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Introduction: This application note Spectral Density of Phase Fluctuations discusses various techniques for the S(f) measurement of phase noise using frequency domain analysis. Typical This is the most basic measure of phase applications areas are characterization of noise. It is the square of the Fourier phase noise in crystal oscillators, phase transform of the time varying phase (t) noise of synthesized sources and phase normalized to a 1 Hz bandwidth. The noise in PLL or other measurement spectrum is normalized because when systems. These methods should give measuring a broadband signal such as good estimates of phase noise for noise, the amplitude of the spectrum frequencies upto 2 GHz. Frequency changes with the bandwidth over which stability in the microwave region is not the measurement is made. Normalizing covered. allows measurements with different bandwidths to be compared. If the noise Concepts of frequency stability: is Gaussian in nature, the amount of noise in other bandwidths may be Instantaneous frequency can be defined approximated by scaling the spectral as the time rate of change of phase, i.e. density by the bandwidth. Using the d(t ) above example of phase modulation, 2 (t ) ( t ) dt S(f) can be written as where (t) is the instantaneous phase of 2 rms ( f ) S ( f ) = the oscillator, and the angular frequency B is where rms = / 2 and B is the 2f . bandwidth (in Hz) used to measure The instantaneous output voltage of a rms. S(f) describes the phase noise at DUT may be written as an offset f on both sides of the carrier. V ( t ) = [Vo + (t )] sin[2v o t + (t )] where Vo and vo are the nominal Single Sideband Phase Noise L(f) amplitude and frequency of the output, and it is assumed that This is the most common way to express (t ) a phase noise spectrum. L(f) is defined << 1 and as the ratio of power in a single 1 Hz Vo sideband at an offset frequency f to the . (t ) total signal power. Typically, when << 1 measuring phase noise, almost all of a 2v o t signal's power is in the carrier, so carrier for s