Lecture 15-Transmission line circuits

Lecture 15-Transmission line circuits - ENEE 381 Lecture#15...

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ENEE 381 Lecture #15 The Smith Chart 9-6 Transmission line circuits 9-4.4
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Input impedance of finite length terminated line Z0 ZL z Z i + - 0 - l Exactly the same equation as for multiple dielectrics For a lossless line This could be another transmission line i V % i I % ( 29 ( 29 0 z z V z V e e γ γ + - = + Γ % ( 29 ( 29 0 0 z z V I z e e Z γ γ + - = - Γ % ( 29 0 l l i V V e e γ γ + - = + Γ % ( 29 0 0 l l i V I e e Z γ γ + - = - % 0 z z i i z z i V e e Z Z I e e γ γ γ γ - - + Γ = = - Γ % % j γ β = ( 29 ( 29 ( 29 ( 29 0 0 0 cos sin cos sin L i L Z l jZ l Z Z Z l jZ l β β β β + = + 0 0 L L Z Z Z Z - Γ = +
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Other forms of the same equation γ = j β for lossless transmission line ( 29 ( 29 ( 29 ( 29 0 0 0 cos sin cos sin L i L Z l jZ l Z Z Z l jZ l β β β β + = + ( 29 ( 29 0 0 0 tan tan L i L Z jZ l Z Z Z jZ l β β + = + ( 29 ( 29 ( 29 ( 29 0 0 0 cosh sinh cosh sinh L i L Z l Z l Z Z Z l Z l γ γ γ γ + = + ( 29 ( 29 0 0 0 tanh tanh L i L Z Z l Z Z Z Z l γ γ + = + 2 2 0 0 0 2 2 1 1 1 1 z z z j z i i z z z j z i V e e e e Z Z Z Z I e e e e γ γ γ β γ γ γ β - - + Γ + Γ + Γ = = = = - Γ - Γ - Γ % %
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Quarter wave line Z0 ZL z Z i 0 -λ/4 Quarter wave transformer ( 29 ( 29 0 0 0 tan tan L i L Z jZ l Z Z Z jZ l β β + = + 2 4 2 l π λ π β λ = = 2 0 i L Z Z Z = 0 i L Z Z Z =
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Half wave line Z0 ZL z Z i 0 -λ/2 The line is having no effect on the impedance of the load ( 29 ( 29 0 0 0 tan tan L i L Z jZ l Z Z Z jZ l β β + = + 2 2 l π λ β π λ = = i L Z Z =
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