2 Mathematical Modeling

The reason for this ground shift phenomenon is explained by looking at the capacitance models of the system. Figure 1 shows a simple diagram of the FDC2214 and its capacitances. In this model, both the sensor and the system are referenced to earth ground where:

• C₀ is the tank capacitance
• C_s is the sensor capacitance
• L₀ is the tank inductance

The oscillator signal alternates between INA and INB, so the circuit configuration is different for each half cycle of the oscillation.

Figure 1. Simplified Model of the FDC2214 EVM Board Referenced to Earth Ground Without a Large Local Ground Plane

Use Equation 1, Equation 2, and Equation 3 for this configuration:

In Phase 1:

Equation 1.

In Phase 2:

Equation 2.

The effective oscillation frequency is the average of the two phases:

Equation 3.

These equations show that if the entire system is referenced to earth ground, because L₀ and C₀ are fixed, the sensor frequency is only affected by variations in C_s, as intended.

A second possible ground configuration is represented by a system that is not referenced to earth ground, but instead is isolated and uses a local ground. This is shown in Figure 2, where:

• C_g is the parasitic capacitance between local and earth ground

Figure 2. Simplified Model of the FDC2214 EVM Board Floating Without a Large Local Ground Plane

Figure 2 shows how the LC resonator interfaces with earth ground through the parasitic and sensor capacitances of C_s and C_g. In addition to the desired sensor capacitance, C_s, the secondary capacitance, C_g, acts as a sensor also, and is affected by the same objects that interact with the intended sensor, C_s.

Because no other branch bridges the circuit with earth ground in either phase of the half-sine wave excitation, C_s and C_g are effectively in series when referenced to local ground. This series relationship is given by C_x characterized by Equation 4:

Equation 4.

where:

Equation 5.

This additional C_g creates the above β factor which reworks the equations to the following:

Equation 6.

Equation 7.

Equation 8.

In order for these equations to match those that characterize the ideal scenario of Figure 1, β should be as close to 1 as possible which means that C_g should be as large as possible. When the entire system is referenced to earth ground, C_g is theoretically infinite which forces β to be 1 and explains why the ground shift phenomenon is not observed. On the other hand, if C_g is not large enough, β will not be equal to 1 and will cause a shift in the frequency, which appears as a ground shift.

The next sections of this applications note will examine several possible ground configurations. To support the discussion, the reference system will be the FDC2214 EVM connected to a laptop through a USB cable.