### PDQ High Speed Charge Drive

The PDQ amplifiers are the first commercially available charge drives for piezoelectric actuators. A charge drive is similar to a voltage amplifier except that piezoelectric hysteresis can be reduced to less than 1%.

In many applications, a charge drive can immediately replace a voltage amplifier when improved dynamic linearity is required. This can reduce or eliminate the need for feedback or feedforward control of hysteresis.

PiezoDrive charge drives are designed for both high-performance and ease-of-use. Compared to a standard high-voltage amplifier, there is only one additional control, the DC-gain, which sets the voltage-gain at low-frequencies.

The PDQ charge drives have the same exceptional bandwidth and output current as the PDX voltage amplifiers. This includes Dynamic Current Control which dramatically improves the maximum output current and allows the reproduction of larger amplitude waveforms with higher frequency.

In addition to the fast response, the PDQ drives also include: comprehensive overload protection; external shutdown; voltage, charge and current monitor outputs; and front-panel bias-voltage adjustment.

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• ### Specifications

 Model PDQ150b PDQ200b Voltage -30V to 150V* -30V to 200V* Peak Current 2A 1.5A Overload Time 100ms 100ms RMS Current 1.6A 1.1A Power Bandwidth 9.5 kHz 7.2 kHz Signal Bandwidth Greater than 80 kHz (1uF Load) Charge Gain 2.2, 6.2, 22, 62, 220, or custom uC/V Voltage Gain 20 - 66 V/V Offset From 0V to Full-Range Input Differential, Zin = 22 kOhm Signal Connectors BNC input, BNC Monitor Outputs, Output Connectors 4mm Plugs and 2-Way LEMO 0B Overload Protection Thermal, current and voltage Noise 3mV RMS Environment 0 - 40 C (32-104 F) Enclosure Desktop, rack compatible Dimensions 212.6 x 304.8 x 132.6 mm (w x d x h) Power Supply 115V or 230V AC (selectable)

### Introduction to Charge Drives

It has been known since the 1980's that piezoelectric transducers respond more linearly to current or charge rather than voltage [1]. However, problems with drift and the floating nature of the load have only been solved recently [2], [3] Since then, charge drives have been demonstrated to reduce the hysteresis of piezoelectric actuators by up to 93% [3]. This corresponds to a maximum non-linearity of less than 1% which can reduce or eliminate the need for feedback or feedforward control in applications that do not require accurate positioning at frequencies below 1 Hz.

Charge Drive Circuit Diagram
The simplified circuit diagram of a charge drive. The piezoelectric actuator is shown in gray.

In the simplified schematic, the piezoelectric load is modeled as a capacitor $$C_p$$ and voltage source $$v_p$$ shaded in gray. The high-gain feedback loop works to equate the applied reference voltage $$v_{in}$$ to the voltage across a sensing capacitor $$C_S$$. Neglecting the resistances $$R_p$$ and $$R_S$$, the charge $$q$$ is $$q = v_{in} C_S .$$ That is, the gain is $$C_S$$ Coulombs/V. This implies an input-to-output voltage gain of $$C_S/C_p$$.

A problem with charge drives is the finite output impedance and dielectric leakage, modelled by $$R_p$$ and $$R_S$$. These resistances cause the output voltage to drift at low frequencies. However, by setting the ratio of resistances equal to the ratio of capacitances, low-frequency error can be avoided. To maintain a constant voltage gain, the required resistance ratio is $$\frac{R_p}{R_S} = \frac{C_S}{C_p} .$$ The parallel resistances effectively turn the charge drive into a voltage amplifier at frequencies below $$f_c = \frac{1}{2 \pi R_p C_p } \text{Hz} .$$ Although the parallel resistances act to stabilize the voltage gain at low frequencies, the amplifier now operates as a voltage source below $$f_c$$ and a charge drive above. A consequence is that reduction of non-linearity only occurs at frequencies above $$f_c$$. Practical values of $$f_c$$ can range from 0.01 Hz to greater than 10 Hz.

The cut-off frequency $$f_c$$ can be reduced by increasing the parallel resistances; however, a practical limit is imposed by the dielectric leakage of the transducer. In addition, excessively high resistance values also reduce the immunity to drift and result in long settling times after turn-on and other transient events. The settling time is approximately $$5 / 2 \pi f_c$$ seconds.

An ideal compromise between excessively long settling times and good low-frequency performance is $$f_c = 0.1~\text{Hz}$$, implying a settling time of 8 seconds after turn-on. This value of $$f_c$$ is adopted in the PDQ charge drives which have a cut-off frequency of between 0.03 Hz and 0.1 Hz, depending on the load capacitance.

### Example application

Comparison of Non-Linearity between Voltage and Charge Drives
The displacement of a 10mm piezoelectric stack actuator in response to a 180V sine-wave. the non-linearity when using a voltage amplifier is 14%; however, this reduces to only 0.6% when a charge drive is applied.

In this example, the response of a 5x5x10mm 200V stack actuator is compared when driven by a voltage amplifier and charge drive. The full displacement range of this actuator is 10.5 um at 200 V. As the actuator capacitance is 330 nF, the 22 uC/V charge range was selected. This corresponds to a voltage gain of 66 and a cut-off frequency of 0.1 Hz.

The voltage- and charge-driven displacement responses to a 100-Hz 150-V sine wave are plotted on the right. Using a voltage amplifier, the maximum difference in position between two points with the same applied voltage is 1.1 um, or 14.3% of the range. Alternatively, when the voltage amplifier is replaced by a charge drive, the non-linearity is reduced to 0.05 um or 0.65% of the range. In many applications, this magnitude of non-linearity can avoid the necessity for feedback or feedforward hysteresis compensation.

### Charge Gain

The PDQ charge drives are preconfigured during manufacture to drive a certain range of capacitance values. This means that the charge-gain, resistance ratios, and transition frequency $$f_c$$ are all optimally preconfigured and do not require user adjustment. The standard capacitance ranges and associated charge-gain, voltage-gain and cut-off frequencies are tabulated below.

 Load Capacitance Transition Frequency Voltage Gain Charge Gain 30 - 100 nF 0.3 - 0.1 Hz 66 - 22 2.2 uC/V 100 - 300 nF 0.1 - 0.03 Hz 60 - 20 6.2 uC/V 0.3 - 1.0 uF 0.1 - 0.03 Hz 66 - 22 22 uC/V 1.0 - 3.0 uF 0.1 - 0.03 Hz 60 - 20 62 uC/V 3.0 - 10 uF 0.1 - 0.03 Hz 66 - 22 220 uC/V 10 - 1000 uF 0.1 Hz 40 Custom

Standard Load Capacitance Ranges

### Power bandwidth

The power bandwidth is the maximum frequency sine-wave that can be reproduced at full voltage. The PDQ150 and PDQ200 are designed to maximize the power bandwidth in general purpose and scanning applications. With a capacitive load, the maximum frequency sine wave is $$f^{max}=\frac{I_{pk}}{V_{p-p} \pi C}$$ where $$I_{pk}$$ is the peak current, and $$V_{p-p}$$ is the peak-to-peak voltage. A table of the approximate power bandwidths for a range of capacitive loads is shown below.

 Capacitance PDQ150 PDQ200 100 nF *9.5 kHz *7.2 kHz 300 nF 9.2 kHz *7.2 kHz 1 uF 4.2 kHz 2.3 kHz 3 uF 1.4 kHz 790 Hz 10 uF 424 Hz 230 Hz 30 uF 141 Hz 79 Hz 100 uF 42 Hz 23 Hz

Power Bandwidth versus Load Capacitance

* With very small loads, the power bandwidth is limited by the slew-rate, which is approximately 4.5 V/us. This can be doubled to 8 V/us if necessary.

Also of interest is the maximum amplitude sine-wave that can be delivered to a capacitive load versus frequency. This relationship is plotted below and can be computed for a specific capacitance by using the links above.

### Frequency Response

The small-signal frequency response for a range of capacitive loads is shown in the figure and table below.

Note that the load capacitance is the maximum permitted under each charge range which results in a voltage gain of 20. When the load capacitance is lower, the voltage gain is increased and the bandwidth may reduce.

 Capacitance Bandwidth No Load 78 kHz 0.1 uF 200 kHz 1.0 uF 84 kHz 10 uF 27 kHz 100 uF 2.7 kHz

Signal Bandwidth versus Load Capacitance

### Signal Conditioning

The differential input circuit eliminates ground-loops and noise resulting from the interconnection of different instruments.

### Enclosure

The PDQ drives are housed in a desktop enclosure that can be bolted together in a side-by-side configuration. Mounting in a standard 19-inch rack is also possible with the addition of rack-mount handles.

### Options

The PDQ drives can be customized to meet a range of industrial or scientific requirements. Specific options include:

• 19-inch rack kit for two amplifiers
• 19 inch rack kit for a single amplifier

### References

[1] C. V. Newcomb and I. Flinn, "Improving the linearity of piezoelectric ceramic actuators," IEE Electronics Letters, vol. 18, no. 11, pp. 442-443, May 1982.

[2] K. A. Yi and R. J. Veillette, "A charge controller for linear operation of a piezoelectric stack actuator," IEEE Transactions on Control Systems Technology, vol. 13, no. 4, pp. 517-526, July 2005.

[3] A. J. Fleming and K. K. Leang, "Charge drives for scanning probe microscope positioning stages," Ultramicroscopy, vol. 108, no. 12, pp. 1551-1557, November 2008.