Output reflection coefficient of a two port network

In the third edition of the textbook Microwave Engineering by David Pozar, example 4.7, it is explained how to use signal flow graphs to find the output reflection coefficient $\Gamma_{out}$ of a two port network. The expression for $\Gamma_{out}$ turns out to be independent of the value of the load impedance, however, I am confused as to how this can be reconciled with the fact that $\Gamma_{out} = b_2/a_2$ and $\Gamma_{load} = a_2/b_2 = 1/\Gamma_{out}$ , making the value of $\Gamma_{out}$ completely determined by that of $\Gamma_{load}$ and consequently by the load impedance $Z_L$. Thanks in advance.

• Including the example you cited, or drawings from the example, would probably help make your question more clear. Partiicularly, enough information to define $a_2$, $b_2$, etc. Oct 22 '15 at 16:07
• Has your text previously defined the S-parameters? Oct 22 '15 at 16:15
• Yes , S-Parameters are defined Oct 26 '15 at 21:52

Most likely, the difference is that $\Gamma_{out}$ is defined when a stimulus is applied from the load side (and the "input" side is properly terminated), while $\Gamma_{load}$ is defined when stimulus is provided from the input side of the DUT.
• From the formula you gave, it looks like your book is defining $\Gamma_{out}$ as the reflection when a matched source is applied on the output side, but accounting for a possibly mismatched source connected on the input side. If the input-side source were perfectly matched, then you'd get $\Gamma_{out}=S_{22}$. Oct 26 '15 at 22:38
• So the difference between $\Gamma_{out}$ and $\Gamma_{load}$ is that one is a response to a stimulus coming from the right and the other is a response to a stimulus coming from the left. But he didn't assume perfect termination on the left like I guessed he would. Oct 26 '15 at 22:39