An inductive-to-digital converter (LDC) senses the change in inductance caused by the movement of a conductive target through the senor’s AC magnetic field. The target movement with respect to the sensor may be either axial or lateral with respect to the plane of the sensor. The characteristics of the sensor, as discussed in the TI application note LDC Sensor Design, determine the characteristics of the sensor’s magnetic field and the overall system measurement resolution and accuracy.

Whenever a conductor interacts with an AC magnetic field, eddy currents are induced on the conductor’s surface. Lenz’s Law states that induced currents will flow in a manner to oppose the magnetic field, which weakens the original magnetic field in a measurable way. LDC devices use an inductor in a resonant circuit to generate an AC magnetic field, as shown in Figure 2-1. Any generated eddy currents will weaken the inductor’s magnetic field, which effectively reduces the inductance of the resonant circuit, which is typically detectable by the LDC. Depending on the device, an LDC measures either the shift in resonance and/or the energy losses in the resonant circuit and in the target (due to the eddy currents).

Figure 2-1 AC Magnetic Field Interaction With Conductor

For many LDC applications, a flat spiral inductor printed on a PCB is an effective sensor design. An example is shown in Figure 2-2. Some of the primary considerations for the sensor include the total inductance, the resonant frequency, and the physical size of the inductor.

Figure 2-2 Spiral PCB Inductor

When a conductive target is brought into the magnetic field of the inductor coil, the eddy currents on the surface of the conductor will flow in the lowest possible impedance path. This path take is composed of concentric loops which match the shape of the sensor.

Figure 2-3 Image Current Flow on Target

Any differences in the image current path compared to the sensor current path will result in a weaker change in the sensor’s magnetic field. For this reason, the strongest target response occurs when the target size larger than the sensor size, as the image current path can better mirror the flow of current in the sensor. If the target size is smaller than the sensor, the change in sensor frequency will be reduced, as shown in Figure 2-4.

Figure 2-4 Sensor Inductance Shift vs Target Radius With Target 1 mm From Sensor

In Figure 2-4, the sensor is a spiral of 10 mm diameter, 25 turns per layer, with 4 layers having an inductance of 36 μH. The targets are stainless steel 304 disks, and held coaxially at a 1 mm distance from the sensor. As always, a larger change in the sensor inductance is desirable, since a larger change allows the target position to be measured with higher resolution. When the target radius is less than 0.1 cm, the sensor measurement changes by less than 1% of its nominal value. Position measurement of such a small target will have lower effective resolution due to the smaller inductance change. When the target size is increased to match the size of the sensor, the sensor measurement changes by >21%. This larger shift can be measured with much greater resolution.

Like all AC currents, the eddy currents induced by the LDC’s AC magnetic field flow near the surface of the conductor, and reduce in amplitude deeper into the conductor. The attenuation of current follows an exponential trend with distance from the surface. The skin depth, δ, is the distance at which the current is reduced to 1/e (~37%) of the density at the surface. Every additional increase of δ from surface will see an additional 1/e reduction in current.

For highly conductive materials, such as metals, the skin depth δ_s can be calculated by:

Equation 1.

where

• μ is the magnetic permeability of the material, which is μo (4π×10-7) multiplied by the conductor’s relative permeability,
• ρ is the resistivity of the conductor, and
• f is the frequency of the AC magnetic field.

Skin depth varies with the material and sensor frequency. At higher frequencies, the skin depth becomes smaller and smaller, which results in the eddy currents concentrating at the surface of the conductor. Poorer conductors, such as carbon, have a larger value for their skin depth, as shown in Figure 2-5. Poorly conductive materials have a limit on skin depth; as an example, silicon never gets below 11 m.

Figure 2-5 Skin Depth vs. Frequency for a Variety of Conductors

A conductor with a thickness equal to 1 skin depth for a given frequency will carry 63.2% of the current of an infinitely thick conductor. With a conductor of 3 skin depths thick, 95% of the total current will be induced, as shown in Figure 2-6.

To achieve best performance, a good rule of thumb is to that the target thickness should be at least 2 to 3 skin depths. To achieve this, either increase the target thickness or sensor frequency.

Figure 2-6 Current vs. Conductor Skin Depth