An analytical and experimental investigation of a frequency- shift-keyed signal generated by a phase-locked-loop with application to narrowband FSK

Abstract

Narrowband communications systems employing frequency-shift-keyed (FSK) carrier modulation demand careful consideration of system transient responses. Discontinuous waveforms or their derivatives, such as produced by frequency modulation, can result in the generation of large transient currents and voltages. These transient conditions produce distortion which interferes with demodulation processes, and may be in excess of the physical limitations on continuous operation of the transmitting terminal.

It has been suggested that a phase-locked-loop (PlL), whose reference signal is instantaneously switched between two discrete frequency sources, be employed as the modulated source of an FSK carrier. The characteristics of the PLL provide signal coherence and a means of "shaping" the modulation waveform, both of which are required in certain FSK transmissions. The investigation undertaken here is primarily concerned with the characterization of such a PLL output signal (exhibiting a finite frequency transition interval). Expressions are obtained for the output signal and the resulting modulation waveform for the case of a single frequency shift. Graphical evidence of the dependence of the modulation waveform on the loop parameters, gain and bandwidth, is presented. In order to facilitate the analysis of linear networks excited by the FS-PLL, an infinite series of damped sinusoidal terms, representing the PLL output signal is developed. This series is also utilized to determine the coefficients of the Fourier series representation of a periodically keyed PLL. Using this result, the signal bandwidth is shown to vary directly as the loop bandwidth.

Application of the FS-PLL as a voltage source is made in the case of the equivalent circuit (a high Q series tuned circuit) of a VLf transmitting antenna. Representative curves are provided which show that the series tuned circuit transient response is in general the superposition of a transient component, resulting from a change in frequency, and a quasi-stationary component.

Finally, an experiment is devised which provides an additional investigative tool. A unique method for achieving demodulation of narrowband signals, while maintaining wideband demodulator response characteristics, is used to experimentally substantiate the predicted modulation waveforms. Experimental data is also obtained, and graphically compared with the theory, to verify the frequency domain analysis of the FS-PLL output as well as the tuned circuit time domain analysis.