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Design >> Analog Design >> Transfer function estimation from AC response
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Message started by didac on Feb 18^th, 2008, 9:15am

Title: Transfer function estimation from AC response
Post by didac on Feb 18^th, 2008, 9:15am

Hi,
Does anybody have references about transfer function estimation from Bode plots(Magnitude and Phase). I did a small program with Matlab that loads the magnitude and phase plots from csv files(generated with spectre) and then applied the usual method to estimate the transfer function(from de frequency where the system crosses -90º and so on...), then I applied a lead compensator(measuring the point of maximum phase difference and deriving a "correction function"-all with Matlab-) and I think that from this point it's a matter of iteration(easily automated) until a "acceptable error" is reached. I was wondering if it exists a more effective way to handle this issue.
Thanks for the help,
PS:the picture shows the results I achieved so far(one iteration of lead compensation)

Title: Re: Transfer function estimation from AC response
Post by vivkr on Feb 18^th, 2008, 11:14pm

Hi didac,

Just a comment. If you are using Spectre as the source for your analysis, you might as well use the PZ analysis to get all the poles and zeros of interest directly.
You may have to get rid of some of the high frequency poles/zeros, but this is easy.

I once had to do transfer function estimation based on data from a PAC analysis. I did it the old fashioned way - by eyeballing the major poles/zeros from the
phase plot and from the magnitude. I compared not only the AC response but also the step response of the resulting system in MATLAB to the response of the
original system. That way, you can see if you caught some pole/zero doublets lurking at low frequencies. These would matter as they would determine the
settling time constants. In my case, the responses matched almost perfectly even though I had just taken rough estimates. The method was also very fast. But
maybe it would be less effective for another system.

If you do make a nice program for estimating the TF, be so kind as to send me a copy :)

Regards
Vivek

Title: Re: Transfer function estimation from AC response
Post by shankar_p on Feb 20^th, 2008, 5:11am

Hi Didac

I have a small query. The Bode plots throw some light to the transfer function if the poles and zeros are real. Can you tell me how your matlab code interprets when the transfer function has imaginary zeros and poles.

Shankar

Title: Re: Transfer function estimation from AC response
Post by didac on Feb 20^th, 2008, 8:21am

Hi first of all thanks for the answers,
Vivek: thanks for the advise of pz analysis I just checked it(i.e. I saw that is here, I need to play with it a little bit and look at documentation).
shankar:at this moment the method doesn't do anything with imaginary zeros or poles, it determines complex poles and adds zeros afterwards.
Let me explain a little bit what I'm doing: the method that I'm applying is something I did in my first or second year of university in Control Theory. There are two methods in fact : one is estimation from the step response were you measure rising time,overshoot,settling time and it's dual is the one I'm applying. From what I know both methods are equivalent. The drawback is that they model the system as a second order function(including complex poles since the method involves measuring the peak gain at the natural frequency) and then a correction function is applied(that includes zero and poles). My aim is not to obtain the exact transfer function,instead a "reasonable" approximation(better that what I could achieve making by hand small signal analysis-and without dying trying to include all the intrinsic parameters of the transistor-).
The problem is that I usually see that method applied to electromechanical systems at low frequency and this is why I'm wondering if it exists a better method.
Thanks for the help,