Formulas for the four-terminal network parameters of uniform ladder networks

THE general theory of four-terminal networks is well known and may appear in any one of several forms, depending on the combinations of external currents and voltages which are to be related. In the present discussion we are interested in specifying the sending-end voltage and current, each in terms of linear combinations of both receiver voltage and current. In the general case of Figure 1, which may be a nonsymmetrical network, the required relations may be written where the notation is that of the figure and A, B´, C´, and D are constants of proportionality. (The primes on B and C are used here merely to allow a uniform notation in the final results.) The theory of smooth lines and recurrent ladder networks is usually given in terms of the surge impedances (two in the case of a nonsymmetrical network) and the propagation function. However, this is an artificial point of view when one is interested in the over-all behavior of the circuit, considered as a four-terminal network, the parameters of equations 1 being more suitable. Occasion will arise in the subsequent discussion to compare the formulas for the ladder network with those for the smooth line. Therefore, we begin by putting the smooth-line parameters into forms suitable to our purpose.