This tool provides an estimate of the Return Loss [1] of a cascade of two RF subsystems.

**Enter the Return Loss (RL) in dB of each element in the RF chain.**

**Formula**

The reflection coefficient for each element is

**Γ = 10 ^{-(RL/20)}**

The cascaded Return Loss is

**RL = −20*Log _{10}(√(Γ_{1}^{2} + Γ_{2}^{2})**

*Reflection coefficient can be calculated from the source and load impedance.*

**Background**

**Return loss** is a measure of the amount of signal loss that occurs due to reflections in a system. It is expressed in deciBels (dB) and represents the ratio of the reflected signal to the incident signal.

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

**RL = 10*Log _{10}(Pi/Pr)**

*Since Pr is always less than Pi, the return loss is always a positive number. *

Practically speaking, when a signal encounters an impedance mismatch or a fault in a transmission line, a portion of the signal is reflected back towards the source. This reflected signal is measured and compared to the incident signal to determine the return loss.

A high value of return loss indicates that a majority of the signal is being absorbed or transmitted through the system, while a low return loss indicates that a significant portion of the signal is being reflected back towards the source.

Mathematically, as the value of **Pr** increases relative to **Pi**, the numerical value of RL decreases.

**At the limit, when all of the power is reflected back**, **Pr = Pi, and RL = 0 dB**

Return loss results are crucial in assessing the quality and performance of a system, particularly in applications where signal integrity is essential, such as in telecommunications or RF systems. By analyzing return loss, engineers can identify and troubleshoot issues such as faulty connectors, impedance mismatches, or other problems that may lead to signal degradation or loss.

**Cascaded return loss takes the effect of two subsystems that are placed back-to-back. It computes the combined Return loss from the input reflection coefficient for each element in the cascade. **

Key assumptions are

- there is no gain, attenuation or impedance transformation in either system [2]
- there is no reflection at the output port (2) of either system

**Example Calculation**

Consider two subsystems. The first one has a return loss of 10 dB while the second has a return loss of 15 dB. The cascaded return loss for the combination is 8.8 dB. The result is worse than it is for either system. *This is because the input signal encounters two reflections – at the input to each system. *

Note that swapping the order of the systems, i.e. RL=15 dB followed by RL=10 dB does not improve the result.

**Notes**

- Return loss can be converted to mismatch loss and the calculator also gives an intuitive sense of the impact by providing the forward and reflected power

**Related **Posts

- How to improve the Return Loss of an amplifier
- Convert S11 to return loss
- Compute Voltage Standing Wave Ratio (VSWR) from Return Loss

**References**

[2] Stack Exchange discussion on How to calculate Cascaded Return Loss and related assumptions