Impedance Matching ZL = Zo No reflections,
desired in power lines and in data lines
Single stub lines
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impedancematching.pdf",
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impedancematching.pdf"D
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impedancematching.pdf
Things to
know : It' s easier to deal with admittances in impedance matching
and on a smith chart,
Smith Chart
Zin_normalized@z + Λ  4D = Yin_normalized@zD
Zin_normalized@zD =
Zo ZL - Zo I Tan@2 Π z  Λ D
Zo Zo - ZL I Tan@2 Π z  Λ D
Zin_normalized@z + Λ  4D =
=
ZL - Zo I Tan@2 Π z  Λ D
Zo - ZL I Tan@2 Π z  Λ D
ZL - Zo I Tan@2 Π Hz + Λ  4L  Λ D
Zo - ZL I Tan@2 Π Hz + Λ  4L  Λ D
ZL + Zo I Cot@2 Π z  Λ D
Zo + ZL I Cot@2 Π z  Λ D
=
=
ZL Tan@2 Π z  Λ D + Zo I
Zo Tan@2 Π z  Λ D + ZL I
I ZL Tan@2 Π z  Λ D - Zo
I Zo Tan@2 Π z  Λ D - ZL
=
=
Zo - I ZL Tan@2 Π z  Λ D
ZL - I Zo Tan@2 Π z  Λ D
= Yin_normalized@zD
Things to
know : Purely reactive impedances are on the outer circle of the
smith chart Hbecause thier real part is 0L
See Smith Chart p90
Ex. 2.12
Zo = 50; ZL = 25 - 50 I;
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Find d, the distance from the load and l,
the length of the short circuit stub used to null out the reflections
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Ex 11.7 HNot from our bookL
antenna load
Zo = 100; ZL = 40 + 30 I;
Find : 1. Required stub admittance
2. Distance between stub and antenna lB
3. Stub length dB
4. VSWR on each segment of system
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Transients - Important for digital or wideband signals
HSmith Charts are useful for single frequency,
harmonic signals in steady stateL
transient response : time record of back and forth travel of voltage pulse
See pages 93 - 98
Pulse : Two parts
u@t_D := UnitStep@tD
vo = 2
2
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p1 = Plot@vo u@tD, 8t, 0, 10<, PlotStyle ® Thick, Filling ® AxisD
4
3
2
1
2
4
6
8
10
p2 = Plot@-vo u@t - 2D, 8t, 0, 10<, PlotStyle ® Thick, Filling ® AxisD
2
-0.5
-1.0
-1.5
-2.0
4
6
8
10
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p2 = Plot@vo Hu@tD - u@t - 2DL, 8t, 0, 10<, PlotStyle ® Thick, Filling ® AxisD
2.0
1.5
1.0
0.5
2
4
6
8
10
I+1 = Vg ‘ HRg + Zo L; V1+ = I+1 Zo = Vg Zo ‘ HRg + Zo L;
http :  webcas.cas.suffolk.edu  engineering  lshatz  public_html  ece403 
transient.pdf
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pdf"D
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After a long time Hsteady stateL
V = Vg ZL ‘ HRL + Rg L; I = Vg ‘ HRL + Rg L;
8
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