The Smith Chart

1
The Smith Chart

• the Smith chart also has a phase angle scale
  measured using distance in units of wavelengths
• link to high res smith chart
• why? because the angle of G is

• direction of increasing l, or equivalently
• away from load
• towards generator

2
Transmission line applets

• various
• http//www.eecg.toronto.edu/bradel/projects/trans
  missionline/
• http//fermi.la.asu.edu/w9cf/tran/
• matching (single stub) http//home3.netcarrier.com
  /chan/EM/PROGRAMS/STUBMATCH/
• Smith chart
• pointer on chart gives gamma and impedance
• http//www.ntu.edu.sg/eee/eee5/el/smithchart/
• http//www.ee.ust.hk/eee/course/elec241/java/Smith
  Chart.html
• local link
• how tos
• http//www.web-ee.com/primers/files/SmithCharts/sm
  ith_charts.htm
• http//cnx.rice.edu/content/m1060/latest/

3
L-C transmission line summary

• lossless L-C transmission line

4
Equivalent models

• can I simplify this complicated transmission line
  circuit?
• can I prevent reflections back to the generator
  using Zmatch?

• what is Z ( Itot/Vtot) in plane C?

• what about ZB?

5
Equivalent models

• so I can simplify the original circuit, replacing
  it with

Zmacth Rmatch jXmatch
generator
Zo2
l2
plane B
plane A
plane B

• what is Z in plane B?

• what about ZA?

6
Equivalent models

• so I can simplify the circuit even further

generator
plane A

• what is the reflection back to the generator?

• then to have zero reflection we must have ZA
  Zint

7
Example for series matching

• lets assume both T-lines have the same
  characteristic impedance Zo, and that the
  generator internal impedance is also Zo

• no reflection at plane A

• does l2 matter?
• NOT THIS TIME!