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Simulators >> Circuit Simulators >> Question on PSS
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Message started by sutapanaki on Jul 10^th, 2011, 7:36pm

Title: Question on PSS
Post by sutapanaki on Jul 10^th, 2011, 7:36pm

Hi,

Since this forum is frequented by the people who came up with the periodic simulations in Cadence, I thought I could get some insight in the meaning of the ideas behind linearizing the circuit around a periodic operating point. We all know what is meant by linearizing at a single operating point - Taylor expansion at that point and leaving only the 1st order term (or maybe more if we care about distortion). But how is this done for a periodically behaving circuits? What is the periodic operating point there? Obviously this doesn't refer to a single operating point. Does it mean that Taylor expansions are done for every point in the simulated period of the circuit (since we talk about analog waveforms, there are infinite number of points)? Or it is something else?
Thanks in advance.

Title: Re: Question on PSS
Post by Ken Kundert on Jul 11^th, 2011, 10:31am

To perform a periodic small signal analysis such as PAC or PNoise the simulator linearizes about the periodic operating point. In this case the word point may be a little confusing. It refers to a point in a waveform space (the space of all possible waveforms). A point in a waveform space is a waveform. Linearizing about the periodic operating point is the same as taking the first term in the Taylor series expansion at that point (again, in this case the point is a waveform).

That is the way it works conceptually. In practice it is more complicated because the simulator needs to solve the circuit equations at individual time points, so the waveforms must be decomposed into time points. Performing a periodic small signal analysis does involve linearizing the circuit at each time point in the periodic operating point, but it is more complicated that just performing a traditional small signal analysis at each time point and summing the result. If it was, the method would not work on switched-capacitor filters, because there is never a time when there is a direct path from input to output. Rather, the result at each time point must account for what is happening at the other time points as well.

-Ken

Title: Re: Question on PSS
Post by sutapanaki on Jul 11^th, 2011, 12:04pm

Thanks, Ken, for the reply. It certainly helps lift the fog a bit. I was wondering if you can put what you said in the context of a simple circuit. For example, a single NMOS transistor with a small signal at the gate and large, square wave clock at the source, so that when clock is high the transistor is off and when low, it is on and operational in saturation. Then, we can look at the drain current as an output. It may not be a practical circuit but probably good enough to further understand the concept of periodic operating point.

Title: Re: Question on PSS
Post by Ken Kundert on Jul 11^th, 2011, 6:16pm

When computing the periodic operating point, you assume that small input signal (at the gate) is zero. Then apply the clock to the circuit (at the source). The circuit reaches its periodic operating point when the circuit reaches steady state. The periodic operating point is then all voltage and current waveforms in the circuit for one full cycle of the clock.

When performing a periodic small-signal analysis, the simulator solves for the periodic operating point, then linearizes the circuit about that periodic operating point. The resulting linearization is periodically time varying and so can exhibit frequency conversion. The simulator then applies the small input signal to the linearized version of the circuit and computes the steady-state response.

-Ken

Title: Re: Question on PSS
Post by sutapanaki on Jul 11^th, 2011, 7:30pm

Thanks again. Now that I have the rough idea how it works, could you please point me to papers/books where I can further read about it?

Title: Re: Question on PSS
Post by Ken Kundert on Jul 12^th, 2011, 12:46am

My attempt to explain it can be found in http://www.designers-guide.org/Analysis/rf-sim.pdf.

-Ken