L-Network Impedance Matching Calculator
Calculate a first-pass low-pass or high-pass RF L-match from real source impedance, real load impedance and design frequency.
RF-008 is a single-frequency lumped matching calculator. It does not model complex loads, Smith chart tuning, transmission-line stubs, π networks, T networks or broadband matching.
Engineering tool
L-Network Impedance Matching Calculator
Calculate narrowband RF L-match quality factor, series reactance, shunt reactance and component values for real source and load impedances.
Result console
- Matching Network Type
- Low-Pass
- Quality Factor
- 1Q
- Series Reactance
- 50Ω
- Shunt Reactance
- 100Ω
- Series Component
- Inductor79.577472 nH
- Shunt Component
- Capacitor15.915494 pF
- Shunt Location
- Load side
- Estimated Fractional Bandwidth
- 1≈1/Q
- Equivalent Circuit
- Low-Pass L-match: series inductor on the low-resistance path; shunt capacitor across the load side.
- Formula Used
- Q = √(Rhigh/Rlow - 1); Xs = Q × Rlow; Xp = Rhigh / Q
An L-network is a single-frequency narrowband matching estimate.
Formula reference
L-Network Matching Formulas
The simple real-resistance L-match model uses the high and low resistance values to calculate Q and reactance magnitudes.
Q = √(Rhigh / Rlow - 1)Xs = Q × RlowXp = Rhigh / QL = X / (2πf)C = 1 / (2πfX)Estimated fractional bandwidth ≈ 1 / QVariable definitions
- Rhigh
- higher of source and load resistance
- Rlow
- lower of source and load resistance
- Q
- loaded quality factor of the matching network
- Xs
- series reactance magnitude
- Xp
- shunt reactance magnitude
- Low-pass topology
- series inductor and shunt capacitor
- High-pass topology
- series capacitor and shunt inductor
- The shunt element is placed on the high-resistance side in this simplified model
Worked Examples
50 Ω to 100 Ω at 100 MHz
Q = 1, Xs = 50 Ω and Xp = 100 Ω. Low-pass gives series L ≈ 79.58 nH and shunt C ≈ 15.92 pF.
50 Ω to 75 Ω at 433 MHz
Q ≈ 0.707, Xs ≈ 35.36 Ω and Xp ≈ 106.07 Ω.
50 Ω to 25 Ω at 915 MHz
Q = 1, Xs = 25 Ω and Xp = 50 Ω. The shunt component is on the 50 Ω source side.
75 Ω to 300 Ω at 100 MHz
Q ≈ 1.732, Xs ≈ 129.90 Ω and Xp ≈ 173.21 Ω.
50 Ω to 200 Ω at 2.4 GHz
Q ≈ 1.732, Xs ≈ 86.60 Ω and Xp ≈ 115.47 Ω. Layout parasitics become very important.
200 Ω to 50 Ω at 2.4 GHz
The same reactance magnitudes apply, but the shunt element belongs on the high-resistance source side.
Auto match
Auto Select uses the low-pass topology as the conservative default for real-resistance matching.
Compare low-pass vs high-pass
Low-pass uses series inductor and shunt capacitor; high-pass swaps those to series capacitor and shunt inductor with the same reactance magnitudes.
Higher Q case
A large Rhigh/Rlow ratio raises Q, narrows bandwidth and increases sensitivity to component tolerances.
Component tolerance
A few percent capacitance or inductance error can move the match away from the target frequency, especially for high-Q networks.
Engineering Notes
- An L-network is a narrowband impedance matching network.
- Matching performance falls away as frequency moves from the design frequency.
- Higher Q generally means narrower bandwidth.
- Component ESR and finite Q affect real insertion loss.
- PCB layout, pad capacitance, via inductance and ground return paths affect high-frequency results.
- Inductor self-resonant frequency and capacitor self-resonant frequency must be above the operating region.
- Component tolerance changes the actual center frequency and return loss.
- Low-pass and high-pass topologies have the same ideal reactance magnitudes but different filtering behavior.
- This calculator assumes real source and load impedances.
- Use VNA measurement and tuning for final RF hardware.
Common Mistakes
- Ignoring Q and assuming the match is broadband.
- Ignoring inductor and capacitor parasitic behavior.
- Choosing low-pass or high-pass topology without considering DC path and harmonic behavior.
- Using components near their self-resonant frequency.
- Ignoring PCB parasitic capacitance and trace inductance.
- Treating complex antenna impedance as a simple resistance.
- Forgetting that the shunt element belongs on the high-resistance side in this model.
- Assuming ideal values will remain exact after tolerance, package and layout effects.
Support reference
FAQ
What is an L-network?
An L-network is a two-reactive-component impedance matching circuit that transforms one real resistance to another at a single design frequency.
How do I match two impedances?
For a simple real-resistance L match, identify the high and low resistance, calculate Q = √(Rhigh/Rlow - 1), then calculate Xs = Q × Rlow and Xp = Rhigh / Q.
When should I use low-pass matching?
Use a low-pass L match when harmonic attenuation is useful or when a series inductor and shunt capacitor fit the RF design better.
When should I use high-pass matching?
Use a high-pass L match when DC blocking, low-frequency rejection or a series capacitor topology is preferred.
What is Q?
Q is the loaded quality factor of the L-network. Higher Q generally means narrower bandwidth and greater sensitivity to tolerance and parasitics.
Does L matching work over a wide bandwidth?
No. A basic L-network is narrowband. Broadband matching often needs multi-section, transformer, distributed or active matching approaches.
How do I choose inductors?
Choose RF inductors with suitable inductance, current rating, Q, self-resonant frequency, tolerance and low parasitic loss at the design frequency.
How do I choose capacitors?
Choose RF capacitors with suitable capacitance, voltage rating, dielectric, Q, tolerance, ESR and self-resonance margin at the design frequency.
Does this calculator handle complex impedances?
No. RF-008 uses a real-resistance L-match model. Complex impedance matching requires additional reactance cancellation or Smith chart analysis.
Why do layout parasitics matter?
At RF frequencies, PCB pads, traces, vias, packages and ground return paths add inductance and capacitance that shift the real match.
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Future Engineering Guide Topics
L Matching Explained
In_DevelopmentLoaded Q
In_DevelopmentBandwidth of Matching Networks
In_DevelopmentChoosing RF Components
In_DevelopmentDisclaimer
This calculator provides first-pass lumped RF matching estimates for real impedances. Final values should be tuned with measured component parasitics, PCB layout, load impedance and VNA data.