The Potential Analogue Method of Network Synthesis

HE problem of network synthesis is the inverse of the much simpler problem of network analysis. If an exponential input voltage, E exp (pl) } is applied to a given network consisting of a finite number of lumped linear elements, we can always calculate the corresponding output voltage, V exp (pt), in terms of the network constants. Then we define a transmission function F{p) as the logarithm of the ratio V/E. In general F(p) is an analytic function in the complex p-plane. Its value on the real frequency axis, p = /a), defines the gain and the phase shift of the network. In the inverse problem we start with an assigned transmission function F(p) and are required to find a network for which F{p) is the transmission function. More frequently we have to design a network with assigned gain or phase characteristics over a prescribed frequency range. Obviously, there will be certain restrictions on the assigned transmission function if the network is to be physically realizable. Further, the solution will not be unique, though certain solutions may be more convenient than others. Engineering and cost requirements usually impose severe limitations on the number of elements that may be used in constructing a physical network, hence it may not be possible to match the given function exactly even within the prescribed range of frequencies. Thus from the practical design point of view the problem of network synthesis may be formulated as follows: To design a network unlit a reasonable number of lumped elements such that its transmission function approximates a given transmission function to a prescribed tolerance in a given frequency range.