NFC antenna tuning - measuring Rp

[Harvs]

I'm working on a integrating Mifare cards into a product at the moment and trying different antenna ideas (within the constraints of the product package.)

I've bought a miniVNA Tiny to do the tuning.  NXP are helpful enough to even have an appnote on how to do it using this particular piece of kit, so it's a bit of a brease.

However, one measurement required for their formulas that they skip over measuring in this appnote is the resistance at self resonance (Rp).  From their examples, it's in the region of a few k.

The miniVNA at the self resonance point of the coil only gives back noise in the resistance plot (totally useless noise, ranging from 0 to tens of k ohms).  From digging around google, it would seem the miniVNA isn't able to give decent measurements up in the kOhms as it's down in the noise floor of the unit.  So I'm guessing that's why NXP helpfully skipped over this measurement and just gave the output of their formula.

In practice, I don't think it's a big deal, as I've just substituted in some notional figures and got component values in the ballpark.  Then used the VNA to measure and adjust the component values to achieve the tuning desired of the complete impedance matching circuit.

However, can anyone provide guidance on how to take this measurement either using the miniVNA or a scope and sign gen?  I can't think of a good way to measure kohms @ 45MHz...

References
NXP app note - using miniVNA to do NFC antenna tuning.
http://www.nxp.com/documents/application_note/AN11535.pdf

NXP Antenna design guide (include excel sheet)
http://data.nxp.com/doc/published_files/1270733179751

[T3sl4co1l]

ESR might be easier?  You can also calculate ESR/EPR from Q, for a given equivalent circuit.

Usual process, as far as I know, is to use a matching network to go from nominal impedance (at the driver pins) to whatever the coil behaves as.

Matching networks are pretty easy to calculate:

Suppose you have a low impedance source, and you attach a series resonant (L-C) tank to it.  The tank will develop a high voltage.  Suppose you put a high impedance load on that "gain" node -- now the tank gets loaded down, and the voltage drops.  If you put on a nominal load, the voltage drops only nominally (ideally, by half -- it's a linear circuit, so power transfer theorem applies).  And then, presumably, you've achieved some sort of impedance matching, at least between the load and the output side of the tank.  Not necessarily at the input side of the tank.

As it happens, the LC values are easy to solve for.  The resonant impedance Zo = sqrt(L/C) must equal the geometric average of the two port impedances, i.e. sqrt(L/C) = sqrt(Rin * Rout).  Literally, the tank impedance is the same ratio above the lower impedance, as it is below the higher impedance.  The lower impedance gets the series branch (series L or C) and the higher impedance gets the parallel branch (C or L to GND).  Obviously, the resonant frequency must be characteristic, and the desired bandwidth will not be more than the loaded Q (which is also more or less equal to that impedance ratio, for obvious reasons).

This is called an "L match" circuit (actually more like capital Gamma, but it looks like an "L" if you turn it around right..).

There is a residual reactance at the feed point, because the inductor or capacitor is in series with the source, AND in resonance with the load and the opposite component.

The residual reactance can be left in (for MFC purposes, it's usually desired to have inductance at the driving pins, since they just drive it with square waves, as far as I know), or it can be canceled out with one more reactance.  This gets you a "Pi match" circuit.  These are very popular for narrow band matching in RF amplifiers; back in the day, they were almost exclusively used for directly matching vacuum tubes (1-10kohm required plate load!) to transmission lines, so the impedance ratio is plenty accessible... assuming you don't mind that the tuning range is squat.  (Which you don't for a fixed MFC thing that squirts out <10kHz of bandwidth, and which you wouldn't for an amateur radio where the entire band is maybe all of 150kHz wide anyway.)

Usually, your antenna is a known inductance and resistance (note: resistance at frequency, not just DCR -- they will be quite different in practice), so you only need to set it up as series resonant (low feedpoint impedance) or parallel resonant (high feedpoint impedance) and match that with a suitable network, potentially including these LC networks.  It may also be desirable to use a balanced network (which, for the NXP parts I've seen, is usually what's suggested?), which reduces stray electric field, and thus radiation and susceptibility.

You can also get "matched" antennas that go to coax or twisted pair.  Beware that the coax ones probably aren't balanced.  You probably still need another matching or coupling network at the chip itself (say, if it wants a slightly higher or lower impedance than what the stock device provides, or if it requires those series inductors I mentioned earlier), so allow for that.

Tim

[Harvs]

Thanks for the info, I'll have a chew over it in the morning.

I did have a win tonight, albeit by accident.  Once the series resistors were added (to control the Q of the antenna to <35), the VNA could now get a reasonable reading at the self resonant point.  In hindsight it makes perfect sense.

[T3sl4co1l]

Of course, now the Rp measurement is largely the impedance transformation of your resistor (with your antenna serving as the L and the resonant cap (if present) serving as the C in the L-match); and the Rr (radiation) part even smaller still!  Not that you need or want much radiation, but...

Speaking of... ideally I suppose you'd measure and tune with the antenna in the intended location (to accommodate distances to PCBs, chassis...), and with the intended load nearby (i.e., a tag in the near field).  Since it will reduce Q (that's the point!) and affect tuning slightly.

And then you could model that equivalent loss as the "radiation" resistance, since although it's not radiative, it's the part that's not staying in the coil, that's the part you're concerned with (i.e., power in this resistance = power in the load!).

Tim