Still Another Method For Transforming Impedances Through Lossless Networks (Correspondence)

The input impedance Z_A and the terminating impedance Z_L of a symmetrical lossless four-terminal network are related by an equation which contains only one additional parameter; namely, the input impedance Z₁ when the network is terminated in any known resistance R₀. Let /Spl Gamma/_A= (Z_A- R₀)/ (Z_A+R₀), /Spl Gamma/_L=(Z_L-R₀)/(Z_L+R₀), /Spl Gamma/₁ = ( Z₁ - R₀)/( Z₁+R₀), and the superscript "*" denote the conjugate. Now [equation] Eq. (1) also relates the voltage reflection coefficients for a lossless two-port junction. This equation provides a basis for a graphical procedure for finding Z_A or Z_L when the other is known.