An Introduction to the Smith Chart for Amateur Radio Jesse Sheinwald, N2CA [email protected] The Smith Chart 0.12 0.13 0.11 0.14 0 1 0.38 .37 0.1 0. 0.39 0.36 5 90 4 100 80 0.3 9 0. 5 0.1 0.0 5 6 0 4 5 1 0 0 7 1 10 0 . 0 0. 1 4 . 0 9 4 1 . 3 . 9 4 . 2 0 0 1 5 2 . 0 8 . 0 . 5 8 08 1 .1 . 0 7 0 1 5 . 4 0 4 . 3 7 . 0 . 42 1 7 6 .3 . 0 0 3 0 2 0 0 1 6 1 . ) 6 6 Yo . 0 0 7 jB/ 1 . 6 + . 1 . .0 ( 6 0 8 0 0 E 3 1 C 0 3 . N 8 . 4 8 A 0 . 3 0. PT .2 0.2 1 2 5 E 0 6 C 5 3 2 S 0 1 . SU 0 0 5 0 . 5 0 6 E 2 . 0 1 .0 IV 9 0 IT 25 0 4 C .3 .4 A 1 0 P A 0 C 7 R 0 O .4 0.4 0 4 4 0 , . 4 ) 4 0 0 5 1 0 o . .0 2 0 Z 0 5 / . .4 jX 0 3 0 + 2 ( 3 T 5 . 0 0 N 3. 7 0 E .6 0.6 N 0 4 O .2 0 3 P . 3 0 1 0 6 0 0 . 4 5 M 0 2 . 1 9 0 O C > 0. 8 E 8 0. 15 0 4 — .0 C .0 8 4 R N O A T 0 T 1 . 0 0 2 A C 0 . 7 1 . 2 2 R A 4 1 . 8 0 E 5 E . 0 0 0 0 . 0 2 5 . 2 R 1 N 0 2 0 5 0 E 6 E 1 8 V G 0 I . 8 . 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S N O B S O R F S S .W C P F L S S O ( , L . ∞ 40 30 20 15 10 8 6 5 4 3 12 1 1 1.1 1.2 1.3 1.4 1.6 1.8 2 3 4 5 10 20 ∞ L F . C [d . K F C O B L A E O E ] F E O I F 0 1 2 3 4 5 6 7 8 9 10 12 14 20 30 ∞ 0 0.1 0.2 0.4 0.6 0.8 1 1.5 2 3 4 5 6 10 15∞ R P C r E F . o F , F P .W M E , S S , E 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 0 0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.5 3 4 5 10 ∞ N F o F r A E I R O 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 0.99 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 T C . M S CENTER N A R 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 T ORIGIN Outline of Presentation 1. What is a Smith Chart? 2. Why should hams care? 1. Understanding antennas, transmission lines, and circuits. 2. Instrumentation marketed to the amateur community. 3. Some mathematical and physical basics 4. Exploring the Smith Chart 5. Representations on the Smith Chart 6. The Smith Chart on the computer 7. An impedance matching example using Smith Chart on the computer What is a Smith Chart? • The Smith Chart is a complex transformation of the transmission line equations on a polar plot with a loci of constant resistance and reactance lines superimposed on a polar plot of of reflection coefficients and angles of reflection coefficients. • Why should the average ham care? • Instruments marketed to the ham community • Sometimes shown in amateur articles and books • Essential if you want to design your own amplifiers Instruments Marketed to the Amateur Community Mathematical and Physical Basics • Scientific Notation • MKS Units • Radian Frequency • Complex Operator • Complex Impedance (Admittance) • Normalization • Lumped and Distributed Components • Wavelength Scientific Notation • A compact way to express either very large or very small numbers as powers of 10. The most important quantities for Smith chart work: • Kilo 103 • Mega 106 • Nano 10-9 • Pico 10-12 • MKS units are based on the meter, kilogram and second. Units used in Smith chart work (although they can be inconvenient) are Ohm (Ω), Farad (F), Henry (H), and Hz. Radian Frequency • In calculations on the Smith Chart, frequency must be expressed as Radians/Sec not Hz. • Do not worry. The conversion is simple and it is, for the most part, transparent to the user. • Radian frequency is expressed as ω, which is the lower case of the Greek letter Omega (Ω).