# Parasitics and Capacitor Selection, Part VIII: Voltage Coefficient for Class II Ceramic Capacitors

General decoupling applications require capacitors with a combination of high capacitance and low reactance (i.e., low equivalent series resistance [ESR] and equivalent series inductance [ESL]) in the circuit. The trend in digital applications for greater data throughput at higher speed is being met by lower voltage logic operating at increasing switching speeds.

Going back to the standard capacitance equation C = KA/d , in which C = capacitance, k = dielectric constant, A = surface area of the capacitor plates, and d = distance between the capacitor plates, we can see that you can achieve higher capacitance by increasing the dielectric constant and/or surface area and decreasing the distance between the plates, the latter of which also results in lower breakdown voltage, which can be very useful in low voltage applications.

Once a voltage is applied in an ideal capacitor (i.e., one with nothing but free space between the plates), opposite charges will build up on the plates, creating an electric field between the two. The amount of charge stored is controlled by the geometry of the plates (i.e., the area and distance between them) multiplied by the dielectric constant of the free space. If the voltage is varied (e.g., if an AC signal is applied), the charges on the plates will oscillate and the AC signal will pass, but the DC signal will be blocked.

Since the dielectric constant of the free space has a very small value, insulating materials capable of increasing the electric field (dielectrics) can be sandwiched between the plates. Many of these materials are classified as para-electric, and may be amorphous or have some degree of crystallinity, but all have the ability to polarize, which is when the internal dipoles of the material align with and increase the electric field. These dipoles may arise from microscopic internal molecular alignment with the field direction (ionic polarization), a smaller effect from the electronic charge distribution in the material (electronic polarization), or an even smaller effect resulting from the internal atomic alignment (atomic polarization).

What dielectrics all have in common is that, although the plate area and separation remain constant, the relative dielectric constant of the material exhibits non-linear variability with temperature and signal frequency. So, apart from the intrinsic capacitance range of a given technology, each dielectric is best suited for different application temperatures and frequencies. Typically, ionic polarization prevails in the 100kHz – 1GHz range, which is useful for digital to general high frequency applications, and electronic polarization prevails in higher frequency RF to optical range: 1GHz – 40GHz.

Many dielectric types fall within the para-electric family: glass, films (polypropylene, polyester, etc.), tantalum and niobium pentoxides (Ta2 O5 and Nb2 O5 ), and Class I ceramics (e.g., those with temperature characteristics NP0, C0G, etc.), and the typical temperature/frequency performance of these materials is well known. Alternately, Class II ceramic dielectrics (e.g., those with temperature characteristics X7R, X5R, etc.), belong to the ferroelectric material family. This family shares the same polarization mechanisms and temperature/frequency characteristics, but has additional material properties that impact several electrical characteristics that are often overlooked.

In the previous blog on ripple current, I noted that the dielectric structure of a Class II ceramic capacitor can be envisioned as a collection of domains with internal dipoles that change alignment in response to an applied AC voltage. So, in the case of a typical Class II material, barium titanate (BaTiO3 ) for example, these micron-size domains have an additional mechanism whereby, under a small electric field resulting from the application of a low DC bias, the titanium ions can actually move within the lattice to create a large dipole moment and, hence, high dielectric constant. Once re-stabilized in the lattice, the ions will remain in their new position and will not relax back into their original site, even after the external field is removed.

This contribution to dielectric constant is significant, providing values of relative dielectric constant over 1,000 times that of some para-electric ceramic materials and associated capacitance values over 1,000 times higher. However, since contribution to the dielectric constant is actually a property of the crystal lattice, its value will be affected by all of the other conditions that affect the lattice, which are more varied than those that only affect molecular distribution (e.g., ionic polarization) or charge distribution (e.g., electronic polarization).

The main factors that affect dielectric constant are the applied electric field and temperature, the first of which is responsible for the voltage coefficient associated with Class II dielectrics. To understand voltage coefficient, it’s important to recognize how Class II dielectrics are used in the majority of applications. Although Class II dielectrics are only one of many dielectric types, they are by far the most general purpose dielectric in the world, accounting for trillions of capacitors produced annually for general filtering and decoupling applications.

We have previously discussed capacitors in terms of both DC and AC applications. A typical DC application could be charging and discharging a capacitor with a known current and having the voltage across it increase or decrease; but, in reality, the majority of general DC applications have an element of AC, in that we are measuring their effect on a small, low voltage, and low frequency signals.

Capacitance is measured with a low voltage bias applied — usually just enough to make sure the signal voltage does not go negative. However, in real world applications, there is often a DC bias applied associated with the line voltage (e.g., 3.3V, 5.5V, 12V, etc.) This is where the additional field effect in Class II ceramics comes into play. As DC bias voltage is increased, an ever-greater number of the crystal lattice domains become locked, which means that the titanium ions are inhibited from movement within the lattice (and thus no longer contribute to the dipole moment) and that the effective dielectric constant (K) of the material reduces. So, in the equation above, Capacitance (C) will vary as the K value varies with frequency and temperature for all dielectrics, but additionally with applied voltage in the case of Class II ceramics.

The chart below shows a typical response curve for the capacitance vs. applied voltage of a Class II dielectric, such as X7R. Once this characteristic is taken into account, choosing the right voltage rating to meet the minimum capacitance target in an application becomes straightforward. For instance, if using a 6V rating on a 5.5V line produces too high a capacitance drop, you can reduce it by using a 10V rated capacitor of the same nominal capacitance rating in the application.

Figure 1

Typical capacitance change vs. applied DC voltage (voltage bias curve) for X7R

The way in which capacitors are designed factors into this too, though. For commercial series, the temperature coefficient (e.g., X7R) and voltage coefficient need to be factored separately. However, more demanding applications allow capacitors to have a conservative voltage design and be represented by a single characteristic combining both temperature and voltage effects, such as the BX characteristic, which can be found in DLA specifications such as MIL-PFR-55681.

Although this concludes our discussion of voltage coefficients for Class II dielectrics, there are several other field and temperature effects that need to be considered beyond those experienced by para-electric dielectrics. So, stay tuned for the next blog in this series, which will address why these other effects are important in low noise and high temperature applications.

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