L04_Frequency Response & Smith Chart_Sp11

L04_Frequency Response & Smith Chart_Sp11 - EEL 4422...

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EEL 4422 / EEL 6427 RF & Microwave Circuits II Lecture #4 ompressed Smith Chart Compressed Smith Chart Normalized ZY Chart Frequency Response 1
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Example for handling r<0 in Smith chart Example 2.2.3: Find the impedance whose reflection oefficient 36 6 6 0 ote at Find 1/ *: coefficient is 2.236/26.56 ( note that | Γ |>0) 11 0.447 26.56  0 26.56 Γ Plot 1/ * on the Smith chart (2.236 26.56 )   Take the values of resistance circles as being negative (i.e. -r) 1 z 2j 1 1    0.447 Γ Take reactance circles as labeled z2 j 1   2 56 . 26 236 . 2 1 1 2 1 1 2 1 1 j j z z Verify:
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Z Chart vs. Y Chart 1 Z Chart: One to one map between impedance (z) and reflection coefficient z1  Chart: One to one map between admittance (y) and reflection coefficient Y Chart: One to one map between admittance (y) and reflection coefficient j y1 e y 1  ΓΓ Γ • The point z=r+jx on the Smith chart corresponds to a given • The point y=g+jb on the Smith chart corresponds to – Γ and – are 180 degrees apart on the Smith chart •- = I , the current reflection coefficient
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Example: z given, find y value using Smith Chart z 1 = 1 + j1 On the IMPEDANCE chart: z 1 +b, +x b, - , - b, x y 1 point y 1 = 0.5 - j0.5 On the ADMITTANCE chart: 4 is the normalized admittance
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Normalized ZY Smith Chart Standard Smith chart can be used as a Z or Y chart, but not both at the +X otate same time ! The “normalized impedance and dmittance Smith chart” or ZY chart Impedance (Z) chart -X Rotate 180 0 j e  ΓΓ admittance Smith chart , or ZY chart, can be used for Z and Y simultaneously The ZY chart contains a Z-chart and a +X -b superimposed Y-chart that is rotated 180 degrees
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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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L04_Frequency Response & Smith Chart_Sp11 - EEL 4422...

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