Impedance matching network calculator
Design L, Pi and T matching networks between two impedances at a frequency, with component values, bandwidth and the nearest standard parts.
Analog, RF, photonics and packagingFree to useHow it worksSourcesWhere it helps
Fills the inputs below with typical figures. Replace any of them with your own.
- L network, low-pass, shunt part next to the source
- shunt capacitor 7.334 pF, series inductor 916.8 pH
- Rounded to E24: shunt capacitor 7.5 pF, series inductor 910 pH
- Network Q
- 2.000
- Higher Q is narrower and more sensitive to part loss
- Return loss after, ideal parts
- 60 dB or more
- Mismatch loss under 0.001 dB
- Return loss after, standard parts
- 33.4 dB
- Reflection 0.0215, mismatch loss 0.002 dB
- Return loss before matching
- 3.2 dB
- Reflection 0.691, mismatch loss 2.816 dB
- Bandwidth at 10 dB return loss
- 687.5 MHz to 1.017 GHz
- 38.0% of the centre frequency, ideal parts
- Loss in the parts
- under 0.001 dB
- Parts are lossless; enter a Q to see the cost
- Source and load used
- 50 + j0 Ω
- Load 10 + j15 Ω
Sign in to save your inputs and come back to them later.
- Ideal parts (solid line, circles)
- Standard parts (dashed line, squares)
- No network (dotted line, triangles)
Show the data as a table
| Frequency | Ideal parts | Standard parts | No network |
|---|---|---|---|
| 434 MHz | 5 | 5 | 3 |
| 448.5 MHz | 5 | 5 | 3 |
| 462.9 MHz | 5 | 5 | 3 |
| 477.4 MHz | 6 | 6 | 3 |
| 491.9 MHz | 6 | 6 | 3 |
| 506.3 MHz | 6 | 6 | 3 |
| 520.8 MHz | 6 | 6 | 3 |
| 535.3 MHz | 6 | 6 | 3 |
| 549.7 MHz | 7 | 7 | 3 |
| 564.2 MHz | 7 | 7 | 3 |
| 578.7 MHz | 7 | 7 | 3 |
| 593.1 MHz | 7 | 7 | 3 |
| 607.6 MHz | 8 | 8 | 3 |
| 622.1 MHz | 8 | 8 | 3 |
| 636.5 MHz | 8 | 9 | 3 |
| 651 MHz | 9 | 9 | 3 |
| 665.5 MHz | 9 | 9 | 3 |
| 679.9 MHz | 10 | 10 | 3 |
| 694.4 MHz | 10 | 11 | 3 |
| 708.9 MHz | 11 | 11 | 3 |
| 723.3 MHz | 12 | 12 | 3 |
| 737.8 MHz | 12 | 13 | 3 |
| 752.3 MHz | 13 | 14 | 3 |
| 766.7 MHz | 14 | 15 | 3 |
| 781.2 MHz | 16 | 16 | 3 |
| 795.7 MHz | 17 | 18 | 3 |
| 810.1 MHz | 19 | 20 | 3 |
| 824.6 MHz | 21 | 23 | 3 |
| 839.1 MHz | 25 | 27 | 3 |
| 853.5 MHz | 31 | 36 | 3 |
| 868 MHz | 60 | 33 | 3 |
| 882.5 MHz | 30 | 26 | 3 |
| 896.9 MHz | 24 | 22 | 3 |
| 911.4 MHz | 21 | 19 | 3 |
| 925.9 MHz | 18 | 17 | 3 |
| 940.3 MHz | 16 | 15 | 3 |
| 954.8 MHz | 15 | 14 | 3 |
| 969.3 MHz | 13 | 12 | 3 |
| 983.7 MHz | 12 | 11 | 3 |
| 998.2 MHz | 11 | 10 | 3 |
| 1.013 GHz | 10 | 10 | 3 |
| 1.027 GHz | 9 | 9 | 3 |
| 1.042 GHz | 9 | 8 | 3 |
| 1.056 GHz | 8 | 8 | 3 |
| 1.071 GHz | 7 | 7 | 3 |
| 1.085 GHz | 7 | 7 | 3 |
| 1.099 GHz | 6 | 6 | 3 |
| 1.114 GHz | 6 | 6 | 3 |
| 1.128 GHz | 6 | 5 | 3 |
| 1.143 GHz | 5 | 5 | 3 |
| 1.157 GHz | 5 | 5 | 3 |
| 1.172 GHz | 5 | 4 | 3 |
| 1.186 GHz | 4 | 4 | 3 |
| 1.201 GHz | 4 | 4 | 3 |
| 1.215 GHz | 4 | 4 | 3 |
| 1.23 GHz | 3 | 3 | 3 |
| 1.244 GHz | 3 | 3 | 3 |
| 1.259 GHz | 3 | 3 | 3 |
| 1.273 GHz | 3 | 3 | 3 |
| 1.288 GHz | 3 | 3 | 3 |
| 1.302 GHz | 3 | 2 | 3 |
Return loss is capped at 60 dB on the chart. The response uses the parts you see in the tables and lets the source and load reactances change with frequency like an inductor or a capacitor.
| Position | Part | Reactance or susceptance | Ideal value | Standard value | Change from rounding |
|---|---|---|---|---|---|
| Shunt | Capacitor | 40 mS | 7.334 pF | 7.5 pF | 2.3% |
| Series | Inductor | 5.00 Ω | 916.8 pH | 910 pH | -0.7% |
| Network | Ideal parts | Standard parts | Q | Return loss, standard parts | Bandwidth, fraction of centre | Note |
|---|---|---|---|---|---|---|
| L network, low-pass, shunt part next to the source | shunt 7.334 pF, series 916.8 pH | 7.5 pF, 910 pH | 2.00 | 33.4 dB | 0.380 | none |
| L network, high-pass, shunt part next to the source | shunt 4.584 nH, series 5.239 pF | 4.7 nH, 5.1 pF | 2.00 | 28.5 dB | 0.214 | none |
| Pi network, low-pass, Q 5 | shunt 18.34 pF, series 3.169 nH, shunt 30.96 pF | 18 pF, 3.3 nH, 30 pF | 5.00 | 23.7 dB | 0.073 | none |
| Pi network, high-pass, Q 5 | shunt 1.834 nH, series 10.61 pF, shunt 2.396 nH | 1.8 nH, 11 pF, 2.4 nH | 5.00 | 18.3 dB | 0.079 | none |
| T network, low-pass, Q 5 | series 18.79 nH, shunt 4.971 pF, series 6.418 nH | 18 nH, 5.1 pF, 6.2 nH | 5.00 | 37.2 dB | 0.104 | none |
| T network, high-pass, Q 5 | series 1.789 pF, shunt 6.763 nH, series 2.821 pF | 1.8 pF, 6.8 nH, 2.7 pF | 5.00 | 18.1 dB | 0.086 | none |
How it works
A matching network makes a source and a load look like conjugates of each other at one frequency, so that all the available power reaches the load. This tool designs the three lumped networks used in practice (L, Pi and T) for complex source and load impedances, rounds the parts to a standard series, and shows the return loss and bandwidth you actually get across frequency.
- Set the terminations. Each side is a resistance and a reactance, or a reflection coefficient on a reference impedance. A positive reactance is an inductor and a negative one is a capacitor, whose reactance is carried across frequency in the response.
Z = Z0 x (1 + Gamma) / (1 − Gamma); Gamma = |Gamma| x (cos(angle) + j x sin(angle)) - Design an L network. An L network has one series and one shunt part. The shunt part must sit on the side with the higher parallel resistance. The series part is next to the other termination. Q follows from the resistance ratio, and the sign of Q gives the low-pass solution (series inductor, shunt capacitor) or the high-pass one. The reactance of a termination is absorbed into the part next to it.
Rp = 1 / Re(1 / Z(shunt side)); Q = sqrt(Rp / Rs − 1); X(series) = ±Q x Rs − X(termination); B(shunt) = ±Q / Rp − B(termination); plus for low-pass, minus for high-pass - Design a Pi or T network. Two L sections back to back through a virtual resistance let you choose the Q. A Pi network uses a virtual resistance below both terminations, set by the Q at the higher one. A T network uses a virtual resistance above both. A higher Q gives a narrower match and more filtering.
Pi: Rv = R(high) / (1 + Q^2); X(series) = ±Rv x (Q1 + Q2), B(shunt) = ±Qk / R(k); T: Rv = R(low) x (1 + Q^2); X(k) = ±Qk x R(k), B(shunt) = ±(Q1 + Q2) / Rv; Qk = sqrt(R(k) / Rv − 1) for Pi and sqrt(Rv / R(k) − 1) for T - Convert to parts and standard values. A positive series reactance is an inductor and a negative one a capacitor; for a shunt part the signs are the other way round. Each value is then moved to the nearest value (by ratio) in the E12, E24 or E96 series, and the response is worked out again with those values.
L = X / (2 x pi x f); C = 1 / (2 x pi x f x |X|); shunt: C = B / (2 x pi x f), L = 1 / (2 x pi x f x |B|) - Find the response across frequency. The ABCD matrices of the parts are multiplied from the source to the load, and the source and load reactances scale with frequency as an inductor or capacitor would. The reflection is the power-wave reflection against the conjugate of the source. A component Q adds a series resistance to each part.
Zin = (A x ZL + B) / (C x ZL + D); Gamma = (Zin − Zs*) / (Zin + Zs); return loss = −20 x log10|Gamma|; mismatch loss = −10 x log10(1 − |Gamma|^2); transducer gain = 4 x Re(Zs) x Re(ZL) / |A x ZL + B + Zs x (C x ZL + D)|^2 - Read the bandwidth. The bandwidth is the span around the design frequency over which the return loss stays at or above the threshold you set. It narrows as Q rises, which is why a Pi or T network is chosen for filtering and an L network for breadth.
fractional bandwidth = (f(high) − f(low)) / f0, where the return loss is at least the threshold between them
Assumptions
- The parts are ideal lumped elements with no parasitics, unless you enter a component Q, which adds a series resistance equal to the part's reactance divided by its Q.
- The aim is maximum power transfer (a conjugate match at the design frequency), not a noise match or a load-pull optimum.
- A termination's reactance changes with frequency like an ideal inductor or capacitor; real antennas and amplifiers have a more complex response.
- Preset impedances are editorial examples. Use measured or simulated values for your parts.
Limits and warnings
- Parasitic capacitance, inductance and self-resonance of real parts matter above a few hundred megahertz; the layout and the part models decide the real result.
- At microwave frequencies and long structures, distributed elements (stubs and transmission lines) replace lumped parts. Use a Smith chart or a simulator.
- A Pi or T network with a loaded Q that is too low for the resistance ratio is not possible; the tool then uses the lowest Q allowed.
- Matching is for one frequency. The reported bandwidth uses the return loss threshold you set and the simple frequency model for the terminations.
- Standard values come in tolerances (for example 2 to 5 percent for capacitors) that are not included; expect to tune the network on the board.
Sources
The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.
- Microwave Engineering, 4th edition (David M. Pozar), chapter 5, Impedance Matching and Tuning (opens in a new tab), John Wiley & Sons, 2012. Matching with lumped elements (L networks), Smith chart methods and the reflection coefficient.
- Application Note 742: Impedance Matching and the Smith Chart, The Fundamentals (opens in a new tab), Maxim Integrated, now Analog Devices, 22 July 2002. The Smith chart as a plot of the reflection coefficient, conjugate matching and a low-pass L network worked on the chart.
- Application Note AN267: Matching Network Designs with Computer Solutions (opens in a new tab), Motorola Semiconductor, now NXP Semiconductors, 20 July 1993. Lumped matching networks for RF power stages with one 50 ohm termination. Listed on NXP's page of modelling application notes.
Where it helps
The lifecycle stages this tool serves: 2 stages in 1 lifecycle.
More analog, rf, photonics and packaging tools
Method notev1Formula, ranges, sources and limits
Designs L, Pi and T matching networks between a complex source and load at one frequency, snaps the parts to a standard series, and reports return loss, mismatch loss and bandwidth.
Formula
Z = Z0 x (1 + Gamma) / (1 − Gamma); Gamma = |Gamma| x (cos(angle) + j x sin(angle)); Rp = 1 / Re(1 / Z(shunt side)); Q = sqrt(Rp / Rs − 1); X(series) = ±Q x Rs − X(termination); B(shunt) = ±Q / Rp − B(termination); plus for low-pass, minus for high-pass; Pi: Rv = R(high) / (1 + Q^2); X(series) = ±Rv x (Q1 + Q2), B(shunt) = ±Qk / R(k); T: Rv = R(low) x (1 + Q^2); X(k) = ±Qk x R(k), B(shunt) = ±(Q1 + Q2) / Rv; Qk = sqrt(R(k) / Rv − 1) for Pi and sqrt(Rv / R(k) − 1) for T; L = X / (2 x pi x f); C = 1 / (2 x pi x f x |X|); shunt: C = B / (2 x pi x f), L = 1 / (2 x pi x f x |B|); Zin = (A x ZL + B) / (C x ZL + D); Gamma = (Zin − Zs*) / (Zin + Zs); return loss = −20 x log10|Gamma|; mismatch loss = −10 x log10(1 − |Gamma|^2); transducer gain = 4 x Re(Zs) x Re(ZL) / |A x ZL + B + Zs x (C x ZL + D)|^2; fractional bandwidth = (f(high) − f(low)) / f0, where the return loss is at least the threshold between them
| Input | Unit | Range it holds for | Comes from |
|---|---|---|---|
| Source given as | choice | rx, gamma | Your figure |
| Source resistance | ohm | 0.01 to 100000 | Your figure |
| Source reactance | ohm | -100000 to 100000 | Your figure |
| Source reference impedance | ohm | 1 to 1000 | Your figure |
| Source reflection coefficient size | ratio | 0 to 0.999 | Your figure |
| Source reflection coefficient angle | degrees | -360 to 360 | Your figure |
| Load given as | choice | rx, gamma | Your figure |
| Load resistance | ohm | 0.01 to 100000 | Your figure |
| Load reactance | ohm | -100000 to 100000 | Your figure |
| Load reference impedance | ohm | 1 to 1000 | Your figure |
| Load reflection coefficient size | ratio | 0 to 0.999 | Your figure |
| Load reflection coefficient angle | degrees | -360 to 360 | Your figure |
| Design frequency | in the unit chosen | from 0 | Your figure |
| Frequency unit | choice | kHz, MHz, GHz | Your figure |
| Network | choice | l, pi, t | Your figure |
| Character | choice | lowpass, highpass | Your figure |
| L network arrangement | choice | auto, loadshunt, sourceshunt | Your figure |
| Loaded Q for a Pi or T network | ratio | 0.1 to 50 | Your figure |
| Standard values | choice | none, E12, E24, E96 | Your figure |
| Inductor Q (0 for ideal) | ratio | 0 to 1000 | Your figure |
| Capacitor Q (0 for ideal) | ratio | 0 to 5000 | Your figure |
| Return loss threshold for the bandwidth | dB | 3 to 40 | Your figure |
Outputs: Network Q (ratio); First inductor (nH); First capacitor (pF); Return loss before matching (dB); Mismatch loss before matching (dB); Return loss with standard parts (dB); Fractional bandwidth at the threshold (fraction).
Assumptions
- The parts are ideal lumped elements with no parasitics, unless you enter a component Q, which adds a series resistance equal to the part's reactance divided by its Q.
- The aim is maximum power transfer (a conjugate match at the design frequency), not a noise match or a load-pull optimum.
- A termination's reactance changes with frequency like an ideal inductor or capacitor; real antennas and amplifiers have a more complex response.
- Preset impedances are editorial examples. Use measured or simulated values for your parts.
Uncertainty: The design equations are exact for ideal lumped parts. Real parts shift the match by parasitics and tolerance, so expect to tune the values on the board; the bandwidth depends on how the terminations vary with frequency, which is only modelled simply here.
Known limits
- Parasitic capacitance, inductance and self-resonance of real parts matter above a few hundred megahertz; the layout and the part models decide the real result.
- At microwave frequencies and long structures, distributed elements (stubs and transmission lines) replace lumped parts. Use a Smith chart or a simulator.
- A Pi or T network with a loaded Q that is too low for the resistance ratio is not possible; the tool then uses the lowest Q allowed.
- Matching is for one frequency. The reported bandwidth uses the return loss threshold you set and the simple frequency model for the terminations.
- Standard values come in tolerances (for example 2 to 5 percent for capacitors) that are not included; expect to tune the network on the board.
Where the method comes from
Follows Pozar, Microwave Engineering, 4th edition, chapter 5 (Wiley, 2012) (opens in a new tab). The platform's version departs from it as follows.
- Complex source and load impedances are absorbed into the part next to each, and Pi and T networks are added with a chosen Q Why: The textbook treats the L network for a complex load on a real line; a design bench needs both terminations complex and a Q choice.
- The response is evaluated across frequency with ABCD matrices, and standard values and component Q can be applied Why: The match matters at the board, where parts come in series values and have loss; showing return loss and bandwidth makes that visible.
Reference example, checked by test: Worked example in this method note, hand-worked in the tool's unit test: 50 ohm to 100 ohm at 100 MHz with a low-pass L network. Q is 1, the series part is a 79.58 nH inductor and the shunt part a 15.92 pF capacitor; the direct connection has a return loss of 9.54 dB. Network Q 1; First inductor 79.5775; First capacitor 15.9155; Return loss before matching 9.5424; Mismatch loss before matching 0.5115; Return loss with standard parts 36.1957; Fractional bandwidth at the threshold 1.1547.
Versions
- v1 (2026-10-25): First version, built from the tool idea.
Terms on this page
- Bandwidth
- In meeting jargon, a person's or team's available working capacity rather than any data rate.
- Impedance matching
- The design of a network that transforms a source or load impedance so that maximum power is transferred and reflections are minimised, normally to a 50 ohm system reference.
- Return loss
- A measure of how much energy reflects back from an impedance discontinuity rather than continuing down the channel, given by S11.
- Load-pull
- A measurement technique that systematically varies the impedance presented to a transistor's output and records power, gain and efficiency, mapping the optimum matching conditions.
- Smith chart
- A polar plot of the complex reflection coefficient overlaid with constant resistance and reactance circles, letting impedance transformations be read graphically.
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