8.1.1 Calculation of Rp_MIN and Rp_MAX

Different sensing applications may have a different range of the resonance impedance Rp to measure. The LDC1041 measurement range of Rp is controlled by setting 2 registers – Rp_MIN and Rp_MAX. For a given application, Rp must never be outside the range set by these register values, otherwise the measured value will be clipped. For optimal sensor resolution, the range of Rp_MIN to Rp_MAX should not be unnecessarily large. The following procedure is recommended to determine the Rp_MIN and Rp_MAX register values.

8.1.2 Output Data Rate

Output data rate of LDC1041 depends on the sensor frequency, f_sensor and 'Response Time' field in LDC Configuration register(Address:0x04).

Equation 6.

8.1.3 Choosing Filter Capacitor (CFA and CFB Terminals)

The Filter capacitor is critical to the operation of the LDC1041. The capacitor should be low leakage, temperature stable, and it must not generate any piezoelectric noise (the dielectrics of many capacitors exhibit piezoelectric characteristics and any such noise is coupled directly through Rp into the converter). The optimal capacitance values range from 20pF to 100nF. The value of the capacitor is based on the time constant and resonating frequency of the LC tank.

If a ceramic capacitor is used, then a C0G (or NP0) grade dielectric is recommended; the voltage rating should be ≥10V. The traces connecting CFA and CFB to the capacitor should be as short as possible to minimize any parasitics.

For optimal performance, the chosen filter capacitor, connected between terminals CFA and CFB, needs to be as small as possible, but large enough such that the active filter does not saturate. The size of this capacitor depends on the time constant of the sense coil, which is given by L/Rs, (L=inductance, Rs=series resistance of the inductor at oscillation frequency). The larger this time constant, the larger filter capacitor is required. Hence, this time constant reaches its maximum when there is no target present in front of the sensing coil.

The following procedure can be used to find the optimal filter capacitance:

1. Start with a large filter capacitor. For a ferrite core coil, 10nF is usually large enough. For an air coil or PCB coil, 100pF is usually large enough.
2. Power on the LDC and set the desired register values. Minimize the eddy currents losses. This is done by minimizing the amount of conductive target covering the sensor. For an axial sensing application, the target should be at farthest distance from coil. For a lateral or angular position application, the target coverage of the coil should be minimized.
3. Observe the signal on the CFB terminal using a scope. Since this node is very sensitive to capacitive loading, it is recommended to use an active probe. As an alternative, a passive probe with a 1kΩ series resistance between the tip and the CFB terminal can be used.
4. Vary the values of the filter capacitor until that the signal observed on the CFB terminal has an amplitude of approximate 1V peak-to-peak. This signal scales linearly with the reciprocal of the filter capacitance. For example, if a 100pF filter capacitor is applied and the signal observed on the CFB terminal has a peak-to-peak value of 200mV, the desired 1V peak-to-peak value is obtained using a 200mV / 1V * 100pF = 20pF filter capacitor.

8.2.1 Axial Distance Sensing Using a PCB Sensor with LDC1041

Figure 16. Typical Application Schematic, LDC10xx

8.2.1.2 Detailed Design Procedure

8.2.1.2.1 Sensor and Target

In this example, consider a sensor with the below characteristics.

Table 19. Sensor Characteristics

PARAMETER	VALUE
Layers	2
Thickness of copper	1 Oz
Coil shape	Circular
Number of turns	23
Trace thickness	4 mil
Trace spacing	4 mil
PCB core material	FR4
Rp @ 1 mm	5 kΩ
Rp @ 8 mm	12.5 kΩ
Nominal Inductance	18 µH

Target material used is stainless steel

8.2.1.2.2 Calculating Sensor Capacitor

Sensor frequency depends on various factors in the application. In this example since one of the design parameter is to achieve output data rate of 78 KSPS, sensor frequency can be calculated as below.

Equation 7.

With the lowest Response time of 192 and output data rate of 78 KSPS, sensor frequency calculated using the above formula is 4.99 MHz.

Now, using the below formula sensor capacitor is calculated to be 55 pF with a sensor inductance of 18 µH

Equation 8.

8.2.1.2.3 Choosing Filter Capacitor

Using the steps given in Choosing Filter Capacitor (CFA and CFB Terminals) filter capacitor for the example sensor is 20 pF. Below waveform shows the pattern on CFB pin with 100 pF and 20 pF filter capacitor.

Figure 17. Waveform On CFB With 100pf

Figure 18. Waveform On CFB With 20pf

8.2.1.2.4 Setting Rp_MIN and Rp_MAX

Calculating value for Rp_MAX Register : Rp at 8mm is 12.5kΩ, 12500×2 = 25000. In Table 4, then 27.704 kΩ is the nearest value larger than 25kΩ; this corresponds to Rp_MAX value of 0x12

Calculating value for Rp_MIN Register : Rp at 1mm is 5kΩ, 5000/2 = 2500. In Table 6 , 2.394kΩ is the nearest value lower than 2.5kΩ; this corresponds to Rp_MIN value of 0x3B

8.2.1.2.5 Calculating Minimum Sensor Frequency

Using,

Equation 9.

N is 227.51, round off to 228 decimal. This value has to be written into Watchdog Timer Register, which is used to wake up the internal circuit when the sensor is saturated.

8.2.1.3 Application Curves

Figure 19. Rp vs Distance

Figure 20. Inductance vs Distance

8.2.2 Linear Position Sensing Application Diagram

Figure 21. Linear Position Sensing

8.2.3 Angular Position Sensing Application Diagram

Figure 22. Angular Position Sensing