Impedance matching calculator (L / π / T)
Online design of L, π and T matching networks for RF and antennas: enter the source impedance Rs+jXs and load impedance RL+jXL to get the network Q, inductor and capacitor values, the approximate −3 dB bandwidth, and a circuit diagram of the chosen topology. Complex source / load reactances are compensated.
Key points
The impedance matching calculator designs the L, π and T passive matching networks commonly used in RF and antennas. Given the source impedance Rs+jXs, load impedance RL+jXL and operating frequency, it applies conjugate matching to compute the network Q and the inductor and capacitor values, along with the bandwidth and a topology diagram. An L network uses just two elements with Q fixed by the impedance ratio Q=√(Rhigh/Rlow−1); π and T networks let you set Q to widen the bandwidth.
Inputs
L: Q = √(Rhigh/Rlow − 1), Xseries = Q·Rlow, Bshunt = Q/Rhigh ｜ π: Rv = Rhigh/(Q²+1), Xseries = Rv(Q1+Q2) ｜ T: Rv = Rlow(Q²+1), Xseries = Q·R ｜ elements: L = X/ω, C = 1/(ωX)Calculation model (updates with parameters)
Smith chart (impedance / admittance grid, updates with parameters)
The trajectory starts at the load: series elements move along a constant-resistance circle, shunt elements along a constant-conductance circle, ending at the source conjugate point (maximum power transfer). Dashed lines are the admittance grid.
| Matching topology | L network · shunt at source + series at load | Place the shunt element on the higher-resistance side |
| Network Q | 2.00 | Fixed by the impedance ratio |
| Shunt element at source | C 63.66 pF | |
| Series element at load | L 31.83 nH | |
| Approx. bandwidth (−3 dB) | 50 MHz | BW ≈ f / Q |
| Impedance transformation Rhigh : Rlow | 5.00 : 1 |
Engineering notes
- The L network uses the fewest parts, but its Q is fixed by the impedance ratio Q = √(Rhigh/Rlow − 1) and the bandwidth cannot be set independently; for wider bandwidth use a π / T network with a higher Q.
- For π / T networks a higher Q gives wider bandwidth and better harmonic rejection, but also more extreme element values and more pronounced loss and parasitics; keep Q about 1.5–5× Qmin.
- Source / load若带Series电抗，工具按其ShuntEquivalent把电纳并入同侧ShuntCNY件、把电抗并入同侧SeriesCNY件，实现单频点精确共轭匹配。
- Results assume ideal lossless elements; real inductors have finite Q and self-resonance, capacitors have ESL, so fine-tune with a VNA before production.
FAQ
- What is Impedance matching calculator (L / π / T) for?
- Online design of L, π and T matching networks for RF and antennas: enter the source impedance Rs+jXs and load impedance RL+jXL to get the network Q, inductor and capacitor values, the approximate −3 dB bandwidth, and a circuit diagram of the chosen topology. Complex source / load reactances are compensated.
- What is the formula for Impedance matching calculator (L / π / T)?
- Core formula: L: Q = √(Rhigh/Rlow − 1), Xseries = Q·Rlow, Bshunt = Q/Rhigh ｜ π: Rv = Rhigh/(Q²+1), Xseries = Rv(Q1+Q2) ｜ T: Rv = Rlow(Q²+1), Xseries = Q·R ｜ elements: L = X/ω, C = 1/(ωX). The tool returns results instantly using this formula and the selected parameters.
- What engineering notes should I keep in mind when using Impedance matching calculator (L / π / T)?
- The L network uses the fewest parts, but its Q is fixed by the impedance ratio Q = √(Rhigh/Rlow − 1) and the bandwidth cannot be set independently; for wider bandwidth use a π / T network with a higher Q. For π / T networks a higher Q gives wider bandwidth and better harmonic rejection, but also more extreme element values and more pronounced loss and parasitics; keep Q about 1.5–5× Qmin. Source / load若带Series电抗，工具按其ShuntEquivalent把电纳并入同侧ShuntCNY件、把电抗并入同侧SeriesCNY件，实现单频点精确共轭…