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Does anyone know of any impedance matching techniques to match at two different frequencies? Where the impedance at both desired frequencies are different (both the real and imaginary components)?

Most of the papers regarding dual impedance matching assume that the impedance is constant across all frequencies.

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    \$\begingroup\$ You asked a very similar question 2 days ago. Generally we'd rather you improve the existing question rather than post a new one. For example, you could provide more information about the actual problem you're trying to solve. \$\endgroup\$ – The Photon Oct 18 '18 at 1:18
  • \$\begingroup\$ I don't actually think its possible to be any more specific. \$\endgroup\$ – user367640 Oct 18 '18 at 3:12
  • \$\begingroup\$ constant across all frequencies makes it too broad to post an answer less than 1,000 pages long. Narrow frequencies down to what you need and it will make things easier for both of us. Infinities are tough to work with. \$\endgroup\$ – user105652 Oct 18 '18 at 3:51
  • \$\begingroup\$ Of course you can be more specific. What is the load? What frequencies? How close do you need to match? What kind of transmission line? Etc. \$\endgroup\$ – The Photon Oct 18 '18 at 4:17
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I think the confusion may be that usually when you have two bands RF engineers gravitate to 'diplexer' and there are a lot more questions to be answered, such as passband width, stop band attenuation, maximum acceptable insertion loss, transition band, etc.

With that said, there are several resources available on the web to get you started. You mentioned you need to fabricate one, but didn't mention your budget, so I'll approach it several ways.

The first is the old fashioned way, by using a Smith Chart, a decent intro is here: http://www.antenna-theory.com/tutorial/smith/smithchartC.php pros: Its' free, relatively easy, if a bit tedious. cons: The optimization techniques are limited in terms of bandwidth. Did I say tedious?

The second is a computer-assisted matching and there is a plethora of software packages (from free to Rolls Royce pricing).

pros: much easier than the manual technique, various data import options, various matching optimization algorithms and options (especially on the $$$ ones). There are some free or low priced packages out there such as: https://imnlab.wordpress.com/ http://www.iowahills.com/9SmithChartPage.html and more, I have no horse in this race BTW (as a disclaimer).
You can literally google "RF impedance matching software" and they pop out by the dozen, you may want to check reviews or send them an email to see if one would meet your specific tuning requirements.

cons:can be pricey, optimization controls can be limited for the cheaper programs, unlike the $$$ (Genesys eg).

But if you're not in the RF business where you're not trying to squeeze that last .02dB to beat the competition that may be enough.

There is a point of diminishing returns once the matching network becomes large, in that you're losing more signal than the matching network is allowing to pass (due to parasitic losses).

As a historical reference: https://ethw.org/History_of_Broadband_Impedance_Matching

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