### Section 4: Voltage versus Power Gain

S-Parameters are ratios of voltage waves, and describe reflections
and transmission of voltages. We can define these ratios of voltage
waves as gains and losses, in the same way we described voltage and
power gain in Lesson 1. The S_{21} parameter is really a voltage gain. The S_{11} parameter relates to the voltage wave that returns back to the source, rather than going on to the output. The S_{11}
is often called the return loss, because it relates to energy that
returns to the source, instead of going to the load- as far as the load
is concerned, that energy was lost.

Because power is related to voltage, one can describe the power gain of a circuit as a function of the S-Parameters. People often use the following equation:

**Optional Note on Power Gains:**

Equation 2.4.1 is not always correct, because it assumes that all of the ports are terminated in the same impedance. Similarly, people use 10*log10 for power gain, and 20*log10 for voltage gain. Often, we deal in systems that are all 50Ώ inputs and outputs. The general equation when the port impedances are not equal (but are real) for the power gain relating the S-Parameters to gain is:

Note that all we have done is preserved the power equation P=V^2 / R. As a side note, if Mason is run with different power impedances, it will adjust the S-Parameters accordingly.

**Main
Point**

A device can be said to have a gain (or a
loss) associated with the voltage waves that go through it. The
S-Parameters are the gain of the voltage waves, either going through the
system (such as an S_{21}) or reflecting off of the device back to the source (such as the S_{11}). When calculating the gain (or loss) of
a circuit, take care to account for the actual impedances of the
system.