Chapter2_Notes

# Based on fundamentals of applied electromagnetics

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Unformatted text preview: and constant reactance. First, reactance may be both positive and negative (unlike resistance). Also, due to the oﬀset center of the circles only parts of the circles show up in the unit circle (remember, our whole world has to be within the unit circle because of how we deﬁned |Γ| ≤ 1). Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 90 Γi xL=2 xL=0.5 xL=1 Γr xL=0 rL=0.5 rL=0 xL=-0.5 rL=2 xL=-1 rL=1 xL=-2 Figure 22: Constant resistance and reactance circles in complex plane. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 91 What have we accomplished with this? With these circles in place we can read Γ directly from the given impedance, or vice versa. Need a ruler and compass! • Note: the radius of the Smith chart is scaled to unity for the purpose of ﬁnding the magnitude of Γ. • A slightly simpliﬁed Smith chart is shown in Fig. 23 while the full version is shown in Fig. 24. • Note the scale at the bottom — it is used to ﬁnd the magnitude of Γ. • If we don’t use the line, then we have to calculate the ratio of the length of Γ and the radius of Smith chart (as explained in textbook). • What about the angle of Γ? Draw a line through a given point starting from the center (origin) all the way through the edge of the Smith chart. Read oﬀ the angle from the scale that gives the Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 92 Angle of reﬂection coeﬃcient in degrees. Same as using protractor. Watch out for the sign! Illustrated in Fig. 25. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Transmission lines 1.0 1.2 1.4 0.9 0.8 0.17 1.6 60 0.33 0.1 1.8 0.2 0.3 2.0 0.5 0.16 0.34 70 50 8 2 0.4 0.2 40 0.3 3.0 0.6 30 4.0 0.21 0.29 1.0 0.2 20 0.8 0.25 0.26 0.24 0.27 0.25 0.24 0.26 0.23 N COEFFICIENT IN 0.27 REFLECTIO DEGR LE OF EES ANG 0.23 0.6 10 0.1 0.4 20 20 5.0 10 4.0 2.0 3.0 1.6 1.4 1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) 0.2 20 0.4 0.1 10 0.6 −20 0.8 1.0 1.0 0.8 1.8 0.2 1.6 CAP AC ITIV E 1.4 −70 1.2 0.34 0.16 0.15 0.35 0.14 −80 0.36 1.0 0 −6 0.9 0.17 0.33 −90 0.13 0.12 0.37 0.8 2 RE AC TA NC E 0.38 0.11 −100 20 −1 0.7 0 8 0.4 3 0.08 0.42 0.41 0.09 −110 0.1 0.0 7 −1 30 CO M PO NE NT (0.5 0.1 0.3 6 0.4 1 0.6 0.3 9 0.1 0.0 0 −4 0.3 4 0.6 3.0 0.2 0.4 4.0 0.47 &lt;— 5.0 0.46 0.04 0.28 0 −3 0.29 0.21 0.3 0.22 0.2 0.4 0.28 5.0 0.22 1.0 2.0 0.4 0.3 0.8 1.8 0.0 6 4 0.35 −5 0.4 VE TI CI PA CA 0.0 —&gt; WAVELEN 0.49 GTHS TOW ARD 0.48 &lt;— 0.0 0.49 GEN RD LOAD ERA TOWA 0.48 ± 180 TO THS 170 R— −170 ENG 0.47 VEL &gt; WA 0.04 160 −160 0.46 IND o) 0.0 UCT 5 15 jB/Y 50 5 IVE 0 0.4 E (−1 RE 0.4 NC 5 AC TA 5 0.0 TA EP 0.1 NC SC EC SU E OM 14 IV 40 0 PO CT −1 NE DU IN NT R (+ ,O jX o) /Z /Z 0.2 o jX 80 9 0.1 1 0.3 R O ), 0.15 0.36 90 0.7 7 3 0.4 0 13 0.14 0.37 0.38 ) 0 /Yo 12 +jB E( NC TA EP SC SU 0.6 0.42 0.0 0.39 100 0.4 110 0.13 0.12 0...
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## This note was uploaded on 09/25/2013 for the course ECE 331 taught by Professor Martinsiderious during the Fall '12 term at Portland State.

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