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ettore

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PXF/PAC for autonomous circuits
Jul 18^th, 2006, 9:17am

Dear All,

I am currently involved in LC VCO development. In this activity I am facing some problem understanding the feasibility of the small signal analysis, like PXF or PAC, in the frame of autonomous circuit simulations.

As already suggested in this forum (see http://www.designers-guide.org/Forum/YaBB.pl?num=1108757064), the PXF analysis can give some quantitative insight on figures like PSRR. I performed the PXF (Relative Harmonic=1, sideband=-1, sweeptype=relative and frequency sweep between 100Hz to 1MHz to simulate the periodic transfer function from the VDD baseband frequency to the carrier frequency range on the output) on my VCO.

I got a similar result reported in http://www.designers-guide.org/Forum/YaBB.pl?num=1092741082, a pretty huge gain at frequencies close to the carrier (100dB). I did not fully understand the explanation given in the topic of the reported link, being the result of PXF a voltage to voltage transfer function does it mean that if I have 1uV sine on VDD I get 100mV sine on the output?

On the other side, when performing the PXF one calculates the transfer function from any source,to a single output. Now the question is what is the meaning of this transfer function in an oscillator, i.e. what is the SOURCE in oscillator circuit? By definition oscillator is autonomous (not-driven) circuit. If I introduce the periodic small signal sinusoidal excitation that I sweep and according to which I want to get the transfer functions, I would lock the phase. This means that my circuit is not autonomous anymore.
So I would say you cannot obtain periodic-steady state transfer function for an oscillator due to fundamental problem of 'what is the transfer function in case of an oscillator circuit?'

I guess I must be wrong in some of my assumptiom and I would be glad to get Your feedback to clarify my ideas on this topic,

Regards,

Ettore

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Ken Kundert

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Re: PXF/PAC for autonomous circuits
Reply #1 - Jul 19^th, 2006, 3:37pm

The huge gain for signals injected near a multiple of fundamental frequency is a characteristic of all oscillators. If you injected a 1μV signal at a frequency Δf where the gain was 100 dB, then you would expect to see a 100mV response at f_o + Δf as well as a 100mV response at f_o - Δf. Furthermore, the phase relationship between these two signals and the carrier would be such that variation would be almost completely in the phase.

As you increase the input signal amplitude, at some point the nature of the coupling changes. For very small input signals the response is linear, meaning that if you double the input amplitude it doubles the output amplitude. But at some point the oscillator starts to go into entrainment, a condition often referred to as injection locking. At this point the response becomes nonlinear and you can no longer use PXF.

-Ken

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wchlee

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Taiwan

Re: PXF/PAC for autonomous circuits
Reply #2 - Dec 19^th, 2006, 6:43pm

The huge AC gain is reasonable and can be clarified by the VCO narrow band PM equation. Consider a VCO with tuning port sensitivity Kv, center frequency fc, and oscillatopn amplitude Ac, now if a sinusoidal with amplitude Am and frequency fm be injected to the tuning port, the resulting sideband amplitude at fc+-fm is (Ac*Am*Kv)/(2*fm), so the more low frequency excitation(fm) will get the more huge Ac gain (Ac*Kv)/(2*fm).

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