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Three winding transformer with symmetrical resonant tanks for isolated dc-dc converter

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elecTomas

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I am trying to derive the gain |Vout/Vin| vs frequency of a dc-dc converter with isolation provided by a three winding transformer. The circuit includes three symmetrical series resonant tanks (same resonant freq.) for each port. If we simplify the system as shown in the figure attached, which approach would you follow to calculate the transfer function in terms of frequency? i.e. Vout1/Vin and Vout2/Vin vs ws (switching frequency [rad/s])

Thank you very much!!

Drawing1.png
 

Each load affects both output voltages. You have to fix load resistance first to calculate both transfer functions. If both loads are equal, you get a single transfer function.

Why not setup an AC simulation to visualize the circuit behavior?
 

FvM said:
Each load affects both output voltages. You have to fix load resistance first to calculate both transfer functions. If both loads are equal, you get a single transfer function.

Why not setup an AC simulation to visualize the circuit behavior?
Click to expand...


Thanks for your reply.

I have already carried out AC simulations to analyze the performance, and as you say when the loads are equal both networks have the same impedance and thus, the same transfer function. The problem I have is that my loads change in between a certain range. So I wanted to derive the Gain vs freq equation to identify the different transfer functions for different loads. But I have not managed to do it.

When both loads are equal, I calculate the impedance of secondary side LCR circuits (let's say Z1 and Z2) and then Z1//Z2. Then using standard equations for series resonant tank gain I get the transfer function, it matches with simulations. But this is not accomplished when R1 and R2 are different.
 

May be your "standard equations" are wrong. It's a simple AC network and can be well calculated.

If you want others to check it, you should post the complete calculation, including a source/derivation of the standard equations.
 

FvM said:
May be your "standard equations" are wrong. It's a simple AC network and can be well calculated.

If you want others to check it, you should post the complete calculation, including a source/derivation of the standard equations.
Click to expand...


I think you are right, I am using a equation which is derived for series resonant converters with only one secondary windings, see pict below.
Where fn=fs/fr and Q=sqrt(L1/C1)/Req.
When R2=R3, if I calculate the parallel equivalent impedance of secondary sides LCR networks it matches. However, for different loads it does not since I guess that the gain equation is not the proper one.

Capture.PNG

Could you give me some hints or references on how to approach the solution? Thank you very much.
 

I see that dual output circuit has higher order and can't be described by a single Q parameter. No chance to derive an equation of similar low complexity like your equation, I guess.
 

How about closely coupling L2 and L3 ?

Then there can only be one resonant frequency and cross regulation and circuit analysis should be much less of an issue.

It would behave much like a single output circuit, but having two halves galvanicly isolated.
 

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