S-parameters
/ ess-pa-RAM-eh-ters /
At low frequencies we describe a two-port circuit (an amplifier, a filter) by voltages and currents at its terminals. At high frequencies you cannot reliably measure those, because where exactly is the voltage on a transmission line that is a wavelength long? So RF engineers switch to a language built from waves instead: how much of a wave sent into a port comes back, and how much comes out the other port. Those wave ratios are the scattering parameters, or S-parameters. Think of shining a flashlight at a window: some light reflects back, some passes through, and S-parameters are exactly those reflect and pass-through fractions, but for electrical waves.
For a two-port there are four S-parameters, written with two subscripts (to, from). S11 is the input reflection: of the wave you send into port 1, how much bounces back, this is the reflection coefficient at the input and relates straight to VSWR. S21 is the forward transmission: how much of the wave into port 1 comes out of port 2, which for an amplifier is its gain. S12 is reverse transmission (how much leaks backward, ideally tiny), and S22 is the output reflection. Each is a ratio of wave amplitudes, usually complex (magnitude and phase) and usually quoted in decibels: an amplifier with S21 = +15 dB has a gain of about 32 times in power, and a well-matched input might have S11 = -20 dB, meaning only 1 percent of the wave reflects.
S-parameters matter because they are what you can actually measure at RF, with an instrument called a vector network analyser, and what every RF datasheet lists. They are defined against a reference impedance (almost always 50 ohms), they plot naturally on a Smith chart, and they let you cascade and design real systems. Honest framing: S-parameters are not a different physics from voltage and current, they are the same circuit described in the wave language that high frequencies force on us, and they are only valid for the reference impedance and, for small-signal versions, only while the device stays linear.
An LNA datasheet lists S21 = +18 dB (gain about 63 times in power), S11 = -15 dB (input reflects about 3 percent, a decent match), and S12 = -30 dB (very little leaks backward, so it is well isolated). Those three numbers summarise its RF behaviour at a stated frequency.
S21 is gain, S11 is input match, S12 is reverse isolation, all measured as wave ratios.
S-parameters are always referenced to a specific impedance (usually 50 ohms) and a specific frequency, and small-signal S-parameters assume the device stays linear. Quote them out of context and they mislead.