Doing an AC analysis in a time-varying circuit.

Dear Ali,

During the oscillation I want to do a frequency domain transfer function (AC analysis).

I have been thinking about your question and request for suggestions to simulate the transfer function over the oscillation period of your VCO. I cannot help but wonder what the motivation for your analysis might be. For any transfer function that I am familiar with for an oscillator, the transfer functions of interest are not meaningful over a portion of the oscillation period. If you are concerned about the sustaining amplifier's open loop or closed loop gain transfer functions, these are only of interest over the entire oscillation period I believe. Why do I suggest this? Basically, one is interested not in whether the sustaining amplifier can support oscillation over just a portion of the period but whether when considering the entire period the sustaining amplifier has sufficient gain to support steady-state oscillation.

If you are considering the initial gain of the sustaining amplifier prior to the establishment of steady-state oscillation (for example in a ring based VCO consisting of several delay stages whose initial states are not known, then a series of actran simulations will serve you well. I have done this before to verify that the combined delay stages provide sufficient gain to establish oscillation. (An example for the motivation for this type of simulation is if one or more stage may be saturated at start-up. In this case, the near zero gain of the saturated delay stage may prevent the buildup of steady-state oscillation.)

Transfer functions of control voltage bandwidth will not be sensitive to any variation in their value over a single VCO period as the VCO modulation bandwidth is typically far less than the frequency corresponding to the oscillation period. Therefore, the transfer function consists of an average over the oscillation period and therefore does not appear to me, anyway, a reason to explore its behavior over a period of oscillation.

Perhaps if you might provide some added insight into the goal of your effort (i.e., its motivation), I can provide some added thoughts. Others, I am sure, will have good suggestions.

I hope I did not misunderstand your request - and apologize if I did!

Shawn

Dear Shawn,

Thanks for your response and sorry If my question was not clear enough. Let me make an example in order to clarify my motivation and what I want to do.

For example I want to plot the impedance of one node of oscillator during one period and see how it's changing during one period of oscillation. Basically I need to know the instantaneous input impedance of a node of oscillation at a fixed frequency.

To make it more clear, for a simple case I want to plot the gm of the transistor during the oscillation period. For this special case although I can use transient but for a general case which the node has some reactance, I couldn't find any solution. 

BTW, I don't care about the phase of the impedance, what I want is only to know how the magnitude of an impedance is changing during a period.

Also, I found a to simulation method, but It's a little tricky. I connect a DC source series to an inductor (which is like forcing the DC node voltages) to each node and define the DC value such that it's equal to it's transient counterpart and run the AC analysis, but the problem is that for each point I have to update the DC values, although It gives me what I want :-).

If you have any other idea or can help me to make it automatic it would be a great help.

Thanks,

Ali

Dear Ali,

> Also, I found a to simulation method, but
> It's a little tricky.


Although my personal thought is that you might be trying to establish the negative resistance margin or amplitude limiting characteristics of your sustains amplifier (and there might be more efficient methodologies to provide insight into these), I believe your "tricky" methodology can be provided using the spectre actran analysis. In this analysis, a transient analysis is performed and you specify one or more times in the analysis to perform an AC small-signal analysis. The small-signal analyses are performed using the DC operating points of the devices at the time of the transient analysis you specify. If you create an AC analysis expression for the impedance at some frequency, following the transient analysis, a plot of the result of that expression over time by ADE-L will be produced. By choosing a number of times over your oscillation period after steady-state oscillation is achieved will plot the parameter over your oscillator period. The actran analysis parameters are entered in the transient analysis dialog box from ADE-L or from the spectre command line as detailed in solution ID:

Solution ID: 11219108

I hope this helps!

Shawn

Dear Shawn,

Thanks for your suggestion, I didn't know about actran and that's exactly what I wanted to do.  I wanted to use this simulation to extract some information about large signal behavior in an oscillator.

It was a great help. Thanks again,

Best,

Ali

Dear Ali,

I am just happy I managed to help you a little!

Please be aware, however, that if you are trying to estimate how much margin your oscillator has to steady-state oscillation by estimating the average gm in a series of small signal simulations, you are probably not accurately capturing the large signal design margin. From my guess as to what your overall objective might be, I think you might be interested in the start-up gain margin or large signal amplitude limiting.

In any case, thank you for letting me know!

Shawn