Recurrent circuits; a method of solution

The paper consists of the statement and illustration of a method of solving recurrent circuits (of which the filter is the simplest example) when operating in the ¿steady-state¿ condition, by reducing each element to a ¿rejector¿ resonant at the operating frequency. The method is stated and is illustrated by the ¿low-pass¿ and ¿high-pass¿ filters. The general case of a filter is solved. Characteristics of the simpler types of filters are stated briefly. The initial sending-end impedancs of the line and the condition for non-reflection are written down from inspection. It is shown that, for one-way working, it is not necessary, or desirable (as is often stated), that the transmitter, receiver, and initial sending-end impedances should all be equal. Line distortion due to reflection is considered briefly. A worked example is given in the Appendix. Although the method is applied here to niters only, it is readily extended to both continuous and loaded lines.