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title = "Analog to Digital Converters"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Electronics]({{< relref "electronics" >}})
## Power Spectral Density of the Quantization Noise {#power-spectral-density-of-the-quantization-noise}
This analysis is taken from [here](https://www.allaboutcircuits.com/technical-articles/quantization-nois-amplitude-quantization-error-analog-to-digital-converters/).
Let's note:
- \\(q = \frac{\Delta V}{2^n}\\) the quantization in [V] (the corresponding value in [V] of the least significant bit)
- \\(\Delta V\\) is the full range of the ADC in [V]
- \\(n\\) is the number of ADC's bits
- \\(f\_s\\) is the sample frequency in [Hz]
Let's suppose that the ADC is ideal and the only noise comes from the quantization error.
Interestingly, the noise amplitude is uniformly distributed.
The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#org5158d30)).
<a id="org5158d30"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
Now, we can calculate the time average power of the quantization noise as
\begin{equation}
P\_q = \int\_{-q/2}^{q/2} e^2 p(e) de = \frac{q^2}{12}
\end{equation}
The other important parameter of a noise source is the power spectral density (PSD), which indicates how the noise power spreads in different frequency bands.
To find the power spectral density, we need to calculate the Fourier transform of the autocorrelation function of the noise.
Assuming that the noise samples are not correlated with one another, we can approximate the autocorrelation function with a delta function in the time domain.
Since the Fourier transform of a delta function is equal to one, the **power spectral density will be frequency independent**.
Therefore, the quantization noise is white noise with total power equal to \\(P\_q = \frac{q^2}{12}\\).
Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we should divide the noise power \\(P\_q\\) by \\(f\_s\\):
\begin{equation}
\int\_{-f\_s/2}^{f\_s/2} \Gamma(f) d f = f\_s \Gamma = \frac{q^2}{12}
\end{equation}
<div class="important">
<div></div>
Finally, the Power Spectral Density of the quantization noise of an ADC is equal to:
\begin{equation}
\begin{aligned}
\Gamma &= \frac{q^2}{12 f\_s} \\\\\\
&= \frac{\left(\frac{\Delta V}{2^n}\right)^2}{12 f\_s} \text{ in } \left[ \frac{V^2}{Hz} \right]
\end{aligned}
\end{equation}
</div>
<div class="examp">
<div></div>
Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz.
The quantization is:
\\[ q = \frac{20}{2^{18}} = 0.000076 \ [V] = 76 \ [\mu V] \\]
\\[ \Gamma\_Q = \frac{q^2}{12 f\_N} = 4.85 \cdot 10^{-14} \quad [V^2/Hz] \\]
</div>
<./biblio/references.bib>

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title = "Digital to Analog Converters"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Electronics]({{< relref "electronics" >}})
<./biblio/references.bib>

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title = "Flexures"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Flexible Joints]({{< relref "flexible_joints" >}})
## Material Used {#material-used}
## Materials {#materials}
- ([Smith 2000](#org0c6025e))
- ([Lobontiu 2002](#org42ce68f))
- ([Henein 2003](#org59d412b))
- ([Cosandier 2017](#org637114f))
## Bibliography {#bibliography}
<a id="org637114f"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org59d412b"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org42ce68f"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org0c6025e"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.

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## Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------|---------------------------------------------------------------------------------------------------------------|
| PCB | [link](https://www.pcb.com/sensors-for-test-measurement/impact-hammers-electrodynamic-shakers/impact-hammers) |
| DJB | [link](https://www.djbinstruments.com/products/instrumentation/impact-hammers) |
| Manufacturers | Links | Country |
|---------------|---------------------------------------------------------------------------------------------------------------|----------|
| PCB | [link](https://www.pcb.com/sensors-for-test-measurement/impact-hammers-electrodynamic-shakers/impact-hammers) | USA |
| DJB | [link](https://www.djbinstruments.com/products/instrumentation/impact-hammers) | UK |
| Dewesoft | [link](https://dewesoft.com/fr/products/interfaces-and-sensors/accelerometers-and-modal-hammers) | Slovenia |
<./biblio/references.bib>

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draft = false
+++
### Backlinks {#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" >}})
- [Inertial Sensors]({{< relref "inertial_sensors" >}})
- [Sensors]({{< relref "sensors" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Inertial Sensors]({{< relref "inertial_sensors" >}})
Tags
: [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" >}})
@@ -18,7 +18,7 @@ Tags
## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors}
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#orgdd1b6d5)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#org0e7fb0d)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@@ -116,9 +116,9 @@ Description:
| Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 |
([Jang and Kim 2017](#orgbcf1569))
([Jang and Kim 2017](#orga6fb604))
<a id="orgf2b5520"></a>
<a id="org22624ed"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
@@ -130,10 +130,11 @@ Description:
| 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 |
| Celera Motion | [link](https://www.celeramotion.com/microe/) | USA |
## Bibliography {#bibliography}
<a id="orgdd1b6d5"></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="org0e7fb0d"></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="orgbcf1569"></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>.
<a id="orga6fb604"></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>.

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title = "Rotation Stage"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Slip Rings]({{< relref "slip_rings" >}})
## Manufacturers {#manufacturers}
| Manufacturers | Links | Country |
|-------------------|-------------------------------------------|---------|
| Huber | [link](https://www.xhuber.com/en/) | Germany |
| LAB Motion System | [link](http://www.leuvenairbearings.com/) | Belgium |
<./biblio/references.bib>

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<https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems/permanent-magnet-shakers/V201>
| Manufacturers | Links |
|--------------------|----------------------------------------------------------------------------------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) |
| The Modal Shop | [link](http://www.modalshop.com/excitation/Electrodynamic-Exciter-Family?ID=243) |
| Deweshop | [link](https://dewesoft.com/fr/products/interfaces-and-sensors/shakers) |
| Bruel and Kjaer | [link](https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems) |
| YMC | [link](http://www.chinaymc.com/product/showproduct.php?id=78&lang=en) |
| BKSV | [link](https://www.bksv.com/en/products/shakers-and-exciters) |
| Vibration Research | [link](https://vibrationresearch.com/shakers/) |
| Sentek Dynamics | [link](https://www.sentekdynamics.com/) |
| Manufacturers | Links | Country |
|--------------------|----------------------------------------------------------------------------------|-----------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) | Australia |
| The Modal Shop | [link](http://www.modalshop.com/excitation/Electrodynamic-Exciter-Family?ID=243) | USA |
| Deweshop | [link](https://dewesoft.com/fr/products/interfaces-and-sensors/shakers) | Slovenia |
| Bruel and Kjaer | [link](https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems) | Denmark |
| YMC | [link](http://www.chinaymc.com/product/showproduct.php?id=78&lang=en) | China |
| Vibration Research | [link](https://vibrationresearch.com/shakers/) | USA |
| Sentek Dynamics | [link](https://www.sentekdynamics.com/) | USA |
<./biblio/references.bib>

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draft = false
+++
### Backlinks {#backlinks}
Backlinks:
- [Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments]({{< relref "tang18_decen_vibrat_contr_voice_coil" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
@@ -32,40 +32,59 @@ Tags
:
## Manufacturers {#manufacturers}
| Manufacturers | Links | Country |
|---------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|
| PI | [link](https://www.physikinstrumente.com/en/products/parallel-kinematic-hexapods/) | Germany |
| Newport | [link](https://www.newport.com/search/?q1=hexapod%3Arelevance%3Acompatibility%3AMETRIC%3AisObsolete%3Afalse%3A-excludeCountries%3AFR%3AnpCategory%3Ahexapods&ajax&text=hexapod) | USA |
| Symetrie | [link](https://symetrie.fr/en/hexapods-en/positioning-hexapods/) | France |
## Stewart Platforms at ESRF {#stewart-platforms-at-esrf}
| Beamline | Manufacturer | Comments |
|----------|--------------|-----------------------------------|
| ID11 | Symetrie | Small, Piezo based |
| ID31 | Symetrie | Large Stroke, Encoders, DC motors |
| ID01 | PI | |
| ID16a | ESRF | Piezo (PI) |
## Flexure Jointed Stewart Platforms {#flexure-jointed-stewart-platforms}
Papers by J.E. McInroy:
- ([O’Brien et al. 1998](#orgaa46d57))
- ([McInroy, O’Brien, and Neat 1999](#org378c866))
- ([McInroy 1999](#org3334ff2))
- ([McInroy and Hamann 2000](#orgbb67e4d))
- ([Chen and McInroy 2000](#org37a21cf))
- ([McInroy 2002](#org8af76b7))
- ([Li, Hamann, and McInroy 2001](#orgd55cfdb))
- ([Lin and McInroy 2003](#orged11f1d))
- ([Jafari and McInroy 2003](#org3d4fb3c))
- ([Chen and McInroy 2004](#orgda0daba))
- ([O’Brien et al. 1998](#org71c69cc))
- ([McInroy, O’Brien, and Neat 1999](#orgd9fe3c1))
- ([McInroy 1999](#org82cce67))
- ([McInroy and Hamann 2000](#orgc17f973))
- ([Chen and McInroy 2000](#org21fffc9))
- ([McInroy 2002](#org2f95611))
- ([Li, Hamann, and McInroy 2001](#org247940b))
- ([Lin and McInroy 2003](#org39928ef))
- ([Jafari and McInroy 2003](#org1e7c00b))
- ([Chen and McInroy 2004](#orgc6995cb))
## Bibliography {#bibliography}
<a id="orgda0daba"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.
<a id="orgc6995cb"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.
<a id="org37a21cf"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org21fffc9"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org3d4fb3c"></a>Jafari, F., and J.E. McInroy. 2003. “Orthogonal Gough-Stewart Platforms for Micromanipulation.” _IEEE Transactions on Robotics and Automation_ 19 (4). Institute of Electrical and Electronics Engineers (IEEE):595–603. <https://doi.org/10.1109/tra.2003.814506>.
<a id="org1e7c00b"></a>Jafari, F., and J.E. McInroy. 2003. “Orthogonal Gough-Stewart Platforms for Micromanipulation.” _IEEE Transactions on Robotics and Automation_ 19 (4). Institute of Electrical and Electronics Engineers (IEEE):595–603. <https://doi.org/10.1109/tra.2003.814506>.
<a id="orged11f1d"></a>Lin, Haomin, and J.E. McInroy. 2003. “Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms.” _IEEE Transactions on Control Systems Technology_ 11 (2):267–72. <https://doi.org/10.1109/tcst.2003.809248>.
<a id="org39928ef"></a>Lin, Haomin, and J.E. McInroy. 2003. “Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms.” _IEEE Transactions on Control Systems Technology_ 11 (2):267–72. <https://doi.org/10.1109/tcst.2003.809248>.
<a id="orgd55cfdb"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In _Smart Structures and Materials 2001: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.436521>.
<a id="org247940b"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In _Smart Structures and Materials 2001: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.436521>.
<a id="org3334ff2"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
<a id="org82cce67"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
<a id="org8af76b7"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
<a id="org2f95611"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
<a id="orgbb67e4d"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
<a id="orgc17f973"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
<a id="org378c866"></a>McInroy, J.E., J.F. O’Brien, and G.W. Neat. 1999. “Precise, Fault-Tolerant Pointing Using a Stewart Platform.” _IEEE/ASME Transactions on Mechatronics_ 4 (1):91–95. <https://doi.org/10.1109/3516.752089>.
<a id="orgd9fe3c1"></a>McInroy, J.E., J.F. O’Brien, and G.W. Neat. 1999. “Precise, Fault-Tolerant Pointing Using a Stewart Platform.” _IEEE/ASME Transactions on Mechatronics_ 4 (1):91–95. <https://doi.org/10.1109/3516.752089>.
<a id="orgaa46d57"></a>O’Brien, J.F., J.E. McInroy, D. Bodtke, M. Bruch, and J.C. Hamann. 1998. “Lessons Learned in Nonlinear Systems and Flexible Robots Through Experiments on a 6 Legged Platform.” In _Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)_, nil. <https://doi.org/10.1109/acc.1998.703532>.
<a id="org71c69cc"></a>O’Brien, J.F., J.E. McInroy, D. Bodtke, M. Bruch, and J.C. Hamann. 1998. “Lessons Learned in Nonlinear Systems and Flexible Robots Through Experiments on a 6 Legged Platform.” In _Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)_, nil. <https://doi.org/10.1109/acc.1998.703532>.

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draft = false
+++
## Backlinks {#backlinks}
### Backlinks {#backlinks}
- [Element and system design for active and passive vibration isolation]({{< relref "zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
@@ -31,4 +31,11 @@ draft = false
Tags
:
## Vibration Isolation Tables {#vibration-isolation-tables}
| Manufacturer | links |
|--------------|-----------------------------------------------------------|
| TMC | [link](https://www.techmfg.com/products/stacis/stacisiii) |
<./biblio/references.bib>

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draft = false
+++
### Backlinks {#backlinks}
Backlinks:
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
@@ -15,13 +15,32 @@ Tags
## Voltage Amplifiers to drive Capacitive Load {#voltage-amplifiers-to-drive-capacitive-load}
### Manufacturers {#manufacturers}
| Manufacturers | Links | Country |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|
| Piezo Drive | [link](https://www.piezodrive.com/drivers/) | Australia |
| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=2085) | USA |
| PI | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) | USA |
| Micromega Dynamics | | Belgium |
| Lab Systems | [link](https://www.lab-systems.com/products/amplifier/amplifier.html) | Isreal |
| Falco System | [link](https://www.falco-systems.com/products.html) | Netherlands |
| Piezomechanics | [link](https://www.piezomechanik.com/products/) | Germany |
| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html) | France |
| Trek | [link](https://www.trekinc.com/products/HV%5FAmp.asp) | USA |
| Madcitylabs | [link](http://www.madcitylabs.com/piezoactuators.html) | USA |
| Piezosystem | [link](https://www.piezosystem.com/products/controller/) | Germany |
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/08.html) | Japan |
### 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](#org7969f96)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#orgf2b344c)).
<a id="org7969f96"></a>
<a id="orgf2b344c"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@@ -41,7 +60,7 @@ Thus, for a specified maximum current \\(I\_\text{max}\\), the "power bandwidth"
- 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](#org310483b).
The maximum voltage as a function of frequency is shown in Figure [2](#org1190638).
```matlab
Vpkp = 170; % [V]
@@ -55,7 +74,7 @@ C = 1e-6; % [F]
56.172
```
<a id="org310483b"></a>
<a id="org1190638"></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\\)" >}}
@@ -69,7 +88,7 @@ If driven at \\(\Delta U = 100V\\), \\(C = 1 \mu F\\) and \\(I\_\text{max} = 1 A
### Bandwidth limitation (small signals) {#bandwidth-limitation--small-signals}
This is takken from Chapter 14 of ([Fleming and Leang 2014](#orga9ea9d3)).
This is takken from Chapter 14 of ([Fleming and Leang 2014](#org2e80fee)).
```matlab
L = 250e-9; % Cable inductance [H]
@@ -92,23 +111,7 @@ Specifications are usually:
The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
| Manufacturers | Links | Country |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|
| Piezo Drive | [link](https://www.piezodrive.com/drivers/) | Australia |
| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=2085) | USA |
| PI | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) | USA |
| Micromega Dynamics | | Belgium |
| Lab Systems | [link](https://www.lab-systems.com/products/amplifier/amplifier.html) | Isreal |
| Falco System | [link](https://www.falco-systems.com/products.html) | Netherlands |
| Piezomechanics | [link](https://www.piezomechanik.com/products/) | Germany |
| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html) | France |
| Trek | [link](https://www.trekinc.com/products/HV%5FAmp.asp) | USA |
| Madcitylabs | [link](http://www.madcitylabs.com/piezoactuators.html) | USA |
| Piezosystem | [link](https://www.piezosystem.com/products/controller/) | Germany |
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/08.html) | Japan |
## Bibliography {#bibliography}
<a id="orga9ea9d3"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
<a id="org2e80fee"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.