# how to calculate the phase margin

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#### michaelhust

##### Junior Member level 1
hello,everyone
the plot is the open loop gain and phase versus frequency and the close loop gain is 18.however, i have many confusions about it.
1:what is the phase margin when the feedback factor is 1/18?
2oes the overshoot cause close loop instability?
3:Is it common to see the phase never achieve 180 degree?
thank you

#### LvW

Hi Michael,

it would be interesting to see the corresponding circuit.
Question: Does the diagram really show the loop gain (the gain of the open loop)?
I doubt because the phase response indicates instability of the simulated circuit (phase jump with positive slope).

#### michaelhust

##### Junior Member level 1
that reminds me I may have the wrong test bench.
I will check the simulation and reply as soon as possible.

#### michaelhust

##### Junior Member level 1
hello all,i have just got back from the national day.
i tried other kinds of test bench, however the simulation kept unchanged.
here i post the main opamp circuit and hope someone can give me some suggestion.
thanks

View attachment ???.bmp

#### LvW

Hi Michael, as mentioned in posting #2 the phase response indicates already instability of the simulated circuit (that means: not just after closing the loop).

#### FvM

##### Super Moderator
Staff member
I'm not sure, if it's actually unstable. The rising phase may be due to feedforward effects as well. But the gain peak shows, that the amplifiers internal compensation is at least near to instability. I'm not familiar with the compensation schemes for telescopic amplifiers, but guess series resistors to Cc can defuse the situation.

#### biff44

The peak in gain near 0dB shows that you need to shift one of your zeros a little lower in frequency. The peaking will cause ringing for any transient waveform, which may be undesireable.

#### michaelhust

##### Junior Member level 1
hi, i don't understand why the circuit could be unstable when the phase jump is positive.
Doesn't instability always happen in the close loop circuit?

---------- Post added at 10:23 ---------- Previous post was at 10:13 ----------

there are two RHP plural poles in the DM transfer function.
I think it is the main reason of the positive phase jump.

---------- Post added at 10:33 ---------- Previous post was at 10:23 ----------

there are two RHP plural poles in the open loop transfer function.
i think it's the main reason of the positive phase jump.
poles ( hertz)
real imag
-801.599 0.
47.0743x 303.468x
47.0743x -303.468x
-530.111x 0.
-3.84233g 0.

zeros ( hertz)
real imag
-255.267x -331.115x
-255.267x 331.115x
360.289x 0.
27.5830g 0.
this is poles and zeroes position when the Cc is 10pf.
all the poles and zeroes that could be canceled have been neglected.
however, it's very confused the RHP poles turn to be LHP poles when the Cc is 1pf.

Last edited:

#### FvM

##### Super Moderator
Staff member
Doesn't instability always happen in the close loop circuit?
The internal feedback forms also a closed loop, and is well able to become unstable in an usuitable design. The open loop characteristic suggests that it's at least near to instability.

#### michaelhust

##### Junior Member level 1
I never knew that.
If there is a internal feedback, where is the close loop?
Does the compensation capacitor form a close loop?

#### FvM

##### Super Moderator
Staff member
It obviously forms a feedback structure. A risk of instability is particularly brought up, if the compensation crosses multiple stages, involving additional poles. This is the case in your design.

#### LvW

Michael, two RHP poles always indicate instability. Often there are internal hidden loops that cannot be identified by visual inspection.
(Example: A simple common collector stage can be unstable due to a feedback lop that is not visible as such). As a result, there is a peak in the magnitude response that is connected with a sharp phase increase. This phase jump is caused by an RHP pole pair. It can be justified by a method that uses some geometrical rules to construct the magnitude and phase response from the pole location. This procedure is described in several textbooks on control theory.

#### michaelhust

##### Junior Member level 1
thanks,maybe i should try to cancel the intermediate voltage shift stage and find what will happen.

---------- Post added at 17:18 ---------- Previous post was at 17:08 ----------

It seems I have a lot of complicated work to do.
I have learned so much from all of you.
thanks very much.

#### michaelhust

##### Junior Member level 1
hello,everyone. I have figured this problem out recently after acquiring the basic knowledge of control theory. I used two port method to compute the loop gain transfer function and find there are four low frequency poles and one zero locating at origin due to feedforward path and feedback path respectively. Utilizing root locus method , I found that one pole goes to origin, one pole goes to infinite, and two poles bend to RHP after the interval loop is closed. So the pole generated by intermediate stage makes the circuit unstable. After I cancelled the intermediate stage,the circuit just behave like regular Ahuja' compensation way.
So thank you all for your suggestions.

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