📶Online Smith Chart - Reflection Coefficient, VSWR, Stub & L-Network Matching

How to use Smith Chart & Impedance Matching

1. 1Choose Z₀ (50, 75 Ω…) and enter the load’s real and imaginary parts, or click on the chart
2. 2Read the reflection coefficient, VSWR, return loss and mismatch loss
3. 3On the line tab set frequency, velocity factor and length to see the input impedance rotate
4. 4Open single-stub or L-network matching to get stub positions and lengths or L and C values, drawn as paths on the chart
5. 5Use the RLC sweep to see how a load moves with frequency, and the standing-wave tab to watch the voltage envelope

FAQ

What does a point on the Smith chart mean?

The chart is the complex plane of the reflection coefficient Γ. The centre, Γ = 0, is a perfect match; the rim, |Γ| = 1, is total reflection (pure reactance, open or short). The red circles and arcs are constant-resistance and constant-reactance lines, so the same point also reads the normalized impedance z = Z/Z₀. The upper half is inductive, the lower half capacitive, the far left is a short and the far right an open.

How are VSWR, return loss and mismatch loss related?

All three depend only on |Γ|: VSWR = (1+|Γ|)/(1−|Γ|), return loss RL = −20 log|Γ| and mismatch loss = −10 log(1−|Γ|²). For example VSWR 2 means |Γ| ≈ 0.333, about 9.5 dB return loss, 11% reflected power and 0.5 dB mismatch loss. Antennas are usually specified below VSWR 2; precision systems want more than 20 dB return loss.

Why does moving along a line trace a circle?

On a lossless line the reflection coefficient a distance l from the load is Γ(l) = Γ_L·e^(−j2βl): the magnitude stays the same and the angle turns once every half wavelength. Moving toward the generator is therefore a clockwise rotation of 4πl/λ radians on the constant-|Γ| (constant-VSWR) circle. The wavelength scale around the rim is there to read that distance.

How does single-stub matching work?

First move a distance d along the line until the admittance becomes 1 + jb, which lies on the g = 1 circle. Then connect a shorted or open stub in parallel there that supplies −jb, cancelling the susceptance so the total admittance is 1. The g = 1 circle generally crosses the constant-|Γ| circle twice, so there are always two solutions. The tool gives both positions and stub lengths, also in metres for the entered frequency and velocity factor.

How do I pick the L-network components?

An L-network is one series reactance X and one shunt susceptance B. If the load resistance is above Z₀ the shunt element goes next to the load; if it is below Z₀ the series element does, and each arrangement has two solutions. Positive X is an inductor (L = X/ω), negative X a capacitor (C = −1/(ωX)); positive B is a capacitor and negative B an inductor. L-networks are narrowband, which you can see by sweeping the frequency.