Frank,

I see your point. Thanks for the insight. If the VCO output is sin(phi), where phi = integral of frequency wrt time, the linearization is

sin(phi)+delta_phi*cos(phi).

Since delta_phi is the output of an integration, it grows with decreasing frequency. Also, since PAC probably only plots the amplitude of the perturbation, the normalized perturbation indeed equals phase perturbation. It seems only the normalized plot has meaning since the absolute plot (in Volts)  implies incorrectly that the amplitude goes to infinity at DC. Right?

svensl,
By "stripping down the circuit" I meant yours. However, my simple circuit should suffice.

Regarding your f0 offset, are you sure you selected the correct sideband? When you change the offset, don't you also change the VCO unperturbed frequency?

Quote:


Yes. It would be nice if one of the SpectreRF experts could confirm my claim.

You are not the first to be confused. If I don't use the tool for a few months I have to dig into the manual or e-mail someone. One of my complaints about the SpectreRF PAC, Pnoise, Pxf GUIs is that although the manual is very clear about sidebands, the GUI does not say which field is the input and which is the output. Thus, I am forced to waste time experimenting with simple circuits or searching for someone who remembers. Anyway, I believe that for PAC, the topmost frequency fields in the GUI are for the input range. The rest is output. For Pnoise and PXF, it is reversed. You must deal with sidebands when you have frequency translation. Since you are injecting a frequency perturbation, you are injecting at baseband. However, you are observing it at RF(i.e. passband). You have frequency translation. I duplicated Frank's observations by specifying a baseband range in the topmost fields and selecting the output range in the lower fields. I believe I used a -1 sideband but I'm not sure, I am not at my workstation. Frank included some netlist lines that answer that question. I believe the +1 side band gives similar results because a sinusoid has output at positive and negative frequencies.

Excellent! Thanks Andrew.

Frank,
Even for small signals and high frequencies, I am still not sure I agree that the PAC analysis in this case is valid in the absolute sense, i.e. when interpreted as the transfer function from frequency perturbation to amplitude perturbation.  How can any perturbation in frequency have any affect on the amplitude of the VCO output? PAC says it can. However, I think we both agree that for high frequency, small signal perturbations, the normalized PAC output can be interpreted as a phase output.

Also, we agree that phase output should go to infinity at low frequency perturbations, and this PAC analysis does just that.

I therefore maintain that the PAC analysis in this case only has meaning when normalized to amplitude and and interpreted as a phase output. I am not convinced that in this case, the interpretation of the PAC output as an amplitude response is valid at any frequency or for any size of perturbation.

To be more specific, in an oscillator PAC will show that both upper and lower sidebands are generated and that they are correlated in such a way as to produce phase noise rather than amplitude noise.

-Ken

Concerning Eugene's comments about how it is difficult to remember how to fill out the forms for the periodic small-signal analyses (PAC, PXF, PNoise, etc): it might be helpful to remember that you are "specifying what is unique".

For example, PAC computes the transfer function from a single input to multiple outputs. So with PAC you must specify both the location of the input and the band of the input. You specify the location by adding a nonzero pacmag to a source and you specify the band by giving the start and stop frequencies on the analysis form. In this case, there is one input band and multiple output bands. So you specify the input band, which is unique.

Similarly with PXF and PNoise. These compute transfer function from multiple inputs to a single output. So with these you specify the output location and output band on the analysis form. Here, it is the output band that is unique.

Finally, with these analyses the sidebands are specified relative to the frequency band you specified.

Hope that helps.

-Ken