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Formula for LDC1000 resonant frequency and frequency counter accuracy

Kris Paxton
Prodigy 225 points

Hi.

The literature and these discussions (and EVM GUI, I believe) seem to be predicated on this formula for the resonant frequency:

f =  [1/(2*pi)]*[1/(L*C)]^1/2

But that's not always true, is it?

I believe the resonant frequency of an LC tank this:

f = [1/(2*pi)]*[1/(L*C) - (Rs/L)^2)]^1/2     

So that first equation is true only when 1/(L*C)  is much greater than (Rs/L)^2 ... but that is not always the case. 

Also, does the LDC1000 require 1/(L*C)  be much greater than (Rs/L)^2 for the frequency counter to do it's job accurately?    I ask because I have a physical L/C tank for which the frequency counter (and GUI inductance measurement) is not accurate.   L= 640.5uH, Rs = 222ohm, C = 1000pF.   These numbers are good.   They were made by independent measurement.

By the numbers this tank should resonate at 191kHz and indeed, I probed the tank (with buffering so as not to significantly disturb the frequency / GUI-measured-inductance) and it is oscillating ~ 187kHz..  Yet f(sensor) from the frequency counter data is 235kHz and the GUI accordingly displays 458uH.

I'd very much appreciate your input.

Thanks.

  • 0
    TI__Expert 4890 points

    Hello,

    Because CRR/L is negligible. And when it's not (heavily damped system), Rp = L/Rs/C(equivalent parallel resistance) is outside of allowed range for LDC.

    Regards ，Sunny

  • 0 in reply to Sunny Qin
    Prodigy 225 points

    Hi Sunny,

    I'm afraid I don't follow.

    C = 1000pF and for no object near, L = 640.5uH and Rs = 222ohm ...

    Rp = L/(Rs*C) = 2.89k ohm

    f = 191 kHz

    Are these outside the allowed range for the LDC1000?

  • 0 in reply to Kris Paxton
    TI__Expert 4890 points

    Hi,

    In this condition, I think you should change the filte cap, because your frequency if low, larger filter cap will be needed. Or you can use a higher frequency.

    Regards, sunny.

  • 0 in reply to Sunny Qin
    Prodigy 225 points

    Hi Sunny,

    Regarding the filter cap, I had already adjusted it so that the CFB voltage is 1V p-p, as advised in the literature.  Let me be clear:   My numbers are with 1V p-p on CFB, my frequency is around 187 kHz and my Rp is 2.89k ohms. 

    The literature says 5kHz < f < 5MHz and 798 < Rp < 3.93M ... my tank is well within these ranges and the oscillator is oscillating at (or quite near) my predicted frequency, yet the Frequency Counter Data is very inaccurate. 

    With my above-stated tank, the LDC1000 measured Fcount is 26113. With my  Response Time of 3072  this gives f(sensor) = 235kHz and the GUI displays L = 458uH accordingly.  But these are way inaccurate.  The actual (measured) frequency of the oscillator is around 187kHz and the actual (independently measured) inductance is 650.5uH. 

    I'm trying to understand the boundaries of the LDC1000 so I can correctly apply it  and be assured it will work predictably and accurately, within know spec's. To do that, I need to know the rules, which normally come from the literature and spec's.

    Are there some as-yet unspoken/unpublished spec's/requirements for the inductance measuring capability to work? 

    I like this part and want to use it, but I need to know the boundaries, the rules and spec's.  Please help.