Control to output transfer function- Ltspice simulation and calculations

Question

Picture 1 shows the simulation of control to output transfer functions of PSFB converter in Ltspice.

Picture 2 shows the calculation made by Verbal Kint for the same the circuit given in Picture 1. I am showing this picture as reference.

Picture 3. shows how to calculate the quadratic pole frequencies, this document is used by the one of the lecturer in Colorado Boulder University. Page 21.

QUESTION :

I know that the way that Verbal Kint does to find quadratic pole is correct.I have no doubt about this calculation given in the red box in Picture 2. He is professional.

But when I follow the calculations given the Picture 3, I have very different results between the calculation given in the document and calculations made by Verbal Kint.

What could be the reason for this difference ?

Picture 1. Simulation of control to output transfer functions
enter image description here
Source: Me

Picture 2. Calculations used by Verbal Kint enter image description here
Above image from answer to "Calculation of control to output transfer function" by Verbal Kint, edited by Mhan and posted on Electrical Engineering Stack Exchange is licensed under CC BY-SA 4.0.

Picture 3. Quadratic pole frequencies, this document is used by the one of the lecturer in Colorado Boulder. enter image description here
Source: https://u.dianyuan.com/bbs/u/28/1113719734.pdf

• periblepsis: It appears you want to know why C. Basso's (Verbal Kint) work product differs from that from a lecturer in Boulder. There also may be something implied by the inclusion of an LTspice run, but if there is an implication I don't see you discussing it, explicitly. Yet I'm sure you have a clear reason in mind for including it. I for one would appreciate more discussion from you because it feels like you are leaving me with a lot of work to do in order to more fully grasp underlying questions. And I suspect you know more details and thoughts than you have shared so far. I'm holding short, for now.
• Voltage Spike: Can you show your calcs for #3 and how they differ?

Answer 1

The reason for the difference is that the equations presented in your picture 3 do not represent poles for the system rather they are equations for approximating the phase response. They would be near where the phase starts to fall and near where it levels off at -180 degrees for a 2 pole system.

• Mhan: Ah, okay the equations in Picture 3 is for phase asymtotes , on the other side the equations in the picture 2 is for magnitude plot, thank you so much @CBOB