Lecture 8 Impedance Matching

# Lecture 8 Impedance - Lecture Lecture8 Transm. Series()and Parallel(stubtuning)models Hayt CH11 McGillECSE352,Fall2011,D.Davis 1 Impedance

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cture 8 Lecture 8 Transm. Line Impedance matching Series (quarter wave transformer) and rallel (stub tuning) models Parallel (stub tuning) models Hayt CH11 1 McGill ECSE 352, Fall 2011, D. Davis

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pedance Matching Impedance Matching e purpose of impedance matching is to The purpose of impedance matching is to maximize power flow into the load. This is one by making the input impedance seen by done by making the input impedance seen by the source be equal to the source impedance. hen the input impedance and the source When the input impedance and the source impedance are equal, there is no reflected aves and the power flow is maximum waves and the power flow is maximum. McGill ECSE 352, Fall 2011, D. Davis 2
pedance Matching Impedance Matching ere are many strategies for impedance There are many strategies for impedance matching. e first one we will investigate is the quarter The first one we will investigate is the quarter wave transformer. e quarter wave transformer is a series The quarter wave transformer is a series connected transmission line inserted between the source and the load. The transmission line has a length l q and a characteristic impedance Z . q McGill ECSE 352, Fall 2011, D. Davis 3

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pedance Matching Impedance Matching e circuit shown below consists of a source The circuit shown below consists of a source connected to a Tx line #1, series connected to quarter wave transformer #2 which is series a quarter wave transformer #2 which is series connected to a transmission line #3. McGill ECSE 352, Fall 2011, D. Davis 4
pedance Matching Impedance Matching order to simplify the problem we will In order to simplify the problem we will assume that the last line is terminated with a load with the same impedance as line #3 and that the impedance of line #1 is the same as the internal impedance of the source. The requirement for the input impedance to ܼ ݏ ൌܼ 1 3 ܮ ܼ 2 ൌܼ ܳ be equal to the source impedance needs to be satisfied. McGill ECSE 352, Fall 2011, D. Davis 5

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pedance Matching Impedance Matching is can be written as: ܼ 3 ൅ ݆ܼ ܳ ݐܽ݊൫ߚܮ ܳ This can be written as: ܼ ݅݊ ൌ ܼ ܳ ܼ ܳ ൅ ݆ܼ 3 ݐܽ݊൫ߚܮ ܳ ൌ ܼ 1 In order to simplify the problem we will set the quarter wave transformer length to a quarter wavelength. ܼ 3 ൅ ݆ܼ ܳ ݐܽ݊ ቀ ߨ 2 ܼ ܳ ܼ ܳ ൅ ݆ܼ 3 ݐܽ݊ ቀ ߨ 2 ൌ ܼ 1 McGill ECSE 352, Fall 2011, D. Davis 6
pedance Matching Impedance Matching is will lead to the following relationship: This will lead to the following relationship: is indicates that if the quarter wave ܼ ܳ 2 ൌܼ 1 ܼ 3 This indicates that if the quarter wave transformer has a characteristic impedance qual to the square root of the product of the equal to the square root of the product of the characteristic impedances of the lines at the input and output end and the transformer is a quarter wavelength long, then the device will match impedances.

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## This note was uploaded on 12/03/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lecture 8 Impedance - Lecture Lecture8 Transm. Series()and Parallel(stubtuning)models Hayt CH11 McGillECSE352,Fall2011,D.Davis 1 Impedance

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