Scattering parameters, often referred to as S-Parameters, are used to characterize the behavior of reflected and transmitted signals in the frequency domain, including both their amplitude and phase. S-Parameters are represented as a complex matrix. We can think of the internal workings of a circuit as a black box, disregarding the internal circuit elements, and use S-Parameters to measure its port characteristics.

## Detailed Explanation of S-Parameters

The naming convention for S-Parameters involves the first number representing the measurement port, and the second number representing the reference port. For example, S21 represents the signal at port 2 when excited relative to port 1. The form of the S-Parameter wave can be power, voltage, or current.

As shown in the image above, S11 and S22 represent the reflection coefficients (reflection/input), while S21 and S12 represent the transmission coefficients (transmission/input).

### S11

S11 refers to the reflection signal at port 1 concerning the incident signal at port 1. It is defined as $$S11=\frac{S_{Reflection}}{S_{Incident}}$$.

### S21

S21 represents the transmission signal at port 2 concerning the incident signal at port 1. It is defined as $$S21=\frac{S_{Transmission}}{S_{Incident}}$$.

### S12

S12 indicates the transmission signal at port 1 concerning the incident signal at port 2. It is defined as $$S12=\frac{S_{Transmission}}{S_{Incident}}$$.

### S22

S22 refers to the reflection signal at port 2 concerning the incident signal at port 2. It is defined as $$S22=\frac{S_{Reflection}}{S_{Incident}}$$.

## References and Acknowledgments

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