Calculator Inputs
This page uses a single-column content flow, while the input area shifts to three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
| Scenario | Source Impedance | Load Impedance | Frequency | Example Output |
|---|---|---|---|---|
| RF quarter-wave case | 50 + j0 Ω | 100 + j0 Ω | 100 MHz | Quarter-wave transformer impedance = 70.711 Ω |
| Step-up L-network case | 25 + j0 Ω | 100 + j0 Ω | 10 MHz | Q = 1.732, with valid low-pass and high-pass options |
| Complex mismatch check | 50 + j10 Ω | 75 − j20 Ω | 2.4 GHz | Direct mismatch, power, VSWR, and return loss only |
Formula Used
1) Complex impedance: Z = R + jX
2) Total series impedance: Ztotal = Zs + ZL
3) Circuit current: I = Vs / Ztotal
4) Load real power: PL = |I|² × RL
5) Reflection coefficient: Γ = (ZL − Z0) / (ZL + Z0)
6) VSWR: (1 + |Γ|) / (1 − |Γ|)
7) Return loss: −20 log10(|Γ|)
8) Quarter-wave transformer impedance: ZT = √(RS × RL)
9) L-network loaded Q: For step-up, Q = √(RL/RS − 1). For step-down, Q = √(RS/RL − 1).
10) Reactance to parts: XL = 2πfL and XC = 1/(2πfC)
How to Use This Calculator
- Enter the source resistance and reactance.
- Enter the load resistance and reactance.
- Provide source RMS voltage, reference impedance, frequency, and velocity factor.
- Press the calculate button to view mismatch metrics, power transfer, quarter-wave sizing, and available L-network values.
Frequently Asked Questions
1) What does impedance matching improve?
It improves power transfer, lowers reflections, and can reduce standing waves. Better matching also protects stages that dislike large reflected energy or poor loading conditions.
2) When is a quarter-wave transformer valid?
It works best for positive, purely resistive source and load values at one design frequency. It is narrowband, so off-frequency behavior can drift away from the target match.
3) Why are some matching values not shown?
L-network and quarter-wave suggestions need specific conditions. If the impedances include reactance or the resistances are unsuitable, the page limits itself to direct mismatch and power calculations.
4) What does VSWR tell me?
VSWR shows how strongly reflections create standing waves on a line. A value near 1 is good, while larger values indicate stronger mismatch and poorer transmission conditions.
5) Why is reference impedance important?
Reflection coefficient, return loss, and VSWR all depend on the chosen reference. In many RF systems that reference is 50 Ω, but other standards also exist.
6) Can this be used for audio circuits?
Yes. The mismatch, voltage, current, and power sections remain useful. Quarter-wave transmission-line sizing is more common in RF, while lumped networks are often more practical in audio work.
7) What is the conjugate match target?
For maximum power transfer, the target load equals the complex conjugate of the source impedance. That means the same resistance with opposite reactance.
8) Does frequency affect component sizing?
Yes. Inductor and capacitor values come from reactance at the selected frequency. Change the frequency, and the part values needed for the same matching reactance will also change.