Primitive Converters Interconnection of Switches & Energy...

Interconnectionof

Switches & Energy Storage Elements

Switched Mode Power ConversionPrimitive Converters

Interconnectionof

Switches & Energy Storage Elements


T1 T2

PL

C

Interconnectionof

Switches & Energy Storage Elementsto

Source and Load


T1 T2

PL

C

VG IG R

Interconnection Rules


Sources may not be OverloadedVoltage Sources are not to be ShortedCurrent Sources are not to be Opened

Conservation of EnergyInductor Currents are not to be Interrupted

Capacitor Voltages are not to be Shorted


T1 T2

P

Voltage sources may not be connectedacross PT1 or PT2

No Short Circuit of Voltage SourcesCapacitors may not be connected across

PT1 or PT2No Disruption of Energy on the Capacitor



T1 T2

P

Current sources may not be connectedin series with T1 or T2

No Open Circuit of Current SourcesInductor may not be connected

in series with T1 or T2No Disruption of Energy on the Inductor



Acceptable Switch-Storage Cells

P

T1 T2

L

C

T1 T2

P

Two possible switch+storage cellsThese are dual of each other


Primitive Voltage to Current Converter

VG

VO

LoadIO

IG PT1

T2

L

Input average quanities: VG and IGOutput average quantities: IO and VO


Strategy of Operation & Control

VG

VO

LoadIO

IG PT1

T2

L

Constant Switching PeriodT1P ON Time TON ; T2P OFF Time TOFF

TON + TOFF = TS


Primitive Current to Voltage Converter

Input average quanities: IG and VGOutput average quantities: VO and IO

VG

VO

Load

IO

IG

PT1

T2

C



VG

VO

LoadIO

IG PT1

T2

L

Ideal Performance Measures



VG

VO

LoadIO

IG PT1

T2

L

First Performance MeasureForward Voltage Conversion Ratio

O

G

V ?V

=



VG

VO

LoadIO

IG PT1

T2

L

Performance MeasuresForward Voltage Conversion RatioReverse Current Conversion Ratio

G

O

I ?I

=


Forward Voltage Conversion Ratio

VG

VOPT1

T2

L

VPVO

t

VPVG

0 TSTON

Average voltage across inductor in one cycle is zero


Forward Voltage Conversion Ratio

VG

VOPT1

T2

L

VPVO

t

VPVG

0 TON TS

( ) ( )G O ON O S ONV V T V T T 0− − − =

O ON

G S

V T DV T

= =


Reverse Current Transfer Ratio

G

O

I ?I

=

Reverse Current Conversion Ratio

PT1

T2

L

IO

iG(t)



PT1

T2

L

IO

iG(t)

IG

t

iG(t) IO

0 TSTON

O ON G SI T I T 0− =

G ON

O S

I T DI T= =


Efficiency of Ideal Converter is Unity

VG

VO

LoadIO

IG PT1

T2

L

G

O

I ?I

= O

G

V ?V

=

O G ON

G O S

V I T DV I T

= = =



Non-Ideality in the Converter Current IO

VG

VO

LoadIO

IG PT1

T2

L

VL


Ripple Current in the Inductor

VG

VOPT1

T2

L

VL

t

IO

VG-VO

0 TSTON

VL

-VO

( ) ( )O OO S ON S

V VI T T 1 D TL L

Δ = − = −

OIΔ


Normalised Ripple Curent

VG

VOPT1

T2

L

VL

( ) ( )( )

SO OS

O O

1 D TI V 1 D TI I L L / R

−Δ= − =

t

IO

VG-VO

0 TSTON

VL

-VO

OIΔ

t


Condition for Ripple Curent to be Low

VG

VOPT1

T2

L

VL

( )( )

SO

O

S

1 D TI 1I L / R

LTR

−Δ=

Switching Period << Circuit Time Constant



Non-Ideality in the Switches – Conduction Drop

VG

VO

LoadIO

IG PT1

T2

L

VL


Switches are Realised by Real Devices

VG

VOPT1

T2

L

VP

PT1

T2

L

IO

T1P Drop is VT; T2P Drop is VD


T1P Drop is VT; T2P Drop is VD

-VDTSTON

VO

t

VPVG-VT

0

PT1

T2

L

IO

Inductor ON State Voltage is VG-VT-VOInductor OFF State Voltage is -VD-VO


Volt-Sec Balance on the Inductor

( ) ( )( )G T O ON D O S ONV V V T V V T T 0− − − + − =

-VDTSTON

VO

t

VPVG-VT

0

PT1

T2

L

IO


Forward Voltage Transfer Ratio

( )G T ON D OFF O SV V T V T V T− − =

PT1

T2

L

IOT D

O GG G

V (1 D)VV DV 1V DV

⎛ ⎞−= − −⎜ ⎟

⎝ ⎠



iG(t)

IG

t

iG(t) IO

0 TSTON


G ON

O S

I T DI T= =

PT1

T2

L

IO


Switch Non-ideality is Series Non-ideality

iG(t)

IG

t

iG(t) IO

0 TSTON

G ON

O S

I T DI T= =

PT1

T2

L

IO

Switch Non-idealities have no Effecton Current Ratio


Efficiency

iG(t)G ON

O S

I T DI T= =

PT1

T2

L

IOO T D

G G G

V V (1 D)VD 1V V DV

⎛ ⎞−= − −⎜ ⎟

⎝ ⎠

O O T D

G G G G

V I V (1 D)V1V I V DV

⎛ ⎞−η = = − −⎜ ⎟

⎝ ⎠



Non-Ideality in the Source & Inductor

VG

VO

LoadIO

IG PT1

T2

L

VL


Source & Inductor Have Internal Resistances

VG

VOPT1

T2

L

VP

Source Resistance is RSInductor Resistance is Rl

VG

VOPT1

T2

L

VP

Rl

RS


Volt-Sec Balance on the Inductor

VG

VOPT1

T2L

VP

Rl

RS

-IORlTSTON

VO

t

VP

VG-IO(RS+Rl)

0

( )( ) ( )( )G O S l O ON O l O S ONV I R R V T I R V T T 0− + − − + − =


Forward Voltage Transfer Ratio

VG

VOPT1

T2L

VP

Rl

RS

( )( ) ( )( )G O S l O ON O l O S ONV I R R V T I R V T T 0− + − − + − =

O

G S l

V RDV R DR R

⎛ ⎞= ⎜ ⎟+ +⎝ ⎠

O

S lG

V 1D DR RV 1R R

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟+ +⎝ ⎠



IG

t

iG(t) IO

0 TSTON


G ON

O S

I T DI T= =

iG(t) PT1

T2L

VP

Rl

RS


Efficiency

iG(t)G ON

O S

I T DI T= =

PT1

T2

L

IO

O O

S lG G

V I 1DR RV I 1

R R

⎛ ⎞⎜ ⎟

η = = ⎜ ⎟⎜ ⎟+ +⎝ ⎠

O

G S l

V RDV R DR R

⎛ ⎞= ⎜ ⎟+ +⎝ ⎠


Efficiency with Switch/Source/Inductor Drops

T D

O O G G

S lG G

V (1 D)V1V I V DV

DR RV I 1R R

−⎛ ⎞− −⎜ ⎟η = = ⎜ ⎟

⎜ ⎟+ +⎜ ⎟⎝ ⎠


Guidelines for Good Efficiency

T D

O O G G

S lG G

V (1 D)V1V I V DV

DR RV I 1R R

−⎛ ⎞− −⎜ ⎟η = = ⎜ ⎟

⎜ ⎟+ +⎜ ⎟⎝ ⎠

T G D O

S l

V V ; V V

R R ; R R


Non-ideality Related to Output Voltage

Output Voltage Ripple is a Function of the Load

PT1

T2

L

VG VO

LoadIO

IG


Evaluation of the Output Voltage Ripple

Capacitor Supported Load is Common

PT1

T2

L

VG VOIO

IG

R


Inductor Current & Output Voltage Ripple

Output Voltage Ripple is ΔVO

PT1

T2

L

VG VOIO+ΔIO

IG

R

O OV V+ Δ

C



IO

0 TSTON

t

IO

0 TSTON

t

ΔVO

Charge causing voltage ripple

( )OO S

VI 1 D TL

Δ = −



IO

0 TSTON

t

IO

0 TSTON

t

Charge causing voltage ripple

( )OO S

VI 1 D TL

Δ = −

O SO

I T1 1V2 2 2 CΔ

Δ =



( )OO S

VI 1 D TL

Δ = −

2O S S O S

OV (1 D)T T V (1 D)T1 1V

2L 2 2 C 8LC− −

Δ = =

2O S

O

V (1 D)TV 8LCΔ −

=


Guidelines for Low Output Ripple

2O S

O

V (1 D)TV 8LCΔ −

=

Switching Period << Natural Frequency

S1TLC


Summary of Steady State Performance

Voltage Gain VO/VG

Current Gain IO/IG

Current Ripple ΔIO/IO

Voltage Ripple ΔVO/VO

Switch Non-idealitySource Non-idealityStorage Non-ideality

Efficiency


Summary of Steady State Performance

Inductor Volt-sec Balance: VO/VG

Current Averaging: IO/IG

Inductor Volt-sec in Sub-period: ΔIO/IO

Capacitor Charge in Sub-period: ΔVO/VO

Inductor Volt-sec Balance with Non-ideality: η

Switched Mode Power ConversionTransistor Amplifiers

Transistor Amplifier Variants

B E

C

βIB

IB

B

E

CIB βIB

EC

B

IB

βIB


Buck, Boost & Buck-Boost Variants


Buck, Boost & Buck-Boost Variants

Date post:	26-Apr-2018
Category:	Documents
Upload:	vantu
View:	216 times
Download:	3 times

Primitive Converters Interconnection of Switches & Energy...

Documents