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QNP3 Hardware Manual
Aerotech specifies the resolution as a 1 sigma (rms) noise, or jitter, value as measured by an external sensor
(either precision capacitance sensor or laser interferometer) at a measurement bandwidth of 1 kHz, unless
noted. The stage servo bandwidth is set to approximately 1/3 to 1/5 of the 1st resonant frequency of the
piezo nanopositioner because this is generally the highest frequency that the servo bandwidth can be
increased to before servo instability occurs. Because the noise is primarily Gaussian, taking six times the 1
sigma value gives an approximation of the pk-pk noise. Unless specified, the measurement point is centered
and at a height of approximately 15 mm above the output carriage. In noise critical applications, measuring at
a lower servo bandwidth will result in a lower noise (jitter).
Values are specified for open-loop and closed-loop resolution. Open-loop resolution is governed only by the
noise in the power electronics whereas closed-loop resolution contains feedback sensor and electronics
noise as well as power amplifier noise.
C.4.3 Repeatability
The repeatability of Aerotech's QNP3 piezo nanopositioning stages is specified as a 1 sigma (standard
deviation) value calculated from multiple bidirectional full-travel measurements. To obtain an approximate
peak-peak value for bidirectional repeatability, multiply the 1 sigma value by 6. For example, a 1 nm value
specified as a 1 sigma repeatability will be approximately 6 nm peak-peak.
C.4.4 Stiffness
The stiffness of a piezo actuator or nanopositioner is specified in the direction of travel of the output carriage.
The stiffness is a function of the piezo stack, stage flexure and amplification mechanism(s) used in the
design. Higher stiffness piezo stages allow for higher dynamics in positioning such as faster move and settle
times and better dynamic tracking performance.
As mentioned in Section 3.1, most longer-travel (>50 μm) piezo flexure stages use lever amplification to
achieve longer travels in a more compact package size. Lever amplification designs cause the stiffness in
the direction of travel (inversely proportional to the square of the lever amplification ratio) to be reduced when
compared to a directly-coupled design. Also, most lever amplification designs cause the stiffness of the
actuator to change depending on location in travel due to the non-linear nature of the amplification gain. For
this reason, along with manufacturing and device tolerances, the stiffness of Aerotech's piezo
nanopositioning stages is specified at a nominal value of ±20%.
Aerotech piezo nanopositioning stages are optimized to provide both premium dynamic performance and a
compact stage package.
C.4.5 Resonant Frequency
The resonant frequency of a nanopositioning stage can be estimated as follows:
Equation 14
where f
is the resonant frequency (Hz), k is the stiffness of the piezo nanopositioner (N/m) and m
n
effective mass of the stage (kg).
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Appendix C
Piezo Engineering Tutorial
is the
eff
55
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