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# THS4541: How to get the eq.1 in TIDA-00294?

Part Number: THS4541

Hi team,

How to get the eq.1 in TIDA-00294? Can you provide the detailed process? What's the target of this equation?

Thanks and best regards,
Charles Chen
Applications Engineer | LED Drivers

• Hi Charles,

yes, good question. Shouldn't be this the correct assumption?

(RS // RT) + Rg+ = Rg-

(RT // Rg+) = RS

with Av = RF / Rg-

" // " means parallel impedance.

I guess something important is missing in the appnote and in the datasheet. Has it to do with the dynamic input impedance of THS4541?

With the above assumption I get:

RT = SQRT ( (RF / Av x RS^2) / (RF / Av - 2 x RS) )

Kai

• In reply to kai klaas69:

Morning Charles,

Hardly anyone ever asks that - oddly enough. In the early FDA days there was a problem with resolving the R values to get both the matched input impedance and gain as the single to differential configuration has an active input impedance. This arises as the input CM voltages move with the input signal. Early solutions by NSM and ADI executed an iterative solution that does work. That seemed odd to me, so back around April 2013 I pounded out the closed form solution you are asking about and it also works very nicely. This solution starts by assuming you want to pick the Rf value for other reasons. However, the nice thing here is if you can let it be anything, solving the denominator for zero will eliminate the Rt element to ground at the input and give you the perfect active match solution for Rg and Rf - this is the lowest noise matched input solution that I also call the active balun.

Anyway, I don't send out the 4 page algebraic derivation anymore, but here is the 1st publication.

https://www.edn.com/wideband-matched-input-impedance-with-ultra-low-noise-using-the-active-match-capability-of-a-new-type-of-amplifier-part-1-of-2/

https://www.edn.com/wideband-matched-input-z-using-active-match-and-a-new-type-of-amplifier-part-two-of-two/

And then I did some videos on this as well that are still out there on the Renesas website. These are all about 4minutes so pretty quick. This is in fact a new op amp function oddly enough - I was pretty excited about it at the time.  You would think with all this public info ADI would migrate to using this equation in their FDA data sheets (like the new ADA4945). Not so for the citadel of NIH.

https://www.renesas.com/us/en/support/videos/isl55210-active-balun-eval-demo-1-video.html

https://www.renesas.com/us/en/support/videos/isl55210-active-balun-eval-demo-2-video.html

https://www.renesas.com/us/en/support/videos/isl55210-active-balun-eval-demo-3-video.html

https://www.renesas.com/us/en/support/videos/isl55210-active-balun-eval-demo-4-video.html

Michael Steffes

• In reply to Michael Steffes:

Hi Michael,

Thanks and best regards,
Charles Chen
Applications Engineer | LED Drivers

Hi Michael, hi Charles,

I found this in the www:

Kai

• In reply to kai klaas69:

Yes Kai, that is just an earlier version of what I did for EDN.

Here is one the national guys did showing the iterative approach

http://www.ti.com/lit/an/snoa948/snoa948.pdf

ADI also uses an iterative approach that is hiding behind the DiffAmp Calculator tool. One of the things I was doing validating the solution I had developed was to test it against the ADI reported R values, they match.

This app note tells you how to use the ADI tool (which is very nice) but not how they are executing the solutions. I of course have built an FDA design tool that does everything and more than the ADI tool - it is populated with the required parameters for all industrywide FDA's. ADI's most recent FDA is the ADA4945 - they describe their iterative approach on page 39. Kind of silly really to stick with that with the closed form solutions (there are no estimates in those equations, they are exact) available.

https://www.analog.com/media/en/technical-documentation/application-notes/AN-1404.pdf

And the TI guys are doing some more recent things - this one is pretty straightforward when you are coming from a low impedance op amp output and not trying to achieve a matched input impedance - that simplifies things considerably,