DFT of ring oscillator giving frequency components that aren't harmonics

Dear Adithya,

Adithya Sunil said:

While taking the DFTs of a VCO I noticed I was getting significant magnitude components on the spectrum at frequencies that aren't harmonics of the fundamental.

Adithya Sunil said:

The oscillator has a fundamental frequency of 3.8536GHz but I see significant magnitudes at 1.5462GHz and 5.4GHz as well and I am not able to explain this conceptually. I have attached my DFT expression also below. Kindly tell me if there is something wrong with the way I am using DFT or explain to me if this is indeed the right behaviour.

Without some type of significant gain control feedback mechanism, there is nothing that requires an oscillator's output waveform contain only harmonics of the fundamental. Put simply, the limiting mechanism of any VCO without gain control is totally non-linear and may contain mixing products with other frequencies present in any of its internal or external waveforms (such as supply noise, kickback noise, control voltage noise, etc...). Looking quickly at your dft() result for your 3.8536 GHz VCO, and running a few checks suggest the 1.5462 GHz spectral component is a mixing product with the 6.161 GHz spectral component (6.161 GHz  mixes with 3.8536 GHz to produce 2.3074 GHz and then 3.8536  - 2.3074 GHz = 1.5462 GHz ). The 5.4 GHz spectral component is a result of mixing the 3.8536 GHz and 1.5462 GHz via 3.8536 GHz + 1.5462 GHz = 5.3998 GHz.

I don't know the specific setup for your simulation (accuracy settings, spectre type/version, strobe points, etc...) and hence I really can't comment on how appropriate your dft() expression may be to accurately capture its output spectrum. I can, however, state a couple of items that are evident:

1. It appears your dft sample does not contain an integral number of oscillator periods. 

2. The dft analysis appears to include the start of the simulation as its second argument is "0". Hence, your spectrum contains the portion of the oscillator waveform associated with its transient settling performance. In essence, the output frequency is changing over time and hence the sample time cannot possible contain an integral number of steady-state periods. I assume you are most interested in the steady-state spectrum and hence I might suggest you choose a dft analysis interval where the oscillator frequency is within its steady-state frequency requirement (depends on your frequency accuracy requirement...+/- 10K ppm?, +/- 1%?...). Including the initial transient in the dft will add frequency components associated with the envelope of the oscillator waveform as it builds to its limiting amplitude.

I hope this helps Adithya and I understood your question!

Shawn

Hey Shawn, 

Thank you for taking the time to answer my query. I understand the reasoning behind the output now. 

I have been able to get better results by using a larger number of samples and taking the DFT such that it is over an integer multiple of the oscillation period as per your suggestion.

Adithya

Dear Adithya,

Adithya Sunil said:

I have been able to get better results by using a larger number of samples and taking the DFT such that it is over an integer multiple of the oscillation period as per your suggestion.

Excellent! I am happy to read this and thank you for letting us know!

Good luck!

Shawn