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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 – Gain 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 Z j = + in Z 71.56 0 0 0 30 60 50 0.2 0.6 2 5 30 60 50 j L L Z Z j j e Z Z j + Γ = = = + = + + + D 2 0 ( ) L j j d d e e θ β Γ = Γ o 2 2 2 (.02) 0.5 3.35 rad 191.99 f d c π β = = = 71.56 191.99 120.43 ( ) 2 5 2 5 j j j d e e e Γ = = D D 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 = Γ 0 1 ( ) 1 0.32 0.55 ( ) 50 14.7 26.7 1 ( ) 1 0.32 .55 in d j Z d Z j d j + Γ = = = − Γ + + 2 d β

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Plotting the Reflection Coefficient 0 0 0 0 0 0 L j L r i L Z Z j e Z Z 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 Z j Z j = → ∞ = = = + 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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