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The Smith Chart Antennas and Propagation

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The Smith Chart Antennas and Propagation Antennas and Propagation The Smith Chart Introduction Origin 1939 P.H. Smith. Graphical method for performing transmission line calculations. (Well before pocket calculators or computers) Today Useful for displaying information: shows reflection coefficient and impedance/admittance simultaneously Helps engineer gain intuition about using transmissions lines / creating matching circuits. Antennas and Propagation Slide 2 Chapter 1 Basics Principle Waves on a transmission line Antennas and Propagation Slide 3 Chapter 1 Basics (2) Im{Γ} Smith Chart Shows 1. Reflection coefficient ∠∠∠Γ |Γ| Re{Γ} Resistance 2. Impedance / Admittance Values Reactance Values Antennas and Propagation Slide 4 Chapter 1 Bascis (3) Smith chart is a graphical implementation of function: Reflection ⇔ Impedance Using same function for admittance Just rotate by 180 degrees Antennas and Propagation Slide 5 Chapter 1 Typical Smith Chart Information Transmission Line Length (wavelengths) βββl / 2π Constant resistance Constant reactance Polar angle (for Γ) Polar radius (for |Γ|) Antennas and Propagation Slide 6 Chapter 1 Combination Smith Chart Two smith charts Rotated by 180 o Can read Y / Z at once Antennas and Propagation Slide 7 Chapter 1 Examples: Z,Y ⇔ Γ o Example 1 26 ZL = 100 + j50 Ω Z0 = 50 Ω zL = 2 + j1 From Chart G = 0.45 ∠ 26 o Exact G = 0.447 ∠ 26.5 o 0.45 Antennas and Propagation Slide 8 Chapter 1 Examples: Z ⇔ Y Example 2 ZL = 100 + j50 Ω Z0 = 50 Ω zL = 2 + j1 What is y? Rotate by 180 o y = 0.4 – j0.2 Exact: (Is exact value) Antennas and Propagation Slide 9 Chapter 1 Impedance Transformations Idea 1. Plot load impedance on Smith chart This gives Γ0 2. Can find gamma at any point on transmission line with Just means rotation on Smith chart Which way do we move with increasing len? 3. Can read new impedance value looking into that point. Note: 1 wavelength ( λ), βl = 2π = 360 o, But on Smith chart, 0.5 λ means 360 o shift in Γ. Why? Antennas and Propagation Slide 10 Chapter 1 Examples: Imp. Transform Example 3 0.418 +0.125 zL = =0.543 0.4 – j0.5 TLine: l/8 = 0.125 zin = 0.32 + j0.25 Exact: zin = 0.332 + j0.248 0.418 Antennas and Propagation Slide 11 Chapter 1 Transmission Line Stubs Idea Length of (lossless) transmission line Open or shorted Presents a reactance / suceptance Recall Open stub (Z L = ∞) Short stub (Z L = 0) Can get any reactance we like with proper length l Antennas and Propagation Slide 12 Chapter 1 Examples: Stub Len. Example 4 Want zstub = -j1.4 Length? Shorted stub: 0.35 λ Open stub: 0.1 λ Antennas and Propagation Slide 13 Chapter 1 Matching Goal Get Γ(z) = 0 (get to origin) Also means zin = 1 (Zin = Z 0) Operations Clockwise rotation Adding transmission line Moving on constant r circle Adding/subtracting reactance (series stub / reactance) Moving on constant g circle Adding/substracting suceptance (shunt stub / reactance) Antennas and Propagation Slide 14 Chapter 1 Examples: Stub Match Example 5 zant = 0.4 – j0.6 l = 0.174 λ + 0.094 λ = 0.268 λ xstub = -1.4 Antennas and Propagation Slide 15 Chapter 1 Examples: Stub Match Example 5 zant = 0.4 – j0.6 l = 0.016 λ ystub = -1.3 Antennas and Propagation Slide 16 Chapter 1 Other Examples? Antennas and Propagation Slide 17 Chapter 1 Other Examples? Antennas and Propagation Slide 18 Chapter 1 Other Uses Smith Chart also Useful For Gain / stability analysis of amplifiers Gain with respect to source / load impedance Constant gain becomes a circle on chart Stability circles. Stable inside, unstable outside Noise figure analysis Constant noise figure circles Antennas and Propagation Slide 19 Chapter 1 Conclusion Smith Chart Graphical tool for doing simple transmission line computations Transmission line transformations / matching For this class Useful mainly for visualization Also, smith chart gives valuable intuition “See” how transmission line works without doing computation Antennas and Propagation Slide 20 Chapter 1.
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    Frank Lynch, W4FAL Smith Charts Frank A. Lynch W 4FA L Page 1 24 April 2008 “SCARS” http://smithchart.org Frank Lynch, W4FAL Smith Chart History • Invented by Phillip H. Smith in 1939 • Used to solve a variety of transmission line and waveguide problems Basic Uses For evaluating the rectangular components, or the magnitude and phase of an input impedance or admittance, voltage, current, and related transmission functions at all points along a transmission line, including: • Complex voltage and current reflections coefficients • Complex voltage and current transmission coefficents • Power reflection and transmission coefficients • Reflection Loss • Return Loss • Standing Wave Loss Factor • Maximum and minimum of voltage and current, and SWR • Shape, position, and phase distribution along voltage and current standing waves Page 2 24 April 2008 Frank Lynch, W4FAL Basic Uses (continued) For evaluating the effects of line attenuation on each of the previously mentioned parameters and on related transmission line functions at all positions along the line. For evaluating input-output transfer functions. Page 3 24 April 2008 Frank Lynch, W4FAL Specific Uses • Evaluating input reactance or susceptance of open and shorted stubs. • Evaluating effects of shunt and series impedances on the impedance of a transmission line. • For displaying and evaluating the input impedance characteristics of resonant and anti-resonant stubs including the bandwidth and Q. • Designing impedance matching networks using single or multiple open or shorted stubs. • Designing impedance matching networks using quarter wave line sections. • Designing impedance matching networks using lumped L-C components. • For displaying complex impedances verses frequency. • For displaying s-parameters of a network verses frequency.
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