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title = "Amplified Piezoelectric Actuators"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
<./biblio/references.bib>

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:
## Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor}
## Piezoelectric Force Sensors {#piezoelectric-force-sensors}
### Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor}
An analysis the dynamics and noise of a piezoelectric force sensor is done in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
## Manufacturers {#manufacturers}
### Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------|---------------------------------------------------------------|
| PCB | [link](https://www.pcb.com/products/productfinder.aspx?tx=17) |
### Signal Conditioner {#signal-conditioner}
The voltage generated by the piezoelectric material generally needs to be amplified.
| Manufacturers | Links |
|---------------|-----------------------------------------------|
| PCB | [link](https://www.pcb.com/products?m=482c15) |
# Bibliography
<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)
## Backlinks {#backlinks}
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Sensors]({{< relref "sensors" >}})
- [Position Sensors]({{< relref "position_sensors" >}})

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### Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------------|------------------------------------------------------------------------------------|
| Cedrat | [link](http://www.cedrat-technologies.com/) |
| PI | [link](https://www.physikinstrumente.com/en/) |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) |
| Noliac | [link](http://www.noliac.com/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) |
| Manufacturers | Links |
|---------------------|----------------------------------------------------------------------------------------------------------------|
| Cedrat | [link](http://www.cedrat-technologies.com/) |
| PI | [link](https://www.physikinstrumente.com/en/) |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) |
| Noliac | [link](http://www.noliac.com/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) |
| PiezoData | [link](https://www.piezodata.com/piezo-stack-actuator-2/) |
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) |
### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org7ef2e50)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
The relation between the applied voltage \\(V\_a\\) to the generated force \\(F\_a\\) is:
\\[ F\_a = g\_a V\_a, \quad g\_a = d\_{33} n k\_a \\]
with:
- \\(d\_{33}\\) is the piezoelectric strain constant [m/V]
- \\(n\\) is the number of layers
- \\(k\_a\\) is the actuator stiffness [N/m]
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in <sup id="5decd2b31c4a9842b80c58b56f96590a"><a class="reference-link" href="#claeyssen07_amplif_piezoel_actuat" title="Frank Claeyssen, Le Letty, Barillot, \&amp; Sosnicki, Amplified Piezoelectric Actuators: Static \&amp; Dynamic Applications, {Ferroelectrics}, v(1), 3-14 (2007).">(Frank Claeyssen {\it et al.}, 2007)</a></sup>:
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgc110fa4)):
> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
> The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in <sup id="849750850d9986ed326e74bd3c448d03"><a class="reference-link" href="#lucinskis16_dynam_charac" title="@misc{lucinskis16_dynam_charac,
author = {R. Lucinskis and C. Mangeot},
title = {Dynamic Characterization of an amplified piezoelectric
actuator},
year = 2016,
}">(Lucinskis \& Mangeot, 2016)</a></sup>.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orge1d2714)).
<a id="orgd9b1a8d"></a>
<a id="org5a5d286"></a>
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a class=\"reference-link\" href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">(Mingxiang Ling {\it et al.}, 2016)</a></sup>" >}}
@@ -57,6 +64,7 @@ A model of an amplified piezoelectric actuator is described in <sup id="84975085
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) |
## Specifications {#specifications}
@@ -121,7 +129,7 @@ with:
### Resolution {#resolution}
The resolution is limited by the noise in the voltage amplified.
The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
@@ -135,53 +143,57 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance}
The electrical capacitance gives the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org3da123f)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgebd19c2)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
<a id="org3da123f"></a>
[Voltage Amplifier]({{< relref "voltage_amplifier" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
<a id="orgebd19c2"></a>
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#orgab6e282)).
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#orgb64bc37)).
<a id="orgab6e282"></a>
<a id="orgb64bc37"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#orgcf60838)):
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#org944d760)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="orgcf60838"></a>
<a id="org944d760"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#orga8ee6e8)).
For piezo actuators, force and displacement are inversely related (Figure [5](#org0a60bcb)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
<a id="orga8ee6e8"></a>
<a id="org0a60bcb"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
# Bibliography
<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)
<a class="bibtex-entry" id="claeyssen07_amplif_piezoel_actuat">Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O., *Amplified piezoelectric actuators: static \& dynamic applications*, Ferroelectrics, *351(1)*, 3–14 (2007). http://dx.doi.org/10.1080/00150190701351865</a> [↩](#5decd2b31c4a9842b80c58b56f96590a)
## Bibliography {#bibliography}
<a class="bibtex-entry" id="lucinskis16_dynam_charac">Lucinskis, R., & Mangeot, C. (2016). *Dynamic characterization of an amplified piezoelectric actuator*. Retrieved from [](). .</a> [↩](#849750850d9986ed326e74bd3c448d03)
<a id="orgc110fa4"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a class="bibtex-entry" id="ling16_enhan_mathem_model_displ_amplif">Ling, M., Cao, J., Zeng, M., Lin, J., & Inman, D. J., *Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms*, Smart Materials and Structures, *25(7)*, 075022 (2016). http://dx.doi.org/10.1088/0964-1726/25/7/075022</a> [↩](#d9e8b33774f1e65d16bd79114db8ac64)
<a id="org7ef2e50"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="orge1d2714"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
## Backlinks {#backlinks}
- [Actuators]({{< relref "actuators" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})

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+++
Tags
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}})
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors}
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance <sup id="3fb5b61524290e36d639a4fac65703d0"><a class="reference-link" href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#orgeaf4a0a)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@@ -44,8 +44,7 @@ Tags
| Interferometer | Meters | | 0.5 nm | >100kHz | 1 ppm FSR |
| Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR |
## Strain Gauge {#strain-gauge}
Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors/).
## Capacitive Sensor {#capacitive-sensor}
@@ -55,42 +54,48 @@ Description:
- <http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html>
- <https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors>
| Manufacturers | Links |
|----------------|-------------------------------------------------------------------------------------------------|
| Micro Sense | [link](http://www.microsense.net/products-position-sensors.htm) |
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/) |
| PI | [link](https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/) |
| Unipulse | [link](https://www.unipulse.com/product/ps-ia/) |
| Lion-Precision | [link](https://www.lionprecision.com/products/capacitive-sensors) |
| Manufacturers | Links | Country |
|----------------|--------------------------------------------------------------------------------------------------|---------|
| Micro Sense | [link](http://www.microsense.net/products-position-sensors.htm) | USA |
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/) | Germany |
| PI | [link](https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/) | Germany |
| Unipulse | [link](https://www.unipulse.com/product/ps-ia/) | Japan |
| Lion-Precision | [link](https://www.lionprecision.com/products/capacitive-sensors) | USA |
| Fogale | [link](http://www.fogale.fr/brochures.html) | USA |
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-sensors) | UK |
| Capacitec | [link](https://www.capacitec.com/Displacement-Sensing-Systems) | USA |
## Inductive Sensor (Eddy Current) {#inductive-sensor--eddy-current}
| Manufacturers | Links |
|----------------|------------------------------------------------------------------------------------------|
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/) |
| Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors) |
| Manufacturers | Links | |
|----------------|-------------------------------------------------------------------------------------------|---------|
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/) | Germany |
| Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors) | USA |
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/sensors/eddy-current-sensors.html) | France |
| Kaman | [link](https://www.kamansensors.com/product/smt-9700/) | USA |
| Keyence | [link](https://www.keyence.com/ss/products/measure/measurement%5Flibrary/type/inductive/) | USA |
## Inductive Sensor (LVDT) {#inductive-sensor--lvdt}
| Manufacturers | Links |
|---------------|--------------------------------------------------------------------------------------------|
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/) |
| Keyence | [link](https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp) |
| Manufacturers | Links | Country |
|---------------|--------------------------------------------------------------------------------------------|---------|
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/) | Germany |
| Keyence | [link](https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp) | USA |
## Interferometers {#interferometers}
| Manufacturers | Links |
|---------------|----------------------------------------------------------------------------------------------------------|
| Attocube | [link](http://www.attocube.com/) |
| Zygo | [link](https://www.zygo.com/?/met/markets/stageposition/zmi/) |
| Smaract | [link](https://www.smaract.com/interferometry) |
| Qutools | [link](https://www.qutools.com/qudis/) |
| Renishaw | [link](https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594) |
| Sios | [link](https://sios-de.com/products/length-measurement/laser-interferometer/) |
| Keysight | [link](https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre) |
| Manufacturers | Links | Country |
|---------------|----------------------------------------------------------------------------------------------------------|---------|
| Attocube | [link](http://www.attocube.com/) | Germany |
| Zygo | [link](https://www.zygo.com/?/met/markets/stageposition/zmi/) | USA |
| Smaract | [link](https://www.smaract.com/interferometry) | Germany |
| Qutools | [link](https://www.qutools.com/qudis/) | Germany |
| Renishaw | [link](https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594) | UK |
| Sios | [link](https://sios-de.com/products/length-measurement/laser-interferometer/) | Germany |
| Keysight | [link](https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre) | USA |
<div class="table-caption">
<span class="table-number">Table 3</span>:
@@ -103,31 +108,33 @@ Description:
| Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 |
<sup id="7658b1219a4458a62ae8c6f51b767542"><a class="reference-link" href="#jang17_compen_refrac_index_air_laser" title="Yoon-Soo Jang \&amp; Seung-Woo Kim, Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: a Review, {International Journal of Precision Engineering and
Manufacturing}, v(12), 1881-1890 (2017).">(Yoon-Soo Jang \& Seung-Woo Kim, 2017)</a></sup>
([Jang and Kim 2017](#org5a2485c))
<a id="org0399c13"></a>
<a id="orgdc4dc3c"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
## Fiber Optic Displacement Sensor {#fiber-optic-displacement-sensor}
## Linear Encoders {#linear-encoders}
| Manufacturers | Links |
|---------------|----------------------------------------------------|
| Unipulse | [link](https://www.unipulse.com/product/atw200-2/) |
| Manufacturers | Links | Country |
|----------------|-----------------------------------------------------------------------|---------|
| Heidenhain | [link](https://www.heidenhain.com/en%5FUS/products/linear-encoders/) | Germany |
| MicroE Systems | [link](https://www.celeramotion.com/microe/products/linear-encoders/) | USA |
| Renishaw | [link](https://www.renishaw.com/en/browse-encoder-range--6440) | UK |
# Bibliography
<a class="bibtex-entry" id="fleming13_review_nanom_resol_posit_sensor">Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106–126 (2013). http://dx.doi.org/10.1016/j.sna.2012.10.016</a> [↩](#3fb5b61524290e36d639a4fac65703d0)
<a class="bibtex-entry" id="collette11_review">Collette, C., Artoos, K., Guinchard, M., Janssens, S., Carmona Fernandez, P., & Hauviller, C., *Review of sensors for low frequency seismic vibration measurement* (2011).</a> [↩](#642a18d86de4e062c6afb0f5f20501c4)
## Bibliography {#bibliography}
<a class="bibtex-entry" id="jang17_compen_refrac_index_air_laser">Jang, Y., & Kim, S., *Compensation of the refractive index of air in laser interferometer for distance measurement: a review*, International Journal of Precision Engineering and Manufacturing, *18(12)*, 1881–1890 (2017). http://dx.doi.org/10.1007/s12541-017-0217-y</a> [↩](#7658b1219a4458a62ae8c6f51b767542)
<a id="orgeaf4a0a"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
<a id="org5a2485c"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>.
## Backlinks {#backlinks}
- [A review of nanometer resolution position sensors: operation and performance]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}})
- [Measurement technologies for precision positioning]({{< relref "gao15_measur_techn_precis_posit" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Inertial Sensors]({{< relref "inertial_sensors" >}})
- [Sensors]({{< relref "sensors" >}})
- [Collocated Control]({{< relref "collocated_control" >}})

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title = "Power Spectral Density"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
Tutorial about Power Spectral Density is accessible [here](https://tdehaeze.github.io/spectral-analysis/).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org8fdb443)).
## Bibliography {#bibliography}
<a id="org8fdb443"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlab’s Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_.

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title = "Shaker"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
## Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------|-------------------------------------------------------------------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) |
<./biblio/references.bib>

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title = "Signal Conditioner"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Force Sensors]({{< relref "force_sensors" >}})
Most sensors needs some signal conditioner electronics before digitize the signal.
Few examples are:
- Piezoelectric force sensors
- Geophone
- Thermocouple, ...
The signal conditioning electronics can have different functions:
- Amplification
- Isolation
- Filtering
- Excitation
- Linearization
## Charge Amplifier {#charge-amplifier}
| Manufacturers | Links |
|---------------|---------------------------------------------------------------------------------------------------------------------|
| PCB | [link](https://www.pcb.com/sensors-for-test-measurement/electronics/line-powered-multi-channel-signal-conditioners) |
## Voltage Amplifier {#voltage-amplifier}
| Manufacturers | Links |
|---------------|------------------------------------------------------------------|
| Femto | [link](https://www.femto.de/en/products/voltage-amplifiers.html) |
## Current Amplifier {#current-amplifier}
| Manufacturers | Links |
|---------------|------------------------------------------------------------------|
| Femto | [link](https://www.femto.de/en/products/current-amplifiers.html) |
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Position Sensors]({{< relref "position_sensors" >}})

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Tags
: [Electronics]({{< relref "electronics" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
From <sup id="3b7899e183dba866e6a6419cf820467f"><a href="#jabben07_mechat" title="@phdthesis{jabben07_mechat,
author = {Jabben, Leon},
school = {Delft University},
title = {Mechatronic design of a magnetically suspended rotating
platform},
year = 2007,
}">@phdthesis{jabben07_mechat,
author = {Jabben, Leon},
school = {Delft University},
title = {Mechatronic design of a magnetically suspended rotating
platform},
year = 2007,
}</a></sup> (Section 3.3.2):
## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#orgd8e3764)) (Section 3.3.2):
> Electronic equipment does most often not come with detailed electric schemes, in which case the PSD should be determined from measurements.
> In the design phase however, one has to rely on information provided by specification sheets from the manufacturer.
@@ -31,5 +22,88 @@ From <sup id="3b7899e183dba866e6a6419cf820467f"><a href="#jabben07_mechat" title
> \\[ S\_{snr} = \frac{x\_{fr}^2}{8 f\_c C\_{snr}^2} \\]
> with \\(x\_{fr}\\) the full range of \\(x\\), and \\(C\_{snr}\\) the SNR.
# Bibliography
<a id="jabben07_mechat"></a>Jabben, L., *Mechatronic design of a magnetically suspended rotating platform* (Doctoral dissertation) (2007). Delft University, . [↩](#3b7899e183dba866e6a6419cf820467f)
<div class="examp">
<div></div>
Let's take an example.
- \\(x\_{fr} = 170 V\\)
- \\(C\_{snr} = 85 dB\\)
- \\(f\_c = 200 Hz\\)
The Power Spectral Density of the output voltage is:
\\[ S\_{snr} = \frac{170^2}{8 \cdot 200 \cdot {10^{\frac{2 \cdot 85}{20}}}} = 5.7 \cdot 10^{-8}\ V^2/Hz \\]
And the RMS of that noise up to \\(f\_c\\) is:
\\[ S\_{rms} = \sqrt{S\_{snr} \cdot f\_c} \approx 3.4\ mV \\]
</div>
## Convert SNR to Noise RMS value {#convert-snr-to-noise-rms-value}
The RMS value of the noise can be computed from:
\\[ N\_\text{rms} = 10^{-\frac{S\_{snr}}{20}} S\_\text{rms} \\]
where \\(S\_{snr}\\) is the SNR in dB and \\(S\_\text{rms}\\) is the RMS value of a sinus taking the full range.
If the full range is \\(\Delta V\\), then:
\\[ S\_\text{rms} = \frac{\Delta V/2}{\sqrt{2}} \\]
<div class="examp">
<div></div>
As an example, let's take a voltage amplifier with a full range of \\(\Delta V = 20V\\) and a SNR of 85dB.
The RMS value of the noise is then:
\\[ n\_\text{rms} = 10^{-\frac{S\_{nrs}}{20}} s\_\text{rms} \\]
\\[ n\_\text{rms} = 10^{-\frac{85}{20}} \frac{10}{\sqrt{2}} \approx 0.4 mV\_\text{rms} \\]
</div>
## Convert wanted Noise RMS value to required SNR {#convert-wanted-noise-rms-value-to-required-snr}
If the wanted full range and RMS value of the noise are defined, the required SNR can be computed from:
\\[ S\_{snr} = 20 \log \frac{\text{Signal, rms}}{\text{Noise, rms}} \\]
<div class="examp">
<div></div>
Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V\\), the corresponding SNR is:
\\[ S\_{snr} = 20 \log \frac{\frac{20/2}{\sqrt{2}}}{10^{-3}} \approx 77dB \\]
</div>
## Noise Density to RMS noise {#noise-density-to-rms-noise}
From ([Fleming 2010](#org68e05a9)):
\\[ \text{RMS noise} = \sqrt{2 \times \text{bandwidth}} \times \text{noise density} \\]
If the noise is normally distributed, the RMS value is also the standard deviation \\(\sigma\\).
The peak to peak amplitude is then approximatively \\(6 \sigma\\).
<div class="exampl">
<div></div>
- noise density = \\(20 pm/\sqrt{Hz}\\)
- bandwidth = 100Hz
\\[ \sigma = \sqrt{2 \times 100} \times 20 = 0.28nm RMS \\]
The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
</div>
## Bibliography {#bibliography}
<a id="org68e05a9"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="orgd8e3764"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
## Backlinks {#backlinks}
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})

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author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
| Manufacturers | Links |
|---------------|---------------------------------|
| Moflon | [link](https://www.moflon.com/) |
<./biblio/references.bib>

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| Beikimco | [link](http://www.beikimco.com/) |
| Electromate | [link](https://www.electromate.com/) |
| Magnetic Innovations | [link](https://www.magneticinnovations.com/) |
| Monticont | [link](http://www.moticont.com/) |
## Typical Specifications {#typical-specifications}

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title = "Voltage Amplifier"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}), [Electronics]({{< relref "electronics" >}})
## Voltage Amplifiers to drive Capacitive Load {#voltage-amplifiers-to-drive-capacitive-load}
### Limitation in Current {#limitation-in-current}
The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org0d9f468)).
<a id="org0d9f468"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
The equation linking the voltage to the current is:
\\[ I = C \frac{dU}{dt} \\]
Suppose we want to drive the piezo with a voltage:
\\[ U(t) = U\_0 \sin(\omega\_0 t) \\]
The required current is:
\\[ I = C U\_0 \omega\_0 \cos(\omega\_0 t) \\]
Thus, for a specified maximum current \\(I\_\text{max}\\), the "power bandwidth" will be:
\\[ \omega\_{0, \text{max}} = \frac{I\_\text{max}}{C U\_0}, \quad f\_{0, \text{max}} = \frac{I\_\text{max}}{C U\_0} \frac{1}{2 \pi} \\]
- Below \\(\omega\_{0, \text{max}}\\), a voltage amplitude \\(U\_0\\) can be applied to the piezoelectric load without reaching the maximum current \\(I\_\text{max}\\).
- Above \\(\omega\_{0, \text{max}}\\), the maximum current \\(I\_\text{max}\\) is reached and the maximum voltage that can be applied decreases with frequency:
\\[ U\_\text{max} = \frac{I\_\text{max}}{\omega C} \\]
The maximum voltage as a function of frequency is shown in Figure [2](#org8625e7c).
```matlab
Vpkp = 170; % [V]
Imax = 30e-3; % [A]
C = 1e-6; % [F]
(1/(2*pi))*Imax/(C * Vpkp/2) % Fmax [Hz]
```
```text
56.172
```
<a id="org8625e7c"></a>
{{< figure src="/ox-hugo/voltage_amplifier_max_V_piezo.png" caption="Figure 2: Maximum voltage as a function of the frequency for \\(C = 1 \mu F\\), \\(I\_\text{max} = 30mA\\) and \\(V\_{pkp} = 170 V\\)" >}}
Similarly, the voltage rise time is determined by the Capacitance of the piezoelectric stack and by the maximum current that the amplifier can deliver:
\\[ t\_c = \frac{\Delta U C}{I\_\text{max}} \\]
with \\(t\_c\\) in seconds, \\(\Delta U\\) in volts, \\(C\\) in Farads and \\(I\_\text{max}\\) in Amperes.
If driven at \\(\Delta U = 100V\\), \\(C = 1 \mu F\\) and \\(I\_\text{max} = 1 A\\), then:
\\[ t\_c = \frac{100 \cdot 10^{-6}}{1} = 0.1 ms \\]
### Amplifiers for Low Voltage PZT {#amplifiers-for-low-voltage-pzt}
Piezoelectric Stack Actuators are behaving like capacitor for the Amplifiers.
Specifications are usually:
- Maximum Current
- DC Gain (usually around 10)
- Output Noise or [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
| Manufacturers | Links |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|
| Piezo Drive | [link](https://www.piezodrive.com/drivers/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=13630) |
| PI | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) |
| Micromega Dynamics | |
| Lab Systems | [link](https://www.lab-systems.com/products/amplifier/amplifier.html) |
| Falco System | [link](https://www.falco-systems.com/products.html) |
| Piezomechanics | [link](https://www.piezomechanik.com/products/) |
| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html) |
| acal | [link](https://www.acalbfi.com/nl/Electronic-test-and-measurement/High-voltage-amplifiers/c/CAT-06-03) |
| Trek | [link](https://www.trekinc.com/products/HV%5FAmp.asp) |
| Madcitylabs | [link](http://www.madcitylabs.com/piezoactuators.html) |
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})