To calculate the mismatch loss (\(ML\)):
\[ ML = 10 \times \log_{10}\left(1 - \left(\frac{VSWR - 1}{VSWR + 1}\right)^2\right) \]
Where:
Mismatch loss occurs when there is an impedance mismatch in the transmission line, which leads to a portion of the transmitted power being reflected back towards the source. This loss is expressed in decibels (dB) and can be calculated using the voltage standing wave ratio (VSWR), which is a measure of how well the transmission line is matched to its load.
Let's assume the following value:
Using the formula:
\[ ML = 10 \times \log_{10}\left(1 - \left(\frac{2 - 1}{2 + 1}\right)^2\right) = 10 \times \log_{10}(1 - 0.1111) = 10 \times \log_{10}(0.8889) = -0.51 \text{ dB} \]
The mismatch loss is -0.51 dB.
Let's assume the following value:
Using the formula:
\[ ML = 10 \times \log_{10}\left(1 - \left(\frac{1.5 - 1}{1.5 + 1}\right)^2\right) = 10 \times \log_{10}(1 - 0.04) = 10 \times \log_{10}(0.96) = -0.18 \text{ dB} \]
The mismatch loss is -0.18 dB.