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Design >> Analog Design >> analysis of time-varying circuits
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Message started by aaron_do on Jun 2^nd, 2008, 8:05am

Title: analysis of time-varying circuits
Post by aaron_do on Jun 2^nd, 2008, 8:05am

Hi all,

I'm interested in studyng analysis of time-varying circuits like mixers. When capacitors/inductors are present, one way seems to be to analyze the circuit in the time domain and then use fourier series to analyze the outputs in the frequency domain. The mathematics gets a little complicated, however. Is anybody familiar with any other good methods for time-varying circuit analysis? I was trying to work out a method using the instantaneous transfer function versus the LO, but i run into a problem when considering capacitors and inductors since their transfer function depends on frequency (input or output?). When i use the input frequency I can get a pretty good approximation of the gain at zero-IF, but not versus output frequency.

thanks for any suggestions,
Aaron

Title: Re: analysis of time-varying circuits
Post by Eugene on Jun 2^nd, 2008, 8:14am

You could try baseband equivalent models. Inductors and capacitors also have baseband equivalent representations. It might help if you explained the purpose of your analysis: Noise? Transients? Stability? Gain? Distortion? All of the above?

Title: Re: analysis of time-varying circuits
Post by aaron_do on Jun 2^nd, 2008, 8:50am

Hi,

thanks for the reply. What i'm looking for is an equation to describe the gain of a passive mixer. Eventually i will move on to nonlinearity and noise analysis, but just gain for now. I preferably want the equation in a form similar to a transfer fucntion, but i think that the problem there is that the input and output frequencies are different...

thanks,
Aaron

Title: Re: analysis of time-varying circuits
Post by Eugene on Jun 2^nd, 2008, 8:08pm

Take a look at
http://designers-guide.org/Modeling/modeling-rf-systems.pdf
There is a section on various ways to define the gain of an up-converter. There are two basic problems with mixers, especially IQ mixers to and from baseband:
1. There are two inputs (outputs) and one output (input).
2. The baseband can be DC while the RF is AC. This makes it hard to use rms quantities.
The solution is to define gain in terms of baseband sinusoids on either side and to clearly specify whether you are defining gain in terms of total baseband power or just the power in one baseband leg.

The situation is further complicated if your input and output units differ. For example, consider the gain of a direct conversion down converter. Your input may be volts but your output could be amps. Let's assume you are defining gain from RF input to just one baseband output. If your output is differential, you still have to say whether you are talking about output differential amps or output circulating amps. The difference is a factor of two.

Also, many times the gain is normalized to the reference impedance. You must clearly specify the reference impedance. Sometimes, the reference impedances for input and output differ, especially if one side is single ended and the other is differential. Then you must really be careful about how you define the gain.

As long as you are consistent, and as long as you clearly define gain to all your team members, you can define gain however you want. In any case, I recommend using behavioral models and test benches to define your gains. That way there is no ambiguity. Another team member need only swap out the behavioral model with his/her device level model to measure gain.