Reflection Coefficient and Return Loss
When a signal meets a mismatch, part of it is reflected. Four numbers describe how much: the reflection coefficient (Γ, or ρ — rho), which is the underlying physical quantity; return loss, the same information in decibels and the number most network analyzers display (as S11); the voltage standing wave ratio (VSWR), which datasheets for cables, connectors and RF modules often quote; and the percentage of power reflected, which is what all of these mean for the signal you are trying to deliver.
These four quantities all describe the same physical situation from different angles. Being able to convert fluently between them is a core skill for reading datasheets, choosing cables and connectors, using a network analyzer or TDR, and checking a termination, and the four calculators in this lesson make it easy.
When a transmission line meets a mismatched load, the reflection coefficient Γ determines what fraction of the incident voltage is reflected. VSWR, return loss, and reflected power percentage are all derived from |Γ|.
View LargerThe Reflection Coefficient
The voltage reflection coefficient Γ (gamma) is the ratio of the reflected voltage wave amplitude to the incident voltage wave amplitude at the load:
- Γ = voltage reflection coefficient (complex in general)
- ZL = load impedance (ohms, may be complex)
- Z₀ = characteristic impedance of the line (real for ideal line)
For the VSWR and power calculations that follow, we use the magnitude |Γ|, also written as ρ (rho). For a purely resistive load:
- If ZL > Z₀: Γ is positive real, 0 ≤ Γ ≤ 1
- If ZL < Z₀: Γ is negative real, −1 ≤ Γ < 0
- If ZL = Z₀: Γ = 0 (perfect match)
- If ZL = 0 (short): Γ = −1
- If ZL = ∞ (open): Γ = +1
- For a complex load: Γ is complex, with |Γ| between 0 and 1
The magnitude |Γ| (always 0 ≤ |Γ| ≤ 1) is what determines VSWR, return loss, and reflected power. The phase of Γ determines where along the line the voltage maxima and minima occur but does not affect the VSWR value.
VSWR from Reflection Coefficient
VSWR is related to |Γ| by two equivalent formulas:
and the inverse:
|Γ| = (VSWR − 1) / (VSWR + 1)A 50-ohm line feeds a 150-ohm resistive load.
Γ = (150 − 50) / (150 + 50) = 100/200 = 0.500
VSWR = (1 + 0.500) / (1 − 0.500) = 1.500 / 0.500 = 3.0:1
Check via inverse: |Γ| = (3.0 − 1) / (3.0 + 1) = 2/4 = 0.500 ✓
Calculator 1: VSWR ↔ Reflection Coefficient
VSWR and Reflection Coefficient Converter
Enter either VSWR (≥ 1) or reflection coefficient magnitude |Γ| (0 to 1) to convert between them.
Return Loss
Return loss is the ratio of the reflected power to the incident power, expressed in decibels. A high return loss is good — it means very little power is being reflected. A low return loss is bad — it means a large fraction is being reflected.
Expressed in terms of VSWR:
Return loss (dB) = 20 × log₁₀((VSWR + 1) / (VSWR − 1))And the inverse:
VSWR = (10RL/20 + 1) / (10RL/20 − 1)- A matched load (VSWR = 1:1) has infinite return loss
- Return loss 20 dB = |Γ| = 0.10, VSWR = 1.22:1
- Return loss 14 dB = |Γ| = 0.20, VSWR = 1.50:1
- Return loss 9.5 dB = |Γ| = 0.333, VSWR = 2.00:1
- Return loss 6 dB = |Γ| = 0.501, VSWR = 3.01:1
Return loss is the preferred measure in professional RF and high-speed digital work. Vector network analyzers (VNAs) typically display S11 — the reflection measured at port 1 — in dB. S11 in dB is the negative of the return loss, so a device with 10 dB return loss displays S11 = −10 dB. High-speed interface standards specify return loss too: a USB or Ethernet connector and cable assembly must keep its return loss above a set limit across the frequency range the signal uses.
Calculator 2: Return Loss from VSWR
Return Loss and VSWR Converter
Enter either VSWR or return loss (dB) to convert between them.
Reflected Power
The fraction of the incident power that is reflected from a mismatched load equals the square of the magnitude of the reflection coefficient:
As a percentage:
% reflected = |Γ|² × 100 = ((VSWR − 1) / (VSWR + 1))² × 100Power delivered to load:
% delivered = 100 − % reflected = (1 − |Γ|²) × 100VSWR 1.5:1 → |Γ| = (1.5-1)/(1.5+1) = 0.5/2.5 = 0.200 → reflected = 0.2² = 4.0% → delivered = 96%
VSWR 2:1 → |Γ| = (2-1)/(2+1) = 1/3 = 0.333 → reflected = 0.333² = 11.1% → delivered = 88.9%
VSWR 3:1 → |Γ| = (3-1)/(3+1) = 2/4 = 0.500 → reflected = 0.5² = 25.0% → delivered = 75%
VSWR 5:1 → |Γ| = (5-1)/(5+1) = 4/6 = 0.667 → reflected = 0.667² = 44.4% → delivered = 55.6%
VSWR 10:1 → |Γ| = 9/11 = 0.818 → reflected = 0.818² = 66.9% → delivered = 33.1%
An important nuance: this reflected power calculation assumes the source simply absorbs any returning reflected power without re-reflecting it. A signal generator or an RF amplifier with a 50-ohm output impedance does approximately this. The reflected power returned to the source is not "lost" in the sense of disappearing — it becomes heat in the source's output stage — but it does mean that only the delivered percentage of the source's power actually reaches the load.
Calculator 3: Reflected Power from VSWR
Reflected Power Calculator
Enter VSWR and source power to calculate reflected power, delivered power, and all related values.
Calculator 4: VSWR from Load and Line Impedances
When you know the load impedance and the line characteristic impedance, you can calculate the VSWR directly. For a purely resistive load, the calculation is straightforward. For a complex load (ZL = R + jX), you need the magnitude of the reflection coefficient.
VSWR from Impedance Values
Enter the line characteristic impedance and the load impedance (with optional reactive component). The calculator returns the VSWR and reflection coefficient.
Quick Reference Table
This table allows quick lookup of all four related quantities for common VSWR values:
| VSWR | |Γ| (rho) | Return Loss (dB) | Reflected Power (%) | Delivered Power (%) |
|---|---|---|---|---|
| 1.0:1 | 0.000 | ∞ | 0.0% | 100.0% |
| 1.1:1 | 0.048 | 26.4 dB | 0.2% | 99.8% |
| 1.2:1 | 0.091 | 20.8 dB | 0.8% | 99.2% |
| 1.5:1 | 0.200 | 14.0 dB | 4.0% | 96.0% |
| 2.0:1 | 0.333 | 9.5 dB | 11.1% | 88.9% |
| 2.5:1 | 0.429 | 7.4 dB | 18.4% | 81.6% |
| 3.0:1 | 0.500 | 6.0 dB | 25.0% | 75.0% |
| 4.0:1 | 0.600 | 4.4 dB | 36.0% | 64.0% |
| 5.0:1 | 0.667 | 3.5 dB | 44.4% | 55.6% |
| 7.0:1 | 0.750 | 2.5 dB | 56.3% | 43.8% |
| 10.0:1 | 0.818 | 1.7 dB | 66.9% | 33.1% |
| ∞ | 1.000 | 0 dB | 100.0% | 0.0% |
Note the disproportionate nature of VSWR and reflected power: even a VSWR of 3:1, which many beginners consider "very bad," only reflects 25% of the incident power. A matched load receives 100% and a VSWR of 2:1 delivers 89% — the difference is only 11%. For power delivery, moderate mismatches cost surprisingly little. For signal integrity it is a different story: a reflection coefficient of 0.33 means a third of every edge comes back as a reflection, which on a fast digital line is more than enough to cause ringing and false triggering. That is why high-speed designs aim for return losses of 15–20 dB or better, not just a “reasonable” VSWR.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.