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 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
DV1-DVL1-DVO-VC2+VC2D =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 .
1 answer
I stopped trying to read your equations after the second undefined term.
In general, start analyzing such things assuming switches, diodes, and the like are ideal. Also consider continuous and discontinuous as two completely separate cases. This will give you a good starting point to see what is going on.
After you have the basic equations for the ideal circuit, you can add complications like offset voltages caused by diodes an the like.
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