Thesis Description of the Operation of the Transfer Current Chopper

NEW SOUTH NALE S

INS TIT UTE 0 F TEe H N 0 LOG Y

SCHOOL OF ELECTRICAL ENGINEEHING

FINAL YEAR PROJECT

NEW CHOPP}~H CONTROL UNIT

STUDENT: Mr. J.A. Dowsett

SUPEHVISOR: Dr. V.S. Ramsden

INTRODUCTION CONTENTS

CHAPTER ONE INTRODUCTION

1-1 OPERATION OF THB TRANS:b"'ER CURItENT CHOPPER 1-1 1-2 M~ EXAMPLE FOR DETERMINING U.F.C. 1-3 1-3 DETERMINING LOSSES 'iVITHIN A CHOPP:ER BY MEANS OP 1-8

CHAPTER TY{O - E(~UATIONS ASSOCIATED WITH THE TRANS FORM Ell CORE

2-1 OPE~~TION OF THE CHOPPER 2-1 2-2 COIvIIVmTATION PERIOD 2-2 2-3 FLUX CHANGES DURING THE COMMUTATION PERIOD 2-3 2-4 WHAT HAPPENS WHEN THE CORE SATURATES IN THE NEGATIVE

DIRECTION 2-5 2-5 DERIVING EXPRESSIONS FOR t 1 , t 2 , and t3 2-6 2-6 CALCULATION FOR PERIOD t 2. 2-9 2-7 VARIATION OF t 1 , t 2 , and t 3 , with K AND H 2-14

CHAPTER THREE - EQUATIONS ASSOCIATED WTTH THE qAPACITOR VOLTAGE OVER THE WHOLE PERIOD

3-1 RISE OF CAPACITOR CURRBT\JT FROM ZERO 3-1 3-2 FALl.; OF CAPACITOR CURRENT TO ZERO 3-3

3-3 REVERSAL OF 'CAPACITOR VOLTAGE 3-7 3-4 VOLTAGE AT THE BEGINNING OF THE COMMUTATION PERIOD 3-12 3-5 ALTERNATE METHODS FOR REVERSING THE CAPACI TOR VOIJTAGE 3-13

CRAPTER FOUR - EXPERIMENTAL RESULTS

4-1 METHODS IN IMPROVING EFFICIENCY OF THE HING-AROUND CIRCUIT 4-1

4-2 FALl, OF CAPACITOR CURHENT TO ZEHO 4-9 4-3 RISE O}' CAPACITOR CURRENT FHOM ZERO 4-16 4-4 DISCUSSION OF RESULTS 4-18

CHAPTER FlyE - FINAL DISCU~QION

5-1 DESIGN }EQUATIONS 5-1 5-2 VOLTAGE STABILITY 5-7 5-3 TRANSFER CUHRENT CHOPPER 5-20 5-4 COMPARISON OF CHOPPERS APPENDIX ONE I'HOT OGRAPRS OF WAVEFORMS

I tJish to extend to the follovIil1e my th1.:11"1ks for their co-operation in to Hrite this project.

Dr. '1 .,~. Har:-lSden.

Hrs. Esma H;w .. l1cll1

'JDd the 'l'echnical ;Staff of Brickfield lliJ~.

INTRODUCTION --------

This project concerns itself with the development of equations which describe the operation of the Transfer Current Chopper. This chopper was first described in a paper written by Mr. M. Akamatsu, Mr. M'" Kumano and Mr. A. Kaza.

The description of the operation of this chopper by Mr. M. Akamatsu and Co. was only basic. Also within his paper, Mr. M. Akamatsu compared the Transfer Current Chopper with other choppers. In this comparison Mr. Akamatsu introduces a new concept, U.F.C. This concept is a useful concept, and more details about D.F.C. will be shown in the following chapters.

This project gives detailed information about the Transfer Current Chopper, describing its operation in detail. Sufficient information can be gained by reading this project to enable a person to design a Transfer Current Chopper. Methods for improving the efficiency of the chopper above what would be normal are explained. (Because of the lack of time available it was not possible to test these methods out fully).

This project is different from most articles which are written on choppers, in that it gives detailed equations and information. Mr. M. Akamatau and Co's article was not sufficient to allow a person to deSign a Transfer Current Ohopper. The reason for this, being that Mr. M. Akamatsu and Co. used state equations to obtain his solution.

By using state equations means that there is a lost in direct relationships between components and waveforms. Relationships with occurences can only be gained by using computers and obtaining curves. Jith this project, state equations were avoided. By using a ferrite core, a general assumption can be made, which allowed the chopper to be modelled by means of lumped components.

Because we are using lumped components in the model, then it is possible to link occurrences directly with components. This leads to easy design.

The metho~ used for the development of expressions for the chopper's current and voltages, consisted of observing the waveforms and then analysinc: what was causing these waveforms. This proved difficult at first, as the core would not saturate in the negative direction.

Because of the influence of Mr. M. Akamatsu, the inductance in series with the commutating capacitor was not large enoup:h. The corrent amount of inductance was found w~en cha~ter two was written. By having the correct inductance in series with the capacitor, the chopper's performance improved greatly. Nowhere in Mr. M. Akamatsu's article does he give an expression for this inductance.

Throught out the project the I'JlcI'..'Iurray Chopper is used as a comparison. By using this chopper which is much simplier in opperation, difficult concepts can be conveyed.

INTRODUQTION (cont'd)

In all, this project offers some interesting reading, describing the operation of the Transfer Current Chopper and the M~Murray Chopper in greater detail and the persons who developed them.

CHAPTER ONE

In this chapter the operation of the transfer current chopper is explained. The period of time for operation is divided into seven intervals. By dividing the period into small intervals a more detailed explanation can be obtained.

It is left to chapters 2 and 3 to describe the operation mathematically and show where the expressions come from. With design it is important to know how expressions were obtained. This allows the designer to estimate whether or not he or she is still working within the original assumptions.

As well as outlining the operation of the transfer current T.C. chopper, the three engineers introduce a new term U.F.C., Utilization Factor of Capacitor Charge. This constant provides for a way of comparing the sizes of commutating capacitors needed for different types of choppers. More will be said about U.F.C. later.

1.1 OPERATION OF THE TRANSFER CURRENT CHOPPER (see figs. 1.1 to i.6j

INITIAL CONDITIONS

The capacitor has a positive voltage across its plate which is slightly less than the supply voltage. Load current Ii is flowing through S.C.R. nCRIt and N? turns of the transformer. The M.M.F. around the transformer core is N Ii. This means the core is saturated in the positive direction. It is assumed that because of the load inductance the load current remains constant over the commutation period;S.C.R. "SCR2" is triggered beginning the commutation process.

PERIOD t1 :

The capacitance current begins to rise and flows through winding N1 and diode D. The rate of rise being affected by the inductance L. As the capacitor current increases, the M.M.F. within the transformer is reduced. The capacitor current finally increases to a valve where the M.M.F. within the transformer is zero. During this period there is a slight reduction in the capacitor voltage. -

PERIOD t2:

As the windings M.M.F. is zero, the transformer core is out of saturation. The transformer can be treated as an ideal transformer. During this period I1N2 = IcN1 and since Ii is constant (because of the loaIT inductance) the capacitor current Ic is constant also, over this particular period. With constant capacitor current, the capacitor voltage decreases at a constant rate. N1 is less than N2 , current flows through diode D, thus reverse biasing S.C.H. ItCR".

1-1

The capacitor voltage is applied accross the transformer winding N1• This vOltage is positive and forces the flux to alter from ¢m to -¢m. The transformer adds the capacitor voltage to the supply voltage

(by means of the winding N ) increasing the output voltage. This period end§ when the flux reaches -¢m.

PERIOD t3:

The core is now saturated and there is little change in flux. The N1 winding now forms a short c.ircui t. Land C form a resonant circuit through diode D, still reverse biasing S.C.R. "CR". The capacitor current rises and falls. The capacitor voltage changes from a positive to negative voltage.

PERIOD t4:

This negative capacitor voltage forces the flux to change from -¢m to ¢m. Again we have an ideal transformer, which results in constant capacitor current. The capacitor voltage decreases at a constant rate, once more. The current flowing through diode "D" is reduced to its low value. Just sufficient to keep the diode ltD" forward biased and S.C.R. "CR" reversed biased. This process continues until the flux within the transformer reaches ¢m.

PERIOD t5:

The ideal characteristics of the transformer disappear. The transformer becomes a short circuit. S.C.R. nCR" is no longer reversed biased, but rather it is strongly forward biased by the commutating capacitor. -

Current flowing through the capacitor flows directly into the load circuit. Since no current flows through the diode D, there is a slight reduction in capacitor current. When the ideal transformer characteristics of the transformer existed the capacitor current was slightly greater than the load current. This extra current was needed for forwarding biasing diode "D".

The duration of this period is extremely small and is neglected in chapters 2 and 3.

PERIOD t6:

Constant load current continues flowing through the S.C.R. nSCR2 11 and the commutating capacitor. This period continues until the capacitor voltage is the negative value of the supply voltage.

PERIOD t7:

At this stage the flywheel diode becomes forward biased and begins to conduct. The capacitor current is no longer constant, as the condu cting diode forms a short circuit.

Under these conditions the inductance L, capacitor C and supply voltage form a resonant circuit. The capacitor current falls and the magnitude of the capacitor voltage rises above that of the supnly voltage. ~hen the capacitor current reaches zero S.C.R. "SCR2" is switched off. The energy stored originally in L is dumped in the capacitor.

1-2

. Vs

+

ClfC',UT

F\!j \-3

t ,

'f./ .

-Ys

/'" / \ / \

---1 i-~T' -. .\. ".,

Capacitor Currenl _ '\

FI~ 1-4- \ t ___ 1 __ > ~-------:-t-3--_ ~t~~:-_-___ -_-:, 1~1~c4 t~ __ 6~_~~1 - .!:~---o-I

I t I ,.I t -~---..4--------~--- t It ~.,.---.-- - I 5J

Transformer

flux- F'St-6

-.... " "- ,

\

\ \

o --1--t--lC---

In the next two chapters the operation of the chopper is examined much more closely. Period t5 is not examined because it is a short period and assumed to be zero.

u. F. o. Returning to the idea of U.F.C.

U.F.C. is defined as:

U.F.C. ==

Where I,is the load current (amps) tcis the commutation period (secs) C is the commutation capacitor (farads)

A Vc is the net change in the capacitor voltage over the commutation period (volts)

From the definition it can be seen that the constant "U.F.C.lI is the ratio of charge that would have flowed through the S.C.R. (that is being commutated), divided by the total charge which flowed through the capacitor. The maximum value for U.F.O. is 1. This means that the smallest{<value of capacitance is being used.

1 .2 An example for determining U. F. C.

The chopper used for this example is a McMurray chopper, which is a close relative of the T.C. chopper.

SCR2.

c Vs

ic

It

FIG 1. 1 IvlcI\TUH.HAY CHOFPEB.

sCR 1

L

FLYWHEEL D\ODE

D

LOAD [NOUCl'ANCE

The capacitor C is initially charged to a voltage Vo. S.C.R.2 i8 triggered, capacitor C and inductor L form an L-C resonant circuit. The discharge path i8 through the diode and load. 'iilien the capaci tor current i8 greater than the load current I j , current flows through the diode D. This means tnat S.C.H.1 is reversed biased. When the capacitor current falls below 11 S.C.R.1 is no longer reversed biased.

the U.F.C. of this chopper

Before we can determine the U.F.C. of the circuit we have to obtain an expression for tc (the commutation period).

the expression for ic(t)

c _---. __ Vo L +

FIG 1.2 BASIC CIRCUIT

-L cs

+ Va 5

res)

lS

FIG 1.3 LAPLACE TRANSFORM OF THE CIRCUIT

::b. = 1(5) ( 5' + ..L \ h. 5 \ Le) 5

TRANSFORMING INTO TIME DOMAIN (see Page 2-9).

1-4-

for 5 =: ~ (Ol'le. pole of +he e:x.pre ss"t 0 1'1 )

JLC

o = _\j~o __ 2. \.-L x L

JjLC

20 - -j'-I{i

angle when "Lc(wt) =1\ is

~ on5le where the capac\tof current Lc.(t) falls below II is

1'1'- ().)"\! . The.refore the toto\ ans\e over whtc.h Lc.lt) "is

greater than 1\ \5 1\- 2-wt/. The tctQ\ current per\od

"5 21'r j lC sec.ond s) so the time for- the. current to PQSS

throu';Jh an an<Jle of 11' - ?-(»t! ra.dians

1-5

is '2.1IJLC (71- 2.wt) 211

tc::; J LC x (1\ - 2. wt./) seconds

tc = 2./LCx (TL - <.uti) sec.e>ncis 2.

:. Sin (w{) = cos( 1l. - 0J\.') = 11. j L 2 'Yo C

.". Ie:: 2- jLC C05-1 {~Jf}

Expression for the U.F.C. of the chopper:

U.F.C.-==-lltc ) ~ Vc = '2. \j 0 (for most chcp~rs)

C l::l Vc

2IJIc cos-'{lL iL} 2. Vo c \/ole

U. EC. ;: .h J L CO:,-\{ lL !L} \Jo c VoJ c

LET Y=-ll fL VoJc

:. U.F.C. =ycos-ty (please note thQt Akamatsu ~ co. have

define 'the U.F.C. for 1his c.hopper- os 'I C05-1 Y wntch. \~ wrOf\C\ Z .J

See. ref. \ pO<je 13

le.t " be the mox\um va\ue of Y J for which the. c.hopper \5

des19n to hond\e. ~1 wou\d be des'H'eab\e to find) for who.t VQ\ue3 of

'A do we ho.ve Q mo'/<.\um. U.F.C .. W'lth Q mQxium \J.f.c.. we have. a

A 0-\ 0-2- 0-3 0-4 0·5 0,6 0'1 o·g 0'9

I\c.o:;\ " 0-(5 0-'2.1 0-38. Q-4f> 0-52. 0-S6 0·56 0·5\ 0-4\ 0 l

1$05-\ '" G-gO 3·65 2·G3 2:\6 \. q \ \·80 \-~O \-q4 2:4(,

TABLE 1-1 U.F.C. Versus A

Th, s chopper- ho.s Q mQx'lmum U. F.e. of 0-56. l'ne. tranSt€r

cu rrent c.hopper- hC\s 0. maXlmum U. r.c. of \ . 1h\s means -that Q

Me Murra.~ chopper wiH t'e9u-l~e. 0.1 led,5 tj a commutotirt<j co pac. \ ror

J·1q ('/0-56) times lQr~er than the c.cmmu:\:o.tin~ copacltor re.9u\red

for 1he 1ransfet current chopper

1-6

Using the concept of U.F.C. for the design of a McMu~ray Chopper.

1-7

eh cose. A. -::. 0-6 (smCl\l c:.opa.c.\tQ'(\c.e. ~ \f\ductonc.e needed')

Y con r-O{\5e be:\"wee.'t\. 0 arLd o· 6

ihevo\ue for c) fo\ UFC=\

C :! 10 tc '2. Yo

::: ,5)¢.40 x \0 .... 6

'2.. x 30

Now the capac\tor needed for the Me. Murray Choppe.r- \5

the loci udonce \lQ~\J€. 0-6 = k) L $0 C

L ::: (,5 -82> }l H

Vs

The concept of U.F.C. can make the design of the McMurray and other choppers an easy matter. Also the concept of U. F. C. and A can be used in comparing the losses within a chopper.

1.3 DETERMINING LOSSES #ITHIN A CHOPPER BY MEANS OF i\

After the capacitor current has fallen below the load current I j , the capacitor voltage continues decreasing. Tnis period is the same as for period t in;~the T.C. chopper. In section 3.2 (Page 3-3) a~ equation is developed which gives the final capacitor voltage.

Yc - Vs + IJ~

Some choppers reduce this capacitor voltage before the next commutation process.

R SCR2 SCR I

+

L C

flywhee\ diode

FIG.1.4 MODI,FlED McMURRAY CHOPPER

This reduction of capacitor vOltage is achieved by the capacitor discharging through resistor R. The capaci tor vol tage will reduce d0w'nto the supply voltage. The value of R is such that the circuit formed by C, Land R is critically dampened.

Hence R =2~ The capacitor voltage is then reversed, ready

for the next commutation. The process of voltage reversal is assumed to be lossless (makes the maths easier). It is quite easy to express the losses of a chopper in terms of ?\

1-8

Load

Maximum losses due to resistor R occur when maximum load current is being chopped. For all loss calculations, the load current is the maximum current the chopper can handle.

Capacitor voltage when S.C.R. "SCR2 rt switches off.

~ Vs

= \ +1&JL Vs C

- , + A

The capacitor voltage after decay is:

Vc.::: Ys

Vc :::; Ys

Energy lossed in the resistor is:

and C can be written in terms of

C :: Ie) tc 2. Ys

The energy loss is:

x 1 A ccs-, A

x Vs 10 tc 4-

How does the losses within the commutation period vary as a function of

As ,,-) 0

1-9

the value of A? .. + 2A --?> }'213 "CQS-t"

The following table lITable 1-2" allows us to see how A (a design parameter) affects the full load losses of the chopper.

A 0 O' j 0-2. 0-3 0-4- 0·5 0-6 0-7 0-8 0·'1

~ + 2;\ f· 273 1·428 \-606 \.g, 7 2-070 2· 381 2'804 3'395 t 35l G~430 Acos-t"

TABLE 1-2 FULL LOAD LOSSES VERSUS J\

In~the previous design example A was chosen to be equal to 0.6

fo~ A=0-6 ~ t 2.b ~ 2. .gO'\Acos-fA

2·BO+ )C \Is 10 t c 4-

;:! 2·804 X 30.x 1 to ~ 40)\ \0-6

4

::; 1·2.E>'2.x to-2. joules Fef' commutat'ton

This means that if the chopper was operating at 500 pulses per second, an average of 6.31 watts would be dissipated in the resistor. With a continuous load current of 15 amps a resistance of 0.028 ohms is needed to dissipate 6.31 watts.

1-10

EQUATIONS COVERING THE OPERATION OF THE TRANSFER CURRENT CHOPPER

WHILE THE CAPACITOR CURRENT ic > ~ (1 + N)

The equations in this chapter describe the operation of the chopper only when the capacitor current is greater than 11(1 + N}. During this period S.C.R. "CR" is reversed biased.

There is one main assumption made throughout this chapter, and this is the magnetic characteristics of the core. Without simplifying the characteristics of the transformer core these equations would become too complex to be of any use for design purposes. The magnetic properties of the core are assumed to be that as shown in Fig. 2. 1 •

8

Bs

-----------------r------________ ~H

-Bs

Fig. 2.1 Magpetic Property of Idealized Transformer

When the flux density within the transformer is greater than Bs and less than - Bs, the relative permeability is unity and there is no magnetic coupling between the coils.

Nhen the flux density isbetween Bs and - Bs the transformer is treated as an ideal transformer. This means that there is no magnetizing current and flux density only changes because of voltage.

2.1 OPERA.TION OF THE CHOPPER

Initially thyristor nCRtt is supplying current to an ,inductive load. This current flows through S.C.R. "CR" and N? turns of the transformer. The M.M.F. around the core is N2Io and hence the core is saturated in the positive direction.

2-1

---

Yeo -~.. __

~C ... ----~:-

~-\jCO Vc.o

2· 3 Waveforo'ts Fig . d the. c\rCUIT onJU\\

,

vVhen S. C.R. "SCR2" is triggered, the capacitor current rises quickly. The capacitor current ic continues increasing until N2Io = N1ic. With the increasing capacitor current there 1S little change in the transformer's flux density.

For the capacitor current to increase further than Io(N2/N1 ) there has to be a large change in the flux dens1ty of the transformer. Therefore for a period of time the capacitor current remains constant and there is zero M.M.F. within the transformer.

vfuile the flux within the transformer is altering from + ¢m to a minimum of ¢m, where ¢m = Bs x A, (A is the cross sectional area of the core).

. ,

L~ = JoN2-N,

LR =' IoN'l.. - 10 N.

n - Nt-Nt N,

. Lc = Io(ltn)

and since the load is inductive can assume that 10 is constant over the commutation period.

Since 10 = constant then ic = constant over this period.

2.2 COMMUTATION PERIOD

The capacitor has a constant current flowing through it of 10(1 + n), then the period for the capacitor voltage to change from Vco to -Vco is easily determined.

2-2

c == 3cVc(t)

d\fc(t) = , dg/, dt edt

d\fc(t) :;; -l \.C C

\IC(t) =: -lc t. + K. c

Vlhen t ~ 0 lfc It} = Veo

Vclt) = Veo - Lc t C

For tfc.(t) = -Veo (end of commutation).

t lc - ZVCO c

t ::. 2.Vco C .. Lc.

T = 2YcoC) which is the period 1o(ntl for commutation

2.3 FLUX CHANGES DURING COMMUTATION PERIOD

Now that we know the period for the commutation process, the next step would be to develop equations concerning the flux within the transformer.

Looking at fig. 2.3, we can see that the flux changes from ¢mto some valve. The peak change of flux occurs half way through the period. It would be desirable to determine what change of flux occurs. This knowledge will allow us to choose the right transformer for the chopper.

2-3

2-4

two basic equations

C d '\fc(t) = -\.1 C

dt

- N I d 0 = Vc (t) dt

- N I d2.0' =- d 1fc.(t) =- -L c dt2 dt C

i • 9~¢ == "L.c.

d t.'1 N:c

~ - Lc. t t K. -dt NtC

-N,de) ::::: Veo for t =-.0 dt d0 ::: Let -Yeo - -dt N.C Nt

¢ 0t: - Ycot + K2.. == Lc - -2N!C N,

for t:::.O ¢-:.¢m

¢ =. i,e. t2. - Ycat. + ¢m lNfC N.

= To(n+ l) t2. -Ycot T {Om 2.N\C. Nl

when t == c Veo IoCntl)

11¢ ~ Io(ntl) X C2. vto -Veo C Veo oj

2N,C It (ntt)2. N\ Toll Tn)

2.. 2.-- Yeo C _ YcoC 2.N, To(lt n) NI1o{t+n)

~¢ 1. :::. -Vco C

2.N,Io(\t n)

~B 2..

Change in :::::! -VeaL flux density 2. N. A ToC' Tn)

Where A is the cross sectional area of the magnetic core of the transformer.

To stop the core from saturating in the negative direction.

~B L 2(5) where 85 _ ~m .:.-

A

2.4 WHAT HAPPENS WHEN THE CORE SATURATES IN THE NEGATIVE DIRECTION

II B = 'J~ C ------- (neglecting minus sign) 2N(AIo(ltn)

Looking at this equation, we see by increasing the voltage, change in flux density will increase. While decreasing the current 10 increases ~ B.

FOR THE FOLLOWING PAGES OF MATHEMATICS IT IS BETTER TO DEAL WITH PER UNIT VALUES.

Assume that we have a value of Vo and 10 which cause the core to reach - ¢m during the commutation period, although there exists many valves of Vo and 10 which will cause B = 2Bs

The two values are 10 and Vo, and from these we will define all our other values.

T, == KTo qnd

Using these quantities can define others

To = 2VcoC Io(nt l)

~ = H To K

It will take a certain time for the flux to go from ¢m to -¢m, and also from -¢m to ¢m.

2-5

When the transformer reaches -¢m the transformer's flux no longer has control over the capacitor's voltage. If it was not for the leakage inductance within the transformer, the transformer would be a short circuit.

The leakage inductance and the commutating capacitor forma resonant L-C circuit through diode "D" and S.C.H. "SCH2" •

Looking at fig. 2.4, we see that the time for the core to alter from ¢m to -¢m is "t1". The period for which the core is saturated is "t2" and the period for the flux to go from -¢m to ¢m is "t3".

2.5 DERIVING EXPRESSIONS FOR~ t2L and t3

To make the initial study simplier, we will assume that H = 1 and find expressions for t1, t2, and t3 in terms of K.

The following method for determining these three periods may appear long but it's the easiest method.

New Expression for flux.

Assume that the core does not saturate in the negative direction. See Fig. 2.5

2-6

At the first origin:

. .

Shifting the origin

t for when

for t= Ti . rJ. = ~m + 0p _ ) lf1 2..

(})m+0p = IT?· 4

(r/Jt¢r) -

Cf; = - ¢m

.1

',:~ '-flm

l

-1-- ,.... '-'

I currEnt '3rea1er l'nOr. 10

curt-ert <2::rJU\ to 10

,t3-lcurrent less than 10

--;----'~-.. t<11 ~~.-

Fig 2.-4- VonatlOn of flux wIth load current

H=-I

F\3 2,-5 WO'leform for derl'l\n<j an

e.xpresSION for f\ ux .

Ip -1-£

H::I K "l'

H::I K:::.I

H.:\ K ~ I

--, \-- I, (t\'t\) ..L

I '\ O~----~------~--------~~~ , / l,... .. r----t.·-z-~----'·"'"il \

\ . / ' \

/ \

o_L_- 1:; ---,... Resoflonr ca~acltQf' curn~n-t Re.sonant o:Jpc\cli.:;:r Vo\ tG:~c.

Flg.1..-G Curn:nt and Vo\t('\fjC '"Yc,'id,xms ., durll\~ r-csoncmtancc

;1

: ~ I i

I I

1.1 -6- } 1L2=. t 2 -~t t T?-II +G 4 4-

o == 1:--lit + T\1.{ 2& 1 Roots of this equation are: 4 G-t 1 5

~ 1i {f ~jl -~ L 2 . \ tG J

=.Tl{ft ~} 2 j I+(;

From this equation we can see that the periods are equal.

t 1+ t3 = 2.t, = t {I ± j: ~ ~ } From Page 2-5 Ll B = 1;42 2Bs

K

:. for H=) 6 ¢ = Qrj;rn k

f/Jmt0p .:. t 20m K

I+~ =-2 f/Jm. K

~ - ~ -1 = l -¢K K G-

G =- K ¢ T\.:. To 2-K K

2-7

Substituting in

Expression for t1 and t3 has been o~tained for constant voltage.

2-8

Note that this equation doesnot exist for K ':?,1\

when K = 1 tltt3:: To

This is easily shown

then

If R .is small then R2 is very small.

for small R.

then J1=K ~ C - ~) for small K.

2.6 CALCULATION FOR PERIOD t2

The capacitator and leakage inductance, neglecting the vOltage drops across the diode "Dff and S.C.R. "SCR2" form a L-C series resonant circuit with zero input. Also the resistance of the circuit is assumed to be zero.

Solving the circuit equations using Laplace transforms:

-'-T CS

Ies) .. Initially the capacitor has a voltage E and the

leakage inductance has a current li(n + 1) following through it.

2-9

Expression for i(t):

£ + L Ilnt\) = (_I + L 5) I(s) S cs

I (5) =f + LI$n+l)

LS +....L cs

E + 5 L I , ( n t ,)

L(SZ +tc)

Standard Transform used is:

Roots of the denominator are:

I(s) = E +- 5 L I\(nt$

L(S+j-L)(S-j-L) ~LC 'fCC

1(5) 0* • f

5- djLc

Finding D using partial fractions:

D

• 4. 2. D

:= t: + 51$0+$ where

(5+ jr2c)L = f t d L 1$(\+1) X JLC

2 >< Jj~C xL

= -dEW + r,(O+I) L

- I.(ntq -j E~

So the angle D~ is between zero and -90 0

5 =-tiftC

The current through the inductor and capacitor rises from Ii to a peak value of:

The current then falls back to its original value ofI,(N+1).

2-10

What happens with the Capacitor voltage:

EXPRESSION FOR Vc(t)

Capacitator voltag~ E - 1(s) 5 cs

Qnd 1(5} = Et SLl\(n+$

(S2+Tc)L

Vc(S) - E - E + SLI,(n+Q S (52-tCc) LCS

;::; LCES2.-E-tE-SLI$n-t-Y

SLC (S2+-tc)

:;: . LeE 52 - S L 1. \ (\ t t) SLC (52. + tc)

= LeE S2 - SLIt C (\ t $ 5 LC CS2.t &c )

Roots of the expression are

For S = 0 we have

J-For S=jJCC we have

\..we E2. - SL It en t\)

SLC (:; t JJEc)

LC E 52 - SL l\(nti) ~ 0 lC.(S2 t tc )

1)~ LIES BETWEEN 0 and 90°

** Pl?ase note D* does not mean the conjugate of D but rather to disassociate it from D which is associated with the current expression.

2-11

The capacitor vOltage alters from E volts to zero, then the voltage will decrease to -E

[5+ = tCln-1pt*l) ~} So the current and vOltage waveforms will look

like those shown in Fig. 2.6.

Getting back to the original problem, Nhat is t2. For the capacitor current to rise from Ii to Ip and then back to Ii, the current must through an angle of 2D2\-

2D4-

Expressing t2 in terms of To, Vo, 10 and K.

E is the voltage on the capacitor at the end of period t1. Voltage across the capacitor when the core is not saturated:

Is given by '"\felt> :: Veo -Klo(\-tn)t

\0 :::: 2Vco( To(lt n)

c

2Vco To

E - Veo - k 2 Vcot\ To

From the expression on page 2-8

2-12

Substituting in for t1.

E = Yo{ \ -~ 10K (I - JI=K)} =VO[I -\ t )I-K}

~VoR

and I, == K 10

Substituting in

To be exact

t2., - Z fLCtan-'{vco JEK rc} It(ntl) "L

Taking the constant 2 JLC and rearranging it

c =- To To (n +1) 2VcQ

2C~ =- To ~V~+I) 2 If = To 10(0+1) JCL

Yeo

hence t2.:::; To 10 (f\ + \) rr. ion'S . VCI.l rc J I-$ } \leo J E L 10(f\1-$ J-C K

\ettinq Q ::: \leo rc J IO(Yltt) JT

2-13

It is possible by choosing Q = 3.2 to have t1 + t2 + t3 To (within 2%) for K <.= \

(See Appendix ':1')

2.7 VARIATION OF t~~ and t3 vVITH K AND H

T, = To)( H K

II B := HZ 2 Bs K

We will have saturation of the core when

2-14

t A... 2. L:\'2. ~ - r ¢m K

k:= 2H'2.-K - ( (/)m l-< G

G =- \.( -~-

. .,

o .. f

\ -G \ tG

2.H2- K

= 10: tl -jH'-H-:..K 1

- T; {H -JH'-~K}

Determining T3

A\so

What is the expression for E?

Capaci tor voltage \Jc It) = V, - It (I t-n) t C

'Veet) = H Veo - KrOll -to) t c

ro(n+') To =- Vco

2.C

E = Veol H -H t jH'L-t<. }

:: Veo{ jHl -K}

From page 2-13 we have:

2. ICC ton-\ { E ;C} 1\(\+0) L

2 jLC tan-\ { Veo J H2-\< } I()(n4l) \(

h :: ~ ton-I { G. JH~-K1

All these equations hold as long as is the condition needed for saturation,

2-H d K which

2-15

The total time for commutation period is:

2-16

EQUATIONS COVERING THE OPERATION OF THE TRANSFER CURRENT CHOPPER OUTSIDE THE COMMUTATION PERIOD

This chapter concerns itself with the capacitor voltages and currents outside the period which SCR "CRn is reversed biased. The voltage on the capacitor varies between the time when SCR "CR" is switched off, and the time when the capacitor is called upon to switch off S.C.H. nCR" again.

This period of time is divided into three sections:-

"RISE OF CAPACITOR CURRENT FROM ZERO" "FALL OF CAPACITOR CURRENT TO ZERO" "REVERSAL OF CAPACITOR VOLTAGEu.

The understanding of these three stages is important to the whole understanding of the workings of the chopper.

3.1 RISE OF CAPACITOR CURRENT FROM ZEHO

In the previous chapter it was stated that the capacitor current rose quickly when S.C.R. t1SCR2 11 is triggered. The current does rise quickly but at a finite rate. As the capacitor current increases to 1 1(1 + N), there is a reduction in the capacitor's voltage.

'vihen S.C.R. "SCR2" is triggered we have a path through S. C .R. "SCR2 1f , leakage inductance ilLU and diode ltD".

This circuit can be reduced to the following: . Lc

+ E c L We have stored

energy in the capacitor and no stored energy in the inductor.

Fig 3.1 BASIC CIRCUIT FOR THE RISE OF CAPACITOR CURRENT

Without using laplace transformers, the capacitor current and voltage can be easily written. The capacitor voltage will reduce until the capacitor current reaches I j (1 + N). The capacitor is the voltage at which chapter 2 takes over.

~fuat we need to know is the capacitor voltage at this time and how long does it take to reach this voltage.

3-1

Expressions for capacitor current and voltage:-

'\fc. (l)= E C05(wt)

Lelt) =- E~ SH\(wt) w = \

JLC

This mode of operation finishes when:-

SJn(wt}:: 1, (\ t n) j L : E C

wt! = sln~l{ Il~+n)j~ }

Capacitor voltage at this time

E' :::. E COS(w'l/)

This expression can be further reduced by considering the following:-

LETs,n¢=O

3-2

cos¢ = )1 -;- D'2.

and sInce E I = E caSe wt')

Looking at this expression, we see, as the current to be chopped increases the voltage at the beginning of the commutation process decreases.

With this voltage the commutation process begins and with little losses within the commutating circuit the capacitor voltage at the end of commutating is -E'.

3.2 FALL OF CAPACITOR CURRENT TO ZERO ( see Fig. 3.2)

Now a second process occurs (we will assume that the end of commutation the magnitude of the capacitor voltage is less than the supply voltage) during this section, the capacitor. current falls from 1 1 (1 + N) t9 zero. When the capacltor current falls to zero S.C.H. "SCR2" is placed in its off state. The question is: What is the capacitor voltage when the S.C.R. "SCR2" is switched off?

As the core goes back into positive saturation the ideal transformer characteristics of the transformer disappear. The diode current ir goes to zero, and the transformer can be treated as if it is not there.

3-3

So the circuit may be redrawn as follows:-

+ Vs

L

Diode. o

Fig. 3.3 HOd THE CIRCUIT WILL LOOK 'dHEN THE CORE OF THE TRANSFORMER GOES INTO POSITIVE SATURATION.

The valve for ic(t) when the core has returned to positive saturation is Ii. The reason for this is that the flywheel diode is reversed biased and no current flows through it. This means that the load current Ii is following through S.C.R. "SCR2" , capacitor "c" and inductance "L"

Current ic(t) remains constant and hence the voltage across inductance ilL" is zero. As the capacitor ncn still has constant current following through it, its voltage increases linearly. This situation keeps going until the capacitor voltage is equal to, or slightly greater than the supply voltage Vs.

When the capacitor voltage is equal to, or slightly greater than the supply voltage Vs, the flywheel diode is forward biased. We have no longer constant current. The current ic(t) will begin to decrease. It can assumed that the diode voltage is zero and the circuit is further reduced to the following:-

Fig.

3-4

L +

Vs

c

3.4 REDUCE EQUIVALENT CIRCUIT FOR ~VHEN Vc(t) IS GREATER THAN Vs

SCR 2.

+ 'Vc It)

Transforming this circuit into laplace transforms assuming zero forward voltage drop across the diode.

+ 'ti. - s + Vs

5

Fig. 3.5 LAPLACE TRANSFORM OF EQUIVALENT CIRCUIT

3-5

Current expression:~

L I\ ::;- I(S) {LS + ~s,}

== 1(5) {S2. t I}L LCs I (5) - I, -

(S2.t ft)

This can be directly transformed into:

What is happening to the capacitor voltage:

Vc(s) -= 1(5) + Vs cs -S

Transforming this back into the time domain:-

for 5=0

for 5=- t j jLf

, • UJe have

Ulh\cn is

VS/L \iL-

=- Vs

. ~ _ VsC + Y2-D ~ J JCC LC L

4xc)(.li jL.C fCC

:: <l I. xL ZJLC

Z 0 := Iff l:.qOo

Iff. c0s(oot-qOO)

Ifc. Sine wt)

(omb'lnlf\S the two So\utlons WQ

hove \fctt)::': Vs T rIff. sin(wt)

¢ for the <urr-ent) tdo\:)"!1 COS (lUt)

s. c~ R~ \\ SC R '- \\ sw\+c.hes or F when the. capa.c't tcr

curren t t c. ('\) 30es to 3e.ro

that \5 UJhen Iccos(wt),:l 0

wt ::: 1</2

t == ¥P The capacItor voltase at this time lS

Vs T ll~

3-6

So as the load current 111 1" increases so does the capacitor final voltage increase. Remember that this equation holds for the capacitor voltage Et is less than the supply voltage Vs.

V'Ie still have one more voltage change in the capacitorts voltage.

3.3 REVERSAL OF CAPACITOR VOLTAGE

At the end of the commutation period the capacitor is at the reversed vOltage for what it should be for the next commutation process. One technique that can be used for reversing the voltage, is using a L.O. circuit. The problem with this method is although the voltage is reversed, the magnitude of the volt~ge is reduced due to losses and the S.C.R.forward voltage drop.

A problem with this circuit is obtaining a model for the S.C.R. over the period. The model has to be simple so as to easily fit into the laplace transform. The model chosen for the SCR is simply just a constant voltage source termed HVSCR".

rrY'Ym

I I L

E J c

T SCR 3

FIG 3.6 BASIC REVERSAL CIRCUIT

<1..-1 mn-n

~ LS

CST ~

+C2 9 YSsCR

FIG 3.7 LAPLACE TRANSFORM OF THE CIRCUIT

The expression for this circuit are not obtained fully but the full expression is not needed. The only real information from this circuit we want is how long does it take to complete the reversal of the capacitor voltage, and what is the voltage of the capacitor at the end of this period.

Obtaining an expression for ic(t) as this will tell us when the S.C.R. will switch off.

3-7

v c - YScf{ -= 1(5) { LS + R. t} 5 5 c 5

Vc - VSCR =- res) {S2 + sR + _, _} L l- L-C

I(s) = Vc -v SCR

(52. tSR + _, )L L LC

Roots of this expression are

= =..fL +-j\ -~ 2.L - J LC 4L1..

tOr- 5 ~ - R t · J l - R'l. 2L J LC 4 r.:-

• • •

D = Vc-VscR

2.'( Ij_' -~} L () ~ LC 4l!-

_ VC - V scR

2JJ!:.- R2 c 4

20 -- Vc - V,CR \ -900

J..h - R2. C 1-

Current expression is:-

teCt) = Vc - VSCf!. eX9 (-R. t) Sine ..L - ~ x t) jt. -RZ- 2L LC 4~ c 4'"

Now that we have an expression for the capacitor current we see that the S.C.R. will switch off when ic(t) = 0

3-8

:.t= 'lr ~====---jtc -4R(,.

The voltage expression for the capacitor is:-

Yc(s) :=. Vc 5

res) cs

_ - ~ Vc (s) =

=

for 5 =0

Vc - Vc - 'ISCR

5 CL5 (5'2..+ SR + _'_) L LC,

Vee CL52.tRCS+I)-Vc fYscR

CLS (;,Zt SR t ~) L LC

VC ( S'-CL + Res) t VSCR.

we have Vscr

for S = -.R t- i )...L - R2. 2L cJ L..C 4~

{ S'2.CL + SRC}

S'l.CL:: CL { R?. - (_' -E-) - 2.jR I - R2. 1 4~ LC 4L'l. 2l IT W f

Best to determine

=

SRC. = -R2c + fKjj~- ~ 2.L LC 4L2.

. . S2CL + SRC = -I

For the denominator we have:

CL {-Ji.. + ft --L - R. 2. } 2J" x).l. -~ 2.L cd LC 41: LC 4l!-

= 2.CL{.::.L + R~ - J' Jl.j~ -..B:.} CL 4~ tL LC 4~

3-9

2D = VSCR. -Vc

{-J +,R'2.C -J' fK: J_l -~} 4L '2. LC 4'-=

However, this is not in the correct form yet, Multiplying top and bottom by:

For the denominator

R4C;tl -2R2.c t R~C - R4 C'-16 t.2- 4L 4L '6 ~

2D ;; (VSCR- YC){-I + j R { J 2./fj t - R2.C :

c 4L

(YC-VSCR.){I-j R 1 4J~_B::

c. 4-

The voltage across the capacitor when SCR is Vc(O) = Vc

The real part of D is 1

3-10

at t = 0 we have:

11c(O) = Vc-VscRtVSCR

Obtaining an expression for capacitor voltage when wt =~. Expression for 2D in the time domain is:

When u:;t= 0 we have 12.D} COS(ct4- D) which is

the real part of 2D. When wt ':. 11 we have

COS(AtB) :; coSAcosB .... s\nAs\nB COS('t( -tlf..P) :,:,coS(4D) X-\

For Ul t .. 11' again we have negative real part of 2D •

• " • Capaci tor voltage = (VSC.R-V~ exp ( - R1l') -t VSCR 2L (>.:)

Substituting for ~

. . Capacitor voltage is

3-11

If there is no resistance within the capacitor, voltage would be reduced by 2Vscr volts.

The last formula can be expressed in the form:

Vf = Yc k - VSCfl(' t K)

where: K:::: exp (-fl' j R2( ) 4L - R'2.(

3.4 VOLTAGE AT THE BEGINNING OF THE COMMUTATION PERIOD

From the last three sections we have seen that the capacitor voltage varies considerably outside the period where S.C.R. "CR" is reversed biased.

The most important capacitor voltage is the voltage E'. That is the voltage on the capacitor when the capacitor current through S.C.R. "SCR2" has reached 1 1 (1 + N) = E' is the same voltage as Vi denotes and from Chapter 2 we can see the importance of knowing how E', Vi will vary with load current.

Obtaining an expression for E',V For section 3.2 the voltage on the capacitor when

S. C.R. nSCR2" switches off.

E= Vs + IJf-The capacitor has to hold the capacitor voltage

between the commutation periods. The dielectric of the capacitor has a finite resistance and hence there is some leakage. The leakage of the capacitor voltage can be expressed as a constant "m".

Therefore voltage at beginning of voltage reversal is:

m is loss of capacitor vOltage between commutating periods.

Before S.C.R. "CRIt is commutated capacitor "C" has its voltage reversed.

Voltage after reversal.

KmVs +I,Km )z - (ItK)VSLR

3-12

S.C.R. "SCR2" is triggered, the capacitor current rises and the inductor current falls. The capacitor vOltage Et when the capacitor current is 11(1 + N) is given by:

Capacitor Voltage at the beginning of commutation is:

From the above expression it can be seen that E' is a function of load current Ii.

3.5 ALTEill~ATE METHODS FOR REVERSING THE CAPACITOR VOLTAGE

From the last sections it has been seen that the voltage Et,V1 is a function of load current. It may be desirable for number of reasons to have different methods for reversing the voltage on the capacitor.

One disadvantage of the L-C circuit and separate S.C.R. is if the main commutating circuit falls to commutates S.C.R. "CR" , the capacitor voltage goes to zero. With the capacitor voltage at zero no further commutation can take place and hence a controlled short circuit.

One way to make sure this does not happen is to have the capacitor Charge up to the supply voltage. The method for doing this is shown in Fig.3.

o CR

c SCR 3

FIG. 38 ALTERNATE METHOD OF REVERSING THE CAPACITOR VOLTAGE

3-13

s. C.R. If SCR3" is triggered. Current will flow, altering the capacitor voltage to the right polarity. The capacitor vOltage will finally be the supply voltage. If the capacitor fails to commutate S.C.R. "CRu , the capacitor voltage will not remain at zero volts and further attempts at commutation can be tried.

There are disadvantages with this system. During short circuit conditions the supply voltage may fall. This means that the capacitor may fall and with highe:r currents commutation becomes increasingly difficult. Also there is the threat of a possible short circuit through S. C.R. "SCR2 f1 and S. C.R. "SCR3" occurinr.

These two problems can be overcome by providing a separate power supply.

SCR2

c SCR 3 Seperate O.C. Supply

FIG. 3.9 ALTERNATE METHOD OF CAPACITOR VOLTAGE REV j1JRSAJ.l •

Although this method has the disadvantage of having to provide a second power supply, it has the advantage, that if the supply voltage has a reasonable source impedance, the commutating capacitor will have the full voltage for commutatiYlg. Also by means of sensing circuits the voltage on the commutating capacitor can be increased to cope with the higher currents.

The main disadvantage of this system is its low efficiency. This circuit loss can be lessly calculated. For the following pages the loss of this circuit is determined.

The above circuit can be reduced to the following:

+ E E

+

FIG. 3.10 REDUCED EQUIVALENT OF THE CIRCUIT

3-14

E + 5

.l cs

R

E

+s

FIG. 3.11 LAPLACE TRANSFORM OF THE CIRCUIT

3-15

Expression for Ic(t):

2 E S

2 SE:: ~C~ ; 1) 1(5)

1(5) = '2 EC Rest)

2E ResT ~c)

for 5 = -\ --RC

:. \-c ( t ) :: '2. E e::x: p ( - t \ R ,(RC-)

f\no\ CapClC\toi \[o\ta~e \5 £

Power O'1\to the s~&tem is ~i'ien 'o~ 00 00 J E x lc(t)d.t = t 1 Lc.(t) d:t

o 0 00 00

1 Lc (t)dt = J 2E e:cp(.:.L)d.t o 0 R RC

OQ

= ~E[-RCexp(R\)J~

- 2~ tRcexpC-oo) + RCexp(o)}

- 2E RC R

- 2EC

:. E JLC(t) dt - 2 El( or (Ktl) E'2.( o

Where KE is the initial capacitor voltage. Comparing this technique with the ring-around

(L-O method) and this present method. For the example assume that the capacitor voltage at the end of commutation is 1.1E.

Losses with separate D.C. supply.

With the ring-around circuit say the capacitor voltage at the end of reversal is O.9E.

3-16

Energy loss - {(l.1)2 - (Q.qy-}X E~C

:: 0·40 E2 C 2.

The separate D.C. supply has more than 10 times the losses of the ring-around system. Normally the ring-around circuit would be needed during normal conditions and under short-circuit conditions a separate power supply would be used to maintain the capacitor voltage, if desired.

3-17

CHAPTER 4 TIXPERIMENTAL RESULTS

In this chapter experimental evidence is presented to show that the equations developed in Chapter 2 and 3 are correct. Also a discussion on how to optimumized the ring-around circuit is carried out.

REVERSAL OF CAPACITOR VOLTAGE

Quite a large amount of work could be done on this section of the chopper alone. However this reversedvoltage section was not designed but rather modelled. To design thi~4section, detailed information about small inductors (10 henrys) has to be obtained. This information was not obtained. So the inductor used was chosen on a trial and error basiS. Out of the coils tried the one used gave the highest efficiency.

c R is the lumped resistance of capacitor C and inductor L.

FIG. 4.1 BASIC CIRCUIT OF THE RING-AROUND

From the above circuit an equation relating initial capacitor voltage and final capacitor voltage was developed. And from this equation we can see how to choose the components, in order to improve efficiency.

Vf =. Vc K - VSCR ( \ + \\)

where Vc = initial voltage Vf = final voltage (after reversal)

4. 1 ly1ETHODS IN IMPHOVING EFFICIENCY:

~imply we want K to approach unity. VSCR would depend upon the type of S.C.R. and the individual S.C.R. so to reduce VSCR may be a fruitless search. As the chopper operating voltage increases the term VSCR(1 + K) will become less important. The value of K plays an important role at high voltages while at low voltages the value of VSCR becomes important.

Lets look at K more closely and see how to force K to unity. The simpliest way is to make R=O, but in every circuit there is some resistance. The connecting leads could be large and short. We could increase Land decrease C, so as to increase K. The value for the capacitance C is fixed by other conditions within the chopper. So the alternative is to increase L.

4-1

As the inductance is increased, the series resistance within the inductor is also increased. The resistance of the inductor is basically proportional to the number of turns per unit length and the inductance is proportional to the square of the number of turns per unit length.

n

looking at the expression

it may be written as

nQ. K~ C

80 the expression for K is independant of the number of turns per unit length (on the inductor) but rather dependant upon the configuration of the inductor (K.?,K1). But, in trying to maximize K, we have to remember tfiat the inductance has not all the resistance. The capacitor also has some series resistance tfRc tl •

5

It is rather difficult to find a value for nn" such that 8 is at a minimum. But looking at the expression we can see some ways to decrease 8.

By making K~ smaller, 8 will also become smaller. This is achieved by increasing the diameter of the wire used to wind the inductor. This decreases the resistance of the inductance.

Decreasing the number of turns has an effect, and depending on the coil configuration it will have two different effec~s2 If the coil is lossy then by decreasing n we decrease n K2 th~s2neducing 8. But if the ~nductors is not a lossy cOlI n K < Rc then by reducing n , the denominator is reduced ~nd hence S will increase. If S increases then K decreases.

From experienced gain in this project values for K greater than 0.9 prove difficult to obtain. dhile values ranging of K from 0.8 to 0.9 proved reasonably easy to obtain. For high values of K the magnitude of the inductor is important and also the method for winding is important.

4-2

An inductance of 405.2 uH was chosen for the ring-a-round circuit. The coil had previously been wound and consisted of a large diameter wire. It was felt that this inductor would be satisfactory.

The 405.2 uH inductor had a G of 15 at 1 Hilohertz, while the capacitor had a value of 10.3 uf and a D of 0.011 at 1 kilohertz.

Determining the resistance within the R-L-C loop

The resistance of the inductor at 1 Kilohertz is:

405x\O-6 XL11 x \03 - 2·54-5..0...

• •

Q - wL F\L

'2.,54-'5 - 0·\1 SL \5

The acceptance of the capacitor at 1 Kilohertz is:

o

, . Rc - o we

6· 4-1 x. \0-2. SL

0'0\1 -6'4-72.)( \0-2

O·17SL

Adding the two resistances together we have R= 0.34 Any improvement gain by lowering of the inductance resistance would be overshadowed by the high value of Rc.

Value for K is:

R=O'34 C=\O·3X\O-6 L= 4OSx\O-G

4-3

This value for K agrees favourably with the measured value.

From the actual ring-around circuit the following results were obtained. These voltages were taken by means of an oscilloscope.

Initial Voltage

50.0 45.0 40.0 37.5 35.0 32.5 30.0

Final Voltage

42.0 37.5 33.25 31.0 29.0 27.0 24.25

Table 4.1 - TABLE OF CAPACITOR VOLTAGES BEFORE AND AFTER REVERSAL OF VOLTAGE.

These results are plotted in graph 4-1. The results agree very well with predicted results. From the gradient of the graph K=0.89, compared with predicted value of 0.92 (error of less than 3.3%). The measured voltage of VSCR is 1.25 which is a reasonable voltage.

Four photographs (C.-1, C-2, C - 3, and 0-4) of the commutating circuit waveforms were taken. From these photographs it can be seen that the capacitor voltage rises and falls slightly towards the end of the conduction of S.C.R. "SCR3".

This variation of capacitor voltage was not predicted by the work done in section 3-3. It was assumed that the S.C.R. would only conduct in the forward direction and switch off at current zero. This however, is not the case as the S.C.R. continued conducting into the negative direction. One Wossible cause for this negative current could be the small charge stored in the S.C.R. This small charge within the S.C.R. is dumped back into the commutating capacitor, reducing the capacitor voltage.

To dump the charge back into the commutating capacitor negative current will be required to flow. From each of the four photographs it can be seen that the S.C.R. does not switch off at current zero, but continues flowing for a short period in the negative direction.

The stored charge as well as the forward voltage drop could explain the eXistance of VSCR. The forward voltage drop across the S.C.R. can be reasonably assumed but it may not explain the full 1.25 volts. Nith the stored charge within the S.C.R. it expresses itself as a VOltage when it's charge is dumped into the commatating capacitor. From graph 4-1 it would appear that this charge is independant of the commutating capacitor voltage.

4-4

I.l0,_ '

); Q)

Cf7 o

'~5 -+\J -0

> I.-0, ...... 'u o 0-o

U ""'0 -J -0

c: lL

/

24 .// 1

30 I

~'ft.

,// /'8

,,/ CI //

"

,/'

// ,//

,/ ,/

/~C~

/'

/'

./'"

"

>' .,/

~'I

y Line of besHit

GrClcll~nt of ihis 1I\"\e. is K /' ...

/ " K = 2.7 - 1d = O· ~q

/. 33- 49 ,//' 27 = 33 X 0-89 - (1-8'\) VSCR

" /./ j-Sq \jc!"p .. " 2.- ~7 ./ 0 -~ \ - .)

// C 2. .'. \j sc H ::-.1' 25

Graph 4-1 Graph of initial & fillQ\ vo\tu5es Determ\\l1r\9 the chorQcterisiks of the iring -,0 ro.und c\rcuit

~'. : .. ' L:

InH'ia\ Capacitor Voltage Vf ~ . ~

35 40 45 50 I I ( I

, .", .., •• '!'" "'CT' - ~:". -''''''''r':::,-~~.", ' ...... -~~.'.''"'":''"~ ""-\"-'-,"-"',1 ."-'--'-'--'-~'-"'~"

.. .. ::

"...

I \ . -I I I:· I

I j I

I

i,

I I

I I I' I' ! I I

From photographs 0-1 to C-4 the voltage before reversal and after reversal were measured as well as the peak current, details of this is listed below.

1 cm division on the oscilloscope reads as 8.43 mm on the photograph. An extra and most important piece of information is that the 10 to 1 probe leads used were not 10 to 1 ratio, but 10.63 to 1 ratio. The inaccuracy of the probe leads introduce some doubt into the accuracy of some of the laboratory results. This doubt disappeared when it was realised that the probes were causing the errors.

INFORMATION FROM THE PHOTOGRAPHS:

Photograph C-1

Current Peak

Initial voltage

=

=

37 mm = 4.39 amps B:43mm

15 mm

20 x 15 mm = 35.59, correcting 8.43

35.59 1.063

= 33.48 volts

Final voltage = 12 mm

20 x 12 mm = 8.43-

28.47 Yolts, correcting 28.47 r.o63

= 26.78

Current peak = 4.39 amps, initial VOltage = 33.48 yolts final voltage = 26.78 volts.

Photogr~ph C-2

Current Peak

Initial voltage

=

=

40 mm = 4.75 amps 8.43 mm

16 mm

20 x 16 mm = 37.97, correcting 37.97 = 35.72 8.43 1.063


20 x 13 mm = 30.85, correcting 30.85 = 29.02 8.43 T:Qb)"

Current peak = 4.75 amps, initial voltage = 35.72 volts final voltage = 29.02 volts.

Photograph C-3

Current peak

Initial voltage

4-5

= 2 x 23 mm = 5.46 amps 8.43

= 18 mm

20 x 18 mm = 42.71, correcting 42.71 = 40.18 8.43- 1.063

final voltage = 15 mm

20 x 15 mm = 35.59, correcting 35.59 = 33.48 8:"43 1.0b3

Current Peak = 5.46 amps, initial voltage 40.18 volts final voltage = 33.48 volts.

Photograph C-4

Current Peak = 49 mm = 5.81 amps 8.43

Initial vOltage = 19.5

20 x 19.5 = 46.27, correcting 46.27 = 43.53 8.43 1.063


20 x t6 = 37.97, correcting 37.97 = 35.72 8:43 1.063

Current Peak = 5.81 amps, initial voltage 43.53 volts final voltage 35.72 volts.

The results for final and initial voltages are plotted on graph 4-1 and marked C-1, C-2, C-3 and C-4. From this graph it can be seen that predicted and actual results agreed well ( maximum error of 2.4%).

Checking the validity of the model by comparing the initial voltage with peak current.

From page 3-8, The capaci tor current is

. Lc ( -t,) = V c - V SC R.

j Ob. _ R2. C 4

exp(-Rt) sinlJ& -~ X t) 2 L ~ LC 4L2-

The value for exp(-~C) when wt:. 1'l' Wo.s

0.92, and hence since current peaks half way through the conduction period when ~t:. 11. the value for

4-6

exp (-R11 ) OlD O'Q6 \2L '2.t..o

'2,

I peak ~MqG (Vc -V5CR) L _ R C +

R= 0-34

?,O_

..... n +-' -o >

+ I u >

~; i CJ.'J

~ g "-•. o

-t-l}

C Ge' r,::l U

u +-

~

. ,..

~"'!' •

Pea!\ capacitor curren,t VBrsus

initlol capacItor vD/tase frraph 4-2 ; ///'

/.;9 , ,;/y'

C4- ;;/ \--- -'1'- -.:;:,

.1.,/ /1'

t{ :.;//1 I . . ,,':,>/ I

L' f b t f' + ~ ,../ In e 0 e s . \ ,./ ./ I /

, /./ ~c:: 6'01 Ip + 4 -2 2 ./ it- - • - - - _.' ,/ ~r, /

/'

"'/ : l .' ,/'/": . , /"-: " :" /

T /' ,/ -::,-

r 'd \ r b t f t I / /' " ' Jecoo 'me or es \ I ,/' /' /

'Ie ~ 7· \3 I-f +1-25 .. c.~/~/;/ /<~redicted ~€slilts c : 'x// ,/ ~ -" 'Vc= G'b7 Ip+ I !..5 I ,/ //1 " I /' /" I ,-

CI 1/'" I

,,/' /' I " , '--;/f'. -;;/ ~ " ,-// .!..11

1.. " . /'. :';7'*" ..-' /'

/.

,/ I .-'I ..-'

. // ' ..... // ,. ,

,/

".

// " ,/ ;/ /,/' , /" Peak CdpaC\tor current -'il" arn:Js

./.. /', (

1 .

. ~ ... , --~._~~v<

",..

./ .'

/'

..... ;J-

Ip

= 6-61 Ip t \-'2.5

This is the predicted relationship between the initial capacitor vOltage and peak capacitor current.

On graph 4.2 the predicted relationship as well as the actual results are graphed. As well as the predicted line of Vc = 6.67 Ip + 1.25 two more lines are drawn Vc = 6.67 Ip + 4.22 and Vc = 7.13 Ip + 1.25.

From graph 4.2 it can be seen that predicted and actual results do not agree closely at all.

There exists two reasons for this discrepancy: The first being the modelling of the voltage drop across the S.C.R. by a constant voltage source. The forward voltage drop across the S.C.R. is high during the early stages of conduction. When the S. C .R. i:$ triggered there is only a small cross-sectional area available for conduction. This area grows with time. As this cross-sectional area grows the charge stored across the junctions increases. So there are many reasons for the vOltage across the S.C.R. not remaining constant.

Also it would be expected that the vOltage drop across the S.C.R. to be higher during the early stages of conduction. This would mean a constant voltage soutce representing the forward vOltage would be higher during the early period.

This is reflected in the equation:

Vc = 6.67 Ip + 4.22

In this expression "VSCR" is 3 volts higher than predicted.

The second reason for this discrepancy could be in the values for Land C. This is shown by the expression Vo = 7.13 Ip + 1.25. Here we are assuming that the VSCR value is correct.

4-7

1 -6 The value for L was given as 405 x .0_6 henrys, and the value for C was given as 10.3 x 10 farads. Assume that the inductor's figure is 5% low and the capacitor figure is 5% high then

true IOd lIctan<:-e va\ue 405 X \O-G - 42.6 X \()b \-\ -0-95

\O·?, 'I.. \0-6 - 9 ·8\ ~ \0-6 F -

\-05

Errors could explain the reason for the difference. For the four measured points shown on the graph, errors of a magnitude of 1mm are displayed. The 1mm represents 1mm on the surface of the each of the individual photographs. 1mm may be a too large an error as to be considered as a typical reading error, but rather. it gives an idea of how sensitive this section is to errors.

To find out what is really occuring and establish a relationship for peak capacitor current versus initial voltage would require developing a much more sophisticated model for the S.C.R. Methods for taking much more accurate measurements would have to be developed.

As far as the chopper design and operation it would be unnecessary to establish a better model. vie have an accurate relationship linking the initial capacitor voltage and the reversed capacitor voltage. But it may prove useful to determine if VSCR is independant of L, C, and the period of conduction.

4-8

4.2 FALJJ OF CAI'ACITOR CUH:aEHT TO Z:8RO

In section 3.2 the expressions for the final voltage on the commutating capacitor was determined.

The expression being:

In this section by using three slightly different transfer choppers experimental evidence shall be used to back up this expression.

In chapter two, we found that by adding extra inductance in series with the capacitor the commutation period is independant of the load current. This extra inductance was effectively added in series with the leakage inductance of the transformer. The sum of the inserted inductance and the leakage indt:Ictance of the transformer go to form the term "Lif.

Three choppers were built, each with different values of inductance. Two chopners were built from the same magnetic core and the third was built with a different magnetic core. The values of the inserted inductance were 68.2uH, 20uH and 5uH.

From the photographs of the chopper waveforms, the capacitor voltage was measured. Two measurements were taken, when S.C.H.."SCR21f was triggered and when S.C.H. "SCR2" was switched off. From these results graphs were drawn.

Before we begin to analyse the results obtained from the photographs, two pieces ai' information. The supply VOltage was approximately 32 volts. The 10 to 1 voltage probes used had a ration of 10.63 to 1.

Results:

For this section of the lab. work we need only know the value of the inserted inductance and the supply voltage.

For the first chopper the inserted inductance had a value of 20uH and the sup0ly voltage was approximately 32 volts the same commutatin~ capaciiance was used for all of the choppers its value being 10.28 ufd.

The first thing to do is obtain the results from the photographs.

Looking at the photographs the point at which S.C.H. "SCH2" is triggered is easily found. But the point where S. C.R. "SCR2" ceases conduction is harder to find. IJooking at the voltage waveform we see that the capacitor peaks negatively and then begins to increase its voltage again. This could be due to the S.C.B.tfSCH2" conductin,q in the negative direction for a period. ~he second ca~acitor voltage is taken just after this negative peaking.

The upper most waveform is the flux waveform. From this waveform it can be seen when the flux has reached zhero. This point is taken as the point in time to measure t e capacltor voltage.

4-9

Seven divisions on the oscilloscope occupy 59mm on the surface of the photograph. Therefore 1 division occupies 59/7 = 8.43 mm.

ACTUAL RESULTS - 20UH

With load current of 10 amps the following results were obtained:

Final voltage 21 mm., initial vOltage 16 mm.

final voltage 21mm, 21mm 8.43

= 49.83 volts correcting 49.83 T.Ob3

46.88 volts, final voltage is 46.88 volts

=

Initial voltage 16mm, 16mm = 8.43

37.97 volts, correcting 37.97 = 1.0b3

35.74 volts, initial voltage is 35.74 volts.

Voltage before reversal of capaCitor voltage.

35.74 = 0.89 x 42.82 - 2.37

42.82 = 0.91 4i;.88

This means that the ©Ommutating capaCitor leaks 9% of voltage between the period when S. C.R. "S CR2" is switched off and when the capaCitor voltage is reversed.

The following results will not be done in such detail as was done for the 10 amps case. The 10 amps measurements were only done in detail so as to show the methods used in converting distances on the photographs to actual voltages.

The next sections will not be done in such details.

~amps:

Final voltage 20 mm 47.46 volts 44.67 volts Initial voltage 15 mm 35.59 volts 33.50 volts Vol tage before reversal - 40.30 volts Means 10% loss of voltage between commutation periods

6 amps:

Final voltage 18.5 mm 43.90 volts 41.32 volts Initial VOltage 14.0 mm 33.22 volts 31.27 volts

Voltage before reversal 37.80 volts

Means 10% loss of voltage between commutation periods.

Final voltage 18 mm 42.71 volts 40.20 volts Initial voltage 13.5mm - 32.03 volts 30. 15 volts

Voltage before reversal - 36.54 volts Means 9% loss of voltage between commutation period.

4-10

4 amps:

Final voltage 17 mm Initial voltage 13 mm Voltage before reversal -

40.34 volts 30.85 volts 35.29 volts

37.93 volts 29.04 volts

Means 7% loss of VOltage between comn}utation period.

,Lamps:

Final voltage Initial voltage

16.2 mm 12. 1 mm




Means 9% loss of voltage between commutation period

Lamps:

Initial voltage 12 mm

_1 amp:

28.47 volts 26.80 volts.

Initial voltage 11.3 mm 26.81 volts 25.23 volts

The results obtained for the final and initial VOltages are graphed in graphs 4.3.

The final voltage curve agrees very closely with predicted results. The transformer adds an extra 3.2uH of inductance. By assuming that the capacitor will loose only 9% of its charge between commutation intervals, an expression for the initial capacitor VOltage (when S. C.R. nSCR2" is triggered) can be obtained.

Final voltage is given by:

E = 32 + 1.511 CapaCitor voltage before reversal is 0.91E

Voltage after reversal is:

0.91 x E x 0.89 - 2.37 which is the initial voltage.

Initial voltage is

(32 + 1.5I1) x 0.91 x 0.89 - 2.37 = 23.55 + 1.22I1

This expression gives results within 3% of the measured values. This is the expression for E* see page 3. 1 2.

ACTUAL RESULTS 5uH

This section concerns itself with the results obtained using an inserted inductance of 5uH.

Because of the lack of forsight there is not sufficient enough information contained within the photographs for this section. But by a bit of assumption and by working our way back then the full characteristics of the chopper can be determined.

4-11

. '

,

t

l-

o .+-'u o Do

LJ

30

./ . ! _/~ .

/ f / ;.- ,/1

I ./ l j

1,/ V i

/ /

/

. / /

. /

/

/

/.

I'

/

. / /

/ .. /

/

. / /

/

/ /

FInal Vo\tQ3~

E J.. .c .... h· l' .. guolion 0: i .:is ! i nc E= 32 t I-SIt

./ / C . \ -1-- C 1.. \. II /' omrnU1Q ,trll

j'-' OP-Qrllor fr-,\7.:oq::: . \ • • 'I' ....... 1'-./ _ l __ , --:

,./ . ~ '1/j..l. ...... (

W-hon C, (R SCR / 'c. \ r'.,"".·,,:". r::.· . 1 t'tt,., ...J ... ....,. \ . .,. _ \"... \-..1' . \ t.,_ ........... '-~ ¥

EC\l\01\On of th\s lIne. .

(32 + I·SI.,JxO·9 \ y. 0'89 -2·37 (32+ I-SII)xO<31 -2~ 37 2.3-55 + 1-2..2 I,

20~ __________ ~ __________ ~, Load Current II

o 510

i---------·---------------------------·--------·-·--- . -----------.------

11.4 amps:

Final voltage Initial voltage

19 mm 14.5mm -


Voltage before reversal - 39.06 volts


Means 8% loss of voltage between commutation period.

Final voltage 18.2 mm 43.19 volts Initial voltage 14 mm 33.22 volts



Means 7% loss of vOltage between commutation period.

L...L~~:

InItial voltage 26.2 mm 31.08 volts

5.7 amps:

Final voltage 33.5mm 39.75 volts Initial vOltage 30.0 volts


29.25 volts



~56 amps:

Initial voltage 24 mm 28.47 volts 26.80 volts

2 amps,:


To fill in the values for the final capacitor voltages it is assumed that the capacitor voltage loose 8% of its voltage between commutation periods.

7.5 Amps:

Initial voltage is 29.25 volts Voltage before reversal is 35.53 volts Final voltage is 35.53/0.92 which is 38.62 volts

3.56 amps:

Initial voltage is 26.80 volts Voltage before reversal is - 32.78 volts Final voltage is - 32.78/022 which is 35.63 volts

2 amps:

Initial voltage is 25.68 volts .Voltage before reversal is 31.5Q volts Final voltage is 31.52/0.92 which is 34.62 volts.

These results are shown with a circle enclosing each one.

The results for final and initial voltages are graphed in graph 4-4.

4-12

>t:, >

'j

501

I

40 .. T OJ OJ CJ

+-

:5? L 0

+-.-c> 0 D-o

U

30

I. I

r

I ! 1

,.

I

~ I I /

1/' 1/ V i

r I I

Finol Vo\tcCJ2-Equation of th\s line

E = '32 + 0-95 I l

./

///

,,/' /

/

~y/ t'

/ 'ca!:,u'C-::2d

/' /

/::-'-1

/ /" .

~// resuits

,//;

/' /.

./ / r_ .... 1·· r ·t· "I'; / •. UJmmUlQ \nO LopGe\ 0\' \OliGQe

/' . J ~

// .when S.C.n \\SCR t' is \r!gs,erEG

/ /'. . Equation of lhis line /'

/ /' . (32+0·qSI,)xO·~2)1.0·B9-2·37 ./ /' /' (32 -+ O·'1510xO·82 - 2·3J

/ /' 23 -83 t 0·781\ ./ #

L .. < // Emili ~ 1uillcl Capac-1tQr' YnlJnc~-r ~ ~~ G.r<lyb- 1- 4-

I

20 L-~.-. o

I

5

Load Current--'P-

:_._-------------_ ....... _-_ .• _.--_._-_ .. _._------_ .. _--------_.------_._----_.

Once again actual results agree closely with the predicted results. The transformer presented a leakage inductance of 4.3uH. This compares with a value of 3.2uH obtained from the previous section.

By assuming a constant reduction of 8% between the commutation periods, it is possible to establish an expression for the initial voltage (Commutating capacitor voltage when S.C.TL"SCR2" is triggered).


E = 32 + 0.951 1

Capacitor voltage before reversal is 0.92E

Voltage after reversal is

0.92 x E x 0.89 2.37 which is the initial voltage

Initial voltage is:

(32 + 0.951 1 ) x 0.92 x 0.89 2.37

= 23.83 + 0.7811

This expression gives results within 2% of the measured values. This is an expression for E* see page 3-12.

ACTUAL RESULTS 68uH

This section concerns itself with the results obtained using an inserted inductance of 68uH. This large amount of inductance was used for investigation work on other sections of the chopper operations.

Again there exists the problem that some photographs do not show final voltages. Similiar tactics are used in this section as was used in the previous section to back calculate final voltages from initial

vol tages.

So far the scaling of distances on the photographs to voltages has remained constant. But it was found that with the photographs taken for this section 7 divisions on the oscilloscopes did not necessarily occupy 59 mm. In fact some occupied 59, 58.5 and 58.2 mm. on the surface of the photograph The individual scaling are marked 59/7, 58.5/7 and 58.2/7

9 amps: 58.2/7

Final voltage 60 volts 56.47 volts Initial vol tage 19.5 mm 46.91 volts 44.15 volts



4-13

8 amps - 58.5/7:

Final voltage 23.5 mm 56.24 volts 52.93 volts Initial voltage 18.8 mm 44.99 volts 42.34 volts


Means 85;0 loss of voltage between commutation periods.

7.4 amps _~~«5/7:

Final vOltage 22.8 mm 54.56 volts 51.35 volts Initial voltage 18 mm 43.08 volts 40.55 volts


Means 6% loss of vOltage between commutation periods.

.Latp~ - 58.5/7:

Initial voltage 32.2 mm 38.53 volts 36.26 volts

5 amps 58.5/7


4 am}2s 58.5/7:


3 amps 58.5/7:


2 am.:e2. __ ....22/7:

Initial voltage 24 mm 2g.47 volts 26.80 volts

1 amR-..::_59/7:


Again to help fill in results for final capacitor voltage it is assumed that loss 8% of its voltage between commutation periods. It may be argued that perhaps 7% to 6% may be a better figure but this is hard to say mainly due to the sensitivity to errors of this figure.

6 amps:

Initial voltage is 36.26 volts Voltage before reversal is 43.40 volts Fina1 voltage is 43.40/0.92, which is 47.17 volts

.2..-amps:

Initial voltage is 33.79 volts Voltage before reversal is 40.63 volts final volta~e is 40.63/0.92, which is 44.16 volts.

4 a!!lps:

Initial voltage is 31.53 volts Voltage before reversal is 38.09 volts Final voltage is 38.09/0.92, which is 41.40 volts.

4.14

3 amps:

Initial voltage is 29.28 volts Voltage before reversal is 35.56 volts }'inal voltage is 35.56/0.92, which is 38.65 volts

L§:!!!ps:

Initial voltage is 26.80 volts Voltage before reversal is32.79 volts Final voltage is 32.79/0.92, which is 35.63 volts

_1_~£:

Initial voltage is 24.57volts Voltage. before reversal is 30.27 volts Final v6Jtage is 30.27/0.92, which is 32.90 volts.

Once again actual and final results agree closely. The transformer added an extra 6uR and once more, by assuming a constant reduction of 8% of capacitor voltage between commutation periods, it is possible to establish an expression for the initial voltage (voltage when S. C.R. tlSCH2 lf is triggered.


E = 32 + 2.681 1

Capacitor voltage before reversal is 0.92E

Voltage after reversal is:

0.92 x E x 0.89 2.37 which is the initial voltage

Initial voltage is:

(32 + 2.6811 ) x 0.92 x 0.89 - 2.37

= 23.87 + 2.211

This expression gives results within 5% of the measured values~ This is an expression for E* see page 3.12. A major part of the 5% error appearsto be slight shift in the supply voltage downwards.

It is interesting to compare these results with those given in Fig. 8 "Maximum Capacitor Vol tage lt Ref. 1. From the work carried out in section 3.2 the maximum capacitor voltage is given by:

This equation by means experimental evidence is correct.

4-15

We can express this equation differently:

E 'Vs

E Vs

+

k{C 'JsJc

',' 't! .

60

52.

t

36

28 /

/ /

/ .

/

/

/ /

/

/ /

.I

,I

;. ,-

/

'2-E/3={f

s L:: 7· \8 A IO'3x 10-

=T4)J.H

\eSIJ\~s / /

/ Equnt;on of tnls line

/ /

/ . I

/ /

/ . /

/ /

/ .. "

"" (32 + '2- G511) x 0-92. x 0-89 - c-3"7

(32 + 2:6911)'1- 0-82. -2-0 37

'2.3 -81 + 2· 2.0 I,

Final ~ loi1Lci1billi~)1cr ~fuJ&~_ b12.uti Inserted ~R~_i~~

'Load Current--r-

20+-__________ ~--------~ o 5 10

This is the same equation as stated by Nilliam McMurray REF:2. If we look at Mr. M. Akamatsu and Co., we see that they have become confused.

If we normalize the load current in terms of Y, we would expect a maximum value for Y of 0.33. This is a typical value for Y for a transfer current chopper. A typical maximum value for Y for McMurray Chopper is between 0.6 to 0.7.

Using the 68uH inductor force the Y value to a high value Y., approaching unity. Mr. Mr. Akamatsu and Co. gives a value of Y greater that unity. However, the chopper does not operate with Y greater that unity.

Looking more closely at figure 8 in ref. 1 we see that the voltage waveforms flatten out for Y less than 0.33. This raises some interesting problems if it was observed in the lab. work. But fortunately it was not observed. Mr. Akamatsu raised no reasons for this flatten section.

RISE OJ? C1LPACITOR CURRENT FROM ZERO

In this section we hope to show that the relationship developed in Section 3.1 is correct and valid. One of the three choppers had a larger than necessary inductance inserted. This was to allow accurate measurements of voltages which are needed for this discussion.

From page 3-3 we have the following expression:

Two voltages E and E' need to be known quite accurately. By having a large inductor L, we achieve a large variation between E' and E. Also because of the large inductance it takes a reasonable amount of time for the capacitor voltage to go from E volts to E' volts.

From page 3-2 we have the time required to go from E to E':

t'

HESULTS:

To test this expression a chopper with 68.2uH of inserted inductance was used. The initial voltage E and the final voltage E* were read from the photographs of the voltage and current waveforms. To make the measurement technique easier E* is the capacitor vol tage when the capaci tor current reaches tlle load current. Ii' instead of measuring the capacitor voltage when the load current reaches 1 1 (n + 1).

4-16

The expression for E* is:

As you can see the expression is slightly different. Although we may not be proving the original equation, if the expression for E* is shown to be correct then the expression for E' should be correct also. The reason for this alteration is the point 011 the current waveform where the capacitor current equals the load current is a lot easier to find than compared with trying to find the point on the current waveform where the capacitor current equals the load current times (n+1), I 1(n+1).

Again the voltage probes had a ratio of 10.63 to 1.

RESULTS FROM THE PHOTOGHAPHS 68uH

7 divisions (70mm on the oscilloscope) occupies 58.2 mm on the photograph. Initial voltage 19.5 mm

Final voltage 15 mm

8 amps (58.5/7):

Initial voltage Final voltage



5 amps (58.5/7):


4 amps (58.5/7):


18.8 mm 14.5 mm

18.0 mm 14.5 mm

32.2 mm 28 mm

30 27

28 26

mm mm

mm mm








TII\,~E TAKEN FOR CAPACITOR CURREN~_TO RIS.}~ TO LOAD CURRENT Ii

9 amps (58~.211l:

Time - 7.2 mm 17.23 u sec.

8 amps (58.5/7):

Time - 7 mm 16.75 u sec.

4-17

7.4 amps (58.5/11:

time: 6.5 mm 15.56 u sec.

6 amps "t2~5/7):

Time: 6 mm 14.29 u sec.

Time: 5.5 mm 13.16 u sec.

4 amps (59/7):

Time: 4.5 mm 10.68 u sec.

])ISCUSSION OF RESULTS

The first set of results concerning initial and final voltages should agree with the following equations:

We know reasonable accurately E, E*, Ii and C. We have a rough idea of the value of L, but its exact value we do not know.

Vie can determine the value for L from the results. Better still we can determine a value for L.

C

Which is given by:

L = E2 _ E*2 C 112

From the results we obtain the following values for L:

15

9 amps 9.83 = L C

8 amps 10. 17 = L 15

7.4 amps 10.55 = L C

6 amps 8.85 = L C

5 amps 8.68 = L 15

4 amps 8.55 = L C

From these results we see that there is a large variation of L/c. The reasons for this variation could be due to a large number of causes. The easiest one to

4-16

understand is errors. All of these measurements are taken from the zero line, on the photograph. When setting up the oscilloscope for measurements, it is attempted to have the VOltage trace zeroed. Unfortunately there is an error associated with the zeroing.

To show how sensitive the results are to errors we shall alter the results for the 9 amps case.

Alter the 19.5 mm to 19.0 mm 2.6% error.

58.2/7:


19.0 mm 15.0 mm


This gives an Llc value of 8.61.

8.61 = L C


compared with previous value of 9.83, which gives an error of 12.4%.

So we can see that the results gives an Llc value which is very sensitive to errors.

The only way we could do is to take the average of the six results. The average of 9.83, 10.17, 10.55, 8.85, 8.68, 8~55 is 9.44 with a standard deviation of 0.85. USing this value for Llc we can calculate the final results which gives us the following results.

load Current Final voltage Calculated Final voltage

34.42 34.47 33.58

Percentage l~rror ---1:-3% 9 amps

8 amps 7.4 amps

6 amps 5 amps 4 amps

TABLE 4.2

33.96 33.79 32.66 31.53 30.41 29.28

31. 19 30.10 29.04

2.0% 2.7% 1 .1% 1 • O~~ 0.8%

COMPARISON OF RESULTS WITH CALCULATED RESULTS USING AVERAGE VALUE OF LIC

From these results it would seem that the value for LIe of 9.44 would see to be a good solution.

Before finally deciding on a value for Llc it would be better, to look at how the times compare with that given by:

This can be reduced by letting L=KC. The value of C is kno~~ to be 10.3 ufds. Combining these two we have

As the capacitor voltage E varies with the load current, it would be a good idea to graph the time required to go from E to E* as a finction of Ii 4-19 E

Load Current

9 8

7.4 6 5 4

Initial Volta~

44.15 42.34 40.55 36.23 33.79 31.53

TABLE 4.3 ELRPSE TIME VERSUS 111E

111E

0.204 0.189 0.182 0.166 0.148 0.127

Time U Secs.

17.23 16.75 15.56 -14.29 13. 16 10.68

The results from table 4.3 are shown in graph 4.6. By means of this graph we can determine a suitable value for K. The previous method of using initial and final vOltages gave a laree variation of K. The mean of this variation being 9.44.

With the glapse times it proves difficult to obtain directly from the readings values for K. It would be impossible to have an expression, involving elapse time, with K as the subject. So to obtain a suitable value for K, using elapse time, is purely a graphical method.

I 1$ 7.4 7.6 7.8 8.0 8.2 8.4 8.6 9.44 0;10 7.72 7.93 8. 14 8.35 8.57 8.78 8.99 9.88 O. 11 8.51 8.75 8.98 9.22 9.45 9.69 9.92 10.91 0.12 9.32 9.57 9.83 10.09 10.35 10.60 10.86 11.95 0.13 10.13 10.41 10.69 10.97 11.25 11.53 11 .81 13.00 0.14 10.95 11.25 11.56 11 .86 12.17 12.47 12.78 14.07 0.15 11.78 12. 11 12.43 12.76 13.09 13.43 13.76 15. 16 0.16 12.62 12.97 13.33 13.68 14.04 -14.39 14.75 16.26 0.17 13.47 13.85 14.23 14.61 15.00 15.38 15.76 17.39 0.18 14.34 14.74 15.15 15.56 15.97 16.38 16.80 18.55 0.19 15.22 15.65 16.09 16.53 16.97 17.41 -17.85 19.73 0.20 16.12 16.58 17.05 17.52 17.99 18.56 18.93 20.94 0.21 17.04 17.53 18.03 ~8.53 19.03 19.53 20.04 22.19

TABLE 4.4 VARIATION OF ELAPSE TIME WITH K and I IE i-

On graph 4.6 the results of table 4.4 are also displayed1from graph 4.6 we can work out values for K for the different 111E values.

Load Current l11E K

9 0.204 7.7 8 0.189 8.15

7.4 0.182 7.9 6 0.166 8 5 0.148 8.3 4 0.127 8

Mean of the results of K is 8.01 with a standard deviation of 0.21. The value of K = 9.44 as far as elapse times is in error. Using the value of K of 9.44 we see from graph 4.6 that the elapse time is much greater than the measured elapse time.

4-20

"

20t 1 I

t /5

I

tf) U QJ (j)

5 0-/

/<1;44

,/ RatIos of l to C

0-/5 0-2

How sensitive are the results in this section to errors?

For the 6 amps case assume we have a reading of 5% low. Actually the reading for E should be 38.04 volts instead of 36.23 volts.

IilE = 0.158 which has time still 14.29 u secs., this glves a value of K of 8.4. The measured value of 1i1E of 0.166 which yields a value of K equal to 8.0, Tlie new result of K is a 5% increase in the value of K.

So this method of measurement is less sensitive to errors. So it would seem that it would be better to trust the value of K gain from this action rather than the results obtained from final and initial voltages.

With an L/c value of 8.0 how do the measured final voltages agree with those measured. The values used for the initial voltages are those measured.

Load Initial Final Caculated C'iirrent Volta£e Vol tage Final Voltage Percent Error ------

9 44.15 33.96 36.07 5.85% 8 42.34 33.79 35.79 5.58% 7.4 40.55 32.66 34.73 5.96% 6 36.23 31.53 32.01 1.50% 5 33.79 30.41 30.69 0.91% 4 31.53 29.28 29.43 0.51%

TABLE 4.5 COIVIPARISON OF PREDI CTED AND MEASURED RESULTS WITH A L7c VALUE OF 8.0

From table 4.5 we can see that there is good agreement with actual and predicted results over half of the resul t·s. With high currents the agreement begins to grey rather dramatically.

But if we consider the eventuation that if we had an error of 2% in the first three results then:

0.98 Load Initial InItial 'Cl:irrent :yolta~ -Yoltage

9 8 7.4

44.15 42.34 40.55

43.27 41.49 39.74

Final Vol tage

33.96 33.79 32.66

Calculated Percent Final Vol tB:E~ Error

34.99 2.94% 34.78 2.85% 33.78 3.32%

TABLE 4.6 COMPARISION OF PREDICTED AND MEASURED RESULTS WITH AN L7 C VALUE O}' 0.8 AND AN ASSUMED EHROR OF 2% IN E

In trying to compare predicted measured results, we have to oontend with a large number of components which have errors. There eXists errors within E, E*, C and Ii' which add together. There is also the disadvantage that we are subtracting errors which increases the percentage error.

4-.21

With these small errors we cannot accurately determine the leakage inductance by measurements. Nor can we determine the effect of the leakage inductance has on the circuit. The value of the leakage inductance is controlled by degree of saturation of the core. With the core of the transformer unsaturated, the leakage inductance is low. With the core saturated the leakage inductance is high. During this period where the capacitor current is rising the transformer core is altering from being saturated to being unsaturated. This means that the leakage inductance is altering. How this altering leakage inductance affects the circuit is hard to determine because of errors.

With the inserted inductance larger than the leakage inductance the varying leakage inductance will have very little effect on the operation of the circuit.

The voltage measurements sgggest a total6series

inductance of 9.44 x 10.3 x 10- = 97.2 x 10- henrys. The elapse time suggest a total series inductance of 8.0 x 10.3 x 10-6 = 82.4 x 10-6 henrys. These two values of inductance give two different values of leakage inductance of 29uH and 14 uR.

Before any accurate figures for leakage inductance can be obtained a much more accurate method of determining the voltages E and E* has to be obtained.

The question may arise that why the value for leakage inductance obtained in the last section cannot be used in this section. Values obtained in the last section are 3.2 uR (20uH), 4.3uR (SuR) and 6uH (68uH). These results are lower than those obtained in this section.

The reason for this is Simply that the capacitor see two different leakage inductances.

4-22

commutq\ infj capaC\1a nee..

\nsertec\

Jnductance

DIFFERENT PATHS OF CAPACITOR CURRENT.

During the rise of the capacitor current (t), the capacitor sees N1 turns of the windings of the transformer. While during the fall of capacitor current (2), the capaCitor sees N1 -N 2 turns of the winding of the transformer. But as the leakage inductance is approximately proportional to the number of turns squared, we would expect a greater difference than that shown by the measured results.

With the chopper with 68uH inserted N1 = 12 turns 2 and N2 = 13 turns. Therefore the ratio of (N1/(N1-N2)) = 144. This is not the case. The greatest ratio of the measured results with the 68uH is 29/6 is 4.8.

At this stage I cannot offer an explanation for this. Perhaps with more accurate methods of measurement an explanation could be obtained.

Equations covering the transformer core have not been discussed:-:::as far as experimental evidence. From chapter two, two basic design equations. From these two equations the two basic components are chosen. The commutating capacitor and the transformer core.

The two equations are:

'2. VcoC

and the period of commutation is given by:

T:: 'L VcoC Ie (\\t \)

where Vco is the initial capacitor voltage at the end of period t i • see page 1-1.

Three choppers were designed as to show diff~rent effects.

The first chopper had an inserted inductance of 68.2uH. This large inductance was used to show capacitor voltage effects during the period t1 (see page 1-1) when the capacitor current is rising from zero to above the load current. Also this large inductance shows how the leakage inductance affected the capacitor voltage as the capacitor current is falling to zero. Periods t 5, t6 and t7 (see page 1-2).

This particular chopper was designed for the following conditions.

The load current 10 = 11 amps, Initial capaCitor voltage (Capacitor voltage when the capacitor current is (1 + n) times the load current Vco = 28 volts.

This chopper used two Phillips E30/15/7 cores with one limb broken away, this gave a cross-sectional area of:

4-23

- 4-.\ )(..\0-5 me..~fes squa.r~d

How many turns do we require for the transformer.

NI -'L

\leo C

Ignoring n initially

NI = 2-\lco C

Normally a person would choose C by means

C IS <jl\Je.n. b'j

To :: 2. \}CC) C Ie en T\)

c ~ \010 2Yco

But in the three choppers built C was picked for different reason~ The capacitor used was larger than the one required by the S.C.R. There are several reasons for this action. The first being that if a smaller capacitor was used then elapsed times within the chopper would have become difficult to observe. Another reason is, by having a larger than necessary capacitor, and hence a long commutation period, the chances of the S.C.R. nSCR1 tt not being commutated are remote. This allows us to see a design which did not meet the original specifications of commutating but still working. Jith the commutating period close to the requirements of the S.C.R. the chances of the chopper not operating are high.

Also by having a large capacitor a large crosssectional area of core can be used. Also a reasonable number of turns may be employed.

If the three choppers built were being built for commercial applications it would then be advisable to use a small capacitor and also a small core. In fact because of the small amount of power being handled by the choppers the transformer core could consist of a toroidal core.

4-24

Jumping back to the design.

With C = 10.3 ufds, and using Phillips grade E-1 magnetic material, Bs = 0.35

This means that

N, - 2.8'2. X \0-3)( \O-b L x 4-. \ )(. \ 0 -5)( 0,( '( \ \

Use 12 turns and let Cn + 1) factor to take care of the decreased number of turns.

- 0-017

the diode current is n 10

0.077 x 11 = 0.85 amps, which is sufficient current to turn diode "DII on.

Using this value for n, we can determine the minimum current before which saturation occurs.

== \0·8<1 amps u.>n\ch \~ ac.ce.ptcb\e

Now what is the commutation period with this capacitor voltage and current?

\0::: 2 "leo C 10

2 X ZB)( \O·3x.\O-b \0·89

If we were designing the chopper to be insensitive to current variations we want Q = 3.2.

L~-25

A -l 3·2.

= 6·65 u\-\

But rather an inductance of 68.2uH was inserted and ignoring any leakage inductance which the core may have.

It would be stupid to value of 0.99 or anywhere From chapter three we lmow will rise above the supply voltage it will reduce the

design a chopper with a as it would not commutate. that the capacitor voltage vOltage. dith this extra value for A (A; \/0..)

From the lab work we know that Vco was not 28 volts but rather it was the order of 34 volts for a 10 amps load current giving a value of A of:

A = ill. J 63 = O-lf> 34- 10-3

Vco throughout chapter 2 is considered as a constant independant of current. Through chapter three and through the early part of chapter four we see that Vco is not independant of load current, but rather very much dependant upon the load current. In chapter five we shall see how to use this dependancy of Vco on load current to reduce capacitor size using the McMurray Chopper.

Unfortunately, this dependancy of the capacitor vOltage "Vcol! on the load current, was not able to be used in the design of the three choppers. The reason being that it was not understood at the time.

To use this dependancy an accurate knowledge of the losses within the circuit would have to be known. Different losses and various values of inductance that the capacitor sees affects the shape and magnitude of Vco versus Ii.

4--26

During the design stages as insufficient information was known about hovY' the capaci tor voltage "Vco" would alter with load current, it was hoped that Vco was not affected to any ereat extent.

Any if Vco was affected to load current to any great extent, it was hoped by means of the circuit resonanting in the negative saturation region. (Period t~, page 1-2), the commutation would remain reasonably independant of the change of Vco with load current.

Load Displacement Commutation Current Scaling on photographs Period

9 amps 58.5/7 22.5mm 53.8 u.sec. 8 amps 58.5/7 23.5mm 56.2 u. sec.

7.4 amps 58.5/7 25.0mm 59.8 u.sec. 6 amps 58.5/7 28.0mm 67.0 u.sec. 5 amps 58.2/7 30.0mm 72.2 u.sec. 4 amps 59.0/7 32.0mm 75.9 u. sec.

TABLE 4.6 VARIATION OF COMMUTATION PERIOD WITH LOAD CURRENT

As we can see from table 4.6, with this chopper the commutation period is not independant of the load current. This is mainly due to the large value of inserted inductance.

The same core with the same number windings was used but with a smaller inserted inductance. Using the criteria that Q = 3.2, we have a value of inserted inductance of:

- 25 ~ \tx\-07rJL:

3-2..

L

5·G2.uH

The actual value used was 5uH.

It would be interesting to see the variation of t1 (commutation period) with load current.

4-27

IJoad Dis~lacement Commutation Current Scaling on rhotographs reriod

9 amps 58.5/7 22.5 mm 53.8 u. sec. 8 amps 58.5/7 23.5 mm 56.2 u.sec.

7.4 amps 58,/5/7 25.0 mm 59.8 u. sec. 6 amps 58.5/7 28.0 mm 67.0 u.sec. 5 amps 58.2/7 30.0 mm 72.2 u.sec. 4 amps 59.0/7 32.0 mm 75.9 u.sec.

TABLE 4.7 V ARIA'rI ON OF COMMUTATION PERIOD :,vITH LOAD CURRENT ---

From Table 4.7 and from the photographs of the waveforms, it can be seen that the core saturates at a lower current than expected. The core saturates between 8 and 10 amps. The calculated value is 10.9 amps. The reason for this is the lower voltage "Vco". For the core to just saturate at say 9 amps, it requires a voltage of:

y2 _ 28'2. q \0-<=\

Looking at the waveforms for 8 amps and determining the capacitor voltage, when the capacitor current has reached

is 22.5 mm with a scaling factor of 59/7 which gives 26.7 volts, correcting this figure for the errors in the voltage probes 26J~g, = 25.1 volts

34

Therefore the core will saturate as than 0.7 teslas.

B is larger

Looking at the waveforms for 10 amps and determining the capacitor voltage, when the capacitor current has reached:

is 12 mm with a scaling factor of 59.1/7 gives 28.43 volts, correcting this for errors in the voltafe probes 28.4 x 32 = 26.7 volts

34-

4--28

( 2.b7i 10

(28)~ \0-9

hence the core will not saturate as 6B is less than 0.7 teslas.

Although the core saturated at a lower current then expected, the commutation period for the currents below 8 amps remain reasonable constant (within 4.6%). The stablization of commutation shows the importance of tho period where the core is negatively saturated. When the core does not saturate with currents greater than 9 amps, the cmmmutation period becomes smaller as the load current is increased.

The photograph of the waveforms for 8 amps shows that it is on the verge of saturation so the ?ormula on page 2-16 applys and also the formula.

2. \fco C 10 (n t \)

10 2." 7.5-1 x \0·3 'A. \O-f,

8 x \·017

50 }J seeS

measured value is 60.6 u.secs. which gives a good agreement between measured and predicted results.

Considering the last chopper which was built; the last two ch6ppers have two 30/15/7 cores with one limb broken off forming the transformer core. With this last chopper two 30/15/7 cores were used but this time the limb was not broken off. This gave a crosssectional area of 6 x 10-5 square metres instead of 4.1 x 10-5 square metres.

The current probe used thro1}.ghout the experimental work, had a limit in that it saturates at 12 amps. So it was decided to desifn a chopper where the saturating current is low. The characteristics chosen were Vco= 28 volts, 10 = 6 amps.

ini tially ignoring n, and determining N1 •

4-29

2 NI - Y..co C -

2l\BAIc

= 2S'L x IQ· 315. \Q-6 2l<O'1x6~\O-sx6

- \~ '02. turns -

We will try Nl = 14 turns and N2 = 15 this gives a value for n of i.0'fi. With this data at what current will the core saturate?

10 ~ - Veo C -2. N\ A LlB Cltn)

- '253 2x lO':,ax \0-6 -

2x \4~ bx. \O-Sx.O·l~ 1·01\

- ~'4 amps -

What should the inserted inductance be using Q=3.2.

L

Vo rL lo(\tn) jT

\b,3uH

The actual inserted inductance used was 20uH. The reason for this, the term (n + 1) was neglected in the calculations.

Ignoring the term (n -j- 1) we have:

L

So with a larger than necessary leakage inductance we would expect the commutation periods at low currents to be longer at higher currents.

4-30

The commutation period is:

Load Current Scali.!}£ ----

':'1 Amps 59.2/7 2 amps 59.2/7 3 amps 59.5/7 4 amps 59.5/7 5 amps 59. 1 /7 6 amps 59.2/7 8 amps 59.1/7

10 amps 59.2/7

TABLE 4.8 VARIATION CUH1{ENT -----

1D :: 2. Yeo 10 (n t\)

2 )( '2.8 ~ \0-'3)C. \O-G 6-4)( \·01\

84· ~).J Sec.5

Dis12lacement Commutation on Photographs Period.

40 mm 94.6 u.secs 41 mm 97.0 u.secs 41.5 mm 97.7 u.secs 41 mm 96.5 u.secs 37 mm 87.7 u.secs 33 mm 78.0 u.secs 27 mm 64.0 u.secs 22 mm 52.0 u.secs

OF COMMUTATION TIME WITH LOAD

From table 4.8 and from the photographs of the waveforms it can be seen that the core saturates earlier than expected. Somewhere around 5 amps and lower the core began to saturate. The calculated value of current for the core to saturate is 6.4 amps. The cause for this is the lower voltage "Vco". For the core to just saturate at say 5 amps required ' a voltage of:

.i! -= 2.8<L 5 b-4-

V - 2.4-8 vo\ts


'·071 X 5 - 5·4- amps

is 10 mm with a scaling factor of 59.1/7 which gives 23.7 volts, correcting this figure for the errors in the voltage probes 23.7 x 32 = 22.3 volts.

-34--

l2.c:3l < (2.8Y~ 5 6-4-

4-31

Therefore the core will not saturate as less than 0.7 teslas.

B as


4-x \-07\ :: 4-3 amps

is 11 mm with a scaling factor of 59.5/7 which gives a voltafe of 25.9 volts. Correcting this figure for errors in the voltage probes 25.9 x 32 = 24.4 volts

34

Therefore the core will saturate as than 0.7 teslas.

B is greater

Althoueh the core saturates at a lower current than expected, the commutation period for currents below 5 aBps remain reasonable constant (within 3.2%) This stablization of commutation period further shows the importance of the period where the core is negatively saturated. When the core does not negatively saturate, with currents greater than 4 amps, the commutation period becomes smaller as the load current is increased.

Calculating the period for a load of 5 amps. The measured value of Vco is 22.3 volts.

To ~ Veo 10 (t\ t\)

?- x ~(:3 x \0-3 X \0-(; 5 x \-01\

8 IS -S \j sess

The measured value being 87.7 u.secs. 2.2% while using the 4 amps value, measured value of Vco is 24.4 volts.

\0

4-32

2. Veo C To (nt))

~ x 24·4-)<. \O'3x\Ob 4- x \-07\

- l11· 3 3 p sees.

The measured value being 96.5u.secs. The reason for the large difference is, with a load current of 4 amps the transformer's core is saturated, reducing the commutation period.

If we take the mean of Veo for 4 amps and 5 amps we should obtain a Vco which is just on the verge of causing the core to saturate.

22-3 + 24-4 2

:: '2. 3· 4- vo\ts

To = 2.x'2.3-4-)(. \0-3)(, \O-b 4--5 'A \-07\

:: \00 y sees.

measured commutation period is approximately 96 usecs, which shows a good relationship with the calculated value of 100 u.secs.

In this section we have shown that by the two equations:

68 '2.. VeQ C

10

are correct and agree closely with measured results. !Ie also have shovm that a value for Vco is hard to obtain. The supply voltage is 32 volts while the Vco voltace is from 24 to 25 volts.

Checking the Q values for any alteration due to the voltages and saturating currents.

4-33

Q- Veo Ic lD(\+n) JT

for the 5uH inserted inductance:

Q -

4 ·18

while for the 20uH case:

23·4 J \0-3 4·5)(\-07\ '2.0

3-4-8

The Q value for the 5uH case appears to be high, but by taking into account the leakage inductance of the trans former. And using the value of L obtained from graph 4-4

L -

Q,. -

3·07

While with the 20uH chopper, from graph 4-3 L=23.2uH.

Q - 2 3·4- fT(;3" 4-·5~\·011j~

- 3-24-

So although the voltage"Vco U was below expectation, the Q values remain around the value obtained in chapter and ap:lendix 1.

4-34

.\

:' 13 L-

<::U Cl-

,-

S)JH \. .. ' .f.--: Cl

/!J5cr.r.::.c/ .t~ '-~ (5 U

\7 .Q

L Q)

CL

c:

20;1l-f -r-~

0

/>.i51?r··!~""(:/ -t----

:::J E c':::

0 4 V

-0 0 I-Q)

CL.

c.: 6Q :/ 0

V)JtT -t- ... G

-1- .. -

itlSCifed .:J c-C e 0 0

q(J

50

I~ I

(f)

U U 1.11

:=i,

!, l.l

gO

so

·f' <...,'J I...J QJ if)

:::t.

0

qO.

SO

t (Ji u ~ ~

0

t ..J

I

I

1

... --~----'.-'---

three grophs of -the COITH'nU rotlon

1lrnCS ve,su.s +he \oe\O cUrrC\,T

forcod .. of -the ~hrce T.e. Chopp':1rs

-'--_______ ~ ________ L_ .. __ . ___ ~_

______ ......L ________ --L __ . ____ .

0 5 \0 LOhO CURRENT Al'lPS

\.

,_. __ ._-------_ .•. _._._----_ ... -. __ ._._ ...... _---_ ..•.. - ..... _-_._._--------_._-------_._--

CHAPTER 5 FINAL DIsCUSSION

In this chapter, the equations in chapter three are grouped together to show that the processes determining the capacitor voltage are stable. Also a detailed comparison between the Transfer Current Chopper and the McMurray Chopper is carried out.

CHAPTBH FIViil

The aim of any engineer is to eventually use his or her knowledge of a system, to design a system to work in a manner which he or she wants. So it is worthwhile to talk about the design of Transfer Current Choppers.

The initial method adopted in the design of these choppers followed these steps.

5-1

(1) Initially ignore the term "n" and let it equal zero.

(2) Guess a value for the voltage "Vco". This voltage will not necessarily equal the supply voltage.

(3) Choose a S.C.I?. with the characteristics you want (Maximum continous current, di/dt, dv/dt and maximum forward and reverse voltage). S. C.R. ' s which have lower commutation times are usually more expensive to buy.

(4) From the chosen S.C.R. we have the minimum required commutation time TO

(5) Calculate the required commutating capacitor from the formula:

The load current 10 is the maximum load current which is required to be commutated.

(6) Knowing the size of capacitance required choose the core using the formula:

68 :: 2 Veo C

The unknown quantities are B, A and N1• From the manufactures data book, the right core to suit the above equation can be found.

(7) Substitute in for "nit and make the appropriate corrections. The diode liD" current is nT • and sufficient current must flow through ihe diode, in order to ensure that it is turned on.

(8) To make the commutation period insensitive to load current variations, have the leakaee inductance such that the commutating capacitor sees, complies with this formula.

3·0h3·2.= Q =- Veo ,K Io(nt\)JT

Where L is the total leakage inductance, inserted inductance plus the leakage inductance of the transformer.

With these steps it is hoped that your Transfer Current Chopper works satisfactorily.

This method was used in the design of three choppers used in the laboratory work. But it was found that the hardest part in the design procedure is choosing the right transformer core.

It was found later, by combining the equations for the magnetic core and the commutating capacitor, a more general equation covering the choice of cores can be obtained.

Derivation of the general equation concerning the magnetic core.

Throughout the project two equations play an important role:

68

To

2 Veo C

2. \leo C It (\+ n)

Changing A to Ac (cross-sectional area of the magnetic core).

Introducing a new cross-sectional area, Aw. Aw is the cross-sectional area of the chopper window.

where Aw x J = J is the current density of the windings used

on the transformer core. Here we are assuming that the transformer is wound as an auto-transformer.

from the defin·'tion of \\ nil

n :::

5-2

henc.e

Now b.B 2. - VcoC - 'LAw r Ac:.

AcAw - v/.o c -'2. T b8

¢ C - \oIt(\tnj -'L'Vee

Sub st 'l t ut \ (\'3 \n TOr- C

AcAw 2-

- Veo '2..6 8 J

2.. = Veo I\ x, To(\tn) 4-T6.B

AcAw - Power x Ta(\+n) 4-J~B

Power- ~ Ac Aw 4TLlB To (\-tn)

From this equation we can see how to change different parameters within the circuit to increase its power handling capability. To increase the power, we would increase Aw, Ac, J and i1B. To also increase the power we decrease To, and n.

5-3

If we go through the core sizes available from Phillips, we can gain an idea of the power that Transfer Current Choppers made from these cores are capable of handling.

From the Phillips handbook "Components and Materials", we can obtain the following information:

Aw, Ac and A B.

The parameter tJ' would have to be determined by both the losses which the chopper can handle and by the acceptable temperature rise of the conductors of the transformer windings. 'To' will be determined by the actual S.C.R. which is being used. tn' will be kept as low as possible as to keep the efficiency of the chopper high.

Now what are the figures for Aw, Ac and ~ B for the various cores. For all cores B = 0.7 teslas.

For core E20/10/5:

1 1 0 -6 1 -6 Ac = 3 .2 x metres square Aw = 27 x 0 metres square

Ac Aw ~B = 31.2 x 10-6 x 27 x 10-6 x 0.7 = 5.90 ~ 10-10

For core E30/15/7:

10- 6 Ac = 59.7 x metres square 1 -6 Aw = 80 x 0 metres square

Ac Aw nB = 59.7 x 10-6 x 80 x 10-6 x 0.7 = 3.34 x 10-9

For core E42/21/15:

Ac = 182 x 10-6 metres square Aw = 178 x 10-6 metres square -6 -6 -8 Ac Aw 6B = 182 x 10 x 178 x 10 x 0.7 = 2.27 x 10

For core E55/28/21:

Ac = 354 x 10-6 metres square Aw = 250 x 10-6 metres square

-6 -6 1-8 Ac Aw 6B = 354 x 10 x 250 x 10 x 0.7 = 4.4 x 10

for Core E65/32/15:

Ac = 532 x 10-6 metres square Aw = 394 x 10-6 metres square

Ac Aw ~B = 532 x 10-6 x 394 x 10-6 x 0.7 = 1.47 x 10-7

Cores Aw Ac B ---E20/10/15 5.9 1 -10 x 0

E 30/15/7 3.34 x 10-9

E42/21/15 2.27 x 10-8

E55/28/21 4.41 x 10-8

E65/32/15 1.47 x 10-7

TABIJE 5.1 LISTING OJ? POWER PARAMETERS FOR THE VARIOUS CORES

5-4

Vie shall deter:~tine what amounts of power that a Transfer Current Cnopper can handle using these cores. Using conservative for J and To, and letting n=O.1

Letting tJt = 2.5 x 106 amps/metre 2

'To' = 40 x 10-6 sec Power = Aw Ac D.B)( 4J

T (1 0

+ n)

4-J = 4 x 2.5 x 106

40 x 10-6 x 1 • 1

= 2.27 x 1011

Using the largest core for the transformer E/65/32/15

Power = 1.47 x 10-7 x 2.27 x 1011

= 3.34 x 104 watts

= 33.4 Kilo-watts

Using less conservative values for J and To, it is possible to bring the amount of power that can be handled to a higher value. 133.6 Kilowatts which is a reasonable load.

Using the E65/32/15 cores and J = 5 x 106 amps/ metres 2 and To x 10-6 sees, and leaving n=O.1

Power = 1.47 x 10-7 x 4 x 5 x 106

20 x 10-6 x 1.1

= 133.6 Kilowatts

While using the smaller cores and conservative values for J gnd To. J = 2.5 x 106 amps/metres 2 , and To = 40 x 10- secs., and leaving n=O.1

.Power = 5.9 x 10-10 x 4 x 2.5 x 106

40 x 10-6 x 1 • 1 -10 2.27 x 1011

== 5.9 x 10 x 2 = 1.34 x 10 watts

= 133.4 watts.

So there is a large variety of power that the chopper can handle

5-5

By using the formula:

PO'Nei - A w Ac 68 4J To(\t\"\)

can sort the cores according to their power level and is an easier method than using

~B - '2.. Veo C

So it appears that the design procedure is a simple one, but from the lab. work it was found that the voltage "Vco n is hard to predict and this leads us into the next part of the discussion involving design.

5-6

5.2 VOLTAGE STABILITY

From chapter three and four it was shown that the capacitor voltage varies considerably over the commutation period. The question is what is the steady state value for "yco n and what determines this voltage.

In many ot~er choppers elaborate methods are used to control the commutating capacitor voltage. (see page 1-8)

It is unfortunate that with the Transfer Current Chopper and The McMurray Chopper the discussion of the control of !tyco" has to be theoretical as the concept and importance of this voltage became known at this later part of this project. The voltage "Yco" plays an import~nt role in the commutation period by having a voltage "Vi!5!O" below the supply voltage we will need a larger capacitor and a larger core. By having Yco higher than the supply voltage we will need a lower capacitor voltage and a smaller core. So there is an advantage in looking into this control of "Yco" as far as the design of the chopper is concerned.

During the operation of the chopper we already know that there is a large variation of the comr~utating capacitor voltage. eg. the fall and rise of the capacitor current. Jith this variation of voltages there are two problems. The first is what is stopping the system, each time commutation occurs to continually build up the capacitor voltage and eventually becoming out of control? The second is what determines the capacitor voltage "Yco"?

An easy chopper to look at to see how this voltage stabili ty occurs, is the I\ITcMurray Chopper.

Earlier it was described by placing a resistance and diode in the circuit, it is possible to bring the commutating capacitor voltage back to the supply voltage. This capacitor voltage is then reversed. The capacitor voltage is then Ys x K, where K is less than one. This voltage Ys x K is not the voltage "Yco".

However, this is a simple mode of operation, it is not the most efficient way. A much more efficient mode is to leave the capacitor voltage above the supply voltage. Reverse the voltage on the capacitor just before it is needed and then use it. This brings up the problem that because of this method the voltage "Yco" could be greater than the supply voltage. During section 3.2, page 3-3 the expression for the capacitor voltage when the capacitor current has fallen to zero was derived and is given again.

This equation only applies to the McMurray Chopper for Yco less than the supply voltage "Ys".

5-7

With the McMurray Chopper, the voltage Vco is the commutating capacitor voltage when the capacitor current equals the load current for the McMurray Chopper. vThile with the Transfer Current Chopner it is the voltage when the capacitor current is equal to (1 + n) times the load current. Vco is also the commutating capacitor voltage when the capacitor current falls below these levels.

Since the ahove equation does not apply for Vco greater than the supply voltage, we shall determine the final commutating capacitor voltage when the capacitor current falls to zero; where Vco is greater than the supply voltage.

5-8

Laplace E9u\vc\en-t of the C\fCU\ t

5 upp\ y - \I s - \J co + l I I

S

\)s - Veo -t II \ 5

l(s) {52 + _\ 1.. L LC} s

I(S) Ys - 'Veo ,. SL1t

~?- t -Cc) L

for <3= ~ J LC

Vs-\Jco t j LIt

JLC

2D -

The curren' passes +hrou5h an o["\~e of

<X. = IT _ tQn-t{ (Veo - Vs) rc} 2 II JT.

(Vco-Vs)!t

D~

Current express \on \5 '-

J

5-9

I?- -t (Yeo - Vs?-L L

Vc(s) -

cas( cut t 04-)

M + Veo cs S

- V s - V co + S L 11 (S'2.+[c)LCS

- Ys - Veo + SLII + \fceel c..:,l£. t \Jeo

CLS(S7. t -bJ \/5 + S LII + 'Icc Cl 52.

C l S ( S 2. + Lc..)

fer s= 0 lUe have Ys

we.. have Ys T ~ L 1:.\ - \}CC0

J[C

Vco-Vs

-IV§-

From pOCje 5 - 9 we have

= tan- l {1' !L} Veo -Vs J c

LC x 2.. ¥~ LC

from the locus diagram on this page we can see that when the capacitor voltage vector has moved through an angle of the capacitor voltage has reached its peak of

5-10

The current vector and hence the voltage vector will move through an angle of ex... ',·'lhen the current vector has moved through an anf~le of 0<....., it will be zero and hence the o.C.R: will switch off.

Combining the voltaGe expressions:-

~rhe voltage when the S. C. H. switches off is

(yeo - Vs) '2. -1- I?- L -\- Vs C

So the final voltage for the commutating capacitor voltage, for Vco greater than the supply voltage is:

Vf - j (Vee -Vsl + 1(- ~ -\- Ys

The equation for the final capacitor voltage, for the voltage "Vco" less than the supply voltage is

Vf V5 t lIfe Note that these two equations agree when the capacitor

voltage equals the supply voltaee.

These two equations can be expressed in a different manner.

v+ (VCO-Vsl + I?- L t 'J2 -2. -Vs \is Vs C Vs

= J (Veo - VsY- + ,'2-\

Vs

\If - Vs t 1-1 IF: - - ~. C Vs Vs

+ Y

So we have expressions for Vf and Vf/Vs. For the following calculations we shall still use Vf

5-11

Vf will be greater than 1 always. Vs

Vs.

After the cRpaCitor current has fallen to zero it must hold its voltage until the next commutation. It will loose some of its vOltage and hence its voltage before reversal is Yf x K1

Vs

The capacitor voltage is then reversed. From chapter three and four it was found that the capacitor vOltage after reversal is given by:

where K2 is related to the losses of the reversal circuit.

Vc Vs

to make the mathematics easier we shall ne~lect the term y~. At high voltages this is a justified

Vs method, but atlower voltage it is not a good aprox-. +. lrnavlon.

K2. \\l VrVs

from the section 3-1 dealing with the rise of the capacitor current.

Veo

Vro Vs

vt - 1'- L \ -C

L C

If Vco is greater than 1 then Vco is greater than Vs- '

the supply voltage.

5-12

With the first example assume that Vco is less than the supply VOltage and Vco/Vs is less than unity.

where

Vc Vs

K\Jf \Is

K Vf '/5

K + KY

- !\<o..'l-( \ + 2.'1 -\- '12) _y1..

as long as K2(1 + 2Y + y2) - y2 remains less than or egual to one, the system will remain static.

Under what conditions does the voltafe "Veo" equal the supply voltage?

for this suitation Veo = 1 Vs

for a given value of Y, what value of K do we need for Veo = 1?

Vs-

K'2. - \ -t y?. -\ t?Yt y7[

\t\ = j \ + '12-\+y

5-13

Y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 K 1 0.91 0.85 0.80 0.77 0.75 0.73 0.72 0.71 0.71 0.71

TABIJE 5. t . TABLE OF K VBRSUS Y FOR VCO/VS EQUAL TO UlifITY

Making Y the subject of the equation:

finding the roots:

y

= -v(2~JK4_(~4_L~'2.t\) \-(2. _\

The particular root we want is:

= y

The expression:

_K2+J~~2-\ K2. - \

K2. - J 2.",2..-t \_\<.'2..

\ _ ",2.

gives values of Y great:er than uni ty vihich cannot physically eXist and the chopper commutate.

The minimum value of K is.r0:5 for any value below this the voltage Vco will never be greater.

K Y

1 o

0.95 0.054

0.90 0.119

0.85 0.2

0.8 0.75 0.308 0.478

TABLE 5. 2 TABLI~ OF Y VERSU_~ K ~OR VCO/v..S EQUAL TO UNITY

5-14

We have an expression for Vco as long as it is less than the supply voltage.

The relation between Vco/Vs to Y and K is shown in Graph 5.1. Looking at these curves, we see some interesting shapes. In a number of the curves the relationship peaks and falls away to zero as Y is increased.

However this graph does not tell us why the commutating capacitor reaches a stable condition. Nor does the graph tell us how the commutating capacitor voltage reach a stable condition. Graph 5-1 shows the steady state conditions for Vco/Vs for various K and Y.

])irectly graph 5-1 is of little use in the design of a McMurray Chopper. :llhe voltage which plays an important role in the operation of the McMurray Chopper is the voltage Vc. This voltage determines the commutation times.

see PQ~e 1-5

~ = (I t Y) v\ Vs

By having Vc greater than the supply voltage a smaller capacitor can be usen. The values fur Y and K for which Vc/Vs is equal to unity are:

\= (ltY)~

1-- \ - Y K

y = 1-\-\ K

K .95 .90 .85 .80 .75 .71 .65 .60 .55 •• 5 Min Y .053 .111 .176 .25 .333 .408 .538 .667 .818 1

TABLE 5-3 VALUES OF Y VEHSUS K SUCH THAT Vc/Vs = 1

The value for a chopper operating with K of 0.65 and a Y of of 0.7 gives~

5-15

Vc = (I + 0·7) x 0'55 = I· IOlj \Is

I-

- -

-\

. t~

i

:! -

'-' A

I l

.~

I ;j I I

1

! ! i i

t ~ ~ ~

05 0,55

o -t----y,--" ------\---'.Q~ o o-s 1-0

Graph 5-/ VcojVs versus Y lor dif'feren f /OS5 cO/1.5fOIl ts /{

'. Fot' Mc/VturrclJ Chopper

(n= 0)

l ____________ . ________ . __ _

~/' -I .,:: ..

For choppers operating with a K equal to or greater than 0.71 and operating at high values of Y it becomes difficult to determine the value of Vc/Vs. The reason for this, is Veo/Vs is greater than~. An equation for Vf, when Vco is greater than the supply voltage was derived earlier. But little can be done with this formula as it proves difficult to obtain Vco/Vs in terms of Y and K.

For conditions where Veo/Vs is greater than one, the final capacitor voltage is given by:

Vf I~co~vsl + ,2- + Vs

\Ie - KJrcCD~;j~ + '(2- + K ---\Is

Veo J(~J~ _ y2. \Is

Veo j K2{j (Yc~Vs)1 t ,Q. + If -y2 Vs

It proves difficult to obtain an expression where Vco/Vs is the subject of the expression. If we were designing a r:lfcMurray chopper we would be interested in the expression for Vc/Vs.

t K

For this expression we need an equation for Vco/Vs in terms of Y and K, which we do not have.

It would be possible by means of a digital computer to obtain curves for Vco/Vs for various K and Y. From the results for Vco/Vs curves for Vc/Vs can be obtained.

Because of time this was not done. However, it can be shown that the McMurray Chopper does achieve voltage stablization, although an equation for steady state values has not been obtained.

Assume that we have a chopper with the following p~rameters. K = 0.8 and Y = 0.6. We will start off with an initial voltage where Vc=Vs and we will trace the capacitor voltage movements.

5-16

5-17

Commutation No. Zero - Vc = 1 Vs

Yeo = J 1'2. - (0·6)'2.. = 0·8 which \5 \ess than one

'Ys

\If - 1-\-0·6 - \-6 \Js

Commutation No. One - Vc = K Vf = 0.8 x 1.6 = 1.28 Vs VB

Veo = J (\·?.ra)~ -(O>6)<L = \-l3} Vs

::J£ - J (0 ·13 \) ~ t (O·6)?. t \ - \. G \ 4-Vs

Commutation No. Two - Vc = 0.8 x 1.614 = 1.291 Vs

Veo = J (\0'2.(11)1- - (00(,)'2. = \ \4-'3 Vs

Vi- = J (0· \4-3)'2.. + (o.~)tt. +, = \·617

Vs

Commutation No. Three - Vc = 0.8 x 1.617 = 1.294 Va

Veo = )(1 0 '2.<14)'" - (0 0 E, f :: to t45 Vs

V f - J ( o· \ 46)2. t (0' b') L + \ = \ ,6 \1 Vs

Commutation No. Four Vc = 0.8 x 1.617 = 1 .294 Vs

J (\-2.94-')'2- - (0'6)'1. Veo - - \. \46 - -Vs

:R - J (0-146)'2. + (0'6)1 +) - \'b\8 - -Vs

Commutation No. Five Vc = 0.8 x 1.618 = 1.294 Vs

From the above results it can be seen that the comrnutating capacitor voltage has stablized, with Vc = 1.294 Vs. It would be a shame to dissipate the extra energy which is associated with the 0.294 volts, through a resistor. This extra voltage can be used in the design of the chopper. It is annoying that there was not sufficient time to find out ways in which the fact that Vc is a function of both load current and losses can be exploited in the design of a McMurray Chopper.

An important conSideration is that Y can Change quickly. Y is proportional to load current. It would be interesting to see how the capacitor voltage alters, when the load current is reduced.

To simulate this condition assume that Vco/Vs = 2 and using the same values for K and Y.

Commutation No. Zero

Veo --Vs

Vf --Vs

Commutation No. One

Vc = 2 Vs

J 2.'2 - (a-())'2. - (·Q08 -

J(O-90Bl t (0-6)?. + \

Vc = 0.8 x 2.088 = 1.671 Vs

Veo - jO-G70'2. - (0 6)'2. Vs

-- L'O«38

Vf - )' (O·55Q)2 + (0'6)2 + \ F \ '520 Vs

5-18

5-19

Commutation No. Two - Vc = 0.8 x 1.820 = 1.456 Vs

Veo - J (\ '45b)~ - (0''0)''- - \,{;)2.7 - -Vs

Vf - j (0' 32.7) 2 + ( 0 '6) L t\ - \·683 --Vs

Commutation No. Three - Vc = 0.8 x 1.683 = 1.347 Vs

V~O - j (1'34-7)2 - (O-t>)'2. = \-2-05 -Vs

j (Q'lOSi- t (0'6)2 Vr - + \ -\Js

Commutation No. Four - Vc = 0.8 x 1.634 = 1.307 Vs

-- \ ·63L)-

Yeo - j ( \ '301)2.. -( o·ro)'1- = \. \ ~'2. Vs

Yf = J (0·\b2.)2 + (O'G)?" 1- \ = \ob'2..\ Vs

Commutation No. Five - Vc = 0.8 x 1.621 = 1.297 Vs

Veo - / (\'<Lq 1')2- - (O'6)L -- ---vs Yf - /(O'\50Y- t (O'b)2' -\- \ -Vs

Commutation No. Six - Vc = 0.8 x 1.618 = 1.295

\.\ 50

- \·6\<a -

;1/hich is the same result obtained by having the initial capacitor voltage equal to the supply voltage. So the commutating capacitor reaches a steady state value of 1.295 - 1.294 times the supply voltage. This voltage is independant of the path followed in getting to the steady state value of Ve. There is another piece of information gained from these two examples. With the first example, withVc/Vs initially equal to one, the Commutating Capacitor Voltage rises quite quickly. In one commutation the voltage HVC tt was within 1.5% of its steady state value. dith the second example with VC/Vs initi~lly equal to two, the commutating Capacitor VOltage fell slowly. In chapter four commutations of the load current, the voltage nVc ll was within 1% of its steady state value.

This information becomes important when the chopper has to deal with a transient load current condition eg. during the start of a D.C. motor. If it is possible to operate a McMurray Chopper such that Vc is greater than the supply voltage it must be able to handly the transient conditions as well as the steady state. This means that the capacitor voltage nvc" must follow the load current quickly. This is very important to have this condition with rising load current. With the load current falling this following is not as important. The only disadvantage being that it decreases the efficiency of the chopper.

TRANSF~R CURRENT CHOPPER

We have talked considerably about the McMurray Chopper, so it is reasonable that we should talk about the Transfer Current Chopper.

It was shown in Chapter Three that the final voltage expression is {for Vco less than supply vOltage1

5-20

Vs + l'if: \jf

Ys +

Vc K Vf

~IL. \Is" C

The formula for Vco is slightly different.

V/o j vl: - I~ (l+n)'2. t

+y

Veo

Vs

The (n + \) '2. "IS -the new te.rm For a full understanding 0 f the opera tioD of the

chopner we have to determine an expression for Vf for Vco greater than Vs. This condition has only been observed and as yet no experimental evidence has been done to analyse the condition and determine exactly what is happening.

Once the commutating SCR, S. C.R. flSCR2" is triggered the commutation process begins. The capacitor current builds up to a current (1 + n) times the load current. The transformer flux begins to alter. The main SCR, S.C.R.ffCR" is commutated. The question is what normally stops the operation of the chopper. The core mayor may not saturate in the negative direction. But it will eventually saturate in the positive direction. dhen the core goes into positive saturation it has no longer its ideal transformer characteristics. The main SCR is forward biased. Since the SCR has had sufficient time to turn off no current flows through the SCR.

This is not the only way of stopping the commutation process. Looking at Fig 1.1 nOutput Voltage Waveform u , we see that by the action of the transformer core, the capacitor vrutage is added to the supply voltage.

:Cquating primary and secondary VOltages

Therefore the output voltape is; V = Vs t (\ +n) E

When the capacitor voltage goes negative, E goes negative. Thus the output voltage begins to reduce.

5-21

When this output voltage goes negative the flywheel diode begins to conduct. The flywheel diode stops the output voltage being any less than the diode's forward voltage drop. As the flywheel diode begins to conduct there is no longer a constant current flowing through the commutating capacitor. Also the transformer's flux cannot increase, as the supply voltage and the flywheel diode will not allow it to. This means that the whole commutation process breaks down.

If we ignore the forward voltage drop across the diode we can determine the capacitor voltage at which this all occurs.

• 4 •

o Vs t (\ + n) E

E -Vs \+ll

The magnitude of the capacitor voltage will be less than the supply voltage, when the commutation process ceases.

So the final voltage will be given by:

W :: Vs + TIff If this is what actually happening we would expect

to see a flux waveform similar to that shown in figure 5. 1 •

+ 0-35

o -----~ ----------------

-0,35

FIG .. 5.1 FLUX CHANGES NITH VCO GREATER THAN THE SUPPLY VOLTAG.8 ----

5-22

The uppermost waveforms shown in the photograph of the chopper for 20uH, are the transformer flux movements. This waveform was achieved by wrapping a few windings around the core and using an intergrator made from a reSistor and capacitor.

With large values of Vc waveforms Similar to that shown. in graph 5.1 were observed. This indicates it was not the positive saturation of the core forcing termination of the commutation process. But as yet carefull analysis of this mode of operation has not been carried out.

This means that the expression for the final voltage has not been tested. The expression for Yf is correct, ignoring any effects due to the core and the SCRs

This means that the expression:

Vf Vs

+~!L VsJc

covers the operation of the chopper when Vco is greater than or less than the supnly voltage. (makes things easier). fiith this, it is possible to write an expression for Vco/Vs and show the factors which affect its steady state values.

Vf Vs

+'Y

Vc - K Vf - K( \ + Y) Vs Vc

Vco= J~'2.(ItY)2. _(I;-n)L'(1... Vs

The term (1 + n)2 introduces a third variable. If n=O, we would have the same curves which were drawn for the r~cIVlurray Chopper. Graph 5-1. Normal design values for n would range from 0.05 to 0.1. Two graphs for Vco/Vs were draw~n, graph 5-2 with n=O.05 and graph 5.3 with n=O.1.

From these two graphs we can see that Vco/Vs is a function of t-<-) J\ and n. Ni th lower values of K and high values of n the dependancy of Vco/Vs is increased. When looking at these graphs it should be remembered that the transfer current chopper normally operates in the low values of Y, normally less than 0.4. In this region Vco/vs is always greater than K. The method of capacitor voltage control is more efficient than just using a reSistor to bleed off the excess voltage, such

5-23

t -

t 0-65

0-60

" .'

o • 0-5 ~ G-raph5-2 \,. \-0

.. r vcojVs

.. tor differenf /0< versus Y For the Tt, ,,'s constants K

fVl7Srer C .. . wIth /1 = 0.05 urrerd Chop,cel"

.... --_ .. - .-.-.~----

f' ,

. I

t (11

> ! . '0--

.U >

1 .' .

. I

0-5

o

0-50

o-s 1-0

Groph 5-3 Vco/Vs versus Y··

for dIfferent \055 constcmts K For the.Tran\;1er Current ChOpy2f

. \\lIth r1 ::: 0,(

as in the McMurray Chopper shown on page 1-8. With that particular McMurray Chopper the voltage ratio Vc/Vs=K

The formula for Vco/Vs would be

Vco Vs

:E1rom this equation alone, it can be seen tha t the voltage would be lower. Any Transfer Curent Chopper using such a methould would be at a disadvantage. Requiring a larger capacitor and with a larger change in capacitor voltage larger losses.

So far with both the McMurray and Transfer Current Choppers only praise has been spoken for havingVc and Vco (respec~ively) greater than the supply voltage. However, there is one disadvantage with this technique. The transfer Current Ci10pper has the disadvantage that with Vco/Vs greater than one the commutation period is decreased. The reason for this being the fact that it is the capacitor vOltage and not the core positively saturating, causing the collapse of the commutating process. This effect might be able to be corrected by adjusting the value of Q. Because of time this was not proven.

5-24

~ __ . COMPARISON OF CHOPPERS

At present there may be some confusion between and Y and Q. To strengthen the definition of Q on page 2-13 we have defined Q as:

Q -

The important terms are the constants Vco and 10. These two constants are the voltages and load currents at which the core just saturates in the negative direction.

The term A was defined as the maximum value of Y on page 1-6. Y was defined as being:

y - LIL vole

It was assumed that the value Vo was constant and in a number of cases the voltape Vo was replaced for the supply voltage Vs. It was fou~d in this chapter that the voltage Vo is a function of the load current. For the purpo~es of showing this

y h/L \is j c

(I represents the load current which is to be commutaied). This means that the previous definition of Y is not being contradicted. It is hoped that you will bear with me, as each chapter is in many ways independant of each other. In each chapter Y and 'J\ Have been defined.

In chapter one the term U.F.e. was introduced. Mr. Akamatsu and Co. used this term to show the advantages of the transfer current chopper. By making generalizations, different types of choppers can be compared using this term D.F.C. The inverse of the U.F.e. can be used as an order of merit.

Example: One chopper having an D.F.C. of 0.8 has a commutating capacitance of C farads. A second chopper has a D.F.e. of 0.3 and a capitance of e t

farads. The ratio of the two capacitors are such that:

0-8e

c

5-25

0-3C I

0-3 c' o·~

O·3<3C'

Higher U.F.O. means a lower value of capacitance. The reason for this is, the chopper with the higher U.F.e. is using the charge on its commutating capacitor more effectively. This means that a lower value of capacitance is required.

As well as considering the size of the commutating capacitor, there is the question of how much loss is caused by the commutating process. Losses within a chopper depend upon the method of commutation and the size of the commutating capacitance. (loases within the chopper circuit are proportional to the size of the capacitance value. A chopper with a high U.?C. will have the advantage of a low value of capacitance and generally lower losses compared with a chopper with a low U.F.C.

The main comnetitor against the T.C. chopper is the McMurray chopper. The McMurray chopper has the highest U.F.C. value outside the T.C. chopper. In some sections of operation, the McMurray U.F.C. is the same as the T.C chopper.

We shall now compare the two choppers generally. With this comparison of the two choppers it is assumed that the capacitor voltages are independent of the load current. That is Vc=Vs (for the McMurray) and Vco=Vs (for the Transfer Current).

The commutation period for the McMurray chopper was derived in chapter one.

tc = 'L JLC C05-1

{ Jsk}

y =~~k

tc ?.JLC (05-$"<)

-1 ( u. F. C of the MclVTurray chopper is Y cos Y see page 1-6) which has a maximum of 0.56 for Y ranging from 0.6 to 0.7.

DETERMINING THE U.F.C. AND T.e. OF THE T.C. G:HOPPER

It is possible with the transfer current chopper to design the circuit such that tc remains independant of the load current. This is only true for currents below a certain value. For the chopper to achieve this situation the leakage inductance (transformer plus inserted inductance) must equal L.

5-26

L must correspond to this equation:

Q ~ 3-0 - Vs /c I(\\+~JL

\

'A Where Io is the load current where the core just

saturates in the negative direction tc is given by:

and also

tc = 2VsC IoCn +$

while the core negatively saturates tc remains constant at this value.

while the core does not negatively saturate (varies with the load current) .

This last expression can be rewritten as:

~ = 2- VsC l !Lc 1$n+$ jil

- ~Vs If -I, (n-u) L

tc - L -JLC Y(fLtt)

VVhile the value for tc wi th Y less than 0.33 is:

Determining the U.F.C. of the Transfer Current Chopper wi th Y ~ 0.33

U.F.C. - l\ tc = 1\ tc.. C 6\Jc C 2.Vs

5-27

with the core not going into negative saturation.

tc - ~ VsC -I((\+f\)

U.F.C. - 11 X ~ \jsC -'LCVs l$\t\$

- --L ~ remO\f\ S CO\\si- an-\:) -\t-n

so for a chopper with n = 0.1 the U.F.C. outside the saturated region is:

U.F.c. - \ - 0·9\ \ -t 0·\

for a transfer current chop~er with n = 0.2

U.F.C. _. \ - 0-S3 1+0·2.

So for a high D.F.O. n has to be kept low.

What is the D.1!'.C. for the T.C. chopper when the core does go into negative saturation?

core

5-28

U.F.C.

Tc C

2Vs Ii

U.F.C.

= 2Vs x C

remains constant remains constant remains constant is the load current which does vary depending upon load condi tions.

= Ii x constant

and hence it is a straight line relationship.

,ilien I = 10 (10 is the minimum current beIore the saturaies).

U.F.C. - -IL l<. _I _ Ie, n t \

If the commutation period remains constant, then the D.F.e. of the chopper is an easy thing to determine. But what happens when Tc does not remain constant, but alters for currents less than the supply voltage. This is especially an occurrence if the chopper is designed to operate with a Q of 1 or 2.

To determine the D.F.G. in these cases we have to determine tc. In Appendix 1, tables for tc in terms of To are given (T is the commutation time when the core just negativelyOsaturates and 10 is the load current at that particular occurrence). 'ro find the particular commutation time tc for a current Ii' you must put the current Ii in per unit terms.

Let K - 11 Io

from the tables for a particular Q and K we obtain tc in terms of To' let this be expressed as:

5-29

p = tc To

From this we can determine the D.F.C. of the circuit

U.F.c. = I\tc - V\. 10 PTo -C 2. Vs C 2. \Is

To - ?.. Vs C -Ie (n t l)

U.F.C. = K IoP X 2 VsC 2.( Vs Ie (f\ -T 0

- 1~P -n + I

K - YO -

Interesting relationship

Example for

Q = 2,

K = Q

Y=.1L!f \fs C

U·r·C. = py~ n t l

working out the

Y = 0.4, n = x y = 0.8

From appendix I, and table

P = 1.11152.

whe.r-e P \s founa from '\-c:\o\es \isted in appe\\chx Olte.

U.}?C. for:

O. 1

for Q = 2 & K = 0.8

U.F.C.= PYG - \'\U52x 0·41< 2. - 0-808 f\+-\ \.\

We have already obtained a relationship for tc/jLC for the McMurray chopper and also one for the transfer current chopper (while the transformer doesnot negatively saturate). We still have to obtain one for the Transfer Current Chopper with Q equal to other values besides 3.2 to 3.0 and with the core negatively saturating.

Again we need the assistance of the tables in Appendix one.

from qppend ix one tc -::: p" to

to - L Ys.C -to (r\tO

Q - Vs ~ -I() L

5-30

tc Pto

tc. - Pt.a -- --fCcfCI

Px'LCxVs n t\ Io

Px~ x 0+1

Vs rc IoJL"

Interesting, maximum of Y is l/G..

From graphs 5.4 and 5.5 we can see how the Transfer Current [-tnd McMurray Choppers, U.:8'.C. and t/JLC values vary with Y. These curves differ from the curves given by Mr. Akamatsu and Co. (see figs. 6 and 7.)

Graphs 5.4 and 5.5 give a rather too optimistic view of the differences. These graphs make the Transfer Current Chop~er appear far more superior than it should be.

It would be better to graph U.F.C. and tc for the two choppers as a function ;f load current. If we are comparing two different types of chopners we should compare them as if they were uSing the same type of S.C.R. and handling the same rang~ of load currents. !he relationships for D.F.e., and tc versus 11 are.shown 1n graphs 5.6 and 5.7. In tnese two graphs the dlfferences between these two choPDers are not as dramatic as would be believed by looking at ~raphs 5.5 and 5.4.

Prom graph 5.4, we see that the Transfer Current Chopper has the advantage of the commutation period remaining constant. Th~ commutation period for the McMurray Chopper varies to a maximum of 1.69T . (the chopper was designed with a A of 1 11.67 = o. g or a ma:ximum of Y equal to 0.6 and a Q of 1.67.)

From graph 5.6 we see that the D.F.C. for the Transfer Current Chopper overlaps the U.F.C. of the McMurray Chopper for per unit currents less than 0.4. From previous discussion in this chapter it could be assumed that the McMurray Chopper is just as efficient as the Transfer Current Chopper for K less than 0.4 (ratio of currents).

This is, however, not the case. From graph 5.7 we see that the McMurray period increases above what is needed to turn the Load S.C.R. off. The dash line II F~ f f e c t i "iT e U. F. C. If S how s the value s for th e U. J!'. C . which is calculated from the commutation period which is necessary to turn the S.C.R. off. This is a further refinement of the definition of U.F.O. It is only wasteful to have extra commutation period than is necessary.

5-31

~I!' •

, u w: :J

G=2. (~::l

-, -. --- -r7;--. )-t-c ---;:-:.:.:-":~ n=D·' ... Q~-~~)," _ .. -;;;r -_. --' n, 0'1

-, 50hd lines indic.clte the '; /r' re3ion C)\J€r' V'Jh\ch chopper- t.Ql\ / operOi€.

11 .-',

0' ' !, I ...... ;

//;1/' ~Q=\-~? "" ~I . \ ,1/ / '

/%1/// Me Murr-a'J \ /1/:() 1 I

flil I J I.

O'L I~',/ I I /V I

olP' I

0,-4:

OJ

0,2

o 0'\ 0·2 0'3 fA O·~ 0'1) (j.( O·~ 0·" H)

'(= 1J.. If ~ \Is. C

VI i 3otion k':lol" .vs\ood cUlren r GRAPH 5-4

. t v\~. .rJt;

~'i'~~~

Scl\d \ines indicate 1ne reSjicn eve. whiclr>. the cbc?pe:-, '. •. ,Call cpel'a.+e .. , ..

6.~37 f'~O 1---- \

\ , , '

5~.t:'lf\:':O\ TC " r ':' :~;urfaj """"",

z L ,:'., ----..-____--'-----.. ---

I t -' ... o III! .....l-..L~ o 0-\ C .. 2 !}3 0·4- 0-5 .0·6 0-1 O'S Q'1 \~()

, y::: lLiS.. ..:..:.. vsJC.- .

Aeve;se bios ft'me charac1~r;5tic5; . vs lood current

Graph 5-5 •• I

.. .... ;i)

.r

I; -I I' I I I

I

I , ' ! I;· i

i I (

I I

!

I

t ,..J u..: -;

\.~,

·':u.,'t

\-0_ ji' --n"o-, 2.10 0-8 L. .' ' /?" _. - n::. 0-2 --.~".~ ....... ' '.' .

. S~'.id. \ine .. s in:j.ic.atc the .... '1·,; C .' ..... ~ ...•..•. ~.}'1.c l'1u .. r.ra.y ... I"'€. '~\on. over W ',11C..b chapper- y" . · ; .. ~: . : :~ ..... J .. " : .. CClnope\"Qte .. " .' "" ______

// ... ' ..•.. ---...;.

. ... /~~~~-M~rtci3· t'To '-----'-~:. ',.

~//" < .. ,," . . ," ....... ,... . .T.e: '. ,//.' ....... ",>/, . ~ .... _ So\idlines ind.\(Qi€; the. .~".~~~~_) 'j

/<1 ./",". .;:. ." .{'€~\onover\.~h(crt \-i:e.,c.noppers :: if ...... ::~::: //" . ./ 0 o' c. eln C'p€ rak .. . . I '" ,« , / -S c .,.' ; ~~ eMu r \' c, " : o 2 ' /" . " E! f . U t:" C ,... (U .. '. i..I . I- /;" ,,/ - I .(lc1IVe • r. _ EC 0-

I /~. ,

I.~~,'''' . .' J

1

- /;, .;/ ,

.- 0 /~' \ -l---.J 1 ---' 0 o 0'2. 0·4 0'6 0'8 1;0 ,0

LoadCurr-eflt K~ 0-'2.: 0-4 0'0' 0-8 1-0

I Load. C~r\E?n1 K~ \.2.. .1·4

"'1-

U li 3ation fad'or vs. \ oad cutt'en.t Commuta1:lon' time V5. \ood .cut'r~Y\-t :.

GRAPH S-6 GRA?H 5:-{

. ~

,

i

I f ,

.~J

Considering the U.F.e. and commutation period for currents less than 10 it is only useful in a comparison and to find methods in improving the operation of the choppers.

The most important points are the maximum current. Both choppers have to be designed to meet this load. This current and the supply voltage will determine the choice of components.

Comnarison of Losses:

Althouf'h the maximum current will determine the components used in the choppers, a comparision of the two choppers losses over the whole current rante would be useful. The chopper may be operating over a narrow range of currents. Meaning, that if one chopper has less losses over part of the current range it may be the better choice if the load current is normally in this region.

For a simple comparlslon of losses there is a large number of approximations. The first is to deal with the capacitor voltage - Vo (McMurray) = Vco (Transfer Current) = Vs (Supply Voltage). The next calculation of losses within the chopper circuit. One way would be to subtract the energy going to the load and subtract it from the energy coming from the supply.

An easier method and the one used is:

Energy lost per commutation = ~ C {\II; -\/"/n }

where Vp is the maximum capacitor Voltage Vm is the minimum capacitor vOltage

So for the comparision of the two choppers we have to design them. In designing a McMurray Chopper there is a range of L & C which can be used. For minimum capacitor size ranges between 0.6 and 0.7. To minimize the inductor size should be kept low, so we will choose A = 0.6.

"A. = 10 /L(m) = Ys ~ C(m)

Where 10 is the maximum current.

0-5

L(m), cCm) are the inductance and capacitance values for the McMurray Chopper.

5-32

Vlhile for the T. C. chopper A = 0-33

10 ~ Vs j C (~~)

0-33

LCto), aCto) are the inductance and capacitance values for the Transfer Current Choppers.

The D.F.C. of the McMurray Chopper is 0.56 (at maximum load current) and the D.F.C. of the Transfer Current is 0.94 with n=0.06. The relative capacitor values are:

0.94 C(tc)

C(to)

= 0.56 C(m)

= 0.6 CCm)

The McMurray Chopper commutating capacitor is bigger. How do the two inductors compare?

L (m) 0-5 0-33

\·68 ((tc) L (tc) C(~c)

3·3\ - L(m) I-GB L (tc)

L (~C.) = O-IS L ('0

The McMurray chopper requires a larger capacitor and inductor, when compared to the Transfer Current Chopper.

To calculate the efficiency of the two choppers a further assumption needs to be made. The third assumption is that the minimum voltage (Vm) for both choppers supply voltage. This is only to make the mathematics easier. Maximum capacitor voltage for the McMurray Chopper is:

Vp - Vs + I I jL(nl) -c em)

- Vs + 1:/ 5-55 L(\:.c) -\·6 <6 c etc)

- Vs -\- I, ~ log?.} L(t~ -C(-tc)

Maximum capaci tor voltape for the McMurray Chopper.

5-33

YY-Vs

- \ + \ -<02. "

The maximum voltage rise on the T.C. Chopper is:

Energy losses

Y-L- \ tY Vs

With the McMurray Chopper -

Energy loss per commutation is:

Wi th the Transfer Curr ent Chopper -

Energy loss per commutation is:

1-Vs etc.

1-

l. Vs et.c 2

Ignorine the term Vs 2 ctc which is common to both expressions, we can have the following relative terms.

Power loss (T.C. chopper)

Power loss (McMurray Chopper) 5-34

6·\ 2.. '{ t 5·5{; \,'2-'L

Ratio of Power Loss (McMurray Chop~ is Power Loss (T.C. Chopper)

6-1[, Y + 5-56 y2-2y +- y2.

The following table allows us to see how these expressions vary with Y.

Y 0.05 O. 1 0.15 0.2 0.25 0.31 0.33 T.C. 0.05 O. 11 0.16 0.22 0.28 0.35 0.38

M O. 16 0.33 0.52 0.72 0.94 1 .17 1 • 31 MIT. C. 3.20 3 3.5 3.27 3.36 3.34 3.41

TABLJ~ 5.4 COMPARISON OF POiVER LOSSES filTH Y.

From table 5.4 we see that the McMurray chopper is more than 3 times the 10 ss of the ~r. C. Chopper. But what do these losses actually represent?

Example: a T.C. Chopper operating with a supply vOltage of 200 volts and a load current of 10 amps. The commutatinf capacitance value is 2uH.

The maximum losses occur when the maximum current is flowing.

Vp = 1 + Y} Y has a maximum value of VB 0.33

Vp = (1 + 0.33) x 200

= 266 volts.

Energy loss is equal {266)2

2

= 3.076 x 10-2 jo~les.

Say the chopper is operating a 1 kilohertz

1 -2 'Z

Loss in Power = 3.076 x 0 joules x 10J

1 second.

:::: 30.76 watts.

The McMurray Chopper wi th ,/\ = 0.6 would dissipate 104.89 watts

104.9 Jf "2" 00 x 10 m e an s a 5. 2'}0 los sin e f f i c i en c y •

26g·~ 10 means a 1.5% loss in efficiency.

So the T.C. Current Chopper does have an advantage over the McMurray Chopper. ~{hen actually comparine losses this method is rough. The S.D.R. forward voltage drop results in losses. Also the minimum capacitor

5-35

voltage falls below the supply voltage.

If losses are important, the following chopper has the least losses of any chopper.

S upp\y IrtQuctGnce

3

I\,.qODIFIED PARALLEL CAPACITOR CH01-:lpEH

4

Load

To commutate S. C.R. "CR", S. C.R.s is 1 & 4 are triggered. On the next commutation S.C.R.s 2 & 3 are triggered. The operation of the chopper is the same as the Parallel Capacitor Chopper.

If there is no inductance in series with the supply, there is no build of capacitor voltage above the supnly vol tage. J:his means that the minimum and maxi mum capaci tor voltages are equal.

The only disadvantage with this chovper is the commutation period.

tc - V~ C It

It is a function of the load current. At low currents the commutation period is large. This makes operation at high frequencies difficult.

5-36

CONCLUSION

In this project detailed information about the Transfer Current Chopper has been discussed. The operation of the chopper has been described in greater detail than Mr. M4 Akamatsu, M. Kumano and A. Kaza cared to describe it in. In chapter four experimental evidence was given to prove the justification of equations derived in chapter three.

It is interesting to note that it takes one chapter (chapter two) to describe the operation of the core. It takes two large chapters (chpter three and five) to describe the operation of the commutating capacitor voltage outside the commutation period. dhat occurs during the commutation period determines what size of commutating capacitor is needed. But capacitor voltage variation outside the commutation period determines the efficiency of the chopper. It also determines the capacitor voltage at the beginning of the commutation period.

The term U.F.C. introduced by Pro M. Akamatsu, M. Kumano and A. Kaza, was used to compare capacitor sizes durinr, this project. In addition it was used in comparing losses, something Mr. M. Akamatsu & Co. did not.

State equations have been successfully avoided providing the designer with a richer understanding of what is occurring. It is unfortunate that equations on page 2-16 and 5-23 have not been combined as to show the full effects of Q and the losses within the chopper.

Another regret is that higher voltages could not have been used. Thus giving a good in the designs. The only source of high voltages which could handle reasonable amounts of power were D.C. motors. These motors have amounts of armature inductance. dhen the capacitor current falls to zero, the large armature inductance produces larg'efinal voltages, which is a disadvantage.

A battery is the ideal vOltafe source. The problem is that Iusti tute batteries have a maximum vol taQ'e of approximately 31 volts. This meant that no expe~ience was gained 'Ni th choppers operating at higher voltages.

Although the results obtained have low errors in them, more ~ccurate results need to be obtained. One such method wonld be to measure the time it takes for a voltage to rise or fall below a certain value. There are several triggering pulses which can be used as starting pulses for the timing circuit.

There has been one assumption made throughout this project, which has not been stated. ~his is, that there is no lumped resistance between the inserted inductance and the commutating capacitance. This allows for simplified expressions. The expressions describing the operation of the T.C. chopper would become complexed. The effects of leaving out this resistance was not observed by the experimental work. Sugf'esting that it is small. Perhaps with more accurate techniques of measurement any effects may be shovm.

CONCLUSION (contd)

Choppers can be treated as a complicated or a simple thing. The deciding factor being what you are going to do with them. Designing a chopper to operate at low frequencies anrt without too much concern about losses would be a simple task. But to design a chopper to operate at high frequencies and with low power dissipation would mean a great deal of work. The characteristics of the load will also affect the design and choice of the type of chopper.

A method for protecting the chopper was developed and it worked. It consisted of a 0.05 ohm resistor, which was used to the load current. When the load reached a prescribed point it was chopped and the triggering circuit did not trigger the main S.C.R. itCH" for a prescribed time. . -

No method was developed to detect a non-commutation (commutation capacitor going to zero). This senSing is important as the load current is no longer under control. Detailed information of how to incorperate such a feature was not given in this project because of time and space reasons.

One final important point "What may be good for a chopper may not necessarily be good for an inverter.tI

J.A. DOWSETT.

( 1) A Thyristor-FoTced COl.m.'1ut:ltion. l'Iethod VIi tIl Commutation Current frel1sformer.

, . 1¥J s};:,:un::n:,su, )/. K rU'!1,TI10 and .::~. Ii [iZ~i.

)

(2) • gdh.:a:ray, D.P. ;3hD .. ttch: I.:J:.E.g. ~C:I·ans. on GOIDLRm. 'Slectronics,

Yolo CE - SO p. 531, No. 1 961

The above Here only 11seful references fO'lmu. References on other choppers cc:m be found at the back of Hel'. (1).

A userul design reference is the fol1o'ltJing

(3) Philips Data Handbook. Components a.:.t1d l:Iaterials 0

Part It", JViarch 1970

APPENDIX ONE

This appendix consists of a listing of the results obtained for the commutation period, with the initial capacitor remaining constant. The variables Q and the load current are varied.

On page 2-16 we have the following equations

T= To{~ -JH?-;K tt~-\t QJH\~-\\1)

\ e t t "\(1g H:::: \

The computer printed the com8utation period in terms of T , for various Q and K. Q varies between and 4.5, wHile K varies between 0.05 and 0.95.

From the results, it can be seen that by having ~ between the values of 3.0 to 3.3, there will be little variation of the commutation period.

The first column of the results is K, the second is the time the core is negatively saturated. The third column is the time where the core is not positively or negatively saturated. The fourth column is the addition of the second and third columns. (The last three columns are in terms of To.)

0001 0002 0004 0005 0006 0007 0008 0009 0020 0030 0040 0050 0060 0070 0080 0090 0100 0110 0120

IJISTING OF PROGRAM USED -"---------Let H=O For Q=1 TO 5.5 Step .1 Let H=H+1 If H < 4 then go to 0020 For Z=1 TO 15 Print Next Z Let H=1 Print Tab(6), "This is QII, W For K=.05 TO .97 step .05 Let T1=SQR(1-K) Let T2=T1/K Let T1=1/K-T2 Let T2=T2*Q IJet T2=ATn(T2) Let T2=T2/Q Print Tab(6), K,T2,T1,T1+T2 Next K Next Q

THIS IS Q 1 .05 1.51954 • 506409 2.02595

• 1 1.46577 .513167 1.97394

• 15 1.40951 .520304 1.92982 .2 1.35081 .527864 1.87867 .25 1.28976 • 535898 1.82566

• 3 1.22651 .544467 1.77098 .35 1.16123 .553641 1.7 1 487 .4 1.09412 .563508 1.65762 .45 1.02541 .574178 1.59958

• 5 .955316 .585787 1.5411 .55 .884043 .593503 1.48255

• 6 .811726 .612574 -1.4243

• 65 .738404 .628295 1.3667 .7 .663954 • 6461 1 1.31006 .75 .588003 .666667 1.25467 .8 .50974 .690933 1.20072 .85 .427538 .720826 1 • 1 4836 .9 .337889 .759747 1.09764 .95 .231167 .81 7256 1.04842

THIS IS Q 1 • 1 .05 1.38563 .506409 1.89204

• 1 1.34115 .513167 1.85431

• 15 1.2945 .520304 1 .8 1 48 1 .2 1.24568 .527864 1.77355 .25 1. 19468 .535898 1.73058

• 3 1.14153 .544467 1. 686

• 35 1.08628 .553641 1 • 63992 .4 1.02899 .563508 1.59249 .45 .969737 .57417'3 1.54391 .5 .908619 .585787 1.49441 .55 .845703 .598508 1.44421 .6 .781022 .612574 1. 3936 .65 .714535 • 628295 1.34283 .7 • 64607 .64611 1.29218 .75 .575226 .666667 1.24189 .3 '-501197 • 690983 1.19218 .85 .422377 .720826 1. 1432 .9 .335286 .759747 1.09503 .95 .230317 .817256 1.04757

THIS IS Q 1.2 .05 1.27339 .506409 1.7798

• 1 1.23598 .513167 1.74915 • 15 1.1967 • 520304 1.717 .2 1.15547 .527864 1.68334 .25 1.11226 .535898 1. 64816

• 3 1.06703 .544467 1.61149 .35 1.01973 .553641 1.57337 .4 .970348 .563508 1.53336 .45 .918865 .574178 1.49304 .5 .865261 .585787 1.45105 .55 .809504 .598508 1.40301 .6 .751527 .612574 1.3641 .65 .691197 .623295 1.31949 .7 • 62827 • 6461 1 1.27433 .75 • 562283 .666667 1.22895 .8 .492394 • 690983 1.18338 .85 .416969 .720826 1 • 1 378 .9 .332515 .759747 1.09226 .95 .229399 .817256 1.04666

THIS IS Q 1 • 3 .05 1.17797 .506409 1.68437

• 1 1 • 14607 .513167 1.65924

• IS 1.11253 .520304 1 • 63284 .2 1.07727 .527864 1. 60514 .25 1.04022 .535898 1.57612

• 3 1.00128 • 544467 t·54575 .35 .960384 .553641 1.51403 .4 .917447 .563508 1.48096 .-45 .872382 .574173 1.44656 .5 .825097 .585787 1.41088 .55 .775475 .598508 1.37398

• 6 .723367 .612574 1.33594 .65 .668555 .628295 1.29685 .7 .610711 .64611 1.25682 .75 .5493 .666667 1.21597 .8 .433412 • 690983 1.1744 .85 .411359 • 720826 1.13218 .9 .329594 .759747 1.08934 .95 .228416 .817256 1.04567

THIS IS Q 1.4 .05 1.09584 • 506409 1. 60224

• 1 1.' 06832 .513167 1 • 58148 • 15 1.03936 .520304 1.55966 .2 1.00887 .527<364 1.53673 .25 .976749 .535898 1.51265 .3 .942904 .544467 1.48737 .35 .907222 .553641 1.46086 .4 .869588 .563508 1 .4331 .45 .829871 .574178 1.40405 .5 • 787925 .585787 1.37371 ;55 .743574 .598508 1.34208 .6 .6966 .612574 1 • 309 1 7 .65 .646715 .628295 1.27501 .7 .59351 • 64611 1.23962 .75 .536378 .666667 1.20304 .8 .474325 .690983 1.16531 .85 .405589 .720826 1.12641 .9 .326538 .759747 1.08629 .95 .227371 .817256 1.04463

THIS IS Q 1. 5 .05 1;02441 .506409 1 • 53081 • 1 1.00043 .513167 1.51359 • 15 .975168 .520304 1.49547 .2 .948542 .527864 1.47641 .25 .920446 .535898 1 .45634

• 3 .890769 .544467 1.43524 • 35 .859385 .553641 1.41303 .4 .826159 .563508 1.38967 .45 .790932 .574178 1.36511 .5 .• 753523 .585787 1.'33931 ;55 .713714 .598508 1.31222 .-6 .671235 .612574 1 • 28381 .65 • 62574 .628295 1.25404 .7 .576756 • 6461 1 1.22287 .75 • 523599 • 666667 1.19027 ;8 .465196 .690983 1.15618 .85 .399696 .720826 1.12052 .9 .323366 .759747 1.08311 .95 .226267 .817256 1.04352

THIS IS Q 1 .6 .05 .961715 .506409 1.46812

• 1 .940631 .513167 1.4538

• 15 .918411 .520304 1.43871 ;2 .894962 .527864 1.42283 ."25 .870184 .535898 1.40608

..... · ..) .843958 .544467 1.38842

.35 .816155 .553641 1 • 3698

.4 .786626 • 563508 1.35013

.45 .755197 .574178 1.32937

• 5 ." 721664 .585787 1.30745 .55 .685782 .598508 1.28429 .6 .647245 .612574 1.25982 .'65 • 605662 .628295 1.23396 .7 • 560506 .64611 1.20662 .75 .511028, • 666667 1 • 1 7769 ';8 .45608 • 690983 1.14706 .85 .393716 .720826 1.11454 ;9 • 320092 .759747 1.07984 ;95 .225108 .817256 1.04236

THIS IS Q 1.7 .05 .906252 .506409 1.41266

• 1 .88757 .513167 1.40074

• 15 .867871 .520304 1.38818 .2 .847066 • 527864 1.37493 .25 .825053 .535898 1.36095

• 3 .801717 .544467 1.34618 ." 35 .776925 .553641 1.33057 .4 .750523 .563508 1.31403 .45 .72233 ;574178 1'-29651 .5 .692129 .585787 1.27792 .55 ." 659657 .598508 1 • 2581 7 .6 .624534 .612574 1.23716 .65 .586488 .628295 1.21478 .7 • 544799 • 6461 1 1.19091 .75 .498715 • 666667 1.16538 '-8 .44702 • 690983 1. 138 .85 • 387681 .720826 1 • 1 0851 .9 .316733 .759747 1." 07648 .95 .223897 .817256 1.04115

THIS IS Q 1.0 .05 .856835 .506409 1.36324

• 1 .840167 .513167 1.35333

• 15 .822584 • 520304 1.34289 .2 .804001 .527864 1.33187 .25 .784319 .535898 1.32022

• 3 .763424 • 544467 1.30789 .35 .741186 .553641 1.29483 .4 .71745 • 563508 1.28096 .45 • 692032 .574178 1.26621 .5 .664711 .-585787 1 • 2505 "55 .635212 .598508 1.23372 .6 .- 603192 .612574 1.21577 ." 65 .568206 • 628295 1.1965 • 7 .529657 • 64611 1.17577 .75 .486698 • 666667 1.15337 .8 .438057 • 690983 1.12904 .-85 • 381 618 .720826 1.10244 .9 .313301 .759747 1.07305 ."95 .222637 .817256 1.03989

THIS IS Q 1.9 .05 .812527 .506409 1.31394

• 1 .797564 .513167 1.31073

• 15 .781775 .520304 1,- 30208 .2 .765077 • 527864 1.29294 .-25 .747375 .535898 1.-28327 .- 3 .728562 .544467 1.27303 .- 35 .708508 .553641 1.26215

.' 4 .687061 .563508 1.25057

.45 .664039 .574178 1.23822

.5 .639218 .585787 1.22501

.'55 .612323 .598508 1.21033

.6 • 583001 .612574 1.19557

.' 65 .550795 .628295 1.17909

.7 .515088 • 64611 1.1612

.75 .475003 • 666667 1.14167

.8 .42922 .690983 1 .' 1 202

.85 .375554 .-720826 1.09638

.9 .309812 .759747 1.06956

.95 .~221333 .817256 1.03859 THIS IS Q 2 .05 .772575 .506409 1.27898

• 1 .759069 .513167 1.27224

• 15 .'744812 .520304 1.26512 .-2 .729727 .527864 1.25759 .25 .713723 • 535898 1.24962

• 3 .696697 .544467 1"24116 .~ 35 .678524 • 553641 1.23217 '-4 • 659057 .563508 1.22257 .45 • 6381 15 .574178 1.21229 .5 .615479 .585787 1.20127 .55 .590872 .598508 1.18938 .6 • 563942 .612574 1.17652 .65 .534225 .628295 1.16252 .7 .501092 • 6461 1 1 • 1472 .-75 .463647 • 666667 1.13031 .8 .420534 .690983 1 • 1 1 1 52 .85 • 369509 .720826 1.09033 .9 .306277 .'759747 1.06602 .95 .219987 .817256 1.03724

THIS IS Q 2. 1 .05 .736367 • 506/109 1.24277

• 1 .724115 .513167 1.23728 • 15 .711178 .520304 1 .23143 .2 .697483 .527864 1.22535 .25 • 682946 • 535893 1,.21884 .3 .667466 .544467 1.21193 .35 .650924 .553641 1.-20457 '-4 .633178 • 563503 1.19669 .45 .614054 .574178 1.18823 .5 .593334 .585787 1 • 1 791 2 .55 .570748 .598508 1.16926

• 6 .545945 .612574 1.15852 .~ 65 .518461 .628295 1.14676 .7 .487662 .64611 1.13377 .75 .452641 .666667 1.11931 .8 .412017 • 690983 1. 103 .85 .363501 .720826 1.08433 .9 .302709 .759747 1.06246 .95 .218603 ;817256 1 .03586

THIS IS Q 2.2 .05 .7034 • 506409 1.20981

• 1 .692235 .513167 1.2054 • 15 .660443 .520304 1.20075 .2 .667955 .527864 1.19582 ~25 .654692 ~" 535898 1. 19059 .3 .640559 .544467 1.18503 .35 ." 62544 • 553641 1.17908 ;4 .609201 .563508 1.17271 .45 .591671 .574178 1.16585 .5 .572641 .585787 1.15843 .55 .551846 .598508 1.15035 ;6 .52894 .612574 1.14151

• 65 .503464 .628295 1.13176 ;7 .474784 .64611 1 • 1 2089 .75 .441989 .666667 1. 10866 ."3 .403685 .690983 1.09467 ~85 .357548 .720826 1.07837 ;9 .299118 .759747 1.05886 .95 .217184 .817256 1.03444

THIS IS Q 2.3 .05 .673258 .506409 1.17967 ~ 1 • 663041 .513167 1.17621 .15 .652249 .520304 1.17255 .2 • 640817 .521864 1 • 16868 .25 .628668 • 535898 1.16457 .3 ;615713 ;544467 1 • 1 6018 .35 .601843 .553641 1.15548 .4 .586929 .563508 1.15044 .45 .570806 .574178 1.14498 .5 .553273 .585787 1.13906 .55 .534071 .598508 1.13258 ;6 .512863 .612574 1.12544 .'65 .489195 .628295 1.11749 .-7 .462442 • 6461 1 1.10855 ;75 ."431692 .666667 1~O9636 .8 • 395549 .690983 1.08653 .85 .351662 • 720826 1.07249 .9 .295514 .759747 1.05526 .95 .215734 .817256 1.03299

THIS IS Q 2.4 .05 • 645593 .506409 1. 1 52

• 1 • 636209 .513167 1. 14938 ;15 • 626294 .520304 1.1466 .2 .615788 .527864 1.14365 ;25 .60462 .535898 1. 14052 .3 .592703 .544467 1.13717 ;35 .579935 ;553641 1. 13358 .4 .566191 .563508 1 • 1 297 .45 ;551316 .574178 1.12549 .5 .535114 .585737 1. 1209 .55 .517335 .598508 1. 1 1 584 .6 .49765 .612574 1 • 1 1022 ; 65 .475617 .628295 1.10391 .7 .450617 • 6461 1 1.09673 .75 .421748 .666667 1.08842 .8 .387614 .690983 1'-0786 ;85 .345855 .720326 1.06668 ;9 .291906 .759747 1.05165 .-95 .214254 .817256 1.03151

THIS IS Q 2.5 .05 .620111 .506409 1 • 12652 .- 1 .611462 .513167 1. 1 2463 ~' 15 .602322 .520304 1. 12263 ~ 2 .592635 .527864 1 • 1 205 .25 .582333 .535898 1.11823 .3 .571335 .544467 1.1158 ;35 .559544 .553641 1.11318 ;4 .54684 .563508 1.11035 .45 • 533074 .574178 1.10725 .5 • 51806 .585787 1.10385 "55 ;501556 .598508 1.10006 .6 .483243 .612574 1.09582 .65 .462689 .628295 1.09098 .7 .439288 .- 64611 1 .0854 .75 .41215 .666667 1.07882 .8 .- 379886 .690983 1.07087 .85 .340135 • 720826 1.06096 .9 .288303 .759747 1.04805 .95 .21275 .817256 1.03001

THIS IS Q 2.60001 .05 .596564 • 506409 t.l0297

• 1 .588567 .513167 1.10173 .15 .580115 .520304 1.-10042 .2 .571154 • 527864 1.09902 .' 25 .561622 .535898 1.09752

• 3 .551441 .544467 1.09591 .35 • 540519 .553641 1.09416 .4 .528742 • 563508 1.09225 ;45 .515969 .574178 1.09015 "5 • 50202 .585787 1.08781 .55 .486662 .598508 1.08517

• 6 .469587 .612574 1.0821 6 ; 65 .450376 .623295 1.07867

• 7 .428436 .64611 1.-07455 .75 .402891 .- 666667 1.06956 .8 .372367 .690983 1.06335 .85 ;334511 .720826 1.05534 .9 .2.84711 .7597,47 1.04446 .95 .211222 .817256 1.02848

THIS IS Q 2.70001 .05 .574739 .506409 1.08 1 1 5 ; 1 • 567323 .513167 1.08049 • 15 .559484 .520304 1.07979 ;2 ;551172 • 527864 1 ~'O7904 .25 .542326 • 535898 1.07822 ;3 .532875 .544467 1.07734 .35 .52273 .553641 1.07637 .4 .511784 .563508 1.07529 .- 45 .499901 .574178 1.07408 ;5 .486909 .585787 1.0727 .55 .472585 .598508 1.07109 .6 .456631 .612574 1.06921 ;65 .438641 .628295 1.06694 ~7 .418037 .6L161l 1 .06415 .75 .393961 .666667 1.06063 .-8 .365057 .- 69098 3 1.05604 .85 .328988 .720826 1.04981 .9 ;281137 .759747 1.04088 .95 .209675 .817256 1.02693

THIS IS Q 2.80001 .05 • 554455 .. 506409 1.06086 ; 1 .547559 .-513167 1.06073 .- 15 .540269 .520304 1.06057 .2 .' 5325 37 .527864 1.0604 .25 .524306 • 535898 1 .0602

• 3 .515509 .544467 1.05998 .'35 • 506062 .553641 1 .0597 .'4 .' 495863 .563508 1.05937 ;45 .484781 .574178 1..05896 .5 .472653 .585787 1.05844 .55 .459264 ;598508 1.-05777 .' 6 .444328 .612574 1.0569 .65 .427451 '-628295 1.05575 '-7 .408072 • 64611 1.05418 .75 .385352 .666667 1.05202 ;8 .357956 .690983 1.04894 .85 • 323571 .720826 1.0444 .9 .. 277586 .759747 1.03733 .' 95 .208111 .817256 1.02537

THIS IS Q 2.90001 .05 .535553 .506409 1.04196 ; 1 .529124 .513167 1.04229

• 15 • 522327 .- 520304 1'-04263 ;2 .515117 .527864 1.04298 • 25 '-50744 .535898 1.04334 .3 .499232 .544467 1.0437 ~' 35 .490413 .553641 1.04405 .4 .480887 • 563508 1.0444 .45 .' 470529 .574178 1.04471

• 5 .459183 .535787 1.04497 .55 .446643 • 598508 1.04515 ~ 6 ;432633 .612574 1.-04521 ;'65 .-416773 .628295 1.04507 .7 '-398519 • 6461 1 1.04463 .75 .377051 .666667 1.04372 .-8 .351062 • 690983 1.04205 '-85 .318263 • 720826 1.03909 .9 .274064 .759747 1.03381 .95 .206532 .817256 1.02379

THIS IS Q 3.00001 .05 • 517898 .506409 1.02431

• 1 .51189 .513167 1.02506 .' 15 • 505538 .520304 1.02584 .2 .498798 .- 5278 64 1'-02666 .25 .491621 • 535898 1.02752 .3 .'483945 .544467 1.02841 .35 .475695 .5536l 11 1.02934 .4 .466777 • 563508 1.03028 .45 .457075 .574178 1.03125 ;5 .446439 .585787 1.03223 ;'55 .43467 .598508 1.03318 ;6 .421506 .612574 1 .03408 .65 .406577 .628295 1.-03437 ;7 .389357 .64611 1.03547 .75 .369049 • 666667 1.03572 .8 • 34437 .690983 1.03535 '-85 .313066 .720826 1.03389 '-9 .270575 .759747 1.03032 '-95 '-204941 .817256 1.0222

THIS IS Q 3.10001 .05 • 50137 .506409 1.00778 .- 1 .495743 • 513167 1.00891

• 15 .489793 .520304 1.0101 .2 .483479 .527864 1 .01 1 34 .25 .476755 .535898 1.01265

• 3 .469561 .544467 1.01403 ':35 .461825 .553641 1.01547 .- 4 .453461 .563508 1.01697

." 45 .444355 .574178 1.01853

• 5 .434365 .585787 1.02015 .- 55 .423301 ." 598508 1.-02181 .- 6 .410909 .612574 1.02348

." 65 ':396835 • 628295 1.02513 ':7 .380563 • 646 I 1 1 .02668 .75 .361333 .666667 t.028 ."8 .337878 .690933 1.02886 • .- 85 ;307982 .720826 1.02881 .9 .267122 .759747 t·02687 ':95 .203341 .817256 1.0206

THIS IS Q 3.20001 .05 .485863 .506409 .992272 .- 1 .480582 .513167 .99375 .- 15 .474998 .520304 .995302 .2 .469072 .527864 .996936 ." 25 .462758 .535898 .998656 .3 .456002 .544467 1.00047 .- 35 .448735 .553641 1 .00238 .4 .440874 .563508 1.00438 .- 45 .- 432312 .574178 1 • 00649 .- 5 .422912 .585787 1 • 0087 .- 55 .412492 .598508 1 .-0 1 1 .- 6 .400807 .612574 1.01338 .' 65 • 387519 • 628295 1.01581 .7 .-372132 • 6461 1 1.01824 • 75: .353893 .666667 1.02056 ':8 .33158 • 690983 1.02256 .85 • 303011 .720826 1.02384 .9 .26371 .759747 1.02346 .-95 .201733 .817256 1.01899

THIS IS Q 3.30001 .05 .471287 .506409 .977696 ;1 .466322 .513167 .979489 ;15 ':46107 .520304 .981374 .2 .455496 .527864 .98336 .25 .'449557 .535898 ."985455 ." 3 .4432 .544467 .987667 ;35 .436361 .553641 .990003 .4 .42896 .563508 .992468 .45 .420895 .574178 .995072 .- 5 .'412033 .585787 .99782 ;55 ." 402204 .593503 1.00071 "/ -0 .39117 .612574 1."00374 ;65 .378605 .- 628295 1~O069 .-7 .364031 .64611 1.01014 ;75 ."346717 .666667 1.01338 .8 .325471 .690933 1.01645 .'85 ."298153 .720826 1.01898 .9 .26034 .759747 1.02009 ;95 .-200119 .817256 1 .01 738

THIS IS Q 3.40001 .05 .45756 .506409 .963969 .' 1 .452882 .513167 .96605 '-15 .447934 • 520304 .968238 '-2 .442683 .527864 .970547 .25 .437086 • 535898 .972984 .3 .-431094 .544467 .975561 .35 .' 424646 .553641 .978283 '-4 '-417666 .563508 '--981174 .-45 .410055 .574178 .984233 .' 5 .401689 .585787 .987476 .55 .392402 .598508 .99091 .6 .381968 .612574 .994541 .- 65 .37007 .. 628295 .998365 '-7 .356248 .64611 1.00236 .75 .339795 .666667 1.00646 ;8 .319547 • 690983 1.01053 .85 .'293409 .720826 1.01424 .'9 '-257016 .759747 1.01676 '-95 .198502 .817256 1'-01576

Tl-ilS IS Q 3~50001 .05 .44461 .506409 .951019 • 1 .'440196 .513167 .953363 • 15 .435526 .520304 .95583 ."2 .430569 .527864 .958433 .25 .425286 .535898 .961184 .3 .419629 .544467 '-964096 '-35 .413539 .553641 .967181 .' 4 .406945 • 563508 .970453 ;45 .399752 .574178 ;97393 '-5 .391842 .585787 .977629 '-55 .383054 .598508 .981561 '-6 .373172 .612574 .985745 • 65 '-361892 .628295 .990187 .7 .348768 • 64611 .994878 ~' 75 .333115 .666667 .999782 '-8 .313801 • 690983 1.00478 .'85 .288777 .720826 1 • 00 9 6 .9 '-253738 .759747 1.01348 ;95 .196883 .817256 1.01414

THIS IS Q 3.60001 .05 .432373 .506409 .938782 .- 1 .4282 .513167 .941367 • 15 ~'423786 .520304 .94409 .2 .4191 .527864 .946964 .25 .414104 .535898 .950003 '-3 .408755 .544467 .953222 .35 .402995 • 553641 .956637 '-4 .396756 .563508 .96026L1 .45 • 389948 .574178 .964126 .5 .382457 .585787 '-968243 .55 .374129 .593508 .972637 ~' 6 .364758 .612574 .977331 .- 65 .354049 .628295 .982344 .7 ·341574 • 6461 1 .987684 .75 • 326668 • 666667 .993334 '-8 .308229 • 690983 .999213 ~'85 .284255 • 720826 1.00508 .9 .250509 .759747 1.01026 .95 .195265 .817256 1.01252

THIS IS Q 3.10001 .05 .420192 .506409 .9212 .~ 1 .416841 .513161 .930008 • 15 .412662 .520304 .932965 .-2 .408225 .521864 .936089 .25 .403494 .535898 .939393 ;3 ;398428 .544461 .942895 .' 35 • 392972 .553641 .946613 .4 .38706 .- 563508 .950568 .- 45 • 380607 .514118 .954185 '-5 ;313503 .585181 .95929 .- 55 .365601 .598508 .964109 .' 6 .356702 .612574 .969276 • 65 .346524 .628295 .914819 ;7 .' 334652 • 6461 1 .'980763 .75 .320442 .666667 .987109 .'8 .- 302826 .690983 .993809 ;85 ;219843 .720826 f.00061 ';9 .241329 .759141 1.00708 .95 .193648 .817256 1 .0109

TaIS IS Q 3.80001 .05 .409814 .506409 .916223 .- 1 .. 406068 .513167 .919236 • 15 .402106 .520304 .92241 .2 • 397899 .527864 .925763 .-25 .393413 .535898 .929312 .3 .- 388608 .544467 .933075 '-'35 • 383432 • 553641 .937014 .4 .311823 .- 563508 .941331 ';45 .371698 ;574178 .945875 '-5 • 364952 .585787 .950738 ;55 ';357445 .598508 .955952 .6 • 348984 .612514 .961558 .65 .339299 .628295 .967594 ;1 .321989 • 6461 1 .974099 .-75 .- 31443 .- 666661 .981096 .-8 .291584 .690983 .988567 .85 .275538 .720826 .996364 ;9 .-2442 .759747 r.00395 ~'95 .192033 .817256 1.00929

THrs IS Q 3.90001 .05 .399395 .506409 .905803 • 1 .395839 .513161 .'909006 ;15 • 392011 .520304 .91238 .-2 • 388082 .521864 .915947 ;25 .383823 .535898 .919121 ';3 • 379259 .544467 .923726 ;35 ~'314342 .553641 .927984 .-4 .- 3690 13 .5635013 .932521 ';45 .363191 .574178 .937369 .- 5 ;356711 ;585187 .942564 ."55 .349636 .598508 .948144 .6 .-341583 .612574 .954157 .65 .332351 .628295 .960652 .1 • 32157 • 64611 .967681 .15 • 30862 • 666667 .975287 .-8 ;292499 • 690983 .983482 ;85 .211339 .720826 •. 992165 .9 .241122 .759747 1.00087 .-95 .190423 .817256 1'-00168

END AT 0120

*

THIS IS Q 4 .05 .389493 .506409 .895902 .- 1 .'386112 .513167 .89928 .- 15 .382536 .520304 .90284 ~2 • 378736 .527864 .906603 ;25 .- 374688 ;535898 .910586 .' 3 .370343 .544467 .914315 .' 35 :365672 .553641 .919313 .4 .360602 .563508 .92411 ;45 • 355062 .574178 .92924

• 5 .• 348957 .585787 .934744 .55 ;'342156 .598508 .940664 ;6 .334482 .612574 .947056 .65 .325683 .628295 .953978 '-7 .315386 • 64611 :961496 :75 .303006 .666667 .969673 ."8 .287565 .690983 .978549 :85 .267243 .720826 .988069 .9 .238096 .759747 .997843 ';'95 .188819 .817256 1.00608

THIS IS Q 4. 1 .05 .380069 .506409 .886478 .; 1 .376852 .513167 .890019 • 15 ';373447 .520304 .893751 ';2 :369832 .527864 .897697 '-25 .365976 ;535898 .901875 :3 .361344 ;544467 .906311 .35 .357392 .553641 .911033 :4 :352562 .563508 .91607 :45 .347285 .574178 .921462 :5 .341466 .585787 .927253 .55 .334982 .598508 .93349 .' 6 .'327661 .612574 .940235 .-65 .319261 .628295 .947556 .-7 .309422 • 6461 1 .955532 :75 ';297578 .666667 ;964244 :8 .282778 .690983 .973761 .-85 .263248 .720826 .984074 :9 .235122 .759747 .994869 :95 .- 187221 .817256 (.00448

THIS IS Q 4.2 .05 .371091 .506409 .8775 .' 1 .' 368025 .513167 .881192 • 15 • 36478 .520304 .885084 .2 '-361335 • 527864 .889199 .'25 .35766 .535893 .893558 :3 .353721 .544467 .898188 .35 .' 349476 .- 553641 .903117 :4 .344871 .563508 .908379 .45 ;'339837 .574178 .914015 '-5 .334286 .585787 .920073 .-55 • 328097 .598508 .926605 .- 6 .321106 • 612574 .93368 :65 :313079 .' 628295 .'941374 .-7 • 303668 .64611 .949779 ;75 '-292327 .666667 .958993 .-8 .27813 .690983 ;969114 ;85 .259351 • 720826 .980177 ."9 ;2322 .759747 .991947 .-95 .185632 .817256 1.00289

THIS IS Q 4.3 .05 • 362527 • 506409 • g 68936

• 1 .' 359602 .513167 ;872769 .' 15 .356506 .520304 .87681 .2 .353219 .527864 .881083 ;25 .349712 .535898 .88561 .3 ~'345953 .544467 .89042 .' 35 ;341902 .553641 .895543 ;4 .337506 .563508 .901014 ;45 .3327 .574178 .906878 .5 ;327398 .585787 .913185 ;55 ;'321485 .598508 .919993 ;6 ~314802 ;612574 .927376 .' 65 .307125 ;628295 .93542 .7 • 298116 .- 64 611 .944226 .75 .287246 .666667 .953913 .8 ;273619 .690983 ;964602 .85 .255551 .720826 .976377 ~·9 .22933 .759747 .989077 .95 • 184051 .817256 1.00131

THIS IS Q 4.4 .05 .354349 .506409 .860758

• 1 .351555 .513167 .864723 • 15 ;348599 .520304 ;868903 .- 2 .345459 .527864 .873323 .-25 .34211 .535898 .878008 .- 3 .338519 .544467 .882986 ;35 .334648 .553641 .'888289 '-4 ~. 330447 .563508 .893955 ;45 '-325853 .574178 .900031 ;5 .320785 .585787 .906571 ;55 .315129 • 598508 .913637 .6 ;308735 .612574 .921309 .' 65 ;301385 .628295 .92968 ;7 .292753 '-64611 '-938864 .-75 .282328 ;666667 .948995 ;8 .269238 .690983 .960222 .85 ;251844 .720826 .97267 ;9 .226512 .759747 .986259 '-95 .182479 .817256 .999736

THIS IS Q 4.5 .05 • 346532 .506409 .852941 ; 1 .343861 .513167 .857028 • 15 ;341035 .520304 .361338 ;2 .338032 .527864 ;865897 ;25 • 33483 • 535898 .870728 ;3 .331396 • 544467 .875863 ;35 .327694 .553641 .1381335 ;4 .323676 .563508 .887184 .45 .319281 .574178 .893459 .5 .31443 .585787 .900217 .- 55 .309016 .598508 .907524 ;6 .302893 .612574 .915467 .65 ;29585 .628295 .924145 ;7 ;287573 .64611 .933683 ;75 .277566 .666667 .944232

; ,! .-8 .264984 .~ 69098 3 .955967 ."85 .248229 .720826 .969055 .- 9 .-223745 .759747 .983492 .-95 .180918 .817256 .998175

PHOTOGRAPH NUMBER ONE.

68.2uH T.C. Chopper.

Load current - 1 amp.

Supply voltage - 32 volts.

Time - 20 usecs. per. div.

(1) Capacitor Voltage, 10 volts per. diva (x 0.941).

(2) Voltage from search coil, around T.X. Core.

(3) Capacitor Current, 1 amp. per. diva

(4)

PHOTOGHAJ?H NUMB1~H T'v'lO.


Load Current - 2 amps.


Time: 20 u.secs. per. dive

(1) Capacitor Voltage, 10 volts per div. (x 0.941) ·


(3) Capacitor Current, 1 amp. per. dive

(4)

PHOTOGRAPH NUMBER THREE.

68.2w{ T.C. Chopper.


Supply Voltage - 32 volts.

Time - 20 u.secs. per. dive

(1) Capacitor voltage, 10 volts per div (xO.941).


(3) Capacitor Current, 3 amps per division.

(4 )

PHOTOGHAPH NUIVIB:;~I1 FOUR



Supply Voltage - 32 volts. Time - 20 u.secs. per. dive

(1 ) Capacitor Voltage, 10 vol ts per di v. (x 0.941) •

(2) Voltage from search coil, around T.L. Core.

(3)

(4) Capacitor Current, 2 amps. per. dive

PHOTOGRAPH NUMBER FIVE




Time - 20 u.secs per. dive

(1) Capacitor Voltage, 10 volts per. dive (x 0.941).


(3)


PHOTOGHAPH NUMB1;;R SIX


Iload Current - 6 amps.


Time - 20 u.secs. per dive

(1) Capacitor Voltage, 10 volts per. div (x 0.941).


( 3)

(4) Capacitor Current, 2 amps per dive

PHOTOGRAPH l'mMBER SEVEN

68.2uH T.C. Chopper ..




(1) Voltage from search coil, around T.X. core.


( 3)


PHOTOGRAPH NUMBER EIGHT






( 2 ) Cap a cit or vol ta ge, 20 v 0 It s per. di v • ( x O. 941 ) •

(3 )

(4) Capacitor Current, 2 amps. per. diVe

PHOTOGRAPH NUIlJIBER NINE







( 3)

(4) Capacitor Current, 2 amps per. diVe

PHOTOGRAPH NUMBER TEN



Supply Voltage 32 volts.


(1) Voltage from search coil, around Tx core.


( 3)


PHOTOGRA:PH NUMBER ELEVEN




Time - 20u.secs. per. dive

(1) Capacitor Voltage, 20 volts per dive (x 0.941) .

(2) Voltage from search coil t around Tx core.

(3 )

(4) Capacitor Current, 2 amps per diVe


Load Current 12 amps.



(1) Capacitor Voltage, 20 volts per. diVe (x 0.941).


( 3)

(4) Capacitor Current, 2 amps per. -dive

j-;HOTOGHAPH NUMBER THIRTEEN

20uH T.O. Chopper.

Load Current - 1 amp.



(1) Transformer Core Flux.

(2) Capacitor Voltage 20 volts per dive (x 0.941).

(3) Voltage across the flywheel diode.

(4) Capacitor Current, 2 amps per. dive

PHOTOGRAPH NUMBER FOUHT~EN

20uH T. C. Chopper.

Load Current - 2 amps. Supply Voltage - 32 volts.

Time - 20 u.secs. per diVe


( 2 ) Cap a cit 0 r Vol t a ge, 20 vol t s per. d i v • ( x O. 941 ) •

(3) voltage across the flywheel diode

(4) Capacitor current, 2 amps per. diVe

PHOTOGHAPH NUIVIBEH FIFTEEN --'~~---"-~----. --_ .. _.,-

20uH T.C. Chopper.








PHOTOGHAJ?H NUMBER SIXTEEN

20uH T.e. Chopper.

IJoad Current - 4 amps.

Supply Voltage - 32 volts. Time - 20 u.secs. per. dive


( 2 ) Ca pa cit 0 r Vol t a ge, 20 vol t s per. d i v • ( x o. 941 ) •

(3) Voltaee across the flywheel diode.

(4) Capacitor current, 1 amp per. diVe

PHOTOGRAPH NUMBEH SEVENTEEN

20uH T.C. Chopper.



Time - 20 u.secs. per div.


(2 ) Capacitor Voltage, 20 volts per. div. (x 0.941).

(3) Voltage across the flywheel diode

(4) Capacitor Current, 1 amp per. div.

PHOTOGRAPH NlITvIBER EIGHTEEN

20uH T.C. Chopper.



Time 20 u.secs. per. dive


(2) Capacitor Voltage, 20 volts per dive ex 0.941).



PHOTOGRAPH NUMBER NINETEEN

20uH. T.C. Chopper.





(2) Capacitor Voltare, 20 volts per dive (x 0.941).



.--

D~~ .

II'

PHOTOGRAPH NUMBBR Tw'ENTY

21. IlV lEu. mVI " D!I, , r.1 .. "" ,II, II ' ',"

I rid -II! .-., i i

II, ! I i , -

I, II i I \i I, I '"

- 111 1 I \ II' • ~ II' I, ~ I' II' I

i IlI1! \ II I

! ; I~ I , I I " . ... . " .. il·· l1' '"IIJ.!!!:.: :IiiiIiiI

I 51· mV 20 I r 20 tiS

20uH T.C. Chopper.

Load Current 10 amps.



I


-

(2) Capacitor Voltage, 20 volts per. div (x 0.94 1 ).



PHOTOGRAPH NUMBER TviENTY ONE

5uH T.C. Chopper.

Load Current - 1 amp.




(2) Capacitor Voltage, 10 volts per dive (xO.941).



PHOTOGRAPH NUMB.En. TIIENTY T,{O

5UH T.C. Chopper.





(2) Capacitor Voltage, 10 volts per. div (x 0.941)

(3) Voltaee across the flywheel diode.


PHOTOGRAPH NUIVIBEH TdENTY THREE

5uH T.O. Chopper.

Load current - 4 amps.




(2) Capacitor Voltage, 10 volts per dive (x 0.941).



PROT OGHAPH NUMBER T ~lENTY FOUR

5uH T.C. Chopper.



Time 10 u.secs. per dive

(1) Voltage fiom search coil, around Tx core.

(2) Capacitor voltage, 10 volts per div (x 0.941).



PHOTOGHAPH NUMBER T'dENTY J?IVE

5uH T.C. Chopper.


Supply VoltaGe - 32 volts.

time - 20 u.secs. per dive





PHOTOGHA~PH NUIvIBEH TWEN~CY SIX

5uH T.C. Chopper.




(1) Capacitor Voltage, 10 volts per dive (x 0.941).




5uH T.C. Chopper.


Supply voltage 32 volts.


(1) Capacitor voltage, 20 volts per dive (x 0.941)




PHOTOGH.APH NUMBER TW}~NTY EIGHT

5uH T.C. Chopper.


Supply Voltage 32 volts.


(1) Capacitor Voltage, 20 volts per. diVe (x 0.94 1 )


(3) Voltafe across the flywheel diode.


C-1

RiEE-a-round Waveforms -(rever-s'al'~ of-- the capaci tor vol tClge)

2 amps (load current) - 20uH.


(3) Capacitor Voltage, 20 volts per dive (x 0.941)

(4) Capacitor Current, 1 amp per. dive

PHOTOGRAPH rTUTvJBER THIRTY ---~,,~-----•.. -~.--~-----

HI 2 ll7V 5li O'iV Ir I ,I ! "" I'~--,1" , . ... . '" . ... . . .

! .. I IIj ! "'-= :.-II Ii M .It ~I ~ !~ g -

,I ~ I ~ III I! iMi II,

I ~ al 1 ~~ l •

t I i ~ M II I ~ 11

" t~ I~ II! .1 I • I .. . il··· I ·m·'i. t"";;;;",, O~· , .... ... . ... . ... . ... . ... .

I l' ~ ... r. l.!'J II) 51, mV 20 50 ·tlS

C-2 4 amps (load current) 20uH.


(3) Capacitor Voltage, 20 volts per. div (x 0.941)


~PHo~r:OGRAPH NUMBER THIRTY ONI!!

- - I"I-~.

I Ir:zi?v III' _ I mg- I, I' ,

f '\ii--, .. . ... . , lB·· ,

II

II I I l ~ .. ~, I i ~

! I , ~ M I I i

t ~ I, ., !

! II i~ I~ II,

I~ -I~i~ ~ I .-:=:

- lit !~~ '~ II i It: III iii --- ~

:1'" ~ I~,

0%' . "a·· .... ... . ... . .., . .. , . ~"' .a. .. ~ .. I; 51· mV 211

a.:.i

i!SI . 50


(3) Capacitor Voltage, 20 volts per. div. (x 0.941)

(4) Capacitor Current, 2 amps per. div.

PHOTOGRAPH NUMBEH. THIHTY TNO

211nv 51 tJ"V I I I t l'lll ~

I II,

II· .. •••• . ... j .. 'I' Ii ' .. 1 , .. . ... t ---+\--i ~ I, ~ ~ 1l1~, :

t ~ III ~ ~~ ! I

111 l r~ r.; ~~ II I I'~ :~ l~ <

~ I Ii

I~ - I .~ ..... '

fi II'Ji ~ 11 I I

, -

l~ , I ! ;

iO 'I":0Il i . ~.~ 0%' ••• .. , . . , .. . , .. . , .. ... . ... . ... . hIa I

w tiS I 11

E 51· mV 211 50


(3) Capacitor Voltage, 20 volts per. div (x 0.941).


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Thesis Description of the Operation of the Transfer Current Chopper

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