AbstractThe paper deals with the problem of finding the immittance functions of a 1‐port for which, in the case of periodic signals of Ω frequency, the voltage and current are orthogonal to one another, and in which the voltage and current have the same norms, i.e. they are related as a pair of Hilbert transforms. The need for the construction of such 1‐ports arises, for example, in connection with the problem of the measurement of the reactive power of nonsinusoidal waves. Three sets of network functions have been found for the networks in which input and output signals are pairs of Hilbert transforms, and it has been proved that one of them is a set of positive‐real and reactance functions, and that one is a set of transfer functions of all‐pass networks composed of orthonormal