Calculator Inputs
Example Data Table
| Z₀ (Ω) | ZL (Ω) | Γ | |Γ| | VSWR | Return Loss (dB) | Reflected Power % |
|---|---|---|---|---|---|---|
| 50 + j0 | 50 + j0 | 0.0000 + j0.0000 | 0.0000 | 1.0000 | Infinity | 0.00 |
| 50 + j0 | 75 + j25 | 0.2308 + j0.1538 | 0.2774 | 1.7676 | 11.1394 | 7.69 |
| 75 + j0 | 35 - j20 | -0.3200 - j0.2400 | 0.4000 | 2.3333 | 7.9588 | 16.00 |
Formula Used
The load reflection coefficient is calculated with the complex impedance relation below:
Γ = (ZL - Z₀) / (ZL + Z₀)
Where Z₀ is the characteristic impedance and ZL is the load impedance. Both may include real and imaginary terms.
Additional outputs use these formulas:
- |Γ| = √(Re(Γ)² + Im(Γ)²)
- Phase(Γ) = atan2(Im(Γ), Re(Γ))
- Return Loss = -20 log₁₀(|Γ|)
- VSWR = (1 + |Γ|) / (1 - |Γ|) for |Γ| < 1
- Reflected Power = |Γ|² × Pin
- Transmitted Power = Pin - Reflected Power
- Mismatch Loss = -10 log₁₀(1 - |Γ|²)
- Voltage Transmission Coefficient, τ = 1 + Γ
Frequency is included as a reference input. It becomes critical when the line or load impedance varies with frequency in practical systems.
How to Use This Calculator
- Enter the characteristic impedance real and imaginary parts for the line or medium.
- Enter the load impedance real and imaginary parts at the measurement point.
- Provide the incident input power to estimate reflected and transmitted power.
- Set a frequency reference if you are analyzing a specific operating condition.
- Choose the sweep resistance range and number of points for the graph.
- Press the calculate button to show results above the form.
- Review Γ, magnitude, phase, VSWR, return loss, mismatch loss, and power split.
- Use the CSV and PDF buttons to export your calculated results.
FAQs
What is the wave reflection coefficient?
It is the ratio of reflected wave amplitude to incident wave amplitude at a discontinuity. It shows how strongly impedance mismatch causes signal reflection.
Why can the reflection coefficient be complex?
Complex values capture both amplitude and phase shift. Real and imaginary parts show how the reflected wave rotates and scales relative to the incident wave.
What does a magnitude of zero mean?
A zero magnitude means perfect matching. No power reflects, return loss becomes infinite, and VSWR becomes exactly 1.0.
What happens when the magnitude approaches one?
Reflection becomes severe. Nearly all incident power returns toward the source, return loss drops, and VSWR rises sharply.
Why is VSWR useful?
VSWR converts mismatch into a familiar standing-wave ratio. Engineers use it to judge line quality, antenna tuning, and load matching performance quickly.
Does frequency always affect the result?
Not directly in this basic formula. Frequency matters when characteristic impedance or load impedance changes with frequency in real systems.
What is mismatch loss?
Mismatch loss is the power-transfer penalty caused by reflection. It shows how much useful forward power is unavailable to the load.
Can I use reactive impedance values?
Yes. Enter real and imaginary impedance parts. The calculator handles complex arithmetic and reports both coefficient magnitude and phase.