Sensor Voltage

From Gauss law, the charge output Qⁱ(t) of the i^th electroplated sensor can be expressed in terms of spatial integration of D₃ over its surface as denotes the element number of the i^th sensor.

	(21.3)

If

	(21.4)

in matrix form may be written as

	(21.5)

Charge for the i^th electroplated sensor. is the electro-mechanical matrix of the i^th sensor.

Elementwise could be written as

	(21.6)

When piezoelectric sensors are used as strain rate sensors, the output charge can be transformed to sensor voltage as

	(21.7)

Where is the constant gain of the charge amplifier of the i^th electroplated sensor.

The combined sensor voltage vector can be expressed as

	(21.8)

N_s is the total number of piezoelectric sensors and

;	(21.19)