IndieRF Match
Smith chart calculator and impedance matching
Plot a load on a Smith chart, from a typed impedance or a Touchstone file, and read the L-network that conjugate-matches it. Part values, component Q, and the matched return-loss band stay on screen.
Last updated 11 October 2026.
How to read the chart
A Smith chart plots the reflection coefficient Γ = (Z − Zref) / (Z + Zref). The chart reference Zref is independent of the source impedance. The match target is the conjugate of the source, Zs*, not necessarily the center of the chart. Admittance circles are the same geometry read as y = 1/z. A constant-Q circle through z = 1 + jQ is centered at (0, −1/Q) and passes through the short and the open. Return loss in decibels is −20 log10|Γ|, and VSWR is (1+|Γ|)/(1−|Γ|).
From a file to an impedance
Drop a 1- to 4-port Touchstone file. The chosen port’s reflection is interpolated in Γ, not in Z, and the frequency is not extrapolated past the file. On a multiport file the other ports are terminated. “file” keeps each port’s own reference so the one-port result is Sii. A numeric termination reduces the network through its Z matrix. If the phase steps more than 20° between samples, the sweep is too coarse to trust the band edges. The reference plane is the plane in the file.
Which network this tool builds
This calculator solves L-sections: two lumped elements, series and shunt. Use it when the band is a modest fraction of the center frequency and the part values land in a range you can buy. Pi and T networks, single-stub tuners, and quarter-wave transformers are not calculated here. A microstrip width for a later distributed match is on the microstrip calculator. Measured files that you only want to plot belong in the S-parameter viewer.
Worked example: 2.45 GHz chip antenna
The demo load is synthetic, not a vendor file. A 10 Ω resistor, 3.2 nH, and 1.5 pF in series, with 0.35 pF in parallel, gives 10.64+j5.558 Ω at 2.45 GHz. Unmatched into 50 Ω that is about 3.7 dB return loss. Only topology A is available, because the resistance is below 50 Ω. These figures are computed by this engine.
| Network | Parts, source to load | RL at 2.45 GHz | ≥ 10 dB |
|---|---|---|---|
| Low-pass, ideal | 2.499pF, 968.4pH | matched | 2.311GHz – 2.584GHz |
| High-pass, ideal | 1.689nH, 2.496pF | matched | 2.331GHz – 2.59GHz |
| Low-pass, RF snap | 2.3pF, 1nH | 23.5 dB | 2.32GHz – 2.606GHz |
| Low-pass, QL = 30, QC = 300 | 2.3pF, 1nH | 27.0 dB | GT -0.24 dB |
The RF grid is 0.1 nH and 0.1 pF through 9.9, then E24. The combined search may pick a neighbor of the nearest value when that neighbor improves the worst |Γ| on the sweep. On this antenna the low-pass capacitor moves off the nearest 2.5 pF step. Constant Q is the default and is labeled that way. Inductors can instead use Q(f) = Q0 · √(f/f0). Capacitors stay at the Q you type. Leave the Q field blank, or type ∞, for an ideal part.
Component Q
Q is the ratio of reactance to series loss: ωL/R for an inductor and 1/(ωC·ESR) for a capacitor. In this tool that resistance is applied when the network is evaluated, not inside the topology solver. It sets the insertion loss, which shows up as transducer gain GT below 0 dB, and it moves the match a little, so the return-loss peak is no longer infinite. A higher nodal Q also narrows the band. The presets in the form are typical starting points near 1–6 GHz. They are not datasheet values. Read the Q-versus-frequency curve for the part and the value you will buy.
- Multilayer chip inductors are the low-Q end, often about 10–25 near 1–6 GHz. Murata’s LQG family is this construction. Reference specification JELF243B-0010 lists a minimum Q of 8 for the 10 nH part LQG15HS10NJ02. The product page for LQG15HS47NJ02, the same series and the same minimum of 8, lists the Q test frequency as 100 MHz. That minimum is not the Q at 2.4 GHz.
- Thin-film inductors, such as Murata LQP, sit above multilayer parts. Murata’s LQP03HQ reference specification lists a minimum Q of 20 for LQP03HQ10NH02 (10 nH), measured at 500 MHz for the 0.5 nH to 30 nH range.
- Wirewound chip inductors are higher, often about 30–70 and sometimes more. Murata notes that the LQW wire-wound structure can reach a higher Q than LQP or LQG. The LQW15AN specification measures Q at 250 MHz for 1.5 nH to 43 nH; LQW15AN9N0 (9.0 nH) has a minimum Q of 25 at that frequency. Coilcraft’s 0402HP series, document 526 revised 20 December 2023, lists a typical Q of 62 at 900 MHz and 90 at 1.7 GHz for 0402HP-10N, measured on an Agilent/HP 4287A with a 16197 fixture.
- C0G/NP0 MLCCs in small picofarad values are often Q of 100 or more in the low GHz. High-Q RF capacitors are higher still. Murata GJM is a high-Q C0G/C0H series aimed at about 500 MHz to 10 GHz. Johanson’s high-Q catalog quotes Q greater than 1,000 at 1 MHz, typically 10,000 below 1,000 pF. ATC’s 600S series quotes Q greater than 2,000 at 1 MHz and plots Q against capacitance at 450 MHz and 2 GHz. Use those curves. A 1 MHz catalog Q is not the Q at 2.4 GHz.
Sources: Murata inductor FAQ, “Why is the Q characteristics of the LQW better than the LQP and LQG”; Murata reference specifications JELF243B-0010 (LQG15HS) and JELF243C-0021 (LQP03HQ); Murata LQW15AN reference specification; Murata GJM series lineup; Coilcraft document 526, 0402HP Series; Johanson Technology high-Q MLCC catalog; ATC 600S Series datasheet. Preset buttons such as “Multilayer ~15” are inside the ranges above. They are not a quoted Q from any of those documents.
Limits
- Ideal lumped elements, plus a series loss from Q and an optional inductor self-resonance. No pad or via parasitics and no electromagnetic simulation.
- No stability circles. A conjugate match of a transistor is not a stability analysis.
- The reference plane is the file plane. Fixture delay is not removed.
- Share links and on-screen results are free. A BOM CSV or a network .s2p asks you to sign in. Measured points stay in the URL hash and are not sent to the server.
References
- P. H. Smith, “Transmission Line Calculator,” Electronics, vol. 12, pp. 29–31, January 1939.
- D. M. Pozar, Microwave Engineering, chapter 5, impedance matching and tuning.
- C. Bowick, RF Circuit Design, chapter 4, L-network matching.
- R. Ludwig and P. Bretchko, RF Circuit Design: Theory and Applications, matching networks.
- R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” Journal of the Franklin Institute, 1950.
The L-network page lists a computed check of Pozar’s Example 5.1. Printed book figures are not copied here until the edition and page are transcribed. Design frequency on the demo is 2.45GHz.
Notes
- How to read a Smith chart. One point, 25 + j50 Ω: |Γ| = 0.620 at 82.9°, return loss 4.15 dB.
- Return loss, VSWR, |S11|, and mismatch loss. A 10 dB return loss is |Γ| = 0.316, VSWR 1.92, and 0.46 dB of mismatch loss.
- Match a 2.4 GHz chip antenna to 50 Ω. The demo impedance, the S1P reference plane, and a 50 ps port extension.
- Why an L-match is narrow, and what Q costs. This antenna’s 10 dB band is 273 MHz. The same parts with Z held still span 1.12 GHz.
- How to design an L-network and choose a solution. DC path, harmonics, and a source whose target is not the center of the chart.
FAQ
How do I use an online Smith chart?
The chart is the reflection-coefficient plane. The center is a perfect match to the chart reference, usually 50 Ω. Circles of constant resistance sit to the right of the short, and arcs of constant reactance leave the right-hand open. Click the chart or type a load, set the design frequency, and the L-network arcs are drawn from the load back toward the source.
How do I get antenna impedance from a NanoVNA?
Save a 1-port Touchstone file and drop it here. Pick the frequency you want to match. The tool reads Γ from the file and converts it with the file’s reference impedance. A NanoVNA calibration is at the connector, not at the antenna feed. This calculator does not remove fixture delay or port extension.
Why does an L-network have two or four solutions?
Each allowed topology has two signs for the reactance that lands on the match circle. A load whose resistance is below the source uses the series-at-the-load topology. A load whose conductance is below the source uses the shunt-at-the-load topology. A complex source can allow both, so up to four networks. A load already on the match circle collapses to one element, and a second valid network can remain.
Can I match a purely reactive load?
No. A lossless network cannot create the real part a conjugate match needs. A negative resistance is rejected for the same reason: this tool matches passive loads.
Which solution has the most bandwidth?
The list is ordered by the measured return-loss band that contains the design frequency, then by nodal Q. The f0/Q figure is only an estimate. The band edges come from the sweep, with linear interpolation of return loss.
How accurate is this compared with a circuit simulator?
The ideal parts are the same closed forms used in textbooks, and every solution is checked by cascading ABCD matrices. Finite Q and an optional inductor self-resonance are lumped models. Pad, via, and layout parasitics are not included, so a simulator or a VNA measurement is still the check before a board spin.