A Theoretical and Experimental Investigation of Tuned-Circuit Distortion in Frequency-Modulation Systems

The problem of distortion introduced into the modulation intelligence by tuned circuits is considered both theoretically and experimentally. Complex equations result when the effect of the intelligence modulation is considered. These equations, while not readily amenable to Fourier analysis, disclose that the distortion parameters are ΔW/BW and λ/BW where, ΔW/2π = peak-frequency swing λ/2π = modulation frequency BW = bandwidth in kilocycles measured at 3 decibels down. Double-tuned circuits critically coupled. If the effect of the modulation frequency is neglected, the equations resulting from a theoretical analysis are somewhat simplified and the distortion due to single- and double-tuned circuits can be formulated. Close agreement between calculated and measured distortion was obtained up to approximately a 5000-cycle-per-second modulation frequency. At this frequency the departure of the observed from calculated values was quite noticeable. Theoretical maximum-distortion limits for the single- and double-tuned circuits are derived. For the single-tuned circuit the theoretical maximum distortion is D
n
max (single-tuned circuit) = 2λ/ΔW·100. For the double-tuned circuit it is D
n
max (double-tuned circuit) = 4λ/ΔW·100 A conservative design figure relating bandwidth to frequency swing in order to insure distortion-free transmission to 15,000 cycles per second was experimentally found to be, ΔW/BW = 1/4.