L03_Smith Chart_Sp11

# L03_Smith Chart_Sp11 - EEL 4422 / EEL 6427 RF & Microwave...

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EEL 4422 / EEL 6427 RF & Microwave Circuits II Lecture #3 mith Chart Smith Chart 1

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Smith Chart A mapping between impedance (z) and reflection coefficient ( ) plane -plane (z-plane) is rectangular coordinate system that represents real and imaginary parts of (z) as x and y axes, respectively lane: lane: Z 0 z e    rj x -plane: z-plane: 1 Z L z z=0 jz Ve   ( z0 ) VV  rx j    zrj  L0 0 ZZ  L 1:1 map between | | 1 and z plane (for r>0 ) L Z z r jx (normalized impedance)   r x x 1 1 1 || 1  z1 1 x  0 Z r 1 2 z 1 1 
Constant-r & constant-x circle: equations z1  1 zrj x 1     3

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Constant-r circles… z-plane -plane x r 4
Constant-x circles… z-plane -plane x r 5

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z ↔Γ : Mapping Examples 6
Smith Chart: Plot of constant-r constant-x circles for all z values (r>0) x 0 45 1 Γ z 1 +X Impedance Coordinates - r 1 Γ X 1 Z 1 Z 0 z 1 = Z 1 /Z 0 = 1+ j2 z z=0 1 VSWR 5.8284 7 0.7071 1 Γ How can you determine | | and VSWR without this scale?

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## This note was uploaded on 01/24/2011 for the course ECE 6936 taught by Professor Mumcu during the Spring '10 term at University of South Florida.

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L03_Smith Chart_Sp11 - EEL 4422 / EEL 6427 RF & Microwave...

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