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I have read at numerous places that S-parameters are used for analyzing systems which deal with high frequency. But why only high frequency? From what I have read, I have understood the following about S-parameters:

When a system is considered a box, then the relationship between the currents and voltages from its ports combined with the impedance at each port result in S-parameters.

How does frequency come into picture here?

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  • \$\begingroup\$ It does not. May it be that you are thinking of the Laplace transform? I don't think so anyway... \$\endgroup\$ – Vladimir Cravero Jun 14 '14 at 13:14
  • \$\begingroup\$ They are not limited to RF. After working on software for my company's network analyser, I then, as a hobby project, developed an audio network analyser using my PC sound card, working with S-parameters, just because I could, which worked just fine, and was more accurate (because of the more general calibration that S-parameters affords) than conventional low frequency component analysers. They work at DC as well, if you like cracking your nuts with sledgehammers. \$\endgroup\$ – Neil_UK 2 days ago
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S-parameters can be used at any range of frequencies that's the first point. The second point is understanding what a simple matrix of s parameters represents because two of the parameters are reflection coefficients and although they are of interest (generalism alert!) at any frequency, they tend to be ignored (because they don't offer any significant benefit) at (say) audio frequencies. The reason is because in audio, outputs tend to be low impedance whilst inputs tend to be high impedance. This kind of makes s-parameters to unwieldy for any circuit analysis other than when matched impedances are used. That leaves RF generally.

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  • \$\begingroup\$ Thanks..your answer led me to find this link. It explains clearly about S parameters and the real world significance. \$\endgroup\$ – Curious Jun 14 '14 at 15:57
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Frequency comes into play simply because the input and output impedances are a function of changing frequency. An active device such as a small signal transistor may exhibit an input impedance of 4 -j25 ohms at 100 MHz while at 200 MHz the resistive part of the impedance drops and the reactance climbs even higher. The device with an input impedance of 4 -j25 ohms at 100 MHz may exhibit an impedance of 2 -j150 ohms at 200 MHz. Just as the input impedance will vary with changing frequency so does the device's output impedance. Scattering parameters came into vogue to replace H, X, Y, and Z parameters simply because the Scattering matrix was referenced to a resistance (normally 50 ohms but may be other values such as 75 which is popular with the CATV industry). H, X, Y, and Z parameters were measured using a short or open on the port opposite of the one being characterized. Once you get to a few hundred MHz the shorts and opens start to exhibit considerable reactance which makes reliable measurements difficult as you go higher in frequency. Another problem with using shorts and opens is many active devices will take off and oscillate when terminated with an open or short. Test equipment which is used to characterize active devices can get all confused when a spurious signal appears at its receive port. Sorry for the length of this but there was method in the madness of S Parameter development and it is not always obvious why.

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  • \$\begingroup\$ You make an excellent point about shorts or opens upsetting many active devices. It's a pity your one paragraph wall of text is difficult to read. Maybe you'd add a few paragraph breaks at judicious points. \$\endgroup\$ – Neil_UK 2 days ago

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