Reflection Coefficient
Γ = (ZL − Z0) / (ZL + Z0)
Quick answer
This calculator solves Γ = (Z_L − Z₀) / (Z_L + Z₀) for Reflection Coeff.. With Load Impedance 0.47 kΩ, Characteristic Impedance 1.03 kΩ, the result is -0.3733. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The reflection coefficient Γ (gamma) quantifies the fraction of an incident wave reflected at an impedance discontinuity. When the load impedance ZL equals the characteristic impedance Z0, Γ = 0 and all power is absorbed (perfect match). An open circuit (ZL = ∞) gives Γ = +1 (total reflection, same polarity). A short circuit (ZL = 0) gives Γ = −1 (total reflection, inverted). The reflection coefficient is directly related to VSWR, return loss, and mismatch loss, and is the fundamental quantity measured by a vector network analyzer (VNA).
Variables
- Γ — Voltage reflection coefficient (−1 to +1, dimensionless)
- Z_L — Load impedance (Ω)
- Z₀ — Transmission line characteristic impedance (Ω)
Practical Notes
Return Loss = −20 × log₁₀(|Γ|) in dB. VSWR = (1 + |Γ|)/(1 − |Γ|). Mismatch Loss = −10 × log₁₀(1 − |Γ|²) in dB. For complex impedances, Γ is a complex number and is plotted on the Smith chart. A |Γ| < 0.1 (VSWR < 1.22, RL > 20 dB) is considered an excellent match. Most RF specifications require |Γ| < 0.33 (VSWR < 2, RL > 9.5 dB).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| gamma | Reflection Coeff. | — | — |
| ZL | Load Impedance | Ω | mΩ, Ω, kΩ, MΩ |
| Z0 | Characteristic Impedance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Load Impedance 0.47 kΩ, Characteristic Impedance 1.03 kΩ
- 2. The relation: Γ = (Z_L − Z₀) / (Z_L + Z₀)
- 3. Substitute: ZL = 0.47 kΩ, Z0 = 1.03 kΩ
- 4. Result: Reflection Coeff. = -0.3733
Worked examples
Minimum range
Given: Load Impedance 1 Ω, Characteristic Impedance 2.2 Ω
Result: Reflection Coeff. = -0.375
Low range
Given: Load Impedance 10 Ω, Characteristic Impedance 22 Ω
Result: Reflection Coeff. = -0.375
Typical
Given: Load Impedance 0.47 kΩ, Characteristic Impedance 1.03 kΩ
Result: Reflection Coeff. = -0.3733
High range
Given: Load Impedance 4.7 kΩ, Characteristic Impedance 10.3 kΩ
Result: Reflection Coeff. = -0.3733
Maximum range
Given: Load Impedance 47 kΩ, Characteristic Impedance 103 kΩ
Result: Reflection Coeff. = -0.3733
Solving for each variable
Solve for Reflection Coeff.
Load Impedance 1 Ω, Characteristic Impedance 2.2 Ω → -0.375
Solve for Load Impedance
Reflection Coeff. 0.025, Characteristic Impedance 2.2 Ω → 2.313 Ω
Solve for Characteristic Impedance
Reflection Coeff. 0.025, Load Impedance 1 Ω → 0.9512 Ω
How Reflection Coeff. changes with Load Impedance
| Load Impedance (input) | Reflection Coeff. (result) |
|---|---|
| 47 Ω | -0.9127 |
| 117.5 Ω | -0.7952 |
| 0.235 kΩ | -0.6285 |
| 0.3525 kΩ | -0.4901 |
| 0.47 kΩ | -0.3733 |
| 0.705 kΩ | -0.1873 |
| 0.94 kΩ | -0.04569 |
| 1.88 kΩ | 0.2921 |
| 3.29 kΩ | 0.5231 |
| 4.7 kΩ | 0.6405 |
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<p><a href="https://vbatpower.com/formulas/reflection-coefficient/">Reflection Coefficient</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Reflection Coefficient?
Use Γ = (Z_L − Z₀) / (Z_L + Z₀). With Load Impedance 0.47 kΩ, Characteristic Impedance 1.03 kΩ, Reflection Coeff. works out to -0.3733.
What is the formula for Reflection Coefficient?
The formula is Γ = (Z_L − Z₀) / (Z_L + Z₀). The reflection coefficient Γ (gamma) quantifies the fraction of an incident wave reflected at an impedance discontinuity.
How do you find Load Impedance when you know the other values?
Rearrange for Load Impedance: with Reflection Coeff. 0.025, Characteristic Impedance 2.2 Ω, Load Impedance is 2.313 Ω.
How do you find Characteristic Impedance when you know the other values?
Rearrange for Characteristic Impedance: with Reflection Coeff. 0.025, Load Impedance 1 Ω, Characteristic Impedance is 0.9512 Ω.
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