Ideal transformers in the synthesis of analog computer circuits

The need for ideal transformers in the solution of network synthesis problems, especially in multi-terminal problems, has long been recognized. Nevertheless, there has been a general feeling that solutions to synthesis problems containing ideal transformers are of little more than academic interest because of the impracticability of constructing transformers good enough to be called ideal. Whenever possible, inductances in the network are associated with the transformer so that it can be replaced by coils having self and mutual inductance. This attitude toward the ideal transformer is inappropriate in at least one branch of electrical engineering where network synthesis techniques are employed, namely in analog computing of the direct analogy (or network analyzer) type. Such computers customarily operate in the audio frequency range and contain high quality passive circuit elements which are adjustable in small steps. In the design of such computers the choice between "ideal" transformers and mutual inductance coils is an easy one to make. The availability of "supermalloy," which has an initial permeability of 70,000 or more makes possible the design of ideal transformers which have parasite effects no more serious in practice than those of an ordinary inductor. The ideal transformer has in its favor a much greater versatility than the mutual inductance (making possible mutual resistance and capacitance) and probably a cost advantage as well, when the adjustability requirement is considered.