Interconnection of Switches & Energy Storage Elements Switched Mode Power Conversion Primitive Converters
Interconnectionof
Switches & Energy Storage Elements
Switched Mode Power ConversionPrimitive Converters
Interconnectionof
Switches & Energy Storage Elements
Switched Mode Power ConversionPrimitive Converters
T1 T2
PL
C
Interconnectionof
Switches & Energy Storage Elementsto
Source and Load
Switched Mode Power ConversionPrimitive Converters
T1 T2
PL
C
VG IG R
Interconnection Rules
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
Interconnection Rules
Switched Mode Power ConversionPrimitive Converters
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
Interconnection Rules
Switched Mode Power ConversionPrimitive Converters
Acceptable Switch-Storage Cells
P
T1 T2
L
C
T1 T2
P
Two possible switch+storage cellsThese are dual of each other
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
VG
VO
LoadIO
IG PT1
T2
L
Input average quanities: VG and IGOutput average quantities: IO and VO
Switched Mode Power ConversionPrimitive Converters
Strategy of Operation & Control
VG
VO
LoadIO
IG PT1
T2
L
Constant Switching PeriodT1P ON Time TON ; T2P OFF Time TOFF
TON + TOFF = TS
Switched Mode Power ConversionPrimitive Converters
Primitive Current to Voltage Converter
Input average quanities: IG and VGOutput average quantities: VO and IO
VG
VO
Load
IO
IG
PT1
T2
C
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
VG
VO
LoadIO
IG PT1
T2
L
Ideal Performance Measures
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
VG
VO
LoadIO
IG PT1
T2
L
First Performance MeasureForward Voltage Conversion Ratio
O
G
V ?V
=
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
VG
VO
LoadIO
IG PT1
T2
L
Performance MeasuresForward Voltage Conversion RatioReverse Current Conversion Ratio
G
O
I ?I
=
Switched Mode Power ConversionPrimitive Converters
Forward Voltage Conversion Ratio
VG
VOPT1
T2
L
VPVO
t
VPVG
0 TSTON
Average voltage across inductor in one cycle is zero
Switched Mode Power ConversionPrimitive Converters
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
= =
Switched Mode Power ConversionPrimitive Converters
Reverse Current Transfer Ratio
G
O
I ?I
=
Reverse Current Conversion Ratio
PT1
T2
L
IO
iG(t)
Switched Mode Power ConversionPrimitive Converters
Reverse Current Transfer Ratio
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= =
Switched Mode Power ConversionPrimitive Converters
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
= = =
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
Non-Ideality in the Converter Current IO
VG
VO
LoadIO
IG PT1
T2
L
VL
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
Non-Ideality in the Switches – Conduction Drop
VG
VO
LoadIO
IG PT1
T2
L
VL
Switched Mode Power ConversionPrimitive Converters
Switches are Realised by Real Devices
VG
VOPT1
T2
L
VP
PT1
T2
L
IO
T1P Drop is VT; T2P Drop is VD
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
⎛ ⎞−= − −⎜ ⎟
⎝ ⎠
Switched Mode Power ConversionPrimitive Converters
Reverse Current Transfer Ratio
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= =
PT1
T2
L
IO
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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 = = − −⎜ ⎟
⎝ ⎠
Switched Mode Power ConversionPrimitive Converters
Primitive Voltage to Current Converter
Non-Ideality in the Source & Inductor
VG
VO
LoadIO
IG PT1
T2
L
VL
Switched Mode Power ConversionPrimitive Converters
Source & Inductor Have Internal Resistances
VG
VOPT1
T2
L
VP
Source Resistance is RSInductor Resistance is Rl
VG
VOPT1
T2
L
VP
Rl
RS
Switched Mode Power ConversionPrimitive Converters
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− + − − + − =
Switched Mode Power ConversionPrimitive Converters
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
⎛ ⎞⎜ ⎟
= ⎜ ⎟⎜ ⎟+ +⎝ ⎠
Switched Mode Power ConversionPrimitive Converters
Reverse Current Transfer Ratio
IG
t
iG(t) IO
0 TSTON
O ON G SI T I T 0− =
G ON
O S
I T DI T= =
iG(t) PT1
T2L
VP
Rl
RS
Switched Mode Power ConversionPrimitive Converters
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
⎛ ⎞= ⎜ ⎟+ +⎝ ⎠
Switched Mode Power ConversionPrimitive Converters
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 = = ⎜ ⎟
⎜ ⎟+ +⎜ ⎟⎝ ⎠
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
Non-ideality Related to Output Voltage
Output Voltage Ripple is a Function of the Load
PT1
T2
L
VG VO
LoadIO
IG
Switched Mode Power ConversionPrimitive Converters
Evaluation of the Output Voltage Ripple
Capacitor Supported Load is Common
PT1
T2
L
VG VOIO
IG
R
Switched Mode Power ConversionPrimitive Converters
Inductor Current & Output Voltage Ripple
Output Voltage Ripple is ΔVO
PT1
T2
L
VG VOIO+ΔIO
IG
R
O OV V+ Δ
C
Switched Mode Power ConversionPrimitive Converters
Inductor Current & Output Voltage Ripple
IO
0 TSTON
t
IO
0 TSTON
t
ΔVO
Charge causing voltage ripple
( )OO S
VI 1 D TL
Δ = −
Switched Mode Power ConversionPrimitive Converters
Inductor Current & Output Voltage Ripple
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 =
Switched Mode Power ConversionPrimitive Converters
Inductor Current & Output Voltage Ripple
( )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 −
=
Switched Mode Power ConversionPrimitive Converters
Guidelines for Low Output Ripple
2O S
O
V (1 D)TV 8LCΔ −
=
Switching Period << Natural Frequency
S1TLC
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
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
Switched Mode Power ConversionPrimitive Converters
Buck, Boost & Buck-Boost Variants
Switched Mode Power ConversionPrimitive Converters
Buck, Boost & Buck-Boost Variants