2022-09-16 15:22 Status: Tags: # S-parameters ## Introduction In RF design, Z,Y,H and other parameters can't be used due to not being able to conduct short/open circuit tests. [^1] >The S-matrix for an N-port contains $N^2$ coefficients (S-parameters), each one representing a possible input-output path. Response due to signal ($S_{21}$ is response at port 2 due to port 1). > The input and output reflection coefficients of networks (such as S11 and S22) can be plotted on the Smith chart. Transmission coefficients (S21 and S12) are usually not plotted on the Smith chart. Signal at a port can be thought of as superposition of 2 waves travelling in opposite directions. $a_i$ is the incident wave to port i and $b_j$ is the wave reflected from port j. Magnitude of these incident and reflection variables can be thought of as 'voltage-like' (*normalised using a reference impedance $Z_0$*). This means that **the square of these magnitudes are equal to the power level of the waves**. If each port is terminated in $Z_0$:   Easy to remember! S = b/a, then just add the subscripts! ## Measurements using a Network Analyser Inject a signal into a port, see the resulting signal level at another port. Since the s-parameters are complex, it is good to use a [Vector Network Analyser](Vector%20Network%20Analyser.md) (the signals can be called vectors). Magnitudes can be presented as *linear* or *dB*. Since they are 'voltage' ratios, $S_{ij}\ (dB)=20\log_{10}|S_{ij}|$ Phase almost always presented in degrees. ## Other S-Parameters There are other S-parameters to worry about, however **small-signal s-parameters** is mostly used. Signals only have linear effects on the network, so there are no non-linearities to model. [^2] ## S11 for Reflection Analysis  A [Vector Network Analyser](Vector%20Network%20Analyser.md) would produce the above plot. This antenna would be best used from 2-3GHz since the reflection is very low. S11 is a measure of the power reflected. [^5]   S11 is the reflection coefficient. No differences. Plotting it on the smith chart lets us look at the matching characteristics of the network. [^4]  [^3] --- # References [^1]: [What are S-Parameters? - everything RF](https://www.everythingrf.com/community/what-are-s-parameters) [^2]: [Microwaves101 | S-parameters](https://www.microwaves101.com/encyclopedias/s-parameters) [^3]: [filter - Interpreting scattering parameters on a Smith chart. - Electrical Engineering Stack Exchange](https://electronics.stackexchange.com/questions/410122/interpreting-scattering-parameters-on-a-smith-chart) [^4]: [Decoding the Smith Chart for Signal Integrity Engineers | 2017-03-29 | Signal Integrity Journal](https://www.signalintegrityjournal.com/blogs/4-eric-bogatin-signal-integrity-journal-technical-editor/post/383-decoding-the-smith-chart-for-signal-integrity-engineers#:~:text=On%20a%20polar%20plot%2C%20S11,circle%20in%20the%20clockwise%20direction.) [^5]: [S-Parameters for Antennas (S11, S12, ...) (antenna-theory.com)](https://www.antenna-theory.com/definitions/sparameters.php)