When exposed to an AC electric field, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the applied field. The frequency at which the ceramic element vibrates most readily, and most efficiently converts the electrical energy input into mechanical energy is known as its  resonance frequency.

The pattern of an element's responses is depicted in the figure above (Figure 1.8 from our text "Piezoelectric Ceramics : Principles and Applications"). As the frequency of cycling is increased, the element's oscillations first approach a frequency at which its electrical impedance is minimized (maximum admittance). This minimum impedance frequency, fm, approximates the series resonance frequency, "fs". "fs" is the frequency at which impedance in an electrical circuit describing the element is zero, if resistance caused by mechanical losses is ignored. The minimum impedance frequency is also considered the elements resonance frequency, Fr. The composition of the ceramic material and the shape and volume of the element determine the resonance frequency. Generally, a thicker element has a lower resonance frequency than a thinner element of the same shape.  Continuing along the curve, we eventually hit a frequency where electrical impedance is maximized.  This is known as the anti-resonance frequency "Fa".

Resonance frequency in a piezo element can be approximated mathematically.  It is necessary to know the speed at which sound travels within the piezo material "N", and the elements geometry (shape) and overall dimensions.  

Fr=N/h

In the above equation, Fr is the piezo elements resonance frequency.  "N" is the speed at which sounds travels in the piezo material in Hz*m or m/s (this is composition and orientation specific and is available in the APC Materials Data section of the website) and "h" is the height (thickness) of the piezo element in meters.  

As an example, we will calculate the thickness resonance frequency of a piezo disk made from APC850 material, with a thickness of 25.4mm.  From the APC Materials section of the website, the speed of sound in 850 material in the thickness mode is 2040 Hz*m.

Fr=2040 Hz*m / .0254m

Fr=80,315 Hz

or

Fr=80.315 kHz

An even quicker way to calculate resonance frequency 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 easy!

For more information about determining the  resonance frequency of your piezo ceramics or if you have any other technical questions related to the application of piezoelectric ceramics,   contact a member of our knowledgeable sales staff!