4 Calculating Resolution

Most LDC devices measure shifts in inductance by measuring the resonant frequency of an LC tank circuit. For this reason, it is most useful to calculate LDC resolution in units of Hz. However, many users will spec their desired resolution in terms of the distance between a target and the sensor coil, and also want to determine the SNR of the frequency shift associated with a target movement. For these reasons, this section will give a set of steps to use FEMM to simulate the sensor inductance, and use the LDC EVM and software GUI to estimate the SNR.

1. Calculate the Frequency:
   1. A real inductive sensor will consist of the sensor coil and fixed, physical capacitor. FEMM accurately calculates the magnetic fields of the coil - and therefore its inductance - but it will not include the effects of the capacitor.

      To work with this limitation, we describe two sets of steps below. The first will assume the sensor coil geometry and the capacitor value are known, but the coil inductance and tank circuit resonant frequency are unknown. The second set of steps will be be based on a known coil geometry and tank circuit resonant frequency, but the coil inductance and the capacitance are unknown. This will allow you to simulate the coil in FEMM to determine its inductance, and then calculate the capacitance.

      Neither approach considers the effect of the capacitor into the FEMM simulations. Instead, a few calculate/simulate steps will be used to to quickly iterate to the final inductance value and resonant frequency.

      (1) - Known Coil Geometry and Capacitor Value

      1. For the first iteration, pick a frequency and a maximum target distance and complete Part 1. Use the FEMM .ans file to calculate the inductance.

      2. Use the known capacitance and the newly calculated inductance to calculate the corresponding resonant frequency as shown in Equation 2:
         Equation 2. $f=\frac{1}{2\pi \sqrt{LC}}$
      3. Use the new frequency and the original target distance in FEMM to calculate a new inductance.
      4. Repeat steps ii and iii until the inductance does not change significantly between iterations.
      5. Move the target by the minimum distance for the desired resolution and repeat steps i-iv. Determine the difference in calculated frequencies between the two target positions.

      (2) - Known Coil Geometry and Tank Circuit Resonant Frequency

   2. Complete Part 1 using the resonant frequency and target distance. Use the FEMM .ans file to calculate the inductance.
      1. Calculate the capacitance using:
         Equation 3. $C=\frac{1}{{\left(2\pi f\right)}^{2}L}$
      2. Move the target by the minimum distance for the desired resolution and perform the steps i - iv in (1) just above. Determine the difference in calculated frequencies between the two target positions.
2. Calculate Resolution Using Simulation Results and Noise Floor Measurements:
   1. Measure the Noise Floor: For inductive sensing applications, the first step is to measure the noise floor for the system. Basic noise floor measurements can be done using the LDC evaluation modules, which can be purchased on ti.com. Accuracy can be improved - with respect to the end application - by making measurements over the expected temperature range, and using a sensor designed for the end application. The default evaluation module, however, will still provide a reasonable noise floor estimate.

   To measure the noise floor using an evaluation module, first download and open the Sensing Solutions GUI. For more detailed installation and use instructions, see the user’s guide associated with the EVM.

   1. Open the GUI and navigate to the Configuration tab.
   2. Configure the RCOUNT setting so that the LDC device will sample the sensor frequency at the desired rate.
      • For non-default sensors, the user must use an oscilloscope now to verify that the sensor oscillation amplitude and the sensor frequency are within the acceptable range for the specific device, as specified in the datasheet.
      • If the sensor oscillation amplitude is outside of the recommended range, the sensor drive current will need to be modified. Please see Setting LDC1312/4, LDC1612/4, and LDC1101 Sensor Drive Configuration for instructions.
      • If the sensor oscillation frequency is outside of the frequency range supported by the device, either the inductor or the capacitor in the LC tank will need to be modified.
   3. Next, navigate to the Data Streaming tab.
   4. Click the Start Streaming button to begin the noise floor measurement.
   5. Ensure that the graph displays Detected Sensor Frequency (MHz), which is controlled by the drop-down menu in the upper left corner.
   6. Click on the Show Statistics button to display the average and standard deviation. The data's standard deviation will be used to estimate the system noise. Increase the number of decimals of the standard deviation until the last digit is rapidly changing.
   Log the data in a .csv file and use your favorite analysis tool (e.g. Excel, MATLAB, etc.) to compute the standard deviation over all variations, including temperature. In general, the noise floor measurements will be more accurate over longer measurement periods.
   1. Calculate the Final Resolution via Signal-to-Noise Ratio (SNR):
      To calculate the SNR, use Equation 4, using three times the measured standard deviation as the total noise.
      • Remember that the SNR should be at least 10 to achieve the desired resolution in a real-world application.
      • Note that resolution significantly increases when the target is closer to the sensor. The FEMM simulations should test the resolution at both the minimum and maximum target distances using one of the two steps in (1) just above.
      • Also note that very fine resolutions may not be achievable at high sample rates. For more information about how sample rate affects resolution, see the Optimizing L Measurement Resolution for the LDC161x and LDC1101 application report.
      • If the FEMM simulations show that the desired resolution is not viable, then the sensor design or the target design must be modified. LDC Sensor Design and LDC Target Design are good resources.
      Equation 4. $SNR = \frac{\Delta f}{3{\sigma }_N}$
      • SNR is the signal-to-noise ratio of the inductive sensing system
      • Δf is the calculated frequency shift from 1
      • σ_N is the measured standard deviation of the noise from 2.a