The synthesis of a network to have a sine-squared impulse response

Abstract

The method of moments, as used in statistics, is applied to the problem of synthesizing a network to have a prescribed impulse response; in particular, to have a sine-squared response. One of the advantages of the method is that the basic delay associated with the output of the network does not have to be specified beforehand but is allowed to vary so as to get the best approximation to the desired waveform from a network of given complexity. A numerical example leads to a design for a network consisting of three inductors and six capacitors in a ladder structure working between resistive terminations. The departure of the impulse response from the sine-squared curve does not exceed 2% of the peak amplitude of the pulse. The approximation could be improved by the use of more components.