Phase Noise and Jitter Simulation

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Jitter and Edge phase noise

[https://community.cadence.com/cadence_technology_forums/f/custom-ic-design/56929/how-to-derive-edge-phase-noise-from-output-noise-in-sampled-pnoise-simulation/1388888]

Phase Noise Aliasing & Integration Limits

These two types of measurements deliver the same rms jitter of \(f_{CK}\)

  • both rising and falling: integrated from \(-f_{CK}\) to \(+f_{CK}\)
  • only the rising (or falling) edges: integrated from \(-f_{CK}/2\) to \(+f_{CK}/2\)

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temporal autocorrelation and Wiener-Khinchin theorem is more appropriate to arise rms value

Y. Zhao and B. Razavi, "Phase Noise Integration Limits for Jitter Calculation,"[https://www.seas.ucla.edu/brweb/papers/Conferences/YZ_ISCAS_22.pdf]

time-average noise (phase-noise) & sampled noise (edge-phase noise or jitter) spectrum

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Time-average noise analysis

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\(S_{\Delta f}(f)\) between \([\Delta f, F_0/2]\) may be less than that of other harmonic window

Sampled noise analysis

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correlation

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VCO Phase Noise

pnoise - timeaverage

  1. Direct Plot/Pnoise/Phase Noise or

    image-20220511112856934

  2. manually calculate by definition

    image-20220511112806122

  3. output noise with unit dBc

    Direct Plot/Pnoise/Output Noise Units:dBc/Hz and Noise convention: SSB

    image-20220511113248984

The above method 2 and 3 only apply to timeaveage pnoise simulation,

pnoise - sampled(jitter)/Edge Crossing

EdgePhaseNoise.drawio

Direct Plot/Pnoise/Edge Phase Noise or

image-20220515214901120

Another way, the following equation can also be used for sampled(jitter)/Edge Crossing

1
PhaseNoise(dBc/Hz) = dB20( OutputNoise(V/sqrt(Hz)) / slopeCrossing / Tper*twoPi ) - dB10(2)

where dB10(2) is used to obtain SSB from DSB

image-20220511150337318

Output Noise of sampled(jitter) pnoise

The last section's Output Noise (V**2/Hz) can be obtained by transient noise simulation

The idea is that sample waveform with ideal clock, subtract DC offset, then fft(psd)

  • samplesRaw = sample(wv)
  • samplePost = samplesRaw - average(samplesRaw)
  • Output Noise (V**2/Hz) = psd(samplePost)

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Expression:

image-20220516185506348

The computation cost is typically very high, and the accuracy is lesser as compared to PSS/Pnoise

Pnoise Sampled(jitter): Sampled Phase Option

  • Identical to noisetype=timedomain in old GUI
  • Use model:
    • Sampleds Per Period: number of ponits
    • Add Specific Points: specific time point, still time points

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pss beat freq = 5GHz

pnoise sweeptype: absolute, from 100k to 2.5GHz

Transient noise

phase noise from transient noise analysis

  1. The Phase Noise function is now available in the Direct Plot form (Results-Direct Plot-Main Form) after Transient Analysis is run
    • Absolute jitter Method
    • Direct Power Spectral Density Method
  2. PN phase noise function
    • Absolute jitter Method
    • Direct Power Spectral Density Method

Absolute jitter Method: Phase noise is defined as the power spectral density of the absolute jitter of an input waveform

and absolute jitter method is the default method

In below discussion, we only think about the absolute jitter method

PSD and Phase Noise

  • phase noise is single-sideband
  • psd is double-sideband
  • Then the ratio is 2

By PSS_Pnoise

jee

1
rfEdgePhaseNoise(?result "pnoise_sample_pm0" ?eventList 'nil) + 10 * log10(2)

convert single-sideband phase noise to psd by multiplying 2 or 10 * log10(2)

By trannoise PN function

1
PN(clip(VT("/Out1") 2.60417e-08 0.000400052) "rising" 1.65 ?Tnom (1 / 3.84e+07) ?windowName "Rectangular" ?smooth 1 ?windowSize 15000 ?detrending "None" ?cohGain 1 ?methodType "absJitter")

double-sideband psd

By trannoise psd and abs_jitter function

1
dB10(psd(abs_jitter(clip(VT("/Out1") 2.60417e-08 0.000400052) "rising" 1.65 ?Tnom (1 / 3.84e+07)) 2.60417e-08 0.000400052 15360 ?windowName "Rectangular" ?smooth 1 ?windowSize 15000 ?detrending "None" ?cohGain 1))

double-sideband psd

abs_jitter Y-Unit default is rad

Comparison

image-20220506225324377

PN's result is same with psd's

RMS value

  • build the abs_jitter function with seconds as the Y axis and add the stddev function to determine the Jee jitter value
  • or integrate psd

The RMS \(x_{\text{RMS}}\) of a discrete domain signal \(x(n)\) is given by \[ x_{\text{RMS}}=\sqrt{\frac{1}{N}\sum_{n=0}^{N-1}|x(n)|^2} \] Inserting Parseval's theorem given by \[ \sum_{n=0}^{N-1}|x(n)|^2=\frac{1}{N}\sum_{n=0}^{N-1}|X(k)|^2 \] allows for computing the RMS from the spectrum \(X(k)\) as \[ x_{\text{RMS}}=\sqrt{\frac{1}{N^2}\sum_{n=0}^{N-1}|X(k)|^2} \]

Remarks

Cadence Spectre's PN function may call abs_jitter and psd function under the hood.

reference

Article (11514536) Title: How to obtain a phase noise plot from a transient noise analysis URL: https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1Od0000000nb1CEAQ

Article (20500632) Title: How to simulate Random and Deterministic Jitters URL: https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1O3w000009fiXeEAI

Cadence, Application Note: Understanding the relations between time-average noise (phase-noise) and sampled noise (edge-phase noise or jitter) in Pnoise analysis

Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals Jens Ahrens, Carl Andersson, Patrik Höstmad, Wolfgang Kropp URL: https://appliedacousticschalmers.github.io/scaling-of-the-dft/AES2020_eBrief/