The Joy of Matching

51 Pages·2015·1.76 MB·English

The Joy of Matching
Steve Stearns, K6OIK
[email protected]
Technical Fellow
Northrop Grumman Corp.
August 28, 2015
Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Topics
• Graphing impedance and admittance on a Smith chart
• Similarities and differences between matching and filtering
• Examples of 2-band matching
– GPS L1 and L2 bands
– Cellular-PCS 900-MHz and 1900-MHz bands
• Examples of 3-band matching
– KM5KG’s 3-frequency match for 80-meter band
– K6OIK’s 3-band match for 75, 60, and 40-meter bands
• Software tools for impedance match circuit design
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Phillip Hagar Smith, 1905-1987
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
The Smith Chart
Developed by
Phillip H. Smith at
Bell Labs 1936.
Published in
Electronics, Jan.
1939 and Jan.
1944.
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Complex Functions
• Basic types of complex functions
– Global Properties
• Linear – lines map to lines
• Bilinear – circles map to circles
– Local Properties
• Conformal – right angles map to right angles
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Mathematical Basis of the Smith Chart
z 1
Γ  • A bilinear conformal complex function
z  1 of a complex variable
z
• Maps normalized impedance to
(r 1)  jx
u  jv= complex reflection coefficient 
(r  1)  jx
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Matching at Two Frequencies
Example 1: GPS L1 and L2 bands
Example 2: Cellular-PCS 900-MHz and 1900-MHz bands
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Example 1: Matching a GPS Antenna on Two Bands
Impedance Graphed from 1220 MHz to 1585 MHz
Black – Before matching
Blue – After matching
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Example 1: Matching a GPS Antenna on Two Bands
1227.6 MHz and 1575.4 MHz, Shown in WinSMITH
1.227 GHz
1.575 GHz 93 + j223
37 + j18
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015
Pause for Demo
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Steve Stearns, K6OIK Foothills Amateur Radio Society (FARS), Los Altos, CA August 28, 2015