HomeCalculatorsElectricalRF & MicrowaveL-section LC Match Calculator
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L-section LC Match Calculator

Narrowband real RL→Z0 L-section match with dual LP/HP solutions. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 2/2 declared partitions (match, invalid-domain) · Matrix
Known limitations
  • Narrowband real RL↔Z0; RL≠Z0
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
L-section LC match for real loads.
Scope
Real ZL; lossless L/C; narrowband
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
1/1 property · digest 426af208bd28
Legacy regression
3/3 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass
Named expert review
Not performed
CVP suite
1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Pozar / matching networks — L-section
  • Bowick — RF Circuit Design — Impedance matching
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX physics/RF review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Q (RL>Z0)Q = √(RL/Z0 − 1)
ReactancesXs = ±Q·Z0 · B = ±Q/RL (topology family)
iNarrowband; complex ZL not supported in v1.

How to use

1

Enter system Z0 and load RL

Both resistances must be greater than zero (ohms).

2

Enter operating frequency

f > 0 sets L and C reactances for the L-section.

3

Read L and C

Uses Q = √(RL/Z0 − 1) style L-match (check which side is stepped up/down).

Example calculations

Common configurations with formula and result.

ϟ

50→100 Ω @ 1 GHz

Q=1

√(100/50−1)
Q=1 · two dual networks

L-section LC Match calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09

Calculation status

Review policy · Evidence · Reviewed by CalculatorX physics/RF review

Definition
For real RL≠Z0, Q=√(|RL/Z0−1|) yields two L-section duals (series-L/shunt-C and series-C/shunt-L).
What it calculates
L-section LC match for real loads.
Inputs
  • Z0_ohm
  • RL_ohm
  • f_Hz
Outputs
  • Q
  • solutions[]
Formula
Q=√(|RL/Z0−1|)
Assumptions
  • Real ZL; lossless L/C; narrowband
Units
  • Ω, Hz → H, F
Boundary conditions
  • RL=Z0 → VALUE_OUT_OF_RANGE
  • non-positive → VALUE_MUST_BE_POSITIVE
Example
Z0=50 RL=100 f=1e9 → Q=1
Validation cases

1 published on this page · 3/3 tests · Production surface contract 4/4 · View evidence

  • Z0=50 RL=100 f=1e9 → Q=1
Sources
  • Pozar / matching networks — L-section
    Supports: Q and dual topologies
  • Bowick — RF Circuit Design — Impedance matching
    Supports: L-section Q=√(Rhi/Rlo−1)
Last reviewed
2026-08-09
Reviewed by
CalculatorX physics/RF review
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Design a narrowband L-section match for real impedances.

Supported and not supported

Supported — Real RL→Z0 · dual solutions · API electrical.rf.lc_match

Not supported — Complex ZL, stub matching, multi-section Chebyshev

Agent / API notes

Capability id: electrical.rf.lc_match · tool id: lc-match · pin 1.0.0.

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Frequently asked questions

Key distinctions behind the calculation.

What if RL = Z0?

No matching network is required; API returns VALUE_OUT_OF_RANGE.