Lect22SmithChart_1 - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 22 2009/10/19 Smith Chart Analysis The Complex Reflection Coefficent Plane Stub Tuning 1 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: Instructor: Dr. Wesley E. Swartz Quarter-Wave Transformers -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 10 20 50 -j0.1 j0.1 -j0. 1 -j0.2 j0.2 2 -j0.3 j0.3 3 -j0.4 j0.4 -j0.5 j0.5 -j0.6 j0.6 -j0.7 j0.7 -j0.8 j0.8 -j0.9 j0.9 -j1.0 j1.0 -j1.2 j1.2 -j1.4 j1.4 -j1.6 j1.6 -j1.8 j1.8 -j2.0 j2.0 -j3.0 j3.0 -j4. 0 j4.0 -j4.0 -j5. j5.0 -j5.0 -j10 j10 -j20 j20 -j50 j50 0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.24 0.26 0.28 0.30 4 6 8 0.46 0.48 ZL | Γ |=0.6 67 Zin Zin=15.6+36.4i; Yin=0.0 9 8-0.0232i { Γ } { Γ } Smith Chart with Impedance and Admit ance Co rdinates for: Swartz Problem Assignments and Prelim 2 Demo 8 (Tuesday, October 20) : Problem 13.27: Sliding-probe measurements with SWR>1. Problem 13.16: Quarter-wave impedance matching. Problem 13.10: Stub impedance matching of a complex load. Workshop 8 (Thursday, October 22) : Problem 13.26: Interpreting SWRs. Problem 13.12: Transmission-line power splitters. Pb l 1 3 1 3 St b t hi f l l d d SWR 2 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: Problem 13.13: Stub matching of a complex load and SWR. No Homework 8 . Prelim 2, Tuesday, October 27, 7:30pm: Covers Lectures 1-21, Text Chapters 1-13, Problem Sets 1-8. No Smith Charts nor transmission line transients of Chapter 13. Impedance Transformations Along Transmission Lines 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 = z L L o L Z Z Γ Γ + = 1 1 or 3 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: 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. z X j z R Z z Z z Z n n o n + = = z z z Z n Γ Γ + = 1 1 or 1 1 + = Γ z Z z Z z n n Normalized resistance Normalized reactance Define a normalized impedance as: Then: Γ -Plane (Complex Plane) Imag ( Γ ) z k j L e z 2 Γ = Γ L z Γ = = Γ 0 Γ ( z ) completes one full revolution in the complex plane when its phase goes through 2 π . 2 2 λ π = = z z k L Γ 4 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: Re ( Γ ) 2 z z z Z n Γ Γ + = 1 1 Therefore, impedance is periodic with distance z with a period equal to half-wavelength. o Z 0 = z z = z L Z L z Γ = = Γ 0 z z z X j z R Z z Z z Z n n o n Γ Γ + = + = = 1 1 Γ -Plane with Normalized Resistance Curves 5 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: The blue curves indicate the values of the normalized resistance R n ( z ) on the Γ -plane From the curves one can read- off the values of R n ( z ) o Z 0 = z z = z L Z z z z X j z R Z z Z z Z n n o n Γ Γ + = + = = 1 1 L z Γ = = Γ 0 Γ -Plane with Normalized Reactance Curves 6 Swartz 09/10/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 22: The red curves indicate the values of the normalized reactance X n ( z ) on the Γ -plane From the curves one can read- off the values of X n ( z ) o Z 0 = z z = z L Z
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2 () L z Γ = = Γ 0 z z z X j z R Z z Z z Z n n o n Γ Γ + = + = = 1 1
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Lect22SmithChart_1 - ECE 3030 Electromagnetic Fields and...

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