It was not enough to just develop a mechanical analogy. This could be applied to problems that were entirely in the mechanical domain, but for mechanical filters with an electrical application it is necessary to include the transducer in the analogy as well. Poincaré (1907) was the first to describe a transducer as a pair of linear algebraic equations relating electrical variables (voltage and current) to mechanical variables (force and velocity). These equations can be expressed as a matrix relationship in much the same way as the z-parameters of a two-port network in electrical theory, to which this is entirely analogous: