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
- Use the S11 to calculate the Voltage Standing Wave Ratio (VSWR)
- VSWR can be used to calculate mismatch loss
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.