Hello,

I have come across a paper which makes a point which confuses me.

In the paper a digital-to-frequency modulator is described. The input to the VCO is the output of a sigma delta modulator (+/-1’s). Thus, the output frequency switches between two frequencies only. Naturally, the output of the SDM will have quantization error. It is stated in the paper (top-right column, 2nd page) that since the VCO will attenuate signals outside its frequency bandwidth, the quantization error will appear attenuated if the frequency of the SDM is high. In essence, the VCO acts like a band-pass filter.

If the frequency of the SDM is high then the pulse-repetition-frequency of the +/-1s stream is high and BOTH the signal and quantization error will get slightly attenuated due to the transfer-function of the VCO which is Kvco/(1+s/w). So, how can only the error get attenuated? On the other hand, I can sort of see his point when considering Leeson’s equation which represents a band-pass transfer function. The noise outside would be attenuated. So which should I consider to be correct: Kvco/(1+s/w) or Leeson’s equation (I mean shaped proportional to 1/w^2).

Cheers,
Sven

The URL for the paper is: http://www.mit.edu/~ddaly/research/files/iscas_paper.pdf

Alex,

Thanks for taking the time to have a look at the paper. You are right that Leeson's equation looks at internal noise sources and was derived with a constant control voltage. I guess what I don’t understand is how the switching effects the bandwidth of the VCO.  I understand that at high switching frequency the VCO cannot respond fast enough and the gain Kvco, which ideally should be constant, will drop at some frequency higher than the modulation bandwidth. Thus, the simple equation Kvco/(1+s/w_o). But this bandwidth w_o does not change with the switching frequency of Kvco, does it? It is rather that Kvco is affected by the switching frequency.

Regards,
Sven