A Fractional Termination for Ladder Networks

When using a uniform ladder network to simulate a smooth transmission line, the possibility is considered of deriving a termination which would be intermediate between the usual mid-shunt and mid-series types and which would have advantages over the latter. It is found that a new termination is possible which gives some improvement throughout a limited frequency range. For the dissipationless case, the range corresponds to a line of less than a quarter wave length. The improvements attainable are of the order of a few per cent and become less significant the greater the number of network sections. Thus, although the formula for the new termination and the estimates of the results which it will accomplish are given for any number of sections, the new termination is of most practical value for circuits of few sections. In arriving at this termination, consideration is given to the variation of each of the elements of the pair on each end; but of these two, the end element is the only one whose variation yields an improvement. For the frequency range for which the modified circuit is an improvement, the distinction between the two original types of termination largely is lost, the modified midshunt and modified mid-series terminations being almost identical. Beyond this range there is a difference between them, and the corresponding original and new networks are nearly equivalent. A possible application of the results is suggested in which the simulation of a smooth line is not involved.