# 329fall08hw13 - ECE 329 Homework 13 Due Thu Dec 4 2008 5PM...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 329 Homework 13 Due: Thu, Dec 4, 2008, 5PM 1. Smith Chart derivation: Since Γ = z- 1 z + 1 = r + jx- 1 r + jx + 1 = [( r- 1) + jx ][( r + 1)- jx ] ( r + 1) 2 + x 2 = ( r 2 + x 2- 1) + j 2 x ( r + 1) 2 + x 2 ≡ Γ r + j Γ i , it follows that Γ r = ( r 2 + x 2- 1) ( r + 1) 2 + x 2 and Γ i = 2 x ( r + 1) 2 + x 2 , where r and x are normalized line resistance and reactance, respectively, and Γ r and Γ i denote the real and imaginary parts of reflection coefficient Γ . Using the above expressions for Γ r and Γ i , it can be shown that the following relations are valid: (Γ r- r r + 1 ) 2 + Γ 2 i = ( 1 r + 1 ) 2 constant r circles (Γ r- 1) 2 + (Γ i- 1 x ) 2 = ( 1 x ) 2 constant x circles a) Smith Chart construction: The equations above describe circles on the complex Γ-plane with r and x dependent centers and radii, respectively. Using a compass, draw constant r circles (on a plane with Γ r and Γ i axes) for the values of r = 0 , 1, 2, ∞ — set the scales of your axes such...
View Full Document

## This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Fall '08 term at University of Illinois at Urbana–Champaign.

### Page1 / 2

329fall08hw13 - ECE 329 Homework 13 Due Thu Dec 4 2008 5PM...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online