Theory of the impulse response of receivers. Application of Heaviside operators and the Duhamel integral

The simple superheterodyne receiver is chosen to illustrate the application of the Heaviside expansion theorem and the Duhamel integral to the determination of the impulse response of receivers in general. For the purposes of analysis the receiver is split into three sections: (a) the aerial and r.f. circuit, (b) the convertor valve and first i.f. transformer and (c) the i.f. amplifier valve and second i.f. transformer. Expressions for the voltage/time response at the output of each section are obtained, the theory being verified by experiment. General conclusions are drawn regarding the shape of the detector output voltage.