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

> Interactive Smith chart: click or type a load to get Γ, VSWR and return loss, rotate along a line, design stub and L-network matches, sweep RLC loads.

- URL: https://qilingtools.com/en/physics/smith-chart
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Click or drag on the chart to place the load, or type R and X, and you instantly get the magnitude and angle of Γ, normalized impedance and admittance, VSWR, return loss and mismatch loss. Enter a line length in wavelengths, electrical degrees or metres (from frequency and velocity factor) and the chart draws the rotation toward the generator and gives the input impedance. It also solves shunt single-stub matching (both solutions), L-network component values, plots the frequency locus of RLC loads and animates the standing wave on the line.

## How to use

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

## Features

- Crisp SVG chart with constant-r circles, constant-x arcs, optional admittance overlay and wavelength scale
- Click or drag the chart to set the load, touch friendly
- Line length in wavelengths, electrical degrees or metres with velocity factor
- Both shorted and open single-stub solutions; up to four L-network solutions with L/C values and a check
- Frequency locus and VSWR curve for series, parallel and other RLC loads
- Animated standing-wave envelope and instantaneous voltage with max/min positions

## 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.

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