Some Optimum Properties of n Ports

It is known that it is impossible to construct certain types of n ports for which too many design contraints are required. For instance, a lossless, reciprocal three port cannot be completely matched. The paper is mainly concerned with n ports that provide an equal power split. Scattering matrices are derived which provide for maximum power transfer for the two limiting cases of zero absorption loss and zero reflection at the input ports. It is shown that the first of these cases corresponds to an absolute maximum power transfer and that no other division of the over-all loss into reflection and absorption loss will yield better results. For matched inputs, it is shown that the optimum transmission can always be improved by going from a reciprocal to a nonreciprocal n port. While no matched, reciprocal three ports (providing an equal power split from all ports) can be built with less than 50 per cent loss, an equivalent nonreciprocal device can have losses as low as 33 1/3 per cent. Similar results are given for n ports in general.