FM Transient Response of Band-Pass Circuits

While in a steady state the output frequency of an amplifier must be the same as its input frequency, transient differences occur whenever the input frequency changes. A general formula has been derived for the output voltage resulting from an abrupt frequency shift; and by manipulating the terms of this formula, the instantaneous frequency deviation has been determined. Detailed computations have been made for large frequency shifts in a single tuned circuit, and for small frequency shifts in amplifiers having various numbers of tuned circuits. For large steps of frequency deviation, the shape of the output deviation depends on the magnitude of the step, the initial frequency (before the step), and whether the step is toward or away from the midband frequency. For small steps near midband, the transient response of a given band-pass filter is the same for frequency modulation as for amplitude modulation, and can be described as the response to a voltage step in an equivalent video circuit. Stagger tuning causes overshoot in the transient response, but such overshoot will be small if the stagger is no more than enough to provide maximally-flat amplitude response in the steady state.