Consider the following signal: v(t) = Acos[ 2πf0t + φ(t) ]. The IEEE defines phase noise as ℒ(f)=Sφ(f)/2 where Sφ(f) is the one-sided spectral density of a signal's phase deviation. In a periodic chirp signal, v(t) = Acos[ 2πf0t + at2 +φ(t) ], is the phase noise is still defined by ℒ(f)=Sφ(f)/2. In this situation, how to measure the phase noise ?
Dear Mr. Cen,
Yes, your considerations are right if you have a chirp modulation. You can simply replace f0 by f(t).
You can measure the phase noise either by the spectral density (use a very high sampling rate and STFT for chirps) or by "counting" zero crossings. Maybe "Time domain analysis and its practical application to the measurement of phase noise and jitter" by Cosart et al or "Calculate Oscillator Jitter by using Phase-Noise Analysis Part 1" by Drakhlis is helpful for you. Both publications treat the case of frequency modulation.
I hope this helps,
Michael Ulrich
Since this is a periodic chirp signal, perhaps the most appropriate questions are: Is it a wide-sense stationary or wide-sense cyclostationary signal? Is it a power spectral density or cyclic spectrum or spectral correlation density function? Apparently, the IEEE definition does not establish these differences.
Dear Sir,
To me, the simplest is to A/D convert the signal with a suitable digital oscilloscope, and then process the signal with some C or Matlab program to calculate the phase noise from that.
The processing needs to mix the signal with another chirp, so that the frequency becomes constant, and then measure the phase noise using conventional methods.
Cheers,
Henri
If the chirp signal is noisy, we can simply use an A/D converter and process with a Matlab. But for a pure, high-center-frequency chirp signal, this method is unacceptable.
The traditional method to method to calculate the phase noise is mostly for a narrow-band signal. These methods may not be suitable for measure a broadband signal.
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