Input band-pass limiting in a PLL: its influence on interference-induced bifurcation

The sum of a desired tone and an interfering, offset in frequency by v radians/second, tone is considered as the input reference signal for a system comprised of an ideal band-pass limiter and first-order PLL combination. Parameter y denotes the ratio of interfering signal to desired signal amplitudes. In the first of two cases, this two-tone reference signal is supplied directly to the PLL. In the second case, the two-tone reference is band-pass limited before application to the loop. In both cases, if ratio y is sufficiently small (i.e., the interference is relatively weak), the PLL can phase lock to the desired tone, and the interfering tone causes a closed-loop, (2π/v)-periodic phase error (i.e., a periodic beat note within the loop). However, as y increases, a point y = y_b is reached where the periodic phase error bifurcates (y_b is the bifurcation point), and the PLL breaks phase lock. A metric of interference rejection ability, the value y_b, is a function of tone frequency spacing v, PLL closed loop bandwidth G, loop detuning wΔ and whether or not input band-pass limiting is employed. Two different algorithms are described for calculating the bifurcation point y_b. The first is based on a numerical solution of the equation that describes the PLL; the second is based on harmonic balance methods. These two algorithms are used to show that, depending on the value of v relative to the PLL closed-loop bandwidth G, input band-pass limiting may, or may not, increase the bifurcation point y_b. Specifically, for detuning wΔ = 0, input band-pass limiting decreases the bifurcation point y_b for a range of v within the PLL closed-loop bandwidth.