### Current and Power Calculator

The spreadsheet below calculates the maximum operating frequency of PiezoDrive amplifiers with a capacitive load. The second spreadsheet calculates the current, power, slew-rate, and approximate actuator heat dissipation.

The spreadsheets do not take all operating conditions in to consideration and should only be used as a guide. More detailed specifications can be found in the amplifier datasheets.

Piezoelectric Stack Actuator

### Current Limit Equations

To avoid damage, piezoelectric drives contain circuitry to limit the maximum output current and power dissipation. These limits impose constraints on the dynamic performance of a piezoelectric actuator. As piezoelectric actuators can be approximated by a capacitance at low frequencies, the required drive current is proportional to the rate-of-change in voltage; that is, the required current is approximately

where C is the capacitance and V is the voltage. For a sine-wave, the maximum required current is

where Vpp is the peak-to-peak voltage. The above equation implies that the maximum sinewave frequency is

If a sinewave spans the full voltage range of the drive, the maximum frequency sinewave is also referred to as the power bandwidth.

Compared to a sine-wave, a triangle wave requires less current, and allows a higher maximum frequency of:

An Example of the Voltage and Current Required to Drive a Piezoelectric Actuator
The voltage and current required to drive a 330nF actuator at 5kHz

An example of the voltage and current waveforms applied to a piezoelectric actuator are shown on the right.

Example: A 1uF piezoelectric actuator is to be driven by a 200Vpp, 30Hz sine-wave, the required current is

### Voltage Range

High-speed nanopositioner developed at the EASY lab, University of Nevada, Reno.
Courtesy of Dr K. K. Leang

The output voltage range is the first consideration to be taken into account when selecting a drive for piezoelectric actuators. To achive maximum displacement, the drive should be capable of developing the full rated actuator voltage.

Popular monolithic stack actuators are available in voltage ratings from 60V to 200V. This rating is the maximum positive voltage or coercive field strength that can be applied. Although higher than rated positive voltages will generally not damage an actuator, excessively high voltages may result in arcing that can erode the actuator and cause intermittent short circuits.

Piezoelectric actuators can also tolerate small negative voltages. This will increase the actuators range but extreme care must be taken not to depolorize the dielectric. Most piezoelectric dielectrics can tolerate a negative voltage of approximately 10% to 20% of the maximum positive voltage.

### Signal Bandwidth

Frequency Response versus Capacitance (in uF)
The magnitude frequency response of a piezoelectric drive for a range of load capacitances (in uF)

When considering small signals that do not exceed the current limit, the maximum operating frequency is dictated by the driver bandwidth. The bandwidth is the frequency where output power has reduced by a factor of two and significant phase-shift is present. For accurate signal reproduction, input frequencies should generally be lower than 10% of the driver bandwidth.

As load capacitance is increased, the bandwith of a piezoelectric drive reduces. This relationship between capacitance and bandwidth can be found in the drive's datasheet. A typical frequency response characteristic is shown on the right.

### Capacitance versus Bias-Voltage and Temperature

The power bandwidth, slew-rate and small-signal bandwidth of a piezoelectric drive are all primarily limited by the actuator capacitance. Larger actuators and actuators with a greater number of internal layers have a higher capacitance.

Care must be taken when interpreting capacitance values since these values are measured at room temperature and under small signal conditions. When an actuator is driven at full range, the effective capacitance can be double the small signal capacitance. Therefore, when predicting the performance of piezoelectric drives, a conservative estimate of the actual operating capacitance should be used. In typical applications, the capacitance value should be multiplied by a factor of two when predicting the required operating current.

In addition to capacitance non-linearity, piezoelectric ceramics are also temperature dependant. For example, the sensitivity and capacitance of common piezoelectric actuators can double with every 50 degrees Celsius increase in temperature. If the ambient temperature is above 25 degrees Celsius, the capacitance increase should be considered. Large temperature increases can also occur when driving piezoelectric actuators at high-speed or full-range.

### Safety

Piezoelectric drives produce hazardous potentials and should be used by suitably qualified personnel under the supervision of an observer with appropriate first-aid training.

Do not operate piezoelectric drives when there are exposed conductors.
Use appropriate signage for Hazardous Voltages.