More about understanding the distortion mechanism of high-K MLCCs

December 23, 2013 // By John Caldwell, Analog Applications Engineer, Texas Instruments
In a previous article [Ref 1] I demonstrated the additional distortion produced when using High-K ceramic capacitors in a system’s signal path. The underlying mechanism causing this distortion is the voltage coefficient of capacitance (VCC) of the capacitor.

The term VCC is used to describe the change in the value of a capacitor with respect to the magnitude of the applied voltage. Power supply designers are well aware of this behaviour as it can directly affect the output ripple or stability of their system, but VCC is often ignored in small-signal circuitry. In order to understand why the capacitance varies with applied voltage and how the VCC varies with other capacitor parameters, it is necessary to first look at a capacitor’s basic structure.

Figure 1. A basic parallel plate capacitor with electrode plates of area A and a separation distance d.

Figure 1 shows a simple capacitor consisting of two plate electrodes of area A, separated a distance d by a dielectric (green). The capacitance of this structure is given by equation 1:

where εo and εr are the permittivity of free space and relative permittivity of the dielectric, respectively. The magnitude of the electric field applied to the dielectric is a function of the applied voltage and the separation distance between the two plates.

The voltage coefficient of many capacitors arises from the electrostatic force on the dielectric when a voltage is applied to the capacitor.

Because the dielectric material cannot be infinitely stiff, it is compressed by this force, reducing the separation distance d and increasing the capacitance [Ref 2]. Multilayer ceramic capacitors, on the other hand, exhibit an additional negative voltage coefficient that arises from other properties of the dielectric.

Ceramic capacitors owe their small size, high capacitance, and low cost to the use of barium titanate in the dielectric, which provides an extremely high relative permittivity [Ref 3]. Unfortunately, this material’s relative permittivity varies depending upon the intensity of the applied electric field. Reference 4 presents an excellent example of this behavior in single barium titanate crystals, reproduced in Figure 2. As the applied electric field is increased, the relative permittivity of the barium