The Joy of Matching. Steve Stearns, K6OIK August 28, Technical Fellow Northrop Grumman Corp.

Transcription

1 The Joy of Matching Steve Stearns, K6OIK Technical Fellow Northrop Grumman Corp. August 28, 2015

2 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 2

3 Phillip Hagar Smith,

4 The Smith Chart Developed by Phillip H. Smith at Bell Labs Published in Electronics, Jan and Jan

5 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 5

6 Mathematical Basis of the Smith Chart u Γ jv= z z (r (r 1 1 1) 1) jx jx A bilinear conformal complex function of a complex variable Maps normalized impedance z to complex reflection coefficient 6

7 Matching at Two Frequencies Example 1: GPS L1 and L2 bands Example 2: Cellular-PCS 900-MHz and 1900-MHz bands 7

8 Example 1: Matching a GPS Antenna on Two Bands Impedance Graphed from 1220 MHz to 1585 MHz Black Before matching Blue After matching 8

9 Example 1: Matching a GPS Antenna on Two Bands MHz and MHz, Shown in WinSMITH GHz 37 + j GHz 93 + j223 9

10 Pause for Demo 10

11 K6OIK s GPS Dual-Band Matching Circuit No. 1 Optimized Values 11

12 K6OIK s GPS Dual-Band Matching Circuit No. 2 Optimized Values 12

13 Dual-Band Matching Result, Shown in Microwave Office L1: MHz L2: MHz Both L1 and L2 frequencies map to origin 13

14 Final Result (Blue), Shown in Ansoft Serenade SV Black Before matching Blue After matching Blue passes through origin twice 14

15 SWR Before and After Matching, Shown in Ansoft Serenade SV 15

16 GPS Antenna Dual-Band Match, Done in WinSMITH GHz 37 + j GHz 93 + j223 16

17 Design Procedure for Two-Frequency Matching Step 1: Move both points onto the unit resistance (conductance) circle with the low frequency point above (below) the high frequency point There are many ways to do this first step. For example, one can use an L-network to move one point to center and then use a transmission line segment to rotate the other point onto a unit resistance or unit conductance circle. Step 2: Add an inductor L and a capacitor C Points on the unit resistance circle, add a series LC Points on the unit conductance circle, add a shunt LC Step 3: Adjust L and C to move both points to center of Smith chart Two frequency points can be brought to center by using no more than a single LC resonator stage Do the above steps manually by using one of the software tools given later. When the points are close to center, use an optimizer to finish fine tuning the parts values. 17

18 Example 2: Cellular and PCS Dual-Band Matching at 900 MHz and 1,900 MHz 18 P.J. Bevelacqua, Dual-Band Impedance Matching, online at

19 SWR Before Matching 19 P.J. Bevelacqua, Dual-Band Impedance Matching, online at

20 Bevelacqua s Solution A 4-Element Matching Network 20 P.J. Bevelacqua, Dual-Band Impedance Matching, online at

21 Smith Chart After Matching 21 P.J. Bevelacqua, Dual-Band Impedance Matching, online at

22 SWR After Matching 22 P.J. Bevelacqua, Dual-Band Impedance Matching, online at

23 Pause for Demo 23

24 The Final Step Fine Tuning Optimized Values Original Values C1 = 3.2 pf L1 = 3 nh C2 = 1.5 pf L2 = 5 nh 24

25 A Perfect Two-Frequency Match, Shown in Microwave Office 900 MHz and 1900 MHz points coincide at origin 25

26 K6OIK s Alternate Matching Network No. 1 Optimized Values 26

27 K6OIK s Alternate Matching Network No. 2 Optimized Values 27

28 K6OIK s Alternate Matching Network No. 3 Optimized Values 28

29 K6OIK s Alternate Matching Network No. 4 Optimized Values 29

30 All Five Networks Achieve Perfect Two-Frequency Match 900 MHz and 1900 MHz points coincide at origin 30 Choice among networks can depend on losses, ease of practical implementation, sensitivity to parts tolerances, statistical yield, or other criteria.

31 Matching at Three Frequencies Example 3: KM5KG s 3-frequency match (QEX, 2001) Example 4: K6OIK s 3-band match for 75, 60, and 40 meters 31

32 Example 3: KM5KG s 3-Frequency Match in 80-Meter Band QEX, Sept /Oct Illustrates pitfalls of attempting wideband matching at fewer discrete frequencies than the order of the network Antenna: An electrically-short vertical monopole KM5KG matched three frequencies in 80-meter band Frequency (MHz) Real (ohms) Imaginary (ohms)

33 Impedance of KM5KG Vertical Monopole Frequency sweep 3.5 to 4 MHz 33

34 KM5KG s 6-Element, 3-Frequency Matching Network Component losses included Capacitors: Q C = 1,000 Inductors: Q L = 800 Components calculated for match at 3.5 MHz, 3.75 MHz, and 4 MHz KM5KG assumed that matching at three frequencies (band edges and midpoint) would result in a broadband continuous frequency match across the 80-meter band 34

35 Matching Result Not Published in QEX Frequency sweep 3.5 to 4 MHz 35

36 A 3-Frequency Match Is Not a Broadband Match! Max SWR 2.99 at MHz 36 This example illustrates the Fano bound. Multi-frequency matching is the wrong approach to broadband continuous frequency matching.

37 Example 4: K6OIK Matching a 98-ft. Dipole on Three-Bands Ward Silver (N0AX) proposed to design an antenna for the 75, 60, and 40-meter bands K6OIK s lazy man solution: Take an existing antenna and design a feedpoint match network for the three bands Antenna: 98.4-foot wire dipole antenna resonant at MHz Frequencies: 3.9, 5.35, and 7.2 MHz Design goal: SWR = 1 at these three frequencies 37

38 Dipole Impedance 38

39 Dipole Impedance on the Smith Chart Frequency sweep 3.8 to 7.3 MHz 39

40 Dipole SWR Before Matching 40

41 Zoom View Dipole SWR Before Matching Points of interest are off the chart 41

42 K6OIK s 5-element, 3-Band Matching Network Parts list C1 = 64.8 pf L1 = 11.8 mh Z1 = 171 W E1 = 1 MHz L2 = 3.93 mh C2 = 83.8 pf 42

43 Impedance After Matching Frequency sweep 3.8 to 7.3 MHz Perfect match at design frequencies 43

44 SWR After Matching Before matching Note match bandwidth conservation due to Fano After matching 44 The total match bandwidth for all frequencies is limited by the Fano bound. By matching more frequencies, the match bandwidth at each frequency shrinks.

45 Design Procedure for Three-Frequency Matching Step 1: Use an L-network to move mid-freq point to R 0 on the Smith chart s real axis Step 2: Add an R 0 -ohm transmission line segment to rotate the outer points until they are both on the same side (left or right) of R 0 and On a resistance circle with the low-frequency point on top, or On a conductance circle with high-frequency point on top Step 3: Add an LC section and adjust L and C to wrap the outer points to center of Smith chart For points on a resistance circle, use a series LC to collapse the points For points on a conductance circle, use a shunt LC to collapse the points This step requires you label and keep track of the endpoints Three points can be brought to center by using no more than two LC resonator stages to double wrap (aka Wheeler triple tuning ) Do the above steps manually by using one of the software tools given later. When the points are close to center, use an optimizer to finish fine tuning the parts values. 45

46 Software Tools for Impedance Match Circuit Design A list of useful software tools with links is at 46

47 Software for Smith Charting and Network Design 47 SimSmith by Ward Harriman AE6TY Free download from Smith Chart Calculator 2.1 by Gorik Stevens Free download from Smith 3.10 by Fritz Dellsperger HB9AJY Free download from QuickSmith 4.5 by Nathan Iyer KJ6FOJ Free download from JJSmith 2.11 by James Bromley K7JEB and James Tonne W4ENE (SK) Free download from linsmith by James Coppens ON6JC/LW3HAZ Free download from XLZIZL by Dan Maguire AC6LA, No longer available. WinSMITH 2.0, Noble Publishing, No longer available. MicroSmith 2.3, ARRL, No longer available.

48 Smith Chart Programs for Ladder Network Design SimSmith Smith 3.10 QuickSmith 4.5 winsmith

49 General RF Circuit Design, Analysis, and Optimization Software for Radio Amateurs Quite Universal Circuit Simulator (QUCS) , 2014 Free download from Serenade SV 8.5 (student version), Ansoft, No longer available. See article by David Newkirk W9VES in QST, Jan ARRL Radio Designer 1.5, ARRL, No longer available. Professional electronic design automation (EDA) software Advanced Design System (ADS), Keysight (formerly Agilent) Microwave Office (MWO), National Instruments, Applied Wave Research High Frequency System Simulator (HFSS), ANSYS (formerly Ansoft Designer and Serenade) 49

50 Comments on Software All Smith chart programs Can draw impedance data on a Smith chart with Z and Y grids Allow the user to define ladder networks and see the effect on an impedance locus A good Smith chart program Has tuning sliders that allow changing parts values and seeing results instantly Allows you to import impedance data as Touchstone.s1p files Can convert impedance data from different file formats to Touchstone.s1p file format Can export impedance data as Touchstone.s1p files A good circuit analysis program Can draw impedance data on a Smith chart with Z and Y grids Can import and export impedance data in Touchstone formats (.s1p,.s2p,.snp) Allows analysis and design of arbitrary network topologies, more complicated than ladder networks, e.g. twin-t, bridged-t, and lattice networks Has a robust optimizer such as the Nelder-Mead amoeba or nonlinear simplex algorithm that can numerically search for optimum parts values that satisfy a userdefined goal criterion 50

51 The End This presentation will be archived at 51