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 janos.ladvanszky@ericsson.com, Gabor.G.Kovacs@Ericsson.com 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*10-3 . 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), 524287 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