This tool computes the Mismatch Loss from Voltage Standing Wave Ratio (VSWR).
Background
Mismatch loss is usually specified in deciBels (dB) and represents the loss in power in an RF circuit due to an impedance mismatch. This typically happens at a transition.
A transition occurs in the following situations
- two cables are connected with an RF adapter
- a microwave cable feeds a radio module like a filter or amplifier.
- at the input to an antenna
If there is an impedance mismatch at a transition, some of the RF power is reflected back to the source, resulting in a loss of power.
Good RF design techniques will ensure a good match. Minimizing mismatch loss is important as it can improve the performance of the system, reduce noise figure, and ensure efficient power transfer.
However this is not easy in practice. The larger the frequency range of operation, the more challenging it is to ensure a good match.
Matching circuits are designed with capacitors and inductors. Although a quick way to match two circuits is with the use of an attenuator. In this post we demonstrate a technique to reduce the VSWR with the use of attenuation.
Practical Example of Impedance Mismatch
A 50 ohm cable might be connected to an antenna with 75 ohm input impedance. As the impedance is not the same, some of the input signal will be reflected and there will be a loss in the input signal to the antenna. As a result there will be a reduction in the radiated power from the antenna and loss of range.
The calculator on this page helps determine the loss and that can be factored into the design or RF link budget.
Formula
The reflection coefficient is calculated from the VSWR and used to compute the mismatch loss in dB as shown below.
Γ = (VSWR – 1)/(VSWR + 1)
Return Loss (dB) = -20*Log10(|Γ|)
Mismatch Loss (dB) = -10*Log10(1 – |Γ|2)
Reflected Power (%) = 100*(|Γ|2)
Transmitted Power (%) = 100*(1 – |Γ|2)
The calculator also provides the percentage of power that is both transmitted and reflected back to the source.
Example Calculation
VSWR (sometimes called SWR) has no units and can be determined using an SWR meter or from the data sheet of the RF module.
The picture below shows data for a band pass filter as a function of frequency (MHz).
The pass band of this filter is from 2200 MHz to 2400 MHz. For this range of frequencies, the VSWR values are close to 1.2 which is ideal. It’s smaller than 1.5 which represents a good match. Outside of this frequency range the value increases. At 300 kHz for example, the number is very large – 14895.30.
Let’s use some of these numbers in the calculator
For a VSWR of 1.2 at 2380 MHz, the mismatch loss is calculated to be 0.04 dB.
99.17% of the input power is transmitted forward, while 0.83% is reflected back into the source. This is expected behavior in the pass band of the filter where the match should be close to ideal.
As the VSWR increases, the quality of the match deteriorates and more power is reflected back.
For a VSWR of around 28 which occurs at 1800 MHz, the mismatch loss is calculated to be 8.76 dB.
In this case, 13.32% of the input power is transmitted forward, while a larger percent 86.68% is reflected back into the source. Ideally input signals in the stop band of the filter are completely rejected. However this is not possible in practice, as can be seen in this example.
Also ideally the VSWR continues to increase as the input frequency moves further away from the pass band. However that is not always the case practically. It can be seen in the above example where at 4 GHz the VSWR is 51 and at 6 GHz the value is lower at 30.
How to Measure Mismatch Loss
The easiest and most cost-effective way to do this is with an SWR meter (shown below).
This product is designed for use with CB radio and therefore the frequency range is limited to under 30 MHz.
Another tool to measure VSWR is a Vector Network Analyzer. The NanoVNA is a cost-effective tool that is used to measure S-parameters.
The difference between the SWR meter and the NanoVNA is the frequency range and power rating. So take that into consideration when picking the tool for your application.
| Hardware | Frequency Range | Max Power (W) | Max Power (dBm) |
|---|---|---|---|
| SWR Meter | 0 to 30 MHz | 100 W | 50 dBm |
| NanoVNA | 10 kHz to 1.5 GHz | 100 mW | 20 dBm |
The NanoVNA is not designed for high power applications.
Related Calculators
- Impedance Mismatch – use the impedance of the source and load to calculate the impedance mismatch.
- VSWR to S11 – use the standing wave ratio to compute the input reflection coefficient.
- VSWR to Return Loss – calculate the return loss in deciBel (dB)
References
[1] Wikipedia article on Mismatch Loss
[2] Wikipedia article on Standing Wave Ratio