Return Loss to Mismatch Loss Calculator

Both return loss and mismatch loss are measures of discontinuity in a Radio Frequency (RF) circuit. In this post we provide a tool to convert from one to the other. We also explain the similarities and differences between the two.

Background

If Pi is the incident power and Pr is the reflected power, the return loss is given by

RL = 10*Log₁₀(Pi/Pr)

As the reflected power increases, the value of return loss (RL) decreases. Conversely when Pr decreases, the ratio between the input signal and the return signal is higher.

The reflection coefficient Γ is Vr/Vi, where Vr and Vi are the voltages of the reflected and incident waves, respectively.

Therefore, Γ² = 1/(Vi/Vr)² and substituting this in the equation for RL gives

Return Loss (dB) = -20*Log₁₀(|Γ|)

From the above equation, |Γ| = 10^(-RL/20)

and the Mismatch Loss is given by ML (dB) = -10*Log₁₀(1-|Γ|²)

What’s the difference between Mismatch Loss and Return Loss?

What is Mismatch Loss?

Mismatch loss (ML) is a measure of the reduction in power due to impedance mismatch. Impedance mismatches can occur at various points in an RF system, such as at the input to an amplifier, antenna, mixer or transmission lines. To minimize mismatch loss, it is important to ensure that all components in the system have the correct impedance and are properly matched. This can be achieved by using impedance matching techniques, such as adding attenuators or matching circuits.

Minimizing mismatch loss is important as it can improve the performance of the system, reduce noise figure, and ensure efficient power transfer.

What is Return Loss?

Return loss (RL) is a measure of the amount of signal reflection that occurs in a system due to an impedance mismatch. It is typically expressed in decibels (dB). When a signal is sent through a transmission line, a portion of it gets reflected back towards the signal source due to impedance mismatches or discontinuities in the line. The reflection coefficient, Γ, which is the ratio of the amplitude of the reflected wave to the amplitude of the incident wave, is used to calculate the return loss. A higher return loss value indicates a lower amount of signal reflection and better impedance matching at a transition in an RF circuit or subsystem.

While both ML and RL are dependent on the incident and reflected power, they represent two different things.

Differences

Mismatch loss is used to compute the effective forward power, while return loss enables a calculation of the reflected power. As the return loss increases ⬆, the mismatch loss decreases ⬇ and vice versa.

In general, an RF circuit design goal is to maximize the numerical value of the return loss while minimizing the mismatch loss.

Similarities

Both ML and RL are positive quantities (greater than 0) and expressed in dB. As well they are both dependent on the reflection coefficient, Γ.

Example Calculation

For a return loss of 10 dB, the mismatch loss is 0.46 dB. In this situation, 10% of the incident power is reflected back to the source while the balance of 90% is transmitted forward.

For a RL of 1 dB, the mismatch loss is increased to 6.87 dB. Here almost 80% of the power is reflected while only 20% is transmitted forward.

0 dB Return loss implies there is either a short or an open circuit and all the power is reflected back.