Question about calculating PLL phase noise

To calculate the PLL output noise we simulate the noise of each PLL blocks and add their contribution to the PLL output together. Then I have a question.

Someone told me that when calculate the resistor (in LPF) noise contribution, it should be 4kTR*|H(s)|^2*2, where H(s) is the close loop transfer function from the LPF to PLL output. And multiplied by 2 is because of double sideband of the resistor thermal noise. Is this true? any reference about this?

Thanks a lot.

Doesn't look right.

Which "LPF" are you talking about? It makes a big difference where this lpf is.

H(S) is a weird nomenclature for a closed loop transfer function! H(S) traditionally refers to the feedback open loop transfer function. Sketch up a block diagram and show me what you mean by H(S).

As far as multiplying by 1 or 2, it depeds on if you are making a single sideband phase noise measurement or not. If you look at a spectrum analyzer, there will be a noise sideband to the left of the carrier, and another noise (almost identical) sideband onthe right hand side of the carrier. That instrument, the spectrum analyzer, is making a SSB phase noise measurement, and as such you do NOT multiply by 2.

biff44,

The LPF is the second order RC loop filter in the attached figure. And the H(s) is the close loop transfer function from vn to vout. It's amplitude bode plot looks like the blue line in the following figure, and the dashed line gives the close loop transfer function from the reference input to vout.

If a noise voltage source add at vn (4kTR, represent the thermal noise of the resistor) then it's phase noise contribution to the PLL will show at vout. My question is when we calculate the nosie contribution is the factor 2 necessary or not?