The response of a network to a frequency-modulated input voltage

If a voltage v(t) is applied to a network of admittance* Y, the resultant current I(t) can be obtained by three different methods: (a) By symbolic calculus, in which an image or transform V of v(t) is found and I(t) is determined by applying the inverse transform to the product VY: this leads to difficulties in the f.m. case because V cannot be conveniently formulated. (b) By the convolution integral derived from v(t) and the response y(t) of the admittance Y to unit impulse. Well-known formulae are here derived by this method, together with an additional formula applicable to a typical amplifier-discriminator system in which the distortion imposed by the admittance is separated from mere delay. (c) By operational calculus, in which the admittance Y is regarded as an operator, a function of d/dt, and the input voltage v(t) is the operand. The same formulae are here derived more simply by operational calculus.