84 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

"VWP; A NEW APPROACH TO SMALL, LIGHT, EFFICIENT,HIGH POWER REGULATED POWER SUPPLIES"

Victor WoukElectronic Energy Conversion Corporation

New York 17, New York

Summary cussed in relationship to dc input, the balance ofthis paper is devoted to dc supplies. The switch-

A regulated power supply has been developed, ing technique, indicated in Fig. 2, does not dissi-employing no mains power transformer, with very pate energy in a series or shunt impedance, as islow power dissipating control elements, and result- done in conventional regulated power supplies. Theing high efficiency. The size and weight are sub- input dc is switched on and off at a rapid rate bystantially less than those of conventional designs switch " s", developing rectangular pulses of volt-for comparable power ratings. age, spaced "T" apart, that are applied to the

choke input filter. With proper inductance designThe mains power is converted directly into dc, so that

and silicon controlled rectifiers are utilized to gen-erate high frequency variable width pulses (VWP) fL;> Rq1)of voltage, for output control, and for line and load 1regulation. Pulse width modulation is used to re- where f = Tduce line frequency ripple. The system is advan-tageous for load power ratings above 2 kw. the voltage Eav developed across the resistor Rl

will equal the average of the rectangular wave,Introduction which is determined by:

Reduction of size and weight is an increasing- Eav = Ei XT = k x Ei, whereK (2)ly important objective in the development of mod -

ern electronic equipment. Where possible, higher If "k" is referred to as the duty cycle, the dc out-operating efficiency is also desirable. The regula- put voltage equals the input voltage times the dutyted power supply system described herein effects cycle. This well established concept is not dis -

a substantial saving in size and weight over con- cussed further herein.ventional designs, by eliminating the main powerfrequency transformer, usually a 50/60 cycle trans- It is important to note that a rectifier CR1 con-former, normally employed to raise or lower the nected as illustrated in Fig. 2, must be employed,line voltage. for this circuit to operate properly. CR1 is com-

monly referred to as a "free-wheeling" rectifier2,The system consists of an input rectifier that or "flyback" diode.

immediately converts the main ac power to dc,(without employing a transformer), a chopping cir- This circuit can be made to regulate the outputcuit that converts the dc to high frequency bi-dir- voltage against input voltage changes and load cur-

ectional pulses, and a high frequency transformer rent changes, by varying the width of the pulse, or

for stepping the output voltage up or down as de- the duty cycle,i. e. ,by varying the time"t". Thissired. In order to increase efficiency, variable is done by allowing the switch "s" to remain openwidth pulses (VWP) are developed to control and or closed for greater or shorter periods of time. Ifregulate the output voltage, rather than utilizing the switching rate is rapid (over 1 kc per second),power dissipative techniques such as in series or the pulse width can be modulated to compensateshunt regulating circuits. The variable width pul- for input dc ripple voltage, when the system is op-ses are available either as an inverter for ac out- erated from rectified ac. Hence, this system ofput, or, when applied to a rectifier and an LC av- output voltage control is referred to as "Variableeraging circuit, as dc output. The over-all systan Width Pulse", (VWP), as the average width is var-is illustrated in Fig. 1, in block form, for dc output. ied to give the average output voltage desired, and

rapid width variations, or pulse width modulation,Basic Variable Width Pulse Switching Technique compensates for perturbations of the output by var-

ious causes.It has been pointed out by Morgan and others,

that very efficient regulation of dc power supplies Although this concept of variable width pulsecan be achieved by switching techniques. This control of dc and ac powerhas been known for overalso applies to ac power supplies; but since the half a centLiry, it has been made practical only byconcepts are more readily comprehended when dis- the development of modern high speed switching

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 85

devices having very low voltage drops when carry- and C of Fig. 3, associated with the turning on anding large amounts of current, and negligible conduc- off of each pulse. Because of this, an invertertion when "off". These switches may be power tran- whose efficiency might be 96% at 120 cps, may besistors, or silicon controlled rectifiers (SCRs). For down to 67% at 1 kc, with the output power ratinghigh power levels, above 2 kilowatts, SCRs are dropping more than 50% from 120 cps to 1 kc. Forsuperior to power transistors, due to, among other maximum efficiency, particularly in dc power sup-reasons, the smaller driving power required for plies, where it is desired to operate at a highSCRs, and the lower voltage drops. switching frequency to reduce the size and weight

of the filter components, a circuit to eliminate thisThe balance of this paper is devoted to analy- commutating power loss is desirable.

ses of circuitry and problems peculiar to the useof SCRs in the variable width pulse (VWP) mode. Such a circuit, and several variations thereof,

have been developed by Wouk and Poss5, a typicalDual Polarity Switching one being illustrated in Fig. 4. In this circuit, it

is important to emphasize, no power at all is in-In the switching technique described for Fig 2, herently lost in the commutating process, (except

and in all dc "choppers" described in other litera- internal SCR and rectifier drops, lead losses, etc.)ture, the output voltage is almost invariably lower All of the commutating capacitor energy p a s s e sthan the input voltage, and single polarity pulses through the load, so that the losses in the commu-are generated for subsequent filtering and smooth- tating capacitor are only those incidental to dielec-ing to the desired output voltage level. Where out- tric losses. Hence, this is inherently a very effi-put voltage greater than the input voltage are de - cient circuit, and is referred to hereafter as "loss-sired, for both dc power supply and inverter appli- less" commutation.cations, it is necessary to employ a transformer tostep the voltage up to the desired level. Also, for The operation of the circuit of Fig. 4 is as fol-very low ratios of output dc to input dc voltage, a lows:step down transformer is usually employed, other-wise very short duration pulses in simple chopper 1: Assume that capacitor C is charged to the po-circuits are mandatory, resulting in extremely high larity and voltage shown, i. e. , equal to the inputpeak currents in the switching device, and conse- supply voltage "E". For simplicity of analysis, itquent uneconomical design. will be assumed that the output transformer is a 1:1

voltage transformer, i. e. , twice as many totalDual polarity pulses must be developed to primary turns, center-tapped, as secondary, or

drive a transformer, as unipolarity pulses will as illustrated, Nl = N2. It is further assumed thatcause the transformer to saturate. If this trans- the system is operating under steady state condi-former is operated at a frequency higher than line tions, and a constant load current, I, is flowing infrequency, the transformer can be much smaller for the output filter choke.a given power rating, than the equivalent 60 cycletransformer. 2: SCRs 1 and 2 are fired, and ead and edg are

zero, to energize what is arbitrarily called thepos-NOTE: It is feasible to obtain output volt- itive power pulse. This is illustrated in Fig. 5, atages higher than input voltages without a the start of the period " t1", as are the fact that thetransformer, by using the well known volt- source current, i5, and the SCR currents i and i2,age multiplier circuit of Greinacher3. All equal the load current, I (due to Nl/N2 =1).these circuits have the disadvantage ofproviding no isolation between the primary 3: After a time tl, SCR3 is fired to deenergizeand secondary circuits. Hence, all the the power pulse. This places point "e" at grounddiscussions hereafter will be limited to potential, and drops point "d" to a voltage -B,transformer input. below ground. This applies a reverse voltage to

SCR1, which ceases conducting in less than 5 mi-Typical of the circuits developed for variable croseconds. The load current which had been flov

width pulse operation is that shown in Fig. 3, from ing through SCRs 1 and 2 now flows through SCRsthe paper by McMurray and Shattuck4. This cir- 2 and 3. This is also illustrated in Fig. 5, as i3cuit employs 4 SCRs in a bridge circuit, to utilize is identical to i2 during this interval.fully the ratings of the SCRs. The improved com-mutation, effected by the diodes, and the general 4: In a rectifier application, with inductance in-performance of the circuit, are described in the put, it can be assumed that the load current is apaper. constant through the inductor as a function of time,

particularly if equation (1) applies. Therefore,There are commutation losses of power in L capacitor C will discharge linearly, and the volt-

146

86 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

age across the transformer input will decrease lin- frequency. This loss is NOT PRESENT in the VVW1Pearly with time to zero. This is also shown in Fig. circuit described herein.5, curve ec, which is also ede.

The operation of the rectifier and pulse averag-5: When the voltage of point "d" reaches that of ing portion of this circuit is hereafter analyzed atthe input voltage,i. e. , "E" volts, SCR2 will cease length, mathematically, because of the fact thatto conduct, as will SCR3, and the power pulse out- the output voltage is a function of the output resis-put will be zero. This is illustrated in Fig. 5, at tance, and therefore the regulation problem isthe end of period t2. somewhat more complex than in non-energy-conser-

ving regulating systems.A very important fact is that at the end of tl,

when SCR3 fires to turn off SCR 1, point "d" is at Waveform And Circuit Analysis-E voltage, and, since SCR 2 is still conducting,the voltage at point "a" is also essentially -E. In Fig. 6 the secondary of the output transfor-However, at the input to the transformer, point "I', mer of Fig. 4 is shown with a full wave bridge rec-the dc voltage is +E. Therefore, there appears a- tifier. The waveform input to the filter is showncross the conducting portion of the primary of the now as unidirectional pulses, the average of whiditransformer a voltage step of 2E, shown in Fig. 5, will appear at the output. This waveform and somein curve exy/ at the beginning of period t2. This of the important parameters, are shown in Fig. 7.is an extremely important phenomenon, as it is theheart of the concept of the zero commutation loss Two of the important parameters of the systemcircuitry, and, although it aids in the efficiency, are the rectangular section duty cycle, kl, and theit introduces several design problems. For exam- triangular section duty cycle, k2.ple, the voltage across SCR4 is momentarily sentto a forward voltage of 3E, and hence a much high- Obviously,er voltage rating is required for this SCR. E 2 Et2 (tl + t2)

Eav =El 2 =E T =E(kl + k2) (4)After a quiescent period, in order to start the T

negative pulse, SCRs 3 and 4 are fired. Then, toturn the negative pulse off, SCRl is fired. Action or,similar to that described for SCRs 1 and 2, and 3,now obtains for SCRs 3 and 4, and 1, as capacitor Eav k3 = kl + k2; as a limitation, kl+k2. l (5)C had been charged, during the turnoff of the posi- Etive pulse, to the correct polarity for the turnoff of This set of parameters is plotted in Fig. 8, withthe negative pulse. further parameter limitations discussed later.

In the curves of Fig. 5, ideal commutating con- In practice, t2 cannot be controlled directly,ditions are assumed, such as no transformer leak- but tl can. With a given input voltage E, the out-age inductance, no circuit "ringing" ,etc. These put voltage is controlled by varying tl. However,effects exist in any practical circuit, and can be this is not the only factor determining the outputcorrected for, where necessary, by standard tech- voltage Eav. It is shown in Appendix I that:nique s.

Since voltages and currents in the SCR3 and k3 = 2( k4 (6)SCR4 branch of the circuit are identical to corres-ponding values in the SCRI-2 branch,shifted 1800, where k 4 - 2RC (7)they are not illustrated in Fig. 5 T

2Note that in both cases of pulse turnoff,the or, Eav =tl +,1X +2RC (8)

energy stored in the commutating capacitor C is E 2T 2T/ Treturned to the load, through the mechanism of thetwice-i nput-voltage triangular pulse shown at the where " C" is the commutating capacitance of Fig.turnoff of each power pulse. 4, and R is the load resistance of Fig. 6, transform-

ed to the primary as indicated in Fig. 4.Further, since the capacitor is charged through

the load circuit, the 1/2 CE2 loss normally asso- Equation (8) shows that the ratio of the averageciated with charging a capacitor from a dc source6 voltage to the input voltage depends not only onactually is dissipated in the load. It is this 1/2 the rectangular portion of the "on" part of the SCRCE2 loss that accounts for the low efficiency of chopping wave, but also depends upon the load re-

conventional "parallel inverter" circuits at high sistance, the commutating capacitance, and the

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 87

repetition period of the pulses. In Appendix I it is shown that the triangularpulse "duty cycle" k2, is a function of the input

Since, in any practical device, the commutat- voltage and load current as follows:ing capacitance is normally fixed, the output aver-age voltage can be controlled to some degree by t2 I2E0 (9)varying the period T. But, since all factors entering Iinto the equation for k3 are inverse functions of In Appendix II it is shown that k2 depends upon klthe period, it is best, from an analytical point of and k4, so that:view, to maintain the period fixed, and vary only lthe nominal pulse on time tl. With T fixed, equa- k2 2+ k(l + k4 (10)tion (6) can be plotted as a series of curves forfixed kl, with k4 varying independently, or vice This relationship is shown in the lower portionversa. If T is varied, this may not be done. of Fig. 9. From this it again is seen that for a giv-

en kl, k2 decreases as the load resistance decrea-The variation of the output voltage as a func- ses, for the load current increases, and hence the

tion of the rectangular portion of the wave, andthe slope of the triangular section is much steeper.ratio of the resistance-capacitance product to theperiod, i. e. , equations (6) and (8), is indicated It will be noted that the curves of Fig. 9 arein the upper part of Fig. 9. It is seen from the up- drawn for a minimum limit of kl = 0.05, and maxi-per half of this drawing, that for a small rectangu- mum kl = 0.95. Although in theory both variableslar duty cycle, kl, the output voltage can vary kl and k2 could extend to 0, and kl and k2 couldover a very wide range, depending upon the load each equal 1, the practical aspects of SCRs re -resistance. Or, for a fixed, narrow duty cycle kl, quire a minimum rectangular pulse width, a mini-the inherent regulation of a dissipationless VWP mum triangular pulse width, and a minimum timedc power supply is very poor. However, the sys- between pulse turnoff of one polarity, and pulsetem is still very efficient. Further, the load re- firing of the next polarity.sistance R may also vary over a very wide rangefor a small kl. Due to the buildup time of gate current of

most SCRs with simple gate pulsing circuits, plusAs the duty cycle, kl, of the rectangular por- the requirement of time for current to build up in

tion is increased, the output voltage increases, the SCR, it is impractical to have tl reliably muchand the permissible variation of k3 decreases.This smaller than 20iis. Similarly, it is unreliable tocorresponds to higher output power, and a narrow- have an off time between pulses much less thaner permissible range of R, at lower resistance val- 20fLs. Finally, t2 must be at least 20Ls, as pre-ues. viously mentioned, otherwise the SCRs may not

turn off, and there may be simultaneous firing ofThis is a limiting factor on the performance of SCRs in different arms of the inverter, which will

this device, namely, operation over a comparative- short the dc supply. A kl of 0.05 at 20Ls wouldly narrow range of output voltages and load cur- correspond to a rectified pulse repetition rate ofrents, without some type of modification of a maj- 2. 5 kc, or an inversion frequency of 1250 cyclesor parameter. per second. For a dc power supply, this operating

frequency will yield substantial reduction in sizeThe triangular period t2, or duty cycle, k2, and weight of the power transformer, and of the out-

is of great practical importance. As stated in eq- put filter components.uation (5), tl + t2 < 1, otherwise the inverter pul-ses will overlap, and both arms of the inverter In order to have smaller values of kl, the in-will conduct simultaneously, causing a short cir- version frequency must be lower, causing a conse-cuit on the dc input. So, t2 must not be too large. quert increase of size of transformer, choke and

capacitor.The turnoff period of the SCRs, i. e. , the time

that the voltage across the SCR being turned off by If the operating frequency is higher, then thethe negative voltage from the capacitor C (e. g. , range of variation of kl and k2, will be smaller,SCRl or 3 in Fig. 4), is negative, must be greater with an even smaller allowable range of load re-than a minimum value, depending on the type of sistance Rl.SCR, among other factors. This period can be aslow as 10 Fs, reliably, under certain favorable con- The curves of the lower half of Fig. 9 furtherditions, or as high as 30 pL s. From curve edg of indicate that for a wide rectangular pulse, orFig. 5, it can be seen that this period is t22_ large duty cycle, kl, the allowable variation ofTherefore, t2, or k2, cannot be allowed to be too load resistance ratio is not great, as for too low alow in value. resistance there will be too low turn off time, k2,

88 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

and for too high a resistance the pulse turn off drawings therein, Figs. 13 - 16. The amplitudes oftime will be too great, causing pulses to overlap. the harmonics are plotted as a percentage of the

rectangular pulse height.For example, with a rectangular duty cycle of

0. 45, the allowable resistance ratio, determined It is seen, for example, that the maximum fun-by k2 max = 0. 5, and k2 min = 0. 05, (from the low- damental harmonic shown in Fig.13, in case of theer curve of kl = 0. 45 of Fig. 9) is from k4 = 0. 45 to dc wave, is 0. 84, occuring with kl = 0.15, at k2 =k4 = 0. 025, or a resistance ratio of approximately 0. 52. As is to be expected, as kl increases be-20:1. However, the voltage will drop from a ratio yond 0. 5, the fundamental drops substantially,andof k3 = approximately 0. 95, to k3 = approximately becomes even smaller as k2 increases. Thus, if a0. 50, almost 2:1. The current swing will be great- design can be such that wide rectangular pulseser than the voltage range, but less than the resis- are used throughout, the filter problem is reducedtance range, a ratio of substantially.

0.48/0.025 0.95/0.5 10:1 The second harmonics, illustrated in Fig.14,show much greater variation as a function of kl and

The a'b-)ove data are all for an UNREGULATED k2 than does the fundamental. Further, after k =system, with fixed kl. 0. 5, the curves repeat for kl intervals of 0. 5. For

the larger kl, since kl + k2 . 1, on any curve theThese curves will also indicate the pulse width terminal point is indicated.

variation necessary for regulation against load cux-rent changes. It is apparent that the closer the de- As is to be expecLed, as the harmonic ordersired output voltage to the input voltage, i. e. , the increases, the convolutions of the curves increasegreater k3, the wider the range of output Current in frequency. Fig. 15 shows the 3rd harmonic, andvariation permissible. An example of the use of Fig. 16 the 4th harmonic.these curves is given in Appendix III.

Invert erThe curves of Figs. 8 and 9 could be called the

"Characteristic Curves" of the VWV\P, "lossless" Since the VWP dc power supply circuit is es-commutating circuit. Fig. 8 has the "Output Volt- sentially an inverter to begin with, it can be usedage Characteristics", and Fig. 9 the "Regulation as an inverter, with the understood limitations ofCharacteristics" (upper curves) and the "Turnoff waveform impurity. Here, the operating frequencyCharacteristics" (lower curves). can be much lower than in a dc output power sup-

ply, and still obtain advantages, namely, of veryFig. 10 shows an experimental run to verify eq- high efficiency. Under these circumstances, i n

uation (6). The data are plotted as a function of most practical cases, it can be assumed that thethe dimensionless parameters kl ,k3 and k4. The current is constant during the commutation period,correlation between theory and experiment is ex- in which case all the formulas previously evolvedcellent. It is seen that the inherent regulation, can be applied. If it is assumed that the outputfor fixed kl, is very poor. waveform consists of rectangles and triangles, but

not rectified, as shown in Fig. 5, curve ex,, thenThe curves of Fig. 11 show regulation in a more the harmonic content can be analyzed to determine

conventional form, i. e. , output voltage versus the necessary filtering for purity of ac output wave-output current. It is seen that the inherent regu- form. This is done in Appendix V, where the equa-lation is much better for wider pulses, as the no- tions for the harmonics are derived, the amplitudesload voltage for all pulse widths tends to the sam as a function of kl and k2 are plotted in Figs. 17-value, corresponding to k3 = 1, per Fig. 9. 20, for the fundamental, 3rd, 5th and 7th harmon-

ic S.

The regulation of the power supply can be madeas good as desired, by standard techniques, illus- Practical Designtrated in block form in Fig. 1. Automatic regulationcircuits are not discussed herein. A dc power supply incorporating the VWP prin-

ciple and the elimination of the 60 cycle transfor-Filtering mer has been built and operated successfully, in

accordance with the block diagram of Fig. 1. TheThe harmonic content of the wave form, of the anticipated advantages of small size, light weight

VWP "lossless" commutation power supply, for and high efficiency were achieved. Because of thevarious rectangular portion and triangular portion cost of the solid state rectifiers and swit-ches, theduty cycles, has been calculated in Appendix IV, system does not become economically competitive,and the first 4 components are indicated in the using SCRs, below an output of 2 kilowatts. There-

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 89

for, a 2 kw design was the first one attempted. (1) Transformer T has a 1:1 ratio of input and out-put, as employed. (2:1 ratio of total input

Fig. 21 is a photographofa 2kw unit, 7" high and output turns).(compared with 15" or more for conventional de -signs), weight 60 pounds, (compared with 200 (2) T is lossless, as are all connecting leads.pounds or more for conventional designs). Theoverall conversion efficiency ac to dc, for 1/2% (3) All SCRs and rectifiers are lossless.regulation is 83%, compared with 70% for conven-tional series impedance designs. Ripple and reg- (4) Choke L is lossless.ulation are less than 1/2%, though they can bemade lower without undue engineering effort. The (5) The current I that flows during commutation isunregulated dc input has 10% ripple at 120 cycles constant.and this is reduced to below the specified valueby pulse width modulation. (6) The change in capacitor C voltage during turn-

off of SCR1 is negligible.This system has the further advantage of op-

erating from a wide range of input frequencies. Then, from equation (5),The lower limit of input frequency is determined by Eav tl t2the amount of output voltage control that may be k3 = E kT + k2 = Tsacrificed due to the requirement of additionalpulse width modulation for derippling. The upper To determine t2, referring to Fig. 7 and Fig.12,limit of input frequency is determined by the in- we use the fact that:put rectifiers' characteristics. Operation rangesfrom 25 cps to 2000 cps are anticipated. dE - Bi- LE since all changes are linear.

dt c atThe one limiting performance factor of the ba-

sic circuit shown in Fig. 1 is transient response Applying this to the triangular portion of thewith respect to load changes, due to the output wave of Fig. 7,filter choke. At 1 kc operating frequency, thetransient recovery time is of the order of tens of E= 2Emilliseconds. However, thiscan be improved byauxiliary circuits to control transient energy. 6t =t2

As an ac-ac inverter, the overall efficiency = Iis 90%. As a dc-ac inverter, operating from 150volts dc, the efficiency is close to 95%. 50 t2 = 2ECsot2 I ,which is equation (9).

Conclusion but I Ea

A new approach to dc and ac pov&e r supplies, 2ECR 2CRregulated and unregulated, resulting in smaller so t2 = Eav k3size, lighter weight, and higher efficiency thanconventional designs, has been developed. Analy- Putting the above into (4) yields:tical approaches, and experimental verification of 2CRtheory, have been described in this paper. As the k3 = kl + 3 Tcosts of solid state devices continue to drop, this 2CRtechnique will prove to be economically competi- Let k4 TCtive with existing devices, and hence more advan- -tageous. Then k3 = kl + k3

2Appendix I k3 klk3 -k4 = 0

Calculation of Ea _ k3 or k kl + kl2 +2RCCalculation of E 3 2 - 2 T

Referring to Fig. 4, when SCR3 is fired and only the + solution is physically acceptable,SCR1 extinguished, a process that takes but a yielding equations (6) and (8). This is plotted infew microseconds, thereafter the circuit can be the upper half of Fig. 9.considered that of Fig. 12. The following assump-tions are made in reference to both Fig. 4 and Fig.12:

90 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS DecemberAppendix II sirable to vary the output voltage over a reasonable

t2 range, say 50-100%, the range of acceptable resis-Calculation of k2 7= tance changes is much less at the lower extreme of

output voltage. In the above case, 50% x . 85 =From equation (4), 0. 425 = k3.

k3 = kl + k2 At k3 = 0. 425, going horizontally to the uppercurve of kl = 0. 05, yields k4 = 0. 165 maximum. As

From equation (6), above, we must determine kl maximum such that2 k . 0. 05. Trying kl = 0. 40 (interpolated), yields

k 3 + ( +k4 k4 =0 . 0 2 and, on the k4 =0. 02 line, the inter-2 2/ section with the LOWER kl-0. 40 curve yields k2 =

Subtracting the above two equations, (6) from (4), 0. 04, too low. So, trying kl = 0. 35 yields k4 =yields: 0. 03, and k2 = 0. 055, satisfactory.

kl1 1l 2k2 + -- - + k4 =0 Hence, the current ratio permissible at the2

kl 2 X lower output voltage is 0. 165/0. 03 = 5. 5/1, foror k2 = ) + k4, which is equation regulation of the output voltage.

(1 0). Appendix IV

This is plotted in the lower half of Fig. 9. Calculations of Harmonics of Rectified DC OutputWaveforms

Appendix IIIReferring to Fig. 7, the waveform e (t) can be

Determination of Pulse Widths Required in VVP expressed in a Fourier series as"Lossless" Commutation Circuit, for Regulation Ao (2irn t (2Trn t'lAgainst Load Changes e(t) =2 + ;1LAn costT /+ Bn sint T j (11)

Referring to Fig. 9, assume k3 = 0. 85, or Eav TE hreA 2 c(2rrn t (2=. 85, a desired ratio of output dc to input dc where An = T e(t) cos T dt (12)(normalized for unity transformer ratio). 0

2 TThen, entering horizontally from k3 = 0. 85, we and Bn = T e(t) sin(. il t) dt (13)

have a range of kl = 0. 85 to 0. 05. This corres- 0ponds to k4 = 0 and k4 = 0. 67. The latter value is f2Wrn t ,acceptable, the former is not, as it requires R=0, or e (t) = < Cn sin T + nJ (14)and k2 =0. n=o

Since k2, as discussed in the main text of this where Co = E (kl + k2) (15)paper, must be greater than a minimum amount, say 9o = 20. 05, we must seek a maximum kl, whose value Cn = [An + Bn2] 1/2 (16)of k4, for k3 0. 85, will yield k2 > 0. 05. -l An

,On= tan 1 An (17)Trying the k 1 =0. 80 curve (interpolated), on Bn

the horizontal line k3 = 0. 85 we find k4 = 0. 04. Following a technique of Parzen (7) to simplifyDescending vertically on the k4 = 0. 04 line, we the mathematical analysis, in Fig. 7 have t = 0 atfind this line intersets the LOWER kl =0. 80 char- the END of the period t2.acteristic line very close to k2 = 0. 05.

Then e(t) = E -T(kl+k2)(t(-k2 (a)So, the range of kl = 0.80 to 0. 05. If T were = -2E t -T k2<t<0 (b) (18

1, 000 pts, this would correspond to a rectangular Tk2 }pulse width of 50 to 800 Ls. The output voltage = 0 0(t<T (l-kl-k2) (c)would be constant for this set of parameters (as-suming the input voltage constant) over a range of Putting equations (18) into (12) and (13), andk4 = 0. 04 to 0. 66, a range of current of approxi- integrating from t = -T (kl +k2) to t =0 (the periodmately 16. 5/1 . 18c can be neglected, as e(t) =0 therein), and ev-

Eav ~~~~~~aluating the intergrals yields:At a lower ratio of EEV corresponding to a

practical power supply design in which it is de-

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 91

An -= [sin f 21T n(k1 + k2) + sin (21T nk2)] - nL2p' k2 [I - cos (2Irnk2)1 (19)

Bn - I-- [cos 21 n(k + k2)) + cos (21T nk2)] sin (2 1T nk2) (20)

On=tan-I An2

The values of (19) and (20), (16) and (17), have Acknowledgementsbeen calculated on a computer, at intervals of 0.05,for 0. 05. kl5 0. 9, and 0.054 k24 0. 9. The coef- The author wishes to acknowledge the valuableficient of Cn, i. e. , equation (16), are plotted in consultation of Mr. Eliasz Poss on circuit and com-Figs. 13 - 16 herewith. mutation concepts, and to Co-nputech, Inc., of

New York City, for assistance in computing the co-Appendix V efficients plotted in curves 13 - 20.

Calculations of Harmonics of Inverter OutputWaveforms

Referring to Fig. 5, waveform exy, the wave-form e(t) can be expressed in a Fourier series as:

e(t) =no [A2n+ cos (2 f (2n1) t) + B2n+ 1 sing21r (2n + 1) (21)

In comparing equation (21) to equation (ll), it Referencesis seen that there is no dc component, and thereare no even harmonics, due to the symmetry around 1. Morgan,R. E. :"A New Power Amplifier Using Athe zero axis. Single Controlled Rectifier And A Saturable

Transformer. " AIEE, 60-410 (1960) .Equation (21) may be rewritten as:

T

00 _ l \ ] 2. Gutzwiller, F. W. ,et al: "Silicon Controllede(t) = n=o C2n+ sinT\ + 2n+j (22) Rectifier Manual. " General Electric Co., (1961).

where C2n+1= FA2+ +B21+ 1/2 (23) 3. Greinacher:"Uber Eine Methode WechselstromLhrn2n+ Bn+ Mettels Elecktrischer Ventile undKondensatorem'2n+ 1 = tan-1 A2n+ 1 (24) in Hochgespannten Gleichstrom Umzerivandeln,"

B2n+1 Zeitschrift Fur Physics. vol. 4,p. 195 (1921).

Using the same technique of Parzen (7), to 4. McMurray,W. ,Shattuck, D. P.:"A Silicon Con-simplify the mathematical analysis, we set t=0 at trolled Rectifier Inverter With Improved Commu-the end of the first period t2, in Fig. 5, waveform tation. " AIEE,61-718 (1961).exy, and from t = -T(kl + k2) to t= T(l-kl-k2), theconditions of equation (18) apply. 5. Wouk,V. :"Energy Wasted In Charging A Conden-

ser. " Communications (April 1944).Hence, H c

pO 6. Poss,E. ,Wouk,V.: Patent Applied for.

A2n+I =2. ) (t) cos(t21(2n+l)tJdt (25)T (kl+k2) 2T

B2n+ 1 20Te(t) s2in)f2nI )t} dt (26) 7. Parzen, P., Plainview, N.Y., private communi-B2n j e(t n ~ dt(6_-T(kl+k2) ~2T cation.

Putting equations (18) into (25) and (26), andintegrating over the limits as shown in (25) and (26)and evaluating the integrals, yields:

A(2n+ 1) = 2 [sin ((2n+l)WT (kl + k2)2 + sin( (2n+)TI k231 4 [1 - cos (2n+ 1)I k2j] (27)(2+ (2n+1l)1rl. (2n+l1) 2wr k2

B(2n+l) = (2n+1)1W [Cos { (2n+ 1))1T (kl +k2) + cosf (2n+l)ff2k2jj -2n sin(2 1)qnk2}(28)

The values of (27),(28),(23) and (24), havebeen calculated and tabulated at intervals for 0.05, Addendumfor 0.05 S kl ' 0. 9, and 0.054 k24 ° 9*. The coef-ficients C2n+1 (equation (23)) are plotted in Figs. TeV17-20 herewith.ThauhrbleethtithVWerut,e

______________________________________ phrase "SCR turnoff" is more accurate than "coin-iThese are available from Electronic Energy Conver- mutation". However, common usage has been fol-sion Corp. lowed.

92 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

1*- ~~2T

TRANSFORMER 2EINPUT CONVERSION VARIABLE & PULSE OUTPUT exyE

TO FILTER WIDTH CONVERSION AVERAGING 0DC 1 0PULSE TO CIRCUIT 2 E

GENERATOR DC

TIMING COMPARISON 0AND AND

PHASING DC AMPLIFICATION2CIRCUITS CIRCUITS

I I ~~~~~~~~~~~~~~~~~~~~~~~~~~~icFig. 1. Block diagram of system employing no main _Oi / __E _

power transformer, and using SCRs for variablewidth pulse generation.

E / 5

in -____L_____{(r+; g I tC,p S r -CRI

Fig. 2. Basic dc switching control and regulating Fig. 5. Waveforms of voltages and currents for Fig. 4.circuit.

LOAD+o 2 ec* *

E N2TurnroFilter Input LI

C Waveform

~~~~~TC ~~~~~~~~~~~Tro nsformer

Fig. 3. Typical VWP circuit, employing SCRs, withinherent commutation losses.

Fig. 6. AC waveform rectifying and filtering circuits,for Fig. 4.

i5

+T T b *-N, turns--- x

SCR2f

C Rj E0 , _ _d - -1 >- Ci v~~~~~~~~~~~~~t --t-

_T 2T k3=v k4=EV 2RC

Fig. 4. SCR circuit for VWP generation, with no Fig. 7. Details of waveform into filtering circuit, forinherent losses. dc output.

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 93

1.0

k Eav.1.0 0.9 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.05 E

- k3

0.9-

0.8 Experimental0.5 - Verificotionnof

0.7 - (+j+k T0.6 -tl =44j.us

T =367JLs k I =t =0.12k3 0.5 E =94V.

04/ Output Characteristic C 8=8afd

0.4 - / / ,/ Curves k3 ki +k2 - =EXPERIMENTAL DATAk3 - Eav CURVE=CALCULATIONS FOR kl=0.120.3 E I CUAi9N FO il0k __ 0 0.5 1.0

0.2 0.05<kl <0.9 kl = T k40 2RCT0.05< k2<0.9 k2 t2

0.1I 0.1 .k3.0.95 TI < k3< 0.95 T Fig. 10. Experimental verification of regulation curve

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 for VWP 'lossless commutation circuit.k2

Fig. 8. Output voltage "characteristic curves' for VWP 90'lossless" commutation circuit. 80

kl fork3 600.95 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.05

0.05 Eav. 0-t0.9 OUT, 40

0.15., OT0.8 30

0.25 kl for k E = 90 Volts t340 400.7 20-

0.3 T 3758 Ic0.6 10/ T=pica us

k2 0.45or 0.5 Ik3 0.5 k2 t2 0 10 20 30 40 50

0.4 Tk4 = 2RC dommutatEav I dc, out, Amperes0.65 k3- Eav.

0.3 N Fig. 91. Typical regulation curves of VWP Elossless"0.75 R = RI (e) commutation circuit, for various rectangular pulse0.2 duty cycles.

010.85

R0.1 ~~~k4 2RC~T

6 .1 062 0.3 0.4 0.6 0.7 0.809 1.0 L__

Fig. 9. Regulation and turnoff 'characteristic curves' + Em Eatfor VWP 'lossless" commutation circuit. E_n Eo

Fig. 12. Simplified circuit during power pulse turnoff.

94 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

0.303rd Harmonic

.80 0.25

0.9~~~~~~~~~~~~~~~~~~~~~~06

0.9 °6 ud nc- 0 15 07

00.8 0. 0 0.40 0.30 0.05

0.7

0.6 015~~~~~~~~~LI 05~~~~~~~~~~~~~~~~~~~~3 501~~~~~~~~~~~~~~~~0.20- E C6utu

0.4 0.10~~~~~~~~~~~~~~~~~~~~~~05503

ci 2nd Hanonc /08 0.85

0.3

60Fundamental-0.2- 0 DCOutput 0. 0.5060.50

z °o 52°5 < <\;1 , ~~~~~~~~~~~060 C400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0k2 k2

Fig. 13. Fundamental of harmonic content of waveform Fig. 15. 3rd Harmonic of waveform of Fig. 7.

of Fig. 7, for dc output.

0.22- 4th Harmonic

0.20~~~.10.45 -2nd Harmonic- 0.1

0.40~~~~~~~DCOtpt0.16 0. 07 .0 0.25,0.50, 0.75

0350 0.0 0.5O050.3 0.55~~~~~~~0.0 080.30 ~~~~0.65 01060 C4 0.1~~~~~~0. 1 .15

0045 0.0 0.45, 0.70

C2 0.2510 0.70~~.500.1-0..0 00710.460900.08 0.150 70.60 .4,07

25~~~~~03i ~~~~~~~0.20,70 0.06 0.10, 0.60,

0.15 - ~~~~~~~~~~~~~~~~~~~~~~~~~~0.35,0.850.10 0.04 0.15, 0.40, 0.65

0.05 09 .506

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.02 0.3 0. .5 0. .7 08k2 1.

k2

Fig. 14. 2nd Harmonic of waveform of Fig. 7. Fig. 16. 4th Harmonic of waveform of Fig. 7.

1962 WOUK: "VWP; NEW APPROACH TO HIGH POWER REGULATED POWER SUPPLIES" 95

1.6 0 0404

1.5 /D 4i 0.35 - y \k)1.4 - / 0.325 -

~~~~~b ~~~~~~~~0.75\/00\ .2

0.310.30 d terminals of curves

(.2 -02507

0.25 0.2 0.3 0.45 0.3 0.05(.0 0.225 -

0.9 ~~~~~Fundamentol-0-000.9 ~~~~~~~~AC0Output .C(

0 C 0 0(175 0.50 0.10

E 0E8k E0.7 0.15

0.6 0.125 - hn

0.5 0.10 output.

0.4 0.075 - 0.40

0.3 0.05 - Oupu0.2 0.25 - 0.35

0. U015 /1 0.200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

I I I I I I ~~~~~~~~~~~k20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

k2Fig. 19. 5th Harmonic, ac output.

Fig. 17. Fundamental of harmonic content of waveformof Fig. 5 for ac output.

0.24 -7hHroi0.6 -ACOiu

0.220.550.75 ~3rd Harmonic- 0i0 040

0.80~~~~~~~~~~~~~~~0.0 07

0.4 .0ACOtu5 ~~~~~~ ~ ~~~~~~~~~0.14.00.006

0.35 .02

E~~~~~~~~~~~~~~~/.50.10 000.25-.4

0.I 0 ~~0.080.25-75 05

0.15 .5 01 -03C 3 0.3 E 6~~~~~~~~~~~~~~~~~~0.7020.110

0.05 0.02.200.1

_____________0_25006.- 0230450.40.7.09.00.10.2 0.3 04 050640. 0.84 0.971.0 k2

0.1 - 0.25~~kFig.1.3rdHarmonc, acoutpu.3 Fi020.thHrm2c acoupu.1

96 IRE TRANSACTIONS ON INDUSTRIAL ELECTRONICS December

Fig. 21. Photograph of 2 kw, dc output, regulated VWPpower supply.