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Reg the transfer function of a down conversion mixer (Read 4044 times)
ULPAnalog
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Reg the transfer function of a down conversion mixer
Jan 28th, 2017, 12:07pm
 
Dear experts

Attached is the schematic of a simple down conversion mixer with the relevant waveforms marked. Also assume that the time constant of the circuit is small enough to simplify the problem.

Since the evaluation of transfer function involves exciting the circuit with a sinusoid and in this case, writing the Fourier transform for the output and calculating the transfer function to the respective harmonic. Consider the following case in (a) where the input is a sinusoid and the output resembles that of a halfwave rectifier. Therefore there exists a DC component and hence the transfer function to DC is non-zero.

However in case (b), the input is phase shifted by 90 degrees and the output has a zero DC component and hence the transfer function to DC.

Now the question is, how does simulator differentiate between these two cases? Is it based on the pac phase? How does the spectrum analyzer measure the transfer function in such cases.

Thanks and regards
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Andrew Beckett
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Re: Reg the transfer function of a down conversion mixer
Reply #1 - Jan 29th, 2017, 2:13am
 
I don't quite understand what you're asking. You just said "how does the simulator differentiate between the two cases" without saying which simulator or which analyses you're running. If it's spectre and it's a PSS analysis, is the sine way large signal (i.e. sinusoidal) or small-signal and simulated in PAC?

A clearer question will get a clearer answer...

Kind Regards,

Andrew.
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ULPAnalog
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Re: Reg the transfer function of a down conversion mixer
Reply #2 - Jan 29th, 2017, 3:32am
 
Hi Andrew

Apologies if the question was not clear. I am referring to PAC analysis and simulator is spectreRF. My understanding is that the transfer function is conceptually evaluated by having a sinsusoid as input and taking the Fourier transform of the output, which then gives the information about the gain to a particular harmonic. Now the question is, does this gain/transfer function depending on the phase of the input sinusoid, for the circuit posted in the previous post.

A similar topic, for a different circuit, has been posted here
http://www.designers-guide.org/Forum/YaBB.pl?num=1451747641

Thanks and regards

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Ken Kundert
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Re: Reg the transfer function of a down conversion mixer
Reply #3 - Jan 30th, 2017, 10:16am
 
So far this seems like a thought experiment. Have you tried it?

-Ken
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Re: Reg the transfer function of a down conversion mixer
Reply #4 - Jan 31st, 2017, 5:41am
 
Dear Ken

Indeed, I simulated it with spectreRF pac analysis. The clock frequency in this simulation is set to 10kHz. Changing pac phase does not change the pac magnitude response. Attached is the response.

However with a input tone at 10kHz and an initial phase of 90 degree, transient analysis gives an output with zero DC component.

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Ken Kundert
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Re: Reg the transfer function of a down conversion mixer
Reply #5 - Jan 31st, 2017, 7:24pm
 
You have to remember that if the frequency in PAC differs at all from the frequency in PSS, then the phase relationship between PSS and PAC becomes meaningless, because the signals are at unrelated frequencies. In this case you get the average behavior. PAC takes that a bit farther. Even if the frequencies are related, it treats them as if they are not. Thus, pacphase is only needed if you have two PAC sources. It allows you to specify the phase difference between the two sources. So it is good for specifying differential signals if you do not use baluns.

-Ken
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Re: Reg the transfer function of a down conversion mixer
Reply #6 - Feb 1st, 2017, 2:51am
 
Dear Ken

Thank you for the detailed explanation. So it is as if the input is sin(2.pi.f.t + phi), where phi is a uniformly distributed random variable over[-pi, pi]. Is that correct? That is perhaps what happens when measuring through a spectrum analyzer -- initial phase being a random variable, giving the average behavior for the frequency response.

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Ken Kundert
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Re: Reg the transfer function of a down conversion mixer
Reply #7 - Feb 1st, 2017, 12:28pm
 
You can think of it that way if you wish. The way I think of it is by considering the PAC response for some low input frequency, say f=1. Since the PAC frequency is not commensurate with the PSS frequency and PAC is a steady state analysis, it will compute the average response where the average is computed over all time. In your example the average value is 0. Then I take the limit as f → 0.

That is not a description of how the mathematics is performed in the simulator (there are no limits taken), but I find it to be a natural conceptual framework.

-Ken
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Re: Reg the transfer function of a down conversion mixer
Reply #8 - Feb 2nd, 2017, 6:00am
 
Thank you Ken for sharing your insights on this.

Quote:
That is not a description of how the mathematics is performed in the simulator (there are no limits taken), but I find it to be a natural conceptual framework.


Is there is a document which outlines the math performed in a typical simulator, that is available in the public domain that you have come across?

Best regards
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Ken Kundert
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Re: Reg the transfer function of a down conversion mixer
Reply #9 - Feb 2nd, 2017, 11:47am
 
Yes, we published most of the ideas behind SpectreRF. A good place to start is Introduction to RF Simulation and its Application.

I find the math behind PAC very interesting and rather unique. But I have never really found it to be that helpful for designers to understand the mathematical underpinnings of SpectreRF beyond the basic concepts.

-Ken
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Re: Reg the transfer function of a down conversion mixer
Reply #10 - Feb 3rd, 2017, 10:11am
 
Dear Ken

Thank you for the pointers and the discussion, in general.

Best regards
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