# Impedance mismatch vs Signal attenuation

I'm currently designing a 50Ω grounded coplanar waveguide (GCPW) which connects an antenna to an LTE modem. My question is: does there exist a standard graph/chart that attempts to generalise impedance mismatch against signal attenuation? Essentially, I'd like to be able to predict the impact of small impedance mismatches on signal strength.

Thanks

The impedance mismatch doesn't cause actual loss, it just makes some of the power reflect away from the load. You are interested in a parameter called "reflection loss" that can be calculated. $$\\Gamma\$$ is the reflection coefficient that tells us how much field (current or voltage) is reflected.

$$\Gamma = (Z_l-Z_0)/(Z_l+Z_0)$$

$$\|\Gamma|^2\$$ is the amount of power reflected. $$\1-|\Gamma|^2\$$ is the rest, i.e., amount of power lost due to reflection. From that, you can calculate the amount of loss due to reflection in dB:

$$L_{refl} = -10 \times log_{10}(1-|\Gamma|^2)$$

I assumed that the $$\Z_l\$$ is real and plotted the reflection loss with Python for that special case. For numbers with a complex load you can use the equations above, or Smith chart as suggested by @The Photon.

If the transmission line is lossy, the high VSWR can cause extra loss, as the power loss in a transmission line is proportional to the square of the current.

• I think I made a mistake, the dB equation should have 10 instead of 20 (fixed above) since the parameter is already a power quantity. – user24368 Sep 30 at 16:54

Impedance mismatch doesn't cause attenuation per se, it causes reflection. Whether the reflection reduces the signal reaching the load depends on how it interferes with reflections from other mismatches or components in the system.

The relationship between impedance mismatch and reflection can be visualized on a Smith chart.