lecture 7 Ch 3

# lecture 7 Ch 3 - EE 4002 RF Circuit Design Chapter 3 Smith...

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EE 4002 RF Circuit Design Chapter 3 Smith Charts

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History of the Smith Chart • Developed in 1930’s by P.H. Smith as a way to plot the reflection coefficient and line impedances. • Today it is widely used to describe passive and active RF/MW components and systems. • Network Analyzers have the option to show measurements in a smith chart format. CAD Programs use smith charts for many purposes: – Display measured circuit impedance – Design matching networks – Real time CAD tuning – Computation of noise figures –G a i n – Plot stability circles
Example 3-2: Finding the input impedance of a terminated TL using derived equations is connected to a 50 transmission line of 2 cm length, operated at 2 GHz. Find assuming the phase velocity to be 50% of the speed of light 30 60 L Zj =+ in Z 71.56 0 0 0 30 60 50 0.2 0.6 2 5 30 60 50 j L L ZZ j je j + Γ= = = + = ++ + D 2 0 () L j j d de e θ β Γ o 2 22( . 0 2 ) 0.5 3.35 rad 191.99 f d c π == = 71.56 191.99 120.43 25 jj j e e −− = DD D Notice only the angle changes as we move down the TL. The amount it changes is twice the electrical length of the line, or 0 d Γ 0 1 ( ) 1 0.32 0.55 ( ) 50 14.7 26.7 1( ) 1 0 . 3 2. 5 5 in dj Zd Z j + Γ− = −Γ + + 2 d

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Plotting the Reflection Coefficient 0 00 0 0 0 L j L ri L ZZ je θ Γ= =Γ +Γ =Γ + The reflection coefficient is a complex number, which can be plotted in a polar coordinate system: (a) 0 (short circuit) (b) (open circuit) (c) 50 (d) 16.67 16.67 (e) 50 150 L L L L L Z Z Z Zj =  →∞ =Ω =− =+ For a transmission line with a line impedance of , we can plot the Reflection coefficient. 0
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## lecture 7 Ch 3 - EE 4002 RF Circuit Design Chapter 3 Smith...

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