The Theory of Biconjugate Networks

Abstract

The properties possessed in common by biconjugate networks are derived. It is shown that all biconjugate networks possess the following properties: (1) Of the six possible transfer impedances only three are independent, one of them being infinite; (2) The magnitudes of the reflection coefficients at each resistance are equal; (3) The phase angles of the transfer impedances are not independent but must satisfy equation (4) of the text. It is shown that biconjugate networks can be divided into two classes depending upon the phase relationship existing between pairs of transfer impedances. One class of networks is such that the responses to two driving voltages consist of one output proportional to the sum of the driving voltage and of one output proportional to the difference of the driving voltages. Waveguide networks, such as hybrid circles, magic tees, and directional couplers, are examples of quasi-biconjugate networks. The 7/2-λ_g hybrid circle is analyzed in detail. Computations yielding all the driving-point and transfer impedances have been made. The results are plotted. Two quantities measuring the deviation of the 7/2-λ_g hybrid circle from the ideal behavior are defined and evaluated. One of these quantities measures the cross coupling between pairs of quasi-conjugate arms. The other quantity measures the degree to which the network fails to take sums and differences.