Dielectric Constant and Capacitance. One material specific property, and one component specific value. How are they related?
One of many ways piezo materials are classified is by their relative dielectric constant, or K value. The relative dielectric constant of a piezo material is a unitless bulk material property that is independent of geometry or part size.
This constant is referred to as relative dielectric constant because it is just that, a constant relative to another constant. In this case, the relative dielectric constant (K) is the ratio of the permittivity (dielectric constant) of the piezo material (ε ) to the permittivity of free space (ε0 ).
In the most basic calculation:
where ε0 =8.85 x 10-12 F/m
In other words, the relative dielectric constant (K) is the ratio of ε (the amount of charge a given material can store) to the absolute dielectric constant ε0 (the amount of charge that can be stored by the same electrodes when separated by a vacuum) considering equal voltage.
Because the relative dielectric constant is an indicator of material charge capacity, it can be used to calculate a piezo components capacitance, even before it is manufactured. The relationship is directly related to the electrode surface area, and indirectly related to the component thickness.
or more commonly:
where ε =dielectric constant, A=component electrode surface area, t=thickness. In the more common expression, C=Kε0 A/t, K=relative dielectric constant (since this is the more widely advertised material property) but it is quickly multiplied by ε0 so the end result is the same.
In practice, let’s calculate what the approximate capacitance of the following APC 850 plate would be:
P-27.50mm x 20.00mm x 5mm – 850
(Plate – L x W x T – APC850 Material)
The relative dielectric constant (K) of APC 850 material is advertised as 1900.
In this equation, all of the (meter) units cancel leaving only charge units of farads (F) remaining.
C=1.850 x 10-9 F or C=1.850 nF (nano-farads)
It’s worth noting that because the relationship is inversely proportional to the part thickness, reducing the thickness of the part actually increases the capacitance of the part. Some say this is counterintuitive, but it is important to remember that the piezo element is essentially a plate capacitor, so the fundamentals of plate capacitors apply.
This is one of the many reasons, when manufacturing components to a capacitance specification, small amounts of latitude in dimensions may be required to achieve the desired capacitance range.
Capacitance is an important value to consider (whether calculated or measured directly) when designing transducers, actuators, and drive circuits.
An even easier way to calculate relative dielectric constant or capacitance of piezo elements is to utilize the APC Piezo Calculator, which is available from the home page of the APC Website. This step by step calculator makes calculating most piezo constants a breeze!
For more information about determining the capacitance or relative dielectric constant of your piezo ceramics or if you have any other technical questions related to the application of piezoelectric ceramics, please contact a member of our knowledgeable sales staff today!