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RFIC_Lecture_Note_No5_p64-p75 (Smith chart, S-parameter)

# RFIC_Lecture_Note_No5_p64-p75 (Smith chart, S-parameter) -...

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ECE695F RFIC Prof. S. Mohammadi Smith Chart normalized impedance characteristic impedance 1 1 1 1 Z Z 0 0 0 L 0 L + = + = + = Γ nL nL L L Z Z Z Z Z Z Z Z rt ω Smith chart is the plot of in complex plane Γ relationship between and Z is a bilinear transformation Γ circle remain circle when they are mapped Impedance Plane ( ) Z Im ( ) Z Re Γ - Plane ( ) Γ Im ( ) Γ Re mapping of constant resistance until circle corresponds with imaging axis in impedance plane mapping of constant reactance 3 = χ 1 = χ 3 1 = χ 0 = χ 3 = χ 1 = χ 3 1 = χ 3 = χ 1 = χ 3 1 = χ χ 3 = χ ( ) 0 Im = Z arc of circle ( ) Γ Im ( ) Γ Re ( ) Z Im ( ) Z Re - 64 -

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ECE695F RFIC Prof. S. Mohammadi Smith Chart 1 = Γ short circuit inductive capacitive (matc hed) = Γ 1 open circuit orthogonal unit circle - ½ Smith chart can be used to calculate impedance transformation You can graphically find the transformed impedance d d Z , 0 0 L Z in Z ) ( d Γ to do so in nin in L j L nL nL L Z to it convert Z find find to d length electrical the twice by rotate clockwise e identify chart smith the on Z locate Z Z rt Z normalize * * ) 2 ( ) ( * * * ) ( * 0 Γ Γ Γ = Γ β ω θ ( ) length electrical d e d e x d j L x L : ) ( ) ( 2 2 β β γ Γ = Γ Γ = Γ loss less - 65 -
ECE695F RFIC Prof. S. Mohammadi * example + = 60 30 j Z L connected to 50 TRL impedance TRL : 2cm length @ 2GHz assume phase velocity 50% of the speed of light ( ) = Γ Γ + = = = Γ = Γ ° = = = = = = = Γ = + = + + + = + = Γ ° ° 7 . 26 7 . 14 1 1 4 . 0 55 . 0 32 . 0 192 2 7 . 83 5 . 0 2 2 2 ? 2 4 . 0 6 . 0 2 . 0 50 60 30 50 60 30 0 120 2 0 1 0 71 0 0 j Z Z e j e d m c f v f cm d e j j j Z Z Z Z in j d j L P j L L L β β π π λ π β difficult to calculate now graphical solution using Smith Chart ° = + = + = + = 192 2 2 . 1 6 . 0

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