# S11 to Reflected Power Calculator

Enter S11 the input reflection coefficient, either as a linear number or dB. The tool will calculate the reflected power as a percentage of the incident power.

## Formula

Γ = S11 (linear)

or

Γ = 10(S11dB/20)

Reflected Power (%) = 100*(|Γ|2)

where Γ is the reflection coefficient and 0 < Γ < 1

## Background

### What is S11?

For a two port network, S11 is the input reflection coefficient (also known as Γ or Gamma) with a value between 0 and 1.

S11 = b1/a1 (when port 2 is terminated – usually in 50 Ω) where a1 is the incident power on port 1 and b1 is the power reflected from port 1. This is shown in the picture below.

## Formula

if S11 is expressed as a linear quantity,

S11dB = 20*Log10(S11linear)

On the other hand, if S11 is expressed in dB

S11linear = 10(S11dB/20)

💡 S11 when expressed in dB is always a negative number

### What is Reflected Power?

This refers to the power that’s reflected back into the source due to an impedance mismatch*. Ideally all the power is transmitted forward and none of it is reflected back. However, in practical systems, a certain percentage of the input power is reflected.

To minimize this reflection in a 50 ohm system for example, it’s important that the input and output impedance of every component is either 50 Ω or matched to it.

*To calculate the mismatch loss from S11

### Can S11 be converted to S21?

No it cannot. S21 represents the forward transmission.

Referring to the picture above, S21 = b2/a1 which has no relation to S11= b1/a1.

## Example Calculation

If S11 is 0.2, 4% of the incident power is reflected.

S11 varies between 0 and 1.

• If S11 is 0, 0% of the power is reflected.
• If S11 is 1, 100% of the incident power is reflected.