ABSTRACT

Z s z s ( ) = ( ) − −( )( ) + ( )

G j j j jω ρ ω ρ ω ρ ω ρ ω2 21 2

2 1 1( ) = ( ) = ( ) = − ( ) = − ( )

Refer to the network configuration of Figure 10.1 where the source is represented either by its Thévenin

As stated in Chapter 9, the output reflection coefficient is given by

(10.3)

where

(10.4)

is the real all-pass function defined by the open RHS poles si (i = 1, 2, …, q) of z2(–s). An all-pass function is a function whose zeros are all located in the open RHS and whose poles are located at the LHS mirror image of the zeros. Therefore, it is analytic in the closed RHS and such that

(10.5)

On the jω-axis, the magnitude of A(jω) is unity, being flat for all sinusoidal frequencies, and we have

(10.6)

and (10.2) becomes

(10.7)

This equation together with the normalized reflection coefficient ρ(s) of (10.3) forms the cornerstone of Youla’s theory of broadband matching [14].