A Simple Model for Weakly Coupled Lossy Transmission Lines of Finite Length

A simple formula for coupling between two parallel lossy wires of finite length above a conducting plane is derived. Weak coupling is assumed. The first wire is driven by a source at one end and terminated with an impedance at the other end. The second wire is terminated with an impedance at each end. The formula is shown to agree well with the results of a previously reported experiment. For low frequencies, the formula reduces to the familiar inductive and capacitive coupling terms plus a term which is contributed by wire losses. For higher frequencies, the lossiness of the wires is shown to be a dominant factor in the coupling mechanism if the undriven wire is terminated by large impedances and the driven wire is terminated by low impedances.