Responses of digital frequency multipliers consisting of coupled‐lines to trains of periodical gaussian pulses

Abstract

AbstractFor the coupled‐line digital frequency multipliers which have been discussed for the impulse train, their output responses are presented for the periodically isolated pulses considered as time‐limited incident signals. In this paper, periodic Gaussian pulse trains are treated as an example. In addition, the physical meaning is given for the nonnegative constant which is determined by the relationship between the reflection and transmission coefficients as the transfer function of the circuit. By means of this constant, it is shown that the attenuation constant of the discrete frequency component passing the circuit is minimum. Similar to the case of unit impulse train input, the input frequency components are discrete at an equal interval on the frequency axis. The amplitude is determined by the Fourier transform of the isolated purse constituting the periodic pulse train. Since the input frequency components are discrete, simulation of the output response requires only the sampled values of the frequency characteristics of the circuit. Since the Fourier transform of a Gaussian waveform is Gaussian, it is possible to determine the transmission frequency range in which most of the energy of the Gaussian pulse train is concentrated. Although the characteristic of the distributed circuit degrades as the frequency is increased, an almost desirable output can be obtained if the frequency characteristics are satisfied within a transmission frequency bandwidth.