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Q&A Transfer function of arbitrary dc-dc converter

I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed . quick analysis goes as written below , 1. M1 on Δ IL2= (V1-VL1-VO)*D/L2......VO=Output ...

1 answer · posted 29d ago by kadamrohan16‭ · edited 29d ago by kadamrohan16‭

Question Analog SMPS power-converter DC-DC-conversion buck-converter

#3: Post edited by

kadamrohan16‭ · 2025-01-22T13:03:36Z (29 days ago)
removed diode drops from equtions

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I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed .
quick analysis goes as written below ,
_1. M1 on_
~~Δ IL2= (V1-VL1-VO)*D/L2~~
Δ IL1= (V1-VL2-VO)*D/L1
_2.M2 Off_
~~Δ IL2= -(VC2+VD2)*(1-D)/L2~~
Δ IL1= -(VO)*(1-D)/L1
**Δ IL2on + Δ IL2closed = 0**
~~(V1-VL1-VO)*D -(VC2+VD2)*(1-D)= 0~~
~~D*V1-D***VL1**-D*VO-VC2+VC2*D-VD2+VD2*D =0 .............eq1~~
**Δ IL1on + Δ IL1closed = 0**
(V1-VL2-V0)*D -(VO)*(1-D)= 0
~~V1*D-**VL2***D-VO*D-VO+VOD=0............eq2~~
~~from above two equations , it looks like VO/Vin transfer function will have either term VL1 or VL2 .~~
how to remove that VL1 or VL2 term from the transfer function ( generally inductor voltage term does not appear in any conventional converters transfer function) or inductor voltage is bound to appear in transfer function of this converter ?
Please advise .
![Arbitrary dc-dc converter](https://electrical.codidact.com/uploads/9kdzu7yvpfj5mfsauo9dma53mq7l)!

I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed .
quick analysis goes as written below ,
_1. M1 on_
Δ IL2= (V1-VL1-VO)*D/L2......VO=Output Voltage , V1=Input Voltage
Δ IL1= (V1-VL2-VO)*D/L1
_2.M2 Off_
Δ IL2= -(VC2)*(1-D)/L2
Δ IL1= -(VO)*(1-D)/L1
**Δ IL2on + Δ IL2closed = 0**
(V1-VL1-VO)*D -(VC2)*(1-D)= 0
D*V1-D***VL1**-D*VO-VC2+VC2*D =0 .............eq1
**Δ IL1on + Δ IL1closed = 0**
(V1-VL2-V0)*D -(VO)*(1-D)= 0
V1* D-VL2* D-VO*D-VO+VO *D=0............eq2
from above two equations , it looks like VO/V1 transfer function will have either term VL1 or VL2 .
how to remove that VL1 or VL2 term from the transfer function ( generally inductor voltage term does not appear in any conventional converters transfer function) or inductor voltage is bound to appear in transfer function of this converter ?
Please advise .
![Arbitrary dc-dc converter](https://electrical.codidact.com/uploads/9kdzu7yvpfj5mfsauo9dma53mq7l)!

#2: Post edited by

kadamrohan16‭ · 2025-01-22T12:24:29Z (29 days ago)

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I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed .
quick analysis goes as written below ,
_1. M1 on_
~~Δ IL2= (VS-VL1-VO)*D/L2~~
~~Δ IL1= (VS-VL2-VO)*D/L1~~
_2.M2 Off_
Δ IL2= -(VC2+VD2)*(1-D)/L2
Δ IL1= -(VO)*(1-D)/L1
**Δ IL2on + Δ IL2closed = 0**
~~(VS-VL1-VO)*D -(VC2+VD2)*(1-D)= 0~~
~~D*VS-D***VL1**-D*VO-VC2+VC2*D-VD2+VD2*D =0 .............eq1~~
**Δ IL1on + Δ IL1closed = 0**
~~(VS-VL2-V0)*D -(VO)*(1-D)= 0~~
~~VS*D-**VL2***D-VO*D-VO+VOD=0............eq2~~
from above two equations , it looks like VO/Vin transfer function will have either term VL1 or VL2 .
how to remove that VL1 or VL2 term from the transfer function ( generally inductor voltage term does not appear in any conventional converters transfer function) or inductor voltage is bound to appear in transfer function of this converter ?
Please advise .
![Arbitrary dc-dc converter](https://electrical.codidact.com/uploads/9kdzu7yvpfj5mfsauo9dma53mq7l)!

I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed .
quick analysis goes as written below ,
_1. M1 on_
Δ IL2= (V1-VL1-VO)*D/L2
Δ IL1= (V1-VL2-VO)*D/L1
_2.M2 Off_
Δ IL2= -(VC2+VD2)*(1-D)/L2
Δ IL1= -(VO)*(1-D)/L1
**Δ IL2on + Δ IL2closed = 0**
(V1-VL1-VO)*D -(VC2+VD2)*(1-D)= 0
D*V1-D***VL1**-D*VO-VC2+VC2*D-VD2+VD2*D =0 .............eq1
**Δ IL1on + Δ IL1closed = 0**
(V1-VL2-V0)*D -(VO)*(1-D)= 0
V1*D-**VL2***D-VO*D-VO+VOD=0............eq2
from above two equations , it looks like VO/Vin transfer function will have either term VL1 or VL2 .
how to remove that VL1 or VL2 term from the transfer function ( generally inductor voltage term does not appear in any conventional converters transfer function) or inductor voltage is bound to appear in transfer function of this converter ?
Please advise .
![Arbitrary dc-dc converter](https://electrical.codidact.com/uploads/9kdzu7yvpfj5mfsauo9dma53mq7l)!

#1: Initial revision by

kadamrohan16‭ · 2025-01-22T09:37:05Z (29 days ago)

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Transfer function of arbitrary dc-dc converter

I am trying to find out the transfer function of below arbitrary dc-dc converter and not able to succeed .

quick analysis goes as written below ,
 
_1. M1 on_

Δ IL2= (VS-VL1-VO)*D/L2

Δ IL1= (VS-VL2-VO)*D/L1

_2.M2 Off_

Δ IL2= -(VC2+VD2)*(1-D)/L2

Δ IL1= -(VO)*(1-D)/L1

**Δ IL2on + Δ IL2closed = 0**

(VS-VL1-VO)*D -(VC2+VD2)*(1-D)= 0

D*VS-D***VL1**-D*VO-VC2+VC2*D-VD2+VD2*D =0 .............eq1

**Δ IL1on + Δ IL1closed = 0**

(VS-VL2-V0)*D -(VO)*(1-D)= 0

VS*D-**VL2***D-VO*D-VO+VOD=0............eq2

from above two equations , it looks like VO/Vin transfer function will have either term VL1 or VL2 .

how to remove that VL1 or VL2 term from the transfer function ( generally  inductor voltage term does not appear in any conventional converters transfer function)  or  inductor voltage is bound to appear in transfer function of this converter ?

Please advise .
 
![Arbitrary dc-dc converter](https://electrical.codidact.com/uploads/9kdzu7yvpfj5mfsauo9dma53mq7l)!

Analog SMPS power-converter DC-DC-conversion buck-converter

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