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https://designers-guide.org/forum/YaBB.pl Design >> Mixed-Signal Design >> question on sigma-delta FM https://designers-guide.org/forum/YaBB.pl?num=1137859429 Message started by svensl on Jan 21st, 2006, 8:13am |
Title: question on sigma-delta FM Post by svensl on Jan 21st, 2006, 8:13am 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 |
Title: Re: question on sigma-delta FM Post by boa on Jan 23rd, 2006, 12:33am Here are my considerations: 1. Regarding quantization noise & signal filtering by VCO - they are saying that: "the VCO bandwidth must be sufficiently large to ensure that it does not cause attenuation in the bandwidth of interest. Ideally, the delta-sigma modulator should be operated at a frequency such that the VCO filters out the quantization noise but not any components of the actual signal. The bandwidth of the VCO is significantly affected by the time it takes to switch between the two frequencies. The VCO should switch smoothly (but not instantaneously) between frequencies with no overshoot" So they are modulating VCO with a 4kHz signal and using 10 (with visible quantization noise in modulated signal) and even 100MHz sampling rate of SDM which allows to filter quantization noise but pass the signal relatively unaffected. 2. Kvco/(1+s/w) vs Leeson's equation: Kvco/(1+s/w) is a simplest first-order model of VCO's transient model, i.e. VCO's response to the change in control voltage. Leeson's equation provides a model of VCO's phase noise with a ideally stable control voltage, i.e. the the phase noise due to noise sources in oscillator itself. Cheers, Alex |
Title: Re: question on sigma-delta FM Post by svensl on Jan 23rd, 2006, 2:06am 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/wo). But this bandwidth wo does not change with the switching frequency of Kvco, does it? It is rather that Kvco is affected by the switching frequency. Regards, Sven |
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