# Module 2a - Impedance matching Module 2a-1 (Sadiku 11.5)...

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1 Module 2a-1 (Sadiku 11.5) Impedance matching Resistive and reactive loads How the reflection coefficient changes along the line Smith chart derivation Locating impedances on Smith charts Locating reflection coefficients Locating standing wave ratios Locating the admittance corresponding to an impedance (inverting an impedance) “Moving” along transmission lines using the Smith chart 1 Impedance matching G =0 when looking into a matched load (Z in = Z 0 ), so all wave power enters the matching network • if the matching network only consists of reactive components (L, C, lengths of lossless T-Line) then no power is dissipated in the network and therefore all power is received by the load Page 2 Impedance matching method For a lossless line, Z 0 is real but Z L is arbitrary (could be complex). – 1) Add a piece of transmission line (or move back along the existing line). – 2) Find a position along the line where the real part of Z in becomes equal to Z 0 – 3) Add a “matching” reactance to cancel out the imaginary part of Z in (resistive part does not change and remains equal to Z 0 ). 3 Impedance matching method Find a value of l so that Z in = Z 0 + jX 0 Add “something” that will cancel X 0 4

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2 For instance Here, Z in = (50 + j100)Ω Here, Z in = 50Ω + j100Ω –j100Ω = Z 0 At this location G = 0 and al power is dissipated In the load (since the line and capacitor are reactive) = 11 +j25Ω Z 0 = 50Ω 5 Graphical tools to help solve T-line problems Manipulating the equation that relates Z in (z) to the line parameters and the load impedance can be a daunting task (even with modern tools). Let’s look at the reflection coefficients instead. At the load, Similarly elsewhere on the line, we can define a local reflection coefficient equal to the ratio of the backward to the forward wave: 6 Equivalent terminated T-Lines Input impedance at an arbitrary point along a T- Line can be used to create an
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## This note was uploaded on 09/27/2011 for the course ENGINEERIN 3600 taught by Professor Victor during the Spring '11 term at Carleton CA.

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Module 2a - Impedance matching Module 2a-1 (Sadiku 11.5)...

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