About this tool
For a transmitter to deliver all its power to an antenna or amplifier, their impedance has to match the source – usually 50 Ω. An L-network made of one inductor and one capacitor transforms any load impedance with positive resistance to that value. The calculator finds all possible L-networks (two to four, depending on the load) and gives the component values at your frequency.
The Smith chart shows the path from the load to the centre: a series element moves the point along a circle of constant resistance, a shunt element along a circle of constant conductance. For each solution the calculator gives the Q – the lower, the wider the bandwidth – and whether it acts as a low-pass (suppressing harmonics) or high-pass.
In the advanced parameters you can enter the load as a reflection coefficient or S11 with magnitude and phase, as a network analyser shows it, round to E12 or E24 standard values and see the remaining return loss and the −10 dB bandwidth. How good the match is without a network is shown by the SWR Calculator. Everything runs in your browser.
How it works
- Enter the load impedance as R + jX, the source impedance (usually 50 Ω) and the frequency.
- Pick one of the solutions and read inductor and capacitor with their position (series or shunt).
- Follow the path on the Smith chart; the advanced parameters show standard values, return loss and bandwidth or take the load as S11.
Frequently asked questions
Why are there several solutions?
An L-network can have its shunt element on the load side or on the source side, and each arrangement has two signs – up to four solutions. Which are possible depends on the load: if its resistance is above the source impedance, the shunt element goes across the load. Solutions with series L and shunt C act as a low-pass and attenuate harmonics, those with series C and shunt L as a high-pass.
What does the Q tell me?
For an L-network Q is fixed by the transformation ratio; for purely resistive impedances Q = √(R_high / R_low − 1). 50 Ω to 200 Ω gives Q = 1.73. The higher Q, the narrower the bandwidth and the larger the circulating currents and component losses. Very large ratios therefore use pi or T networks or several L sections.
How do I read the Smith chart?
The centre is exactly the reference impedance (e.g. 50 Ω), the rim is pure reactance. Points in the upper half are inductive, in the lower half capacitive. The distance from the centre is the magnitude of the reflection coefficient: the further out, the worse the match. A series inductor moves the point clockwise along its resistance circle, a shunt capacitor clockwise along its conductance circle.
What happens if I use standard values?
Components only come in series such as E12 or E24. The advanced parameters round both values to the nearest standard value and show the remaining return loss. Above about 20 dB (SWR below 1.22) this is usually enough; otherwise combine two parts in parallel or series, or use a trimmer.