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lecture22 - Lectur 22 RF and Microwave Circuit Design-Plane...

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1 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Lectur 22 RF and Microwave Circuit Design Γ -Plane and Smith Chart Analysis In this lecture you will learn: Γ -plane and Smith Charts • Stub tuning • Quarter-Wave transformers ECE 303 – Fall 2005 – Farhan Rana – Cornell University o Z s Z s V 0 = z z ( ) [ ] t j s s e V t V ω Re = L Z ( ) z k j L z k j L o e e Z z Z 2 2 1 1 Γ Γ + = 1 1 + = Γ 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 Γ = Γ Γ ( 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 Γ Γ + = 1 1 or ( ) ( ) ( ) 1 1 + = Γ z Z z Z z n n Normalized resistance Normalized reactance
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