Coupling factor

When working with piezoelectric materials, one of the most important constants is the coupling factor. It describes the relation between the stored energy and converted energy. To recapitulate: piezoelectrics convert electrical energy to mechanical energy, and vice versa.

The coupling factor k is defined as:

     converted energy
k² = ----------------
      stored energy

From the electrical viewpoint, a piezo is a capacitor. From the mechanical viewpoint it is a spring. When converting from electric to mechanical energy, the "stored energy" is in the form of a charged capacitor. When converting from mechanical to electrical energy, the "stored energy" is in the spring. Only a portion, k², of this stored energy is converted to the other domain.

For example, let's charge the capacitor by applying a voltage V. The stored energy E_C is:

E_C = ½CV²

As a result the piece of piezo will bend, and it will contain a mechanical energy E_K of:

E_K = ½Kx² = E_C·k²

List of parameters:

C = capacity of the piezo
V = voltage applied
K = spring constant
x = spacial displacement