I did consider doing it analytically and looking for poles in the right hand
half of the s plain. But I settled for numerical analysis just adding a
feedback block to the transfer function (TF) as B or B/s (90deg lag, I did
not try s/B for the lead case). Then adjust the constant B while I looked
for zero or 180 phase points that have gains more than one the condition for
oscillation when you connect the output to the input. I am rusty on what
happens if the gain is greater than one but with the wrong phase. So I
closed the loop and used the classic A/(1+A/B) checking with B and -B
varying the feedback gain and looked for peaks. Got two at the spit
frequencies. That case looks like it would only oscillate the center
frequency with a fancy filter in the loop say a PL which can also provide
the 90 deg phase shift. I failed to confirm that the polarity of the
feedback determines which pole it oscillated at???
I have now tried the primary current feed back case now. TF from Vin to Ip.
Three zero phase points the two outer with the same slope and opposite to
the middle one. This could have the potential to oscillate at the mid
frequency or one or other or both of the split frequencies depending on the
polarity of the feedback. Close the loop again with a variable gain block
and adjust polarity. 90 deg phase shift not required this time. Then add a
block for Ip to output voltage
Initial results produce the same two outer peaks independent of the
polarity of the feedback ????? I need to check the equations again. I
favor current feedback because it guarantees softswitching , no extra
connections and provides better isolation from the vagaries of the secondary
caused by streamers and ground strikes.