How do you read and use a Smith chart?
The Smith chart, published by Phillip H. Smith in 1939, plots the complex reflection coefficient Γ inside the unit circle and overlays circles of constant normalized resistance r and arcs of constant normalized reactance x, where z = Z/Z0 = (1 + Γ)/(1 − Γ).[1][2] The center is a perfect match, the left edge a short, the right edge an open, the upper half inductive and the lower half capacitive.
How do you read a point on the chart?
Normalize the impedance by Z0 (e.g., 25 + j50 Ω on 50 Ω is 0.5 + j1). Find the r = 0.5 circle and the x = +1 arc; their intersection is the point. Its distance from the center is |Γ| and its angle is ∠Γ. A circle around the center through the point is a constant-VSWR circle.[2]
What moves do matching elements make?
- Series inductor / capacitor: move along a constant-r circle, clockwise (up) for L, counter-clockwise (down) for C.
- Shunt capacitor / inductor: move along a constant-conductance circle on the admittance chart (the impedance chart rotated 180°); shunt C moves clockwise, shunt L counter-clockwise.
- Series transmission line of Z0: rotate clockwise about the center (“toward generator”), one full revolution per λ/2.
- Stub: add a susceptance, like a shunt L or C.
How do you design an L-network on the chart?
Example: match ZL = 100 Ω to 50 Ω. Normalized zL = 2 lies on the real axis. A shunt capacitor moves it on the g = 0.5 circle until it reaches the r = 1 circle at 1 − j1; a series inductor of x = +1 then moves it to the center. At 1 GHz on 50 Ω: shunt susceptance b = 0.5 gives C = 0.5/(50·2π·109) ≈ 1.59 pF; x = 1 gives L = 50/(2π·109) ≈ 7.96 nH. See L-network matching.
What else is plotted on Smith charts?
Measured S11/S22 versus frequency from a VNA, constant-gain and constant-noise circles, stability circles and load-pull contours.[3]
Frequently asked questions
Who invented the Smith chart?
Phillip H. Smith of Bell Telephone Laboratories, published in Electronics in January 1939.
Which direction is toward the generator?
Clockwise.
What is outside the unit circle?
Negative resistance (|Γ| > 1), relevant to oscillators and instability.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Transmission Line Calculator”. P. H. Smith, Electronics, vol. 12. January 1939.
- “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
- “Microwave Transistor Amplifiers: Analysis and Design, 2nd ed.”. G. Gonzalez, Prentice Hall. 1997.