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What exactly is the scattering matrix in a microwave amplifier. I tried to deduce from lectures what it is used for in a microwave amplifier, but all I found were the formulas corresponding to the calculation of such matrices. Does anyone have any specific information on what this matrix is and why we need it for the topic of microwave amplifiers?

MagicMan
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  • Forget about microwave amplifiers, what have you gathered the scattering matrix (also known as S-parameters) are in general? – Shamtam Feb 15 '21 at 00:29
  • Thank you for comment. I know that amplifiers for small signals can be described by a scattering matrix. The scattering matrix is defined as the relationship between the waves reflected at each port and the waves incident on each port. I also know that when all the port are matched then the reflection coefficients are zero. This is what I have gathered from the lectures + of course the formulas (S11, S12, S21 and S22) – MagicMan Feb 15 '21 at 00:36
  • Are you familiar with the concept of a "black box?" – Shamtam Feb 15 '21 at 00:43
  • No, I never heard of it – MagicMan Feb 15 '21 at 00:43
  • Wikipedia has a fairly straightforward (well, as straightforward as this topic can be) explanation of S parameters. You might want to look that over first, then come back with specific questions. – SteveSh Feb 15 '21 at 00:51
  • I know, I saw a description of these parameters during the lecture as well, but I didn't find an answer to what exactly the scattering matrix itself is and why it is used specifically when describing microwave amplifiers.. – MagicMan Feb 15 '21 at 00:58
  • One of the usefulness of S parameters is that you can chain together multiple devices using their respective scattering matrices and come with the overall end-to-end S matrix for the entire system. – SteveSh Feb 15 '21 at 02:45
  • Obligatory Microwaves101: https://www.microwaves101.com/encyclopedias/s-parameters – Shamtam Feb 15 '21 at 02:49

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Scattering parameters (S parameters) are a way of describing the behavior of a multi-ported circuit at a single frequency. In general, S parameters will tell you what happens when RF energy in the form of a sine wave is injected into any combination of ports - how much is reflected and with what phase angle, and how much makes it through to each of the other ports. It's really used for just about every RF component (filters, splitters/combiners, etc.), not just amplifiers.

You can use scattering parameters to reason about device performance (gain, isolation, etc.) and what happens when multiple devices are connected together.

alex.forencich
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