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I just come across learning Microwave Amplifier. And I encounter two similiar coefficients: source reflection coefficient and input reflection coefficient. Illustration below from Microwave Engineer, Pozar, 4th edition

Two-port network

From what I learn this is how 2 coefficients is definded:

\$\Gamma_{s} =\frac{V_1^+}{V_1^-} \$ and \$\Gamma_{in} =\frac{V_1^-}{V_1^+} \$

This make me feel headache since the way they defined mean I suppose they depend on each other: \$\Gamma_{in} =\frac{1}{\Gamma_{s}} \$ but it is stated that they are calculated independently: \$\Gamma_{in}\$ by \$Z_{in} \$ and \$\Gamma_{s}\$ by \$ Z_{s} \$

So what exactly are these two coefficient, and why they are independent even the definition is kind of similar?

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  • \$\begingroup\$ Independent yet both dependent on a common ideal value with 3 sections \$\endgroup\$ May 27 '19 at 5:58
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    \$\begingroup\$ what is that "a common ideal value"? \$\endgroup\$
    – tintin
    May 27 '19 at 6:08
  • \$\begingroup\$ Whatever is standard for that medium 50Ω, 75Ω, 100Ω, 120 or it can be custom for impedance matching. \$\endgroup\$ May 27 '19 at 6:23
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what exactly are these two coefficient,

The source reflection coefficient is the reflection coefficient of the source.

The input reflection coefficient is the reflection coefficient of the input port of the amplifier.

why they are independent

They're independent because the source reflection coefficient is a property of the source, and the input reflection coefficient is a property of the amplifier.

They're independent because if you attached the source a different amplifier it would still have the same reflection coefficient. And if you attached the amplifier to a different source, it would still have the same input reflection coefficient.

even the definition is kind of similar

The definitions are similar because the source is connected to the same wires as the amplifier input. So the source reflection and amplifier input reflection can both be expressed in terms of the travelling wave voltage on those wires.

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  • \$\begingroup\$ so when they connect, they can be expressed by travelling wave voltage. Isn't it mean they can be calculated by simply calculate just source reflection coef, then input reflection coef is inversed? \$\endgroup\$
    – tintin
    May 27 '19 at 6:07
  • \$\begingroup\$ No, because \$\Gamma_s\$ is defined with Vs=0. When you want to solve the system with the two parts connected, you need to consider Vs non-zero as well. \$\endgroup\$
    – The Photon
    May 27 '19 at 6:17

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