Generalised characteristics of linear networks

Networks consisting of inductances, capacities and resistances are employed frequently to provide characteristics which vary with the frequency of the applied voltages. In the usual way it is necessary to draw curves for the characteristics of such a network, the curve being peculiar to the values of the items employed. In the present paper, the performance of a whole group of networks of any one form is given by a single curve for each characteristic required. If we consider an inductance in parallel with a resistance, then by defining f0 as the frequency at which the reactance of L in ohms = R, i.e., Lomega0 = R, the equation for the impedance of the network is given by Z = RLJomega/(R + jLomega) and this reduces to Z = R [((omega2/omega02)/(1 + (omega2/omega02))) + j(omega/omega0)/(1 + (omega2/omega02))] The quantity in brackets is characteristic of all possible networks of this type and it is possible to plot the real and imaginary parts separately as functions of omega, taking omega0 as unity and expressing omega as a fraction of omega0. The impedance can then be read from this curve by obtaining the characteristic frequency f0, calculating the ratio omega/omega0 and reading off the real and imaginary parts and adding. The method is applied to many types of network and the voltage transfer ratio is evaluated for 4-terminal networks.