Effect of distortion on the Bessel-zero method of frequency-deviation measurement

The Bessel-zero technique for f.m. deviation measurement is often used as the standard for the calibration of carrier-deviation and f.m.-signal-generator instruments. Error in the calculation of the deviation arises owing to harmonic distortion in the modulating signal, which results in a change in the value of the modulation index at which the carrier amplitude is zero. Similar errors occur when spurious amplitude modulation arises because of variation in the loading and dynamic impedance of the tuned circuit during frequency modulation. The paper examines quantitatively the effects of both types of distortion on the modulation index. It is considered that, in practice, zeros greater than, say, the 12th, are rarely used, and percentage distortions greater than 10% are very unlikely. Using these assumptions, `worst-case¿ errors are calculated. The largest error appears to arise from spurious amplitude modulation at the second harmonic of the modulating frequency, and is less than 4% for up to 10% distortion. The actual measurement of the errors is very difficult because they are extremely small. The theoretical analysis confirms this, and indicates the tolerable distortion for a given accuracy of the method.