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Phase noise mechanisms (Read 260 times)
Alberto-G
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Phase noise mechanisms
May 08th, 2017, 5:22am
 
Hello, I have some general questions about phase noise. I'm a beginner on this topic and I would like to share the following points.

1) can split noise in AM-PM be considered a general way to treat noise in any circuit?

2) In case of an ideal amplifier is it possible to consider only amplitude additive noise just because PM component is neglected?(noise is about white)

3) AM noise in resonators is often neglected and all noise is supposed to be PM. Is it true because we suppose to have a complete conversion AM to PM due to the feedback?

4) Additive PM noise spectral density depends on the input signal level, instead multiplicative noise is independent on the input signal level. Is this also true for FM white noise generated from white phase noise?

Thanks
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Ken Kundert
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Re: Phase noise mechanisms
Reply #1 - May 9th, 2017, 2:09pm
 
Your questions are very open ended, so my response will necessarily be somewhat vague.

Quote:
1) can split noise in AM-PM be considered a general way to treat noise in any circuit?

The noise is the noise, and while you can always choose to interpret it as either AM or PM noise, or some combination of the two, the circuit itself will not care. Thus, you tend to only decompose noise into its components when displaying the noise. The circuit and the simulator itself will use the undecomposed noise.

Quote:
2) In case of an ideal amplifier is it possible to consider only amplitude additive noise just because PM component is neglected?(noise is about white)

In the case of a time-invariant non-distorting amplifier the noise added by the amplifier will be stationary, which means it will have equal amounts of AM and PM noise. As such, when considering the noise produced by an such an amplifier, we would never decompose it into its components. However, the input of the amplifier may contain noise that has unequal AM and PM components, in which case that will also be true at the output.

Quote:
3) AM noise in resonators is often neglected and all noise is supposed to be PM. Is it true because we suppose to have a complete conversion AM to PM due to the feedback?

Resonators are generally linear circuits, so the noise they produce is stationary, meaning that it contains equal amounts of AM and PM noise. So again, if we were considering the resonator alone, we would never decompose the noise into its components.

But I suspect that is not the question you are asking. Presumably by resonator, you actually mean resonant oscillator? Except in rare cases, the noise at the output of oscillators is almost purely in the phase. The natural amplitude control mechanisms of the oscillator act to suppress the amplitude variations. (It is wrong to say the feedback converts the amplitude noise to phase noise, the feedback suppresses the amplitude noise.)

Quote:
4) Additive PM noise spectral density depends on the input signal level, instead multiplicative noise is independent on the input signal level. Is this also true for FM white noise generated from white phase noise?

I really do not like the term 'Additive PM noise'. I usually associate 'additive' noise as stationary noise. AM and PM noise only springs from modulation processes, which are more aptly described as 'multiplicative'.

PM and FM noise are the basically the same thing. It is just the FM noise is scaled by the frequency. Generally we talk about FM noise at the output of an frequency modulator. And a frequency modulator is the same as a phase modulator where the input signal has been passed through an integrator.

-Ken
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Alberto-G
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Re: Phase noise mechanisms
Reply #2 - May 10th, 2017, 4:39pm
 
Thank you for your helpful answers.

In question 3 you are right I meant resonant oscillator.
Regarding 3-4 I would be more specific:

Part I
Considering an ideal liner amplifier in a small signal regime, it can be
described as a LTI system with transfer function H(s).
If one neglects environment contributions, all noise can be calculated adding voltage and current generators whose values are related to the power spectral density.
Now in this context I would like to look at the AM and PM components without any particular circuit constrains.
Noise power is equally divided in two degree of freedom amplitude and phase.
Now I can write the input signal plus noise in phase and noise in quadrature at the amplifier input.
I have an available power noise of N=kT (ideal noiseless amplifier otherwise FkT).
So total power in bandwidth B is NB thus I can write the AM and PM PSD as:

s(t)=A(1+α)cos(ω0t+θ)=Acos(ω0t) + nI(t)cos(ω0t) - nQ(t)sin(ω0t)

α=nI/A
θ=nQ/A

Sα(f)=NB/P
Sθ(f)=NB/P

P carrier power.
From this model additive noise spectrum (spectrum analyzer measure) is independent from the carrier power (noise is still present even without carrier) but phase PSD and amplitude PSD are inversely proportional to the carrier power.
Is this reasoning correct?

Part II
When there are non-linear effects in the circuit is it correct to say that multiplicative noise mechanisms take place?
If I consider a non linear model system based on polynomial truncated at the n degree and I substitute a pure sine wave plus I and Q noise components, it turns out that the PSD of PM and AM components are in this case independent from the carrier power (nearly).
Now instead the noise spectrum depends on the carrier power but PM and AM PSD are quite independent from it.
Is this reasoning correct?

Part III
In resonant oscillators if I suppose linearity and time invariance, invoking the general feedback theory and approximating the bandwidth near the resonant frequency as f0/(2Q) a slow phase fluctuation is converted in frequency fluctuation and this leads to the 1/f^2 phase noise slope (leeson's equation).
Hence only the phase fluctuations with frequency from DC to f0/(2Q) are converted with this mechanism.
Leeson's equation takes into account only resistor noise and the loop effect.
The same conversion is exhibited also in a long chain digital delay line due to the accumulated jitter process.

It is correct to say that in the an oscillator phase noise is accumulated in time and this mechanism is related to the group delay of the feedback?

Sorry for the long post

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« Last Edit: May 11th, 2017, 12:01am by Alberto-G »  
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Ken Kundert
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Re: Phase noise mechanisms
Reply #3 - May 11th, 2017, 9:52am
 
First a few clarifications ...
Presumably in part 1 by 'ideal liner amplifier' you mean ideal linear amplifier and not ideal limiter amplifier.
Also in part 1 you equate 'additive noise spectrum' to 'spectrum analyzer measure'. This is incorrect. A spectrum analyzer measures the time-average noise, and it measures it regardless of whether the noise was generated through additive or multiplicative processes. Since it is measuring the time-average noise, it cannot distinguish between amplitude and phase noise.

Part I:
Yes, if you apply a noise free input signal to a noisy linear time-invarient amplifier the noise at the output will be independent of the amplitude of the input signal. This follows directly from the fact that the amplifier is linear. In this case, there are no modulation processes active, so we generally do not decompose the noise into AM and PM components. If we did, they would always be equal because the noise is stationary rather than cyclostationary.

Part II:
If instead you apply a noise free input signal to a noisy nonlinear amplifier, then the noise generally will be affected by the input signal's amplitude. In the situation where the amplifier saturates, the AM components will be suppressed and so will be smaller than the PM components. The nonlinearity is modulating the noise, making it cyclostationary.

Part III:
Yes it is correct to say that the oscillator phase noise is accumulated in time. It is a direct result of the phase being unconstrained. That explains the 1/Δf 2 slope. However, if the oscillator were linear, as you suppose, then the noise would be distributed evenly between amplitude and phase noise. However, all practical oscillators are nonlinear, and it is the nonlinearity that acts to suppress the amplitude noise, with result being almost purely phase noise.

-Ken
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Alberto-G
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Re: Phase noise mechanisms
Reply #4 - May 11th, 2017, 12:33pm
 
Thank you so much for this clarification.
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