1. Software Based Separation of Amplitude and Phase Noises in Time Domain
ISCAS’2011 Rio de Janeiro, Brazil
Software Based Separation of Amplitude and Phase Noises in Time Domain
J. Ladvánszky, G. Kovács, Ericsson R&D, Budapest, Hungary
Abstract: Using the modern analysis tool Matlab, amplitude and phase noises have been extracted separately from the measured time domain output voltage of a sinusoidal oscillator. Analyzing the auto and cross correlations of the extracted amplitude and phase noises as functions of time, now we know how oscillator noise can be modeled for system analysis.
Keywords: Signal process-ing, noise, quadrature demodulation, noise skirt
Introduction
Goal: accurate modeling for system analysis
Ergodicity postulate
A simple noise extraction algorithm
Accuracy test
Analysis of measured data
Closed form expression for power spectrum of a noisy sinusoid
Reason of the noise skirt
Accuracy test
Simulation example: White Gaussian phase noise only, σφ2=2*10-3
Closed form expressions for autocorrelation and power spectrum of the oscillator voltage
Rξξ(τ)
Rφφ(τ)
Variance σφ2 of the detected phase noise.
Horizontal axis: time in seconds, vertical axis: σφ2.
The curve well approximates the preliminarily
given value of 2* Relative accuracy is about 10-4
Analysis of measured data
Rξφ(τ)
Variance σξ2 of the detected amplitude noise that should be zero in this example. This Figure represents numerical error. Horizontal axis: time in seconds, vertical axis: σξ2. As there is only phase noise, σξ2 << σφ2
A 3 transistor quartz oscillator at 10 MHz
Measured by sampling scope Agilent
54854A (40 GS/sec option), samples
Evaluated by Matlab/Simulink
Matlab/Simulink realization
Noise extraction algorithm
Sξξ(f) dB
Reason of the noise skirt is correlation and not phase noise as originally believed
Determine A and ωc accurately
Sφφ(f) dB
Results
- Ergodicity postulate allows closed form calculations
- Amplitude and phase noises are separately extracted using quadrature demodulation
- Reason of the noise skirt is correlation
Quadrature demodulation has never been used for noise extraction before