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I'm trying to design a Delta-Sigma Modulator for frequency synthesizer applications and am (just right now) figuring out how to properly configure a first order DSM in Simulink. I've made a few small variations that I've seen (with the unit delay in the integrator in different paths and one configuration without a delay in the feedback path) but have arrived at a similar conundrum. The 20dB/decade rolloff expected of a 1st order DSM isn't present, and I see very pronounced harmonic tones in the PSD. Specifically, for when I sample at 1MHz (which for a DC input, I'm not entirely sure is needed, but I digress), I see spurs at 100, 200, 300, and 400KHz.

The pictures below are of the Simulink model, followed by the PSD of the three configurations in the model.

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Jack
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  • A one-bit first order DSM with a 0.1 input will give you output components at multiples of fs/10, though the first order case is so straightforward that a time domain rather than spectral domain makes more sense for analysis. Life doesn't get 'interesting' until you have higher order. When higher order, a one bit DSM only works well for inputs in the 0.25 to 0.75 range, where 0 and 1 are the outputs of the feedback DAC, otherwise the output run lengths become excessive, pushing the noise down into the low frequency region you're trying to keep clean. – Neil_UK Jan 13 '21 at 03:52
  • This is what I was worried was happening; I wasn't sure if it was an issue with the model or just how the 1st order DSM behaved. I thought there would at least be some apparent 20dB/decade roll-off as I've seen mentioned in textbooks. I actually did simulate a 2nd order DSM in another simulation (where I was trying to simulate a 2-1 MASH) and saw the output spectrum of the 2nd order (roughly) followed that 40dB/decade rolloff I expected. Is a 1st order DSM even of any value when it comes to toggling the modulus of a PLL, then (I suppose it depends on the PLL's loop filter)? – Jack Jan 13 '21 at 04:33
  • Also, I've noticed that you've replied to many of my DSM questions in the past few weeks; I can't thank you enough for filling in some of the gaps that some of the textbooks/papers I've read have left, Neil. – Jack Jan 13 '21 at 04:34
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    If I was an academic, I would have written some of the books, but I was an engineer and a lot of this was confidential. First order DSM can be used for specific synthesis situations, or with a correction DAC. I made a point of mentioning 'number stream' because there are different ways of making one. A counter can give the same results as a DSM-1, and the first fracN synthesis used counters. Read [this](https://www.microwavejournal.com/articles/3314-fractional-n-synthesizers) and follow the references at the end. Compare fig4 and fig6. I worked with Wells and Owen. Ref8 is me. – Neil_UK Jan 13 '21 at 10:09

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