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Which way of getting the target fundamental frequency is correct after simulating a VCO design?

Alex Liao

Hi,

I have two ways of getting the fundamental frequency if I am not wrong.

1. I use the provided function which is 'plot fundamental frequency' from the RF manual and get a equation if set this as output. Something like this: (L0 is the inductor connected to the output pin).

harmonic(xval(getData("/L0/PLUS" ?result "pss_fd")) '1)

The first-order Harmonic would be the fundamental wave.

2. I use a DFT transfer to transfer the transient output waveform to a discrete waveform, bar plot. By observing it, one could notice a high magnitude value at (or around) a frequency because the property of waveform being discrete. (X-axis is the frequency and Y-axis is the Magnitude). At that frequency with the highest Y value,  I think it is the fundamental target frequency.

With a 'pss' analysis simulation result, I could compare the values from the two methods. There are some mismatch of the two acquired frequencies which I can understand. DFT only gives values at fixed frequency steps dependent on user specific settings. For instance, If I applied 'ymax' which will return the x values corresponding to the maximum Y values in the DFT resultant waveform, I got  4.6G (method 2.) , but the method 1. gave me 4.70118G.

(a) I am wondering which way is the correct way to get the target fundamental frequency of a VCO design? It looks the method 1. gives more accurate result. (1. is better)

 (b) I also noticed there are some energy (Y-axis values in the DFT waveform) at the Zero Frequency. Sometimes if not properly designed, the target frequency's energy (the magnitude of the complex number representing the DFT resultant waveform) is smaller than the energy at the Zero Frequency. Like Mag@4.6G = 1 < 1.3 = Mag@0. I understand according to the definition of the Discrete Fourier Transformation, there are always some energy at the Zero Frequency. If the Magnitude at the target frequency is smaller than that at 0, it means the energy of the oscillation at the target Feq. is not strong enough. Therefore if using the method 2. I may get the target fundamental frequency with low energy which is smaller than the energy at the Zero frequency.  At this point, on the contrary to (a), it looks method 2. is better and secure.

Does anyone have a clear understanding on this?

Thank you,

Alex

  • Alex,

    The first approach will be much better. PSS is solving for the oscillator frequency, and the expression is directly telling you the fundamental (it actually doesn't matter which signal you pick because the xval is retrieving the x-axis - the frequency axis - so any signal will do).

    Doing an FFT on a transient signal over an arbitrary period will only give you the resolution of the observation interval - plus you'd need to do windowing as the chances are the result wouldn't be an exact period. The zero-frequency value is simply telling you the DC component - that's not necessarily a problem as you may just have a DC offset. If your supplies are 0 and 1.8V, you may have a 0.5V amplitude sine wave oscillator biased around 0.9V - the FFT of this would then have a magnitude of 0.9 at 0, and 0.5 at the oscillation frequency.

    If you use PSS, you can also plot the spectrum of the oscillation - so you can check offsets and harmonic content, and the magnitude of each harmonic, This will be in terms of harmonics of the oscillation frequency - exactly what you want, in other words.

    Regards,

    Andrew.

  • Andrew,

    Very Clear Reply.

    Thank you,

    Alex

  • in reply to Andrew Beckett

    Hi Andrew,

    I'd like to know how pss spectrum gets the phase and magnitude of different harmonic content? I thought it was DFT at at fitst, but one can only get magnitude from DFT, so how to get phase in frequency domain?

    Thank you,

    Clara

  • in reply to Alex Liao

    Dear Clara,

    Clara Dong said:
    but one can only get magnitude from DFT, so how to get phase in frequency domain?

    I thought I might comment on the portion of your posting I've shown above as I wanted to prevent any confusion. A DFT does provide phase information. The output of a DFT is, in general, a complex quantity having both real and imaginary parts. Hence, phase information is available. However, some caution is required when computing the phase from the samples due to the nature of the atan() function and due to potential round-off errors. These two considerations are discussed in an article by Mathuranathan Viswanathan at URL:

    https://www.gaussianwaves.com/2015/11/interpreting-fft-results-obtaining-magnitude-and-phase-information/

    Since the result of a converged pss solution is a time-domain waveform of the signal specified as the output of your pss analysis, it will inherently contain phase information and its DFT will also provide phase information.

    Does this help Clara? I hope so!

    Shawn

  • in reply to ShawnLogan

    Dear Shawn,

    Yes! Thank you for detailed explanation~

    Clara

  • in reply to Clara Dong

    Dear Clara,

    Clara Dong said:
    Yes!

    Great!! Thank you for letting us know and good luck!

    Shawn

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