Network response to transient frequency modulation inputs

When an f-m (frequency modulated) signal is transmitted through a linear passive network, the output signal is hybrid, having both amplitude and frequency variations. The output expression can be written in terms of the input through use of circuit equations. However, the relationship is sufficiently complex that an evaluation of a direct solution of these equations is not possible except in simple cases. When the input modulation is periodic, or has a discontinuous step or impulse form, direct solution of the equation is useful; however, in other cases, approximations prove helpful in obtaining a solution.