Hello:
For problem 7.15:
What is the method used to derive Gvg from the average switch small signal model? I am not able to derive a transfer function because in my model, the positive side of the inductor is connected to the negative side of the primary, the positive side (dot) of the secondary, and the tail of the arrow for the current source.
I am trying to manipulate this into the canonical form, and I am able to push the current source to the primary side. However, it is not apparent on how to push the inductor to the secondary.
Does the transformer need to be split apart into two transformers?
Thanks,
Alex
Hi Alex,
ReplyDeleteHere is my tentative way of solving the problem. That way of connection of inductor gives out some equivalent inductance, which is in serial connection with the secondary coil.
The method of calculating the equivalent inductance is: 1 Assuming the primary is shorted 2 gives secondary coil a small AC current in the form of sine wave and calculate the resulting voltage that given out on the secondary. 3 Assuming the turns ratio between the primary and the secondary is 1:x, then the equivalent inductance is L*(1+x)^2.
Zhiyuan
It's a little late now, but you can do circuit manipulation as follows to convert to the Fig 7-16 model (d-hat sources zeroed out), and convert that further to a transformer followed by LCR low pass (with new L value):
ReplyDelete1. Starting with the averaged switch model in the circuit, it's helpful to express the transformer currents in terms of the inductor current, since the transformer forces a i*D and i*D' ratio.
2. The transformer primary-secondary link can be broken, and the inductor can be split in two, one element for each side of the transformer, provided the voltages across the inductors remain as before. With L/D and L/D', all node voltages and all other currents are unchanged, thanks to the transformer.
3. With primary and secondary circuits separated, you can replace the original transformer with any combination of ideal transformers you want, provided the overall turns ratio remains the same (and overall dot phasing is preserved). 1:D connected to D':1 allows the two inductors to be pushed into the middle, where L*D and L*D' sum to L, leaving a circuit like Fig 7-16.