L-Network Impedance Matching Calculator
To match 50 Ω to 200 Ω at 1 GHz you need a network Q of 1.73: a 13.78 nH series inductor with a 1.378 pF shunt capacitor (low-pass), or a 1.838 pF series capacitor with an 18.38 nH shunt inductor (high-pass).
For practitioners
Network
- Loaded Q of the network
- 1.732
- Shunt element goes across
- the load (200 Ω side)
- Series element goes in
- the source line
Low-pass solution (series L, shunt C)
- Series inductor
- 13.78 nH
- Shunt capacitor
- 1.378 pF
High-pass solution (series C, shunt L)
- Series capacitor
- 1.838 pF
- Shunt inductor
- 18.38 nH
Real source and load resistances only. Parts are ideal: real inductors and capacitors have loss, self-resonance and tolerance, so tune on the bench or simulate with S-parameter models. Bandwidth is narrow and shrinks as the transformation ratio grows.
How to use the calculator
Enter the source resistance, the load resistance and the frequency. The calculator shows the network Q, tells you which port gets the shunt element, and gives two complete solutions with series and shunt element values in engineering units. Each solution transforms the load into the source resistance (or the reverse) at exactly the frequency you entered.
What an L-network does
An impedance matching network lets a source deliver its maximum power to a load by presenting each side with the resistance it expects. The L-network is the starting point for nearly every other matching technique. It uses one series reactance and one shunt reactance. The shunt element is placed across the port with the higher resistance and the series element is placed on the side of the lower resistance.
Think of it as a resistance step-down: a shunt reactance in parallel with the high resistance lowers its apparent resistance, and the series reactance then cancels the leftover reactive part. The amount of transformation sets the network Q:
The two reactances follow directly:
For the low-pass version the series element is an inductor and the shunt element is a capacitor. For the high-pass version the series element is a capacitor and the shunt element is an inductor. Component values come from the reactances at the design frequency f, with ω = 2πf:
Worked example: 50 Ω to 200 Ω at 1 GHz
The ratio is 200/50 = 4, so Q = √3 = 1.732. The shunt element sits across the 200 Ω port.
- Series reactance: 1.732 × 50 = 86.6 Ω. Shunt reactance: 200 / 1.732 = 115.5 Ω.
- Low-pass: series inductor L = 86.6 / (2π × 10⁹) = 13.78 nH, shunt capacitor C = 1 / (2π × 10⁹ × 115.5) = 1.378 pF.
- High-pass: series capacitor C = 1 / (2π × 10⁹ × 86.6) = 1.838 pF, shunt inductor L = 115.5 / (2π × 10⁹) = 18.38 nH.
You can check a solution by hand. Put 1.378 pF in parallel with 200 Ω at 1 GHz: the admittance is 5 mS + j8.66 mS. Convert back to impedance and you get 50 Ω in series with −j86.6 Ω. The 13.78 nH inductor adds +j86.6 Ω, and the reactance cancels, leaving a pure 50 Ω. The calculator's solutions are checked this way automatically in the project's tests.
Q and transformation ratio
| Resistance ratio | Network Q |
|---|---|
| 2 | 1.00 |
| 4 | 1.73 |
| 10 | 3.00 |
| 20 | 4.36 |
| 50 | 7.00 |
| 100 | 9.95 |
A higher ratio means a higher Q, a narrower bandwidth (see how to evaluate matching bandwidth), higher circulating currents and more sensitivity to component tolerance and loss. If the ratio is large, consider two L-sections in series: they transform through an intermediate resistance and have a lower Q for each stage.
Choosing between low-pass and high-pass
- Low-pass networks attenuate harmonics, which is useful at the output of an amplifier. The series inductor also provides a DC path, so a bias or a DC level passes through.
- High-pass networks block DC and low frequencies, which can protect a stage from DC, but they pass harmonics and low-frequency noise more easily.
- Component practicality matters too. At 1 GHz, 13.78 nH and 1.378 pF are practical values, but at much higher frequencies the inductor can become too small to realize without its parasitics dominating, and at low frequencies it may become too large to be practical.
What the ideal solution leaves out
The values you get are for ideal, lossless parts at one frequency. Before you build, remember:
- Real inductors and capacitors have loss. Inductor Q limits insertion loss, and the loss grows with the network Q.
- Self-resonance. Every part has parasitics. A capacitor behaves like an inductor above its self-resonant frequency, and an inductor like a capacitor.
- Tolerance. A 5% capacitor and a 5% inductor shift the match frequency and degrade the return loss, more so at high Q.
- Layout. Pad capacitance and trace inductance act as extra elements. Short, tight placement and a consistent ground reference are essential.
- The load is rarely a pure resistor. Real antennas and transistors are complex and change with frequency, so the calculated network is a starting point. Verify it with measured S-parameters or a simulation of the actual parts, then tune. A Smith chart shows the effect of each element step by step.
For the real-world steps, measure the matched circuit's S11 and compare it with your target using the VSWR and return loss calculator to translate between VSWR and return loss. RF View's matching tools use S2P models of real components so you can include their loss and parasitics in the simulation.
In plain words · for students and beginners
Impedance matching in plain words
The problem
Two parts of a circuit, such as an amplifier and an antenna, each prefer to work with a certain resistance. If their preferences differ, part of the signal bounces back and is wasted. Impedance matching adds a small circuit between them that makes each side see the resistance it expects. You can compare it to the gears between two machines that turn at different speeds: the matching network is the gear pair that makes them work together.
What the two parts do
An L-network has just two parts. One sits in the path of the signal (the series part) and one is a side branch to ground (the shunt part). One of them is a coil (inductor) and the other a small capacitor. Together they change the resistance the signal sees, from the load's value to the source's value, at one chosen frequency.
Why it works at only one frequency
A coil and a capacitor respond differently as the frequency changes, so the cancellation that gives you a perfect match happens at one frequency and gets worse on either side. Think of pushing a swing: it works best at the swing's own rhythm. The bigger the change in resistance you need, the narrower the range of frequencies that works well. That narrowness is the network's Q.
The example in words
To match 50 ohm to 200 ohm at 1 GHz, the calculator gives a coil of 13.78 nH and a capacitor of 1.378 pF in the low-pass version, or a capacitor of 1.838 pF and a coil of 18.38 nH in the high-pass version. These are tiny values, so on a real board the length of the traces and the pads of the parts make a visible difference.
Low-pass or high-pass
The two versions give the same match at the design frequency. The low-pass version also lets a steady (DC) level through and weakens higher frequencies, which can help against harmonics. The high-pass version blocks DC, which helps when a stage must not see a DC level.
Mistakes beginners make
- Expecting a wide frequency range from one L-network.
- Forgetting that real coils and capacitors have losses and that their values drift with temperature and tolerance.
- Trusting the calculated values without a simulation or a measurement of the real parts.
Remember
- A bigger resistance ratio means a higher Q and a narrower bandwidth.
- Two parts, two solutions: pick low-pass or high-pass by what else the circuit needs.
- The numbers are a starting point. Always check the result on the bench.
Related pages on RF View
Matching guides
- How to design an L-network
- How to design a Pi-network and a T-network, for lower Q or wider bandwidth
- How to design stub matching
- How to evaluate matching bandwidth
- How to use the real-component match feature to include real part loss and parasitics
- How to interpret a Smith chart
Glossary
Calculators
The microstrip impedance calculator gives the line widths that connect a matching network, and the VSWR and return loss calculator converts a measured result into the units used in specifications.
Frequently asked questions
What is an L-network?
It is the simplest matching network: one series element and one shunt element that transform one resistance into another at a single frequency. Two reactance arrangements are possible, a low-pass and a high-pass version.
Which solution should I choose, low-pass or high-pass?
Choose the low-pass version when you also want to attenuate harmonics or need a DC path through the series inductor. Choose the high-pass version when you need to block DC or low-frequency signals. Component values, size and parasitics can also decide it.
How wide is the bandwidth of an L-network?
It is narrow and gets narrower as the resistance ratio grows, because the network Q rises. A ratio of 4 needs a Q of 1.73, while a ratio of 100 needs a Q of nearly 10. For wider bandwidth use several L-sections in cascade or a different topology.
Can I match a load with a reactive part?
Yes, by absorbing the load reactance into the network. A load with parallel capacitance can use that capacitance as part of the shunt element, and a load with series inductance can use it as part of the series element, so the part you add is the calculated value minus the load's own reactance.