Gain peaking after gain roll-up

[Debdut]

I have a feedback circuit whose open loop transfer function characteristic looks as follows



The closed loop transfer function is as follows



If looked closely, the closed loop transfer function exhibits peaking



I want to understand what is causing this peaking. What is its effect? I searched books. I could only find peaking at gain roll-off, which is caused for insufficient open loop phase margin. What is the cause in this case?
Please help in this regard.

 

[Dominik Przyborowski]

Your opamp has a LHP zero for frequencies ≈ 200kHz. I don't know what your circuit is, but try to calculate closed loop response with 2pole-1zero opamp transfer function.

 

[Debdut]

Dear Dominik, thank you for the reply. I am trying to find the transfer function of output phase vs VCO phase noise of a PLL. I am following Razavi's book on RF Microelectronics.
The open loop transfer function has two poles at zero frequency, and some poles outside the 0dB cutoff frequency of the PLL.
The closed loop transfer function is having some peaking. Can you say whether it will affect the stability of the system.

 

[FvM]

To check for stability, you'll look at the loop gain, which isn't shown in your post. Because the closed loop gain implements a high pass, there will be usually another pole in the feedback factor, reducing the feedback loop phase margin.

In case of a single feedback loop, a finite peaking tells you that the circuit is still stable.

 

[Debdut]

I have made a mistake in the first post. The first graph shown is the curve of loop gain.

"In case of a single feedback loop, a finite peaking tells you that the circuit is still stable." - Is there any expression or theory for it? I mean, explanation for the peaking after closed loop response is rising. I know if there is peaking before the response falls down, it is due to insufficient phase margin of the loop gain.

Thank you.

 

[FvM]

If the curve is loop gain, then it's complying with stability criterion. Overshoot in time domain or peaking in frequency domain can nevertheless happen.