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I've been using xnec2c to model antenna characteristics in Linux and the latest version is able to create a CSV by frequency of SWR, Zr/Zi, dB gain, and other metrics.

I was thinking it would be neat to convert the CSV to a 1- or 2-port touchstone format (.s1p or .s2p) and import it into my favorite RF software as a circuit component to see the whole signal behavior for an amplifier we are modeling including final output through the antenna. (This is a STEM project with my son.)

Certainly the CSV has enough information to provide a 1-port network with return loss alone (.s1p), but could it make sense to model a 2-port network (.s2p) from the CSV data?

The first two S-parameters make sense to me:

  • S11: return loss
  • S21: antenna gain in the direction we care about

But what about the other two?

  • S12: The effect of the air (port2) on the feedpoint (port1):
    • is it the same as S21?
    • is an antenna considered a passive network?
  • S22: I'm not sure how to consider the reflection of inbound signal bouncing off the antenna back into the air. Could this the same as S11?

What would be a meaningful way to represent S12 and S22?

Other considerations?

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2 Answers 2

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  • S12: The effect of the air (port2) on the feedpoint (port1):
    • is it the same as S21?
    • is an antenna considered a passive network?

Yes, an antenna is considered a passive (and lossy) network, and it's reciprocal. Be very sure you take mental note of the fact that the reference impedances on both ports are different!

S22: I'm not sure how to consider the reflection of inbound signal bouncing off the antenna back into the air. Could this the same as S11?

Not only back into the air, back into the same preferred direction (according to your definition up there - one could have defined port 2 as the total radiation in all directions, instead).

It's probably not going to be the same. The antenna can, for example, exhibit a different mismatch to the transmission line impedance, and to free space impedance.

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  • \$\begingroup\$ Interesting. Related questions: (1) Would port2 have an impedance of freespace (376.73 ohms)? (2) Is there a way to derive S22 and S12 from S11 and S21 even if we have to make some assumptions? (3) You mentioned that an antenna is considered lossy, but where: is the loss in the antenna material (copper in this case) or somewhere else? \$\endgroup\$
    – KJ7LNW
    Oct 8, 2021 at 20:36
  • \$\begingroup\$ (1) well, the "transmission line" you imagine being attached to that port has freespace impedance! (2) S12=S21 in reciprocal devices, other things are, as far as I can see, impossible to derive, (3) yes! (it's lossy in the material, but it's also lossy in that it might radiate in directions you don't want) \$\endgroup\$ Oct 8, 2021 at 21:01
  • \$\begingroup\$ Since it sounds like the only thing we can't assume is S22. Assuming we don't care about the S22 measurement, what side effects might there be during simulation if I made S22=S11, or perhaps made S22 very small like =-999 dB ? \$\endgroup\$
    – KJ7LNW
    Oct 8, 2021 at 21:14
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What you are trying to do is somewhat misguided. Just because free space has an 'impedance' doesn't mean that it is a suitable port for a scattering matrix. Ports for a scattering matrix have well defined incident and reflected waves (think coax cable, waveguide, or an idealised circuit theory port of two wires), there is no single wave that you can use to represent free space. You have to talk about some propagating wave. As far as the suggestion that you could define port 2 as the total radiation in all directions, there is no single mode that propagates isotropically that is a solution to Maxwells equations (that I'm aware of).

That said, there has been a lot of work done around the scattering matrix representation of antennas, but the free-space 'ports' are an infinite-dimensional set of radiating modes. This sounds like a bit more than a STEM project, but if you are interested, read Dicke's work in the MIT Radiation Series classic:

MIT-Radiation-Lab-Series-V8-principles-of-microwave-circuits.pdf

starting on p317.

This type of work is useful for the military, for example, who would like their radio antennas not to reflect/scatter enemy radar. It is a fundamental problem, to be able to couple to a radiating mode for transmission/reception, but to minimize interaction with a radar beam.

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  • \$\begingroup\$ Wow, what an amazing reference. Page 333 (section 9.4) says "It can be easily verified that the scattered power is always equal to the absorbed power, independently of the mode of excitation." Does this mean that S12 == S22? If so, that is strange because I sort of expected S12 to equal S21. \$\endgroup\$
    – KJ7LNW
    Oct 9, 2021 at 22:37
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    \$\begingroup\$ You have to be careful, it is difficult to apply some of these theoretical concepts to unrestricted practical situations. Your quotation applies to minimum scattering antennas, which, to my understanding, is not most practical antennas. It is a statement about conservation of power, so you can't say S12 = S22, but simply that scattering matrix is unitary. It is also unlikely that if an antenna radiates to, say, a dipole mode, that you will excite it with a dipole mode - more likely a plane wave. \$\endgroup\$
    – Tesla23
    Oct 11, 2021 at 1:57

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