A widespread test of the phase-locked loop (PLL) FM demodulator under Gaussian modulation is simulated using the Monte Carlo method. Unified noise-free and noise performance analyses of the PLL FM demodulator are presented. Substantial reduction of the modulation limit by the input bandpass filter is reported in the region of the input bandwidth of practical interest. Bessel bandpass filters of order greater than two are shown to compare favorably with Butterworth filters in front of the PLL FM demodulator relative to the intermodulation (IM) distortion. A lower bound on the loop noise bandwidth is found by minimizing the output click rate for given IM distortion specifications. FM threshold of 4 and 7 dB for the root-mean-square (RMS) frequency deviation-to-message bandwidth ratio 0.1 and 1.0, respectively, is reported on the worst-case IM distortion of 45 dB.

A formula suitable for numerical evaluation is derived for the mean cycle slip time of a first-order loop with state-dependent spectral density of the loop noise. The formula is applied to a synchronizer with sinusoidal type limiter phase detector. The accuracy of the asymptotic expression due to Moeneclaey (1985) is evaluated. Better cycle slip performance of the considered synchronizer compared to that with multiplier phase detector is reported at the loop signal-to-noise ratio (SNR) /spl alpha/>2.

The qualitatively different behavior of the PLL phase error variance reported by Yoon and Lindsey (1982) and Sarkar (1990) under the same assumptions is examined. An error which appeared in Yoon and Lindsey is identified and corrected.>