An EM field can be generated using an L-C resonator, or L-C tank. One topology for an L-C tank is a parallel R-L-C construction, as shown in Figure 46.
A resonant oscillator can be constructed by combining a frequency selective circuit (resonator) with a gain block in a closed loop. The criteria for oscillation are: (1) loop gain > 1, and (2) closed loop phase shift of 2π radians. The R-L-C resonator provides the frequency selectivity and contributes to the phase shift. At the resonance frequency, the impedance of the reactive components (L and C) cancels, leaving only RP, the lossy (resistive) element in the circuit. The voltage amplitude is maximized at this frequency. The RP can be used to determine the sensor drive current for a given oscillation amplitude. A lower RP requires a larger sensor current to maintain a constant oscillation amplitude. The sensor oscillation frequency is given by:
The value of Q can be calculated by:
Texas Instruments' WEBENCH design tool can be used for coil design, in which the parameter values for RP, L and C are calculated. See http://www.ti.com/webench.
RP is a function of target distance, target material, and sensor characteristics. Figure 47 shows an example of RP variation based on the distance between the sensor and the target. The graph represents a 14 mm diameter PCB coil (23 turns, 4 mil trace width, 4 mil spacing between traces, 1 oz. copper thickness, on FR4 material). This curve is a typical response where the target distance scales based on the sensor size and the sensor RP scales based on the free-space of the inductor.
It is important to configure the sensor current drive so that the sensor will still oscillate at the minimum RP value (which typically occurs with maximum target interaction). As an example, if the closest target distance in a system with the response shown in Figure 47 is 1mm, then the sensor current drive needs to support a RP value is 5 kΩ. Both the minimum and maximum RP conditions should have oscillation amplitudes that are within the device operating range. See section Sensor Current Drive Control for details on setting the current drive.
The inductance that is measured by the LDC is:
Figure 48 shows an example of variation in sensor frequency and inductance as a function of distance for a 14 mm diameter PCB coil (23 turns, 4 mil trace width, 4 mil spacing between traces, 1 oz copper thickness, FR4 material). The frequency and inductance graphs will scale based on the sensor free-space characteristics, and the target distance scales based on the sensor diameter.
The Texas Instruments Application Notes LDC Sensor Design and LDC Target Design provide more information on construction of sensors and targets charactersitics to consider based on system requirements.