Impedance Matching Designer
Synthesize and verify L matches or a quarter-wave transformer at one design frequency.
- Typical inputs
- Design frequency, real system impedance, complex load, topology, response, loaded Q, and component Q.
- Calculated output
- Valid branch values, schematic, residual impedance/Γ, estimated loss warning, and frequency sweep.
- Model status
- Release C · documented and numerically tested
Which lossless branch transforms this load to the selected real system impedance?
Single-frequency matching synthesis
The objective is zero voltage-wave Γ for a positive real system impedance. That is not a claim of arbitrary complex-source power-wave or conjugate matching.
50 Ω→series
L 79.5775 nH→shunt
C 15.9155 pF→Load
100 + j0 Ω
- Exact synthesis residual
- 0 Ω
- Practical Zin
- 50.00000 + j0.00000 Ω
- Practical Γ / VSWR
- 0.000000 / 1.00000
- Practical return loss
- ∞ dB
- Ideal insertion loss
- 0.000000 dB includes residual mismatch; ideal reactive parts
- Lossy response, Q 100
- 0.08664 dB series-loss component model
- Worst corner, ±1.00%
- 42.9672 dB RL
- Design frequency
- 100.0000 MHz
| Branch | Exact components | Forward residual |
|---|---|---|
| 1. Series L then shunt C | series L 79.5775 nH; shunt C 15.9155 pF | 0 Ω |
| 2. Series C then shunt L | series C 31.831 pF; shunt L 159.155 nH | 0 Ω |
| Component | Voltage | Current |
|---|---|---|
| 1. series L 79.5775 nH | 223.607 mVrms | 4.47214 mArms |
| 2. shunt C 15.9155 pF | 316.228 mVrms | 3.16228 mArms |
Calculation path
- The exact network is independently solved as a circuit; preferred values, tolerance corners, and finite-Q parts are then evaluated separately.
- Perfect f₀ math excludes interconnect, pad/via parasitics, self-resonance, bias, temperature, and measured load movement.
- Verify the assembled network with a calibrated VNA at the intended reference plane.
What this calculator is doing
Ideal reactive networks are synthesized at one frequency and independently re-evaluated with the complex circuit model. L branches accept complex loads; the bounded π/T implementation states its real-load condition.
How to read the result
Choose a branch for harmonic response, bias paths, parasitics, stress, and available component Q. Verify the built network at its real reference plane.
Equations & conventions
- Z0 is positive real source/system resistance; ZL = R + jX is the load.
- Q is loaded network selectivity for π/T synthesis.
- Component Q estimates first-order reactive loss, not full parasitics.
Independently checked example
Checked example: matching 100 + j0 Ω to 50 Ω at 100 MHz yields two ideal L branches; both re-evaluate to 50 + j0 Ω within floating-point tolerance.
Common mistakes
- Assuming a single-frequency match guarantees bandwidth.
- Ignoring component self-resonance and layout parasitics.
Assumptions, validity & omissions
- The source/system reference is positive and real.
- L matches are narrowband ideal lumped models.
- Quarter-wave synthesis requires real positive terminal resistances.
Sources & model provenance
- Keysight, Matching Network Yin-Yang — Part 1 (opens in a new tab) — L-network topology coverage and matchable regions. Accessed 2026-09-05.
- Keysight, Understanding the Fundamental Principles of Vector Network Analysis (opens in a new tab) — Reflection, S-parameters, Smith charts, and group delay. Accessed 2026-09-05.