Scattering matrix of a directional coupler with ideal transformers

A directional coupler suitable for operation in the low radio frequency range (1–100 MHz) can be built by using a combination of two transformers. An analysis of such a device, under the assumption that the transformers are ideal, leads to explicit equations for the scattering parameters of the directional coupler. Two different applications are analysed, one with a loose coupling and another with 3 dB coupling.