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Unformatted text preview: 1 ECE 303 Fall 2005 Farhan Rana Cornell University Lectur 22 RF and Microwave Circuit Design Plane and Smith Chart Analysis In this lecture you will learn: plane and Smith Charts Stub tuning QuarterWave transformers ECE 303 Fall 2005 Farhan Rana Cornell University o Z s Z s V = z z ( ) [ ] t j s s e V t V Re = L Z ( ) z k j L z k j L o e e Z z Z 2 2 1 1 + = 1 1 + = o L o L L Z Z Z Z and l = z Impedance Transformations in Transmission Lines Define a position dependent reflection coefficient as: ( ) z k j L e z 2 = ( z ) is a complex number of magnitude never greater than unity Define a normalized impedance as: ( ) ( ) ( ) ( ) z X j z R Z z Z z Z n n o n + = = Then: ( ) ( ) ( ) z z z Z n + = 1 1 or ( ) ( ) ( ) 1 1 + = z Z z Z z n n Normalized resistance Normalized reactance 2 ECE 303 Fall 2005 Farhan Rana Cornell University Plane (Complex Plane) Imag ( ) Re ( ) ( ) z k j L e z 2 = ( ) L z = = ( z ) completes one full revolution in the complex plane when its phase goes through 2 2 2 2 = = z z k ( ) ( ) ( ) z z z Z n + = 1 1 Therefore, impedance is periodic with distance z with a period equal to halfwavelength o Z = z z L Z l = z o Z = z z L Z l = z L ECE 303 Fall 2005 Farhan Rana Cornell University Plane with Normalized Reactance Curves ( ) ( ) ( ) ( ) ( ) ( ) z z z X j z R Z z Z z Z n n o n + = + = = 1 1 The red curves indicate the values of the normalized reactance X n ( z ) on the plane From the curves one can read off the values of X n ( z ) ( ) L z = = o Z = z z L Z l = z o Z = z z L Z l = z 3 ECE 303 Fall 2005 Farhan Rana Cornell University Plane with Normalized Resistance Curves The blue curves indicate the values of the normalized resistance R n ( z ) on the plane From the curves one can read off the values of R n ( z ) ( ) L z = = o Z = z z L Z l = z o Z = z z L Z l = z ( ) ( ) ( ) ( ) ( ) ( ) z z z X j z R Z z Z z Z n n o n + = + = = 1 1 ECE 303 Fall 2005 Farhan Rana Cornell University Plane with Normalized Resistance and Reactance Curves The Smith Chart ( ) L z = = The Smith Chart enables one to readoff values of both the normalized resistance R n ( z ) and the normalized reactance X n ( z ) values on the plane ( ) = z Z n o Z = z z L Z l = z o Z = z z L Z l =...
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 RANA
 Electromagnet, Impedance

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