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Add "fron matter" to specify zettels category
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content/zettels/acquisition_systems.md
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title = "Acquisition Systems"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Analog to Digital Converters]({{< relref "analog_to_digital_converters" >}})
: [Analog to Digital Converters]({{<relref "analog_to_digital_converters.md#" >}})
## Manufacturers {#manufacturers}

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title = "Active Isolation Platforms"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
: [Vibration Isolation]({{<relref "vibration_isolation.md#" >}})
## Manufacturers {#manufacturers}

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Links to specific actuators:
- [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
- [Piezoelectric Actuators]({{<relref "piezoelectric_actuators.md#" >}})
## How to choose the correct actuator for my application? {#how-to-choose-the-correct-actuator-for-my-application}
For vibration isolation:
- In ([Ito and Schitter 2016](#orga71edd4)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
- In ([Ito and Schitter 2016](#orge96c061)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{<relref "ito16_compar_class_high_precis_actuat.md#" >}}))
## Brush-less DC Motor {#brush-less-dc-motor}
- ([Yedamale 2003](#org0ac1a74))
- ([Yedamale 2003](#org9fa946a))
<https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html>
@@ -30,6 +30,6 @@ For vibration isolation:
## Bibliography {#bibliography}
<a id="orga71edd4"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
<a id="orge96c061"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
<a id="org0ac1a74"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.
<a id="org9fa946a"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.

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content/zettels/analog_to_digital_converters.md
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author = ["Thomas Dehaeze"]
keywords = ["electronics"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Types of Analog to Digital Converters {#types-of-analog-to-digital-converters}
<https://dewesoft.com/daq/types-of-adc-converters>
- Delta Sigma ([Baker 2011](#org60f0e22))
- Delta Sigma ([Baker 2011](#orgbdb61af))
- Successive Approximation
@@ -32,9 +33,9 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati
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](#orgee08810)).
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](#org4bd731c)).
<a id="orgee08810"></a>
<a id="org4bd731c"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@@ -89,4 +90,4 @@ The quantization is:
## Bibliography {#bibliography}
<a id="org60f0e22"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.
<a id="orgbdb61af"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.

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title = "Cables"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Connectors]({{< relref "connectors" >}})
: [Connectors]({{<relref "connectors.md#" >}})
## Typical Cables {#typical-cables}

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content/zettels/capacitive_sensors.md
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title = "Capacitive Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Description of Capacitive Sensors {#description-of-capacitive-sensors}

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content/zettels/charge_amplifiers.md
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title = "Charge Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Description {#description}
@@ -17,19 +18,19 @@ This can be typically used to interface with piezoelectric sensors.
## Basic Circuit {#basic-circuit}
Two basic circuits of charge amplifiers are shown in Figure [1](#org7d016e2) (taken from ([Fleming 2010](#org467f88f))) and Figure [2](#orgb83f736) (taken from ([Schmidt, Schitter, and Rankers 2014](#org80f2485)))
Two basic circuits of charge amplifiers are shown in Figure [1](#org0d411fa) (taken from ([Fleming 2010](#org7834496))) and Figure [2](#org1c3e25d) (taken from ([Schmidt, Schitter, and Rankers 2014](#orgd26dd11)))
<a id="org7d016e2"></a>
<a id="org0d411fa"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit.png" caption="Figure 1: Electrical model of a piezoelectric force sensor is shown in gray. The op-amp charge amplifier is shown on the right. The output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
<a id="orgb83f736"></a>
<a id="org1c3e25d"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit_bis.png" caption="Figure 2: A piezoelectric accelerometer with a charge amplifier as signal conditioning element" >}}
The input impedance of the charge amplifier is very small (unlike when using a voltage amplifier).
The gain of the charge amplified (Figure [1](#org7d016e2)) is equal to:
The gain of the charge amplified (Figure [1](#org0d411fa)) is equal to:
\\[ \frac{V\_s}{q} = \frac{-1}{C\_s} \\]
@@ -50,6 +51,6 @@ The gain of the charge amplified (Figure [1](#org7d016e2)) is equal to:
## Bibliography {#bibliography}
<a id="org467f88f"></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="org7834496"></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="org80f2485"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="orgd26dd11"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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title = "Connectors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Cables]({{< relref "cables" >}})
: [Cables]({{<relref "cables.md#" >}})
## Manufacturers {#manufacturers}
@@ -19,8 +20,8 @@ Tags
## BNC {#bnc}
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgd1b23d3).
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgf757f74).
<a id="orgd1b23d3"></a>
<a id="orgf757f74"></a>
{{< figure src="/ox-hugo/bnc_50_75_ohms.jpg" caption="Figure 1: 75Ohms and 50Ohms BNC connectors" >}}

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content/zettels/digital_to_analog_converters.md
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title = "Digital to Analog Converters"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})

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title = "Eddy Current Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Manufacturers {#manufacturers}

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title = "Encoders"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
There are two main types of encoders: optical encoders, and magnetic encoders.

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@@ -12,33 +12,43 @@ Tags
Books:
- ([Lobontiu 2002](#org0e711a7))
- ([Henein 2003](#org4fb65e1))
- ([Smith 2005](#orgbf46163))
- ([Soemers 2011](#orgf482067))
- ([Cosandier 2017](#orgf099485))
- ([Lobontiu 2002](#orgb45af18))
- ([Henein 2003](#org8ce4916))
- ([Smith 2005](#orgccbed32))
- ([Soemers 2011](#org772b663))
- ([Cosandier 2017](#org7ebf41f))
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From ([Chen and McInroy 2000](#org14378b5)):
From ([Chen and McInroy 2000](#org64f8175)):
> To avoid the extremely non-linear micro-dynamics of joint friction and backlash, these hexapods employ flexure joints.
> A flexure joint bends material to achieve motion, rather than sliding of rolling across two surfaces.
> This does eliminate friction and backlash, but adds spring dynamics and limits the workspace.
## Materials {#materials}
- ([Smith 2000](#org299921c))
- ([Lobontiu 2002](#orgb45af18))
- ([Henein 2003](#org8ce4916))
- ([Cosandier 2017](#org7ebf41f))
## Bibliography {#bibliography}
<a id="org14378b5"></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="org64f8175"></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="orgf099485"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org7ebf41f"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org4fb65e1"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org8ce4916"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org0e711a7"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgb45af18"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgbf46163"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org299921c"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.
<a id="orgf482067"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.
<a id="orgccbed32"></a>———. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org772b663"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.

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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](#org903194d))
- ([Lobontiu 2002](#org353b748))
- ([Henein 2003](#org26cb408))
- ([Cosandier 2017](#org684f025))
## Bibliography {#bibliography}
<a id="org684f025"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org26cb408"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org353b748"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org903194d"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.

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title = "Force Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Modal Analysis]({{< relref "modal_analysis" >}})
: [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}), [Modal Analysis]({{<relref "modal_analysis.md#" >}})
## Technologies {#technologies}
@@ -17,9 +18,9 @@ There are two main technique for force sensors:
The choice between the two is usually based on whether the measurement is static (strain gauge) or dynamics (piezoelectric).
Main differences between the two are shown in Figure [1](#orgd4cde6e).
Main differences between the two are shown in Figure [1](#orgc9e9a88).
<a id="orgd4cde6e"></a>
<a id="orgc9e9a88"></a>
{{< figure src="/ox-hugo/force_sensor_piezo_vs_strain_gauge.png" caption="Figure 1: Piezoelectric Force sensor VS Strain Gauge Force sensor" >}}
@@ -29,7 +30,7 @@ Main differences between the two are shown in Figure [1](#orgd4cde6e).
### 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 ([Fleming 2010](#org6f75dec)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org024e377)) ([Notes]({{<relref "fleming10_nanop_system_with_force_feedb.md#" >}})).
### Manufacturers {#manufacturers}
@@ -45,7 +46,7 @@ An analysis the dynamics and noise of a piezoelectric force sensor is done in ([
### Signal Conditioner {#signal-conditioner}
The voltage generated by the piezoelectric material generally needs to be amplified using a [Signal Conditioner]({{< relref "signal_conditioner" >}}).
The voltage generated by the piezoelectric material generally needs to be amplified using a [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}).
Either **charge** amplifiers or **voltage** amplifiers can be used.
@@ -78,4 +79,4 @@ However, if a charge conditioner is used, the signal will be doubled.
## Bibliography {#bibliography}
<a id="org6f75dec"></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="org024e377"></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>.

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title = "Granite"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags

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content/zettels/inertial_sensors.md
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title = "Inertial Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Review of Absolute (inertial) Position Sensors {#review-of-absolute--inertial--position-sensors}
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orga092f9a))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#orgef1075b))
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orgc1383e0))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#org7b301f5))
<a id="org9a5fa73"></a>
<a id="orgf969bc3"></a>
{{< figure src="/ox-hugo/collette12_absolute_disp_sensors.png" caption="Figure 1: Dynamic range of several types of inertial sensors; Price versus resolution for several types of inertial sensors" >}}
@@ -35,7 +36,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="org1693047"></a>
<a id="orga2a662e"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_accelerometers.png" caption="Figure 2: Characteristics of commercially available accelerometers <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@@ -52,7 +53,7 @@ Wireless Accelerometers
| [Guralp](https://www.guralp.com/products/surface) | UK |
| [Nanometric](https://www.nanometrics.ca/products/seismometers) | Canada |
<a id="org6d70737"></a>
<a id="org431a804"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_geophone.png" caption="Figure 3: Characteristics of commercially available geophones <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@@ -60,6 +61,6 @@ Wireless Accelerometers
## Bibliography {#bibliography}
<a id="orga092f9a"></a>Collette, C., S. Janssens, P. Fernandez-Carmona, K. Artoos, M. Guinchard, C. Hauviller, and A. Preumont. 2012. “Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement.” _Bulletin of the Seismological Society of America_ 102 (4):1289–1300. <https://doi.org/10.1785/0120110223>.
<a id="orgc1383e0"></a>Collette, C., S. Janssens, P. Fernandez-Carmona, K. Artoos, M. Guinchard, C. Hauviller, and A. Preumont. 2012. “Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement.” _Bulletin of the Seismological Society of America_ 102 (4):1289–1300. <https://doi.org/10.1785/0120110223>.
<a id="orgef1075b"></a>Collette, C, S Janssens, B Mokrani, L Fueyo-Roza, K Artoos, M Esposito, P Fernandez-Carmona, M Guinchard, and R Leuxe. 2012. “Comparison of New Absolute Displacement Sensors.” In _International Conference on Noise and Vibration Engineering (ISMA)_.
<a id="org7b301f5"></a>Collette, C, S Janssens, B Mokrani, L Fueyo-Roza, K Artoos, M Esposito, P Fernandez-Carmona, M Guinchard, and R Leuxe. 2012. “Comparison of New Absolute Displacement Sensors.” In _International Conference on Noise and Vibration Engineering (ISMA)_.

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title = "Instrumented Hammer"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Modal Analysis]({{< relref "modal_analysis" >}}), [Force Sensors]({{< relref "force_sensors" >}})
: [Modal Analysis]({{<relref "modal_analysis.md#" >}}), [Force Sensors]({{<relref "force_sensors.md#" >}})
And instrumented hammer consist of a regular hammer with a force sensor fixed at its tip.

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title = "Interferometers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@@ -24,12 +25,12 @@ Tags
## Reviews {#reviews}
([Ducourtieux 2018](#orgba5debb), [2018](#orgba5debb); [Bobroff 1993](#org9cfc0be), [1993](#org9cfc0be); [Thurner et al. 2015](#org9f4a3ed), [2015](#org9f4a3ed); [Loughridge and Abramovitch 2013](#org2c02ae6))
([Ducourtieux 2018](#org538e4dc), [2018](#org538e4dc); [Bobroff 1993](#org9f4652e), [1993](#org9f4652e); [Thurner et al. 2015](#orgdcf4929), [2015](#orgdcf4929); [Loughridge and Abramovitch 2013](#orgd91ce9e))
## Effect of Refractive Index - Environmental Units {#effect-of-refractive-index-environmental-units}
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#org9f4a3ed))).
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#orgdcf4929))).
<a id="table--tab:index-air"></a>
<div class="table-caption">
@@ -64,16 +65,16 @@ Typical characteristics of commercial environmental units are shown in Table [2]
## Interferometer Precision {#interferometer-precision}
Figure [1](#org1406d51) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#orgcfb1fbe))).
Figure [1](#org24527f3) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#org0cf5512))).
<a id="org1406d51"></a>
<a id="org24527f3"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
## Sources of uncertainty {#sources-of-uncertainty}
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#orgba5debb)).
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org538e4dc)).
It includes:
@@ -83,10 +84,10 @@ It includes:
- Pressure: \\(K\_P \approx 0.27 ppm hPa^{-1}\\)
- Humidity: \\(K\_{HR} \approx 0.01 ppm \% RH^{-1}\\)
- These errors can partially be compensated using an environmental unit.
- Air turbulence (Figure [2](#org690599c))
- Air turbulence (Figure [2](#org1d0f37d))
- Non linearity
<a id="org690599c"></a>
<a id="org1d0f37d"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="Figure 2: Effect of air turbulences on measurement stability" >}}
@@ -94,12 +95,12 @@ It includes:
## Bibliography {#bibliography}
<a id="org9cfc0be"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” _Measurement Science and Technology_ 4 (9):907–26. <https://doi.org/10.1088/0957-0233/4/9/001>.
<a id="org9f4652e"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” _Measurement Science and Technology_ 4 (9):907–26. <https://doi.org/10.1088/0957-0233/4/9/001>.
<a id="orgba5debb"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” <https://doi.org/10.13140/rg.2.2.21044.35205>.
<a id="org538e4dc"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” <https://doi.org/10.13140/rg.2.2.21044.35205>.
<a id="orgcfb1fbe"></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="org0cf5512"></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="org2c02ae6"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In _2013 American Control Conference_, nil. <https://doi.org/10.1109/acc.2013.6580402>.
<a id="orgd91ce9e"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In _2013 American Control Conference_, nil. <https://doi.org/10.1109/acc.2013.6580402>.
<a id="org9f4a3ed"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
<a id="orgdcf4929"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

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title = "Linear Guides"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@@ -14,5 +15,3 @@ Tags
|----------------------------------------------------------------------------------------------------------------------------|---------|
| [Bosch Rexroth](https://www.boschrexroth.com/en/xc/products/product-groups/linear-motion-technology/topics/linear-guides/) | Germany |
| [THK](https://www.thk.com/?q=eng/node/231) | Japan |
<./biblio/references.bib>

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title = "Linear variable differential transformers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Manufacturers {#manufacturers}

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title = "Parallel Manipulators"
author = ["Thomas Dehaeze"]
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:

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title = "Piezoelectric Actuators"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Actuators](actuators.md), [Voltage Amplifier](voltage_amplifier.md)
: [Actuators]({{<relref "actuators.md#" >}}), [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}})
## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
@@ -32,7 +33,7 @@ Tags
### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgc916f93)) ([Notes](fleming10_nanop_system_with_force_feedb.md)).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgd563065)) ([Notes]({{<relref "fleming10_nanop_system_with_force_feedb.md#" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@@ -56,14 +57,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator /
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgaaabf8d)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgb463c4c)):
> 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 ([Lucinskis and Mangeot 2016](#org8ca201e)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2bf81f0)).
<a id="org5d92181"></a>
<a id="org77a46eb"></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 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).\">ling16_enhan_mathem_model_displ_amplif</a></sup>" >}}
@@ -141,9 +142,9 @@ with:
### Resolution {#resolution}
The resolution is limited by the noise in the [Voltage Amplifier](voltage_amplifier.md).
The resolution is limited by the noise in the [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}).
Typical [Signal to Noise Ratio](signal_to_noise_ratio.md) of voltage amplifiers is \\(100dB = 10^{5}\\).
Typical [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
\begin{equation}
@@ -155,58 +156,58 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance}
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org2c60a2d)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgca6870e)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[Voltage Amplifier](voltage_amplifier.md) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
[Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}) 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="org2c60a2d"></a>
<a id="orgca6870e"></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](#org7af4476)).
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](#orge05f5e6)).
<a id="org7af4476"></a>
<a id="orge05f5e6"></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](#org97370ea)):
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](#orgfcd374f)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="org97370ea"></a>
<a id="orgfcd374f"></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](#org8c01425)).
For piezo actuators, force and displacement are inversely related (Figure [5](#orgada6c4c)).
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.
<a id="org8c01425"></a>
<a id="orgada6c4c"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Driving Electronics {#driving-electronics}
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier](voltage_amplifier.md).
Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems](fleming14_desig_model_contr_nanop_system.md).
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}).
Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{<relref "fleming14_desig_model_contr_nanop_system.md#" >}}).
## Bibliography {#bibliography}
<a id="orgaaabf8d"></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 id="orgb463c4c"></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 id="orgc916f93"></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="orgd563065"></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="org8ca201e"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org2bf81f0"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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+++
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" >}})
: [Inertial Sensors]({{<relref "inertial_sensors.md#" >}}), [Force Sensors]({{<relref "force_sensors.md#" >}}), [Sensor Fusion]({{<relref "sensor_fusion.md#" >}}), [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}), [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}})
## Types of Positioning sensors {#types-of-positioning-sensors}
High precision positioning sensors include:
- [Interferometers]({{< relref "interferometers" >}})
- [Capacitive Sensors]({{< relref "capacitive_sensors" >}})
- [LVDT]({{< relref "linear_variable_differential_transformers" >}})
- [Eddy Current Sensors]({{< relref "eddy_current_sensors" >}})
- [Encoders]({{< relref "encoders" >}})
- [Interferometers]({{<relref "interferometers.md#" >}})
- [Capacitive Sensors]({{<relref "capacitive_sensors.md#" >}})
- [LVDT]({{<relref "linear_variable_differential_transformers.md#" >}})
- [Eddy Current Sensors]({{<relref "eddy_current_sensors.md#" >}})
- [Encoders]({{<relref "encoders.md#" >}})
## 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](#orgbadb097)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#org654bd0b)) ([Notes]({{<relref "fleming13_review_nanom_resol_posit_sensor.md#" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@@ -57,7 +57,7 @@ High precision positioning sensors include:
Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors/).
<a id="org2b23cef"></a>
<a id="orgff7dc3a"></a>
{{< figure src="/ox-hugo/position_sensors_thurner15.png" caption="Figure 1: Overview of range and precision of different position displacement sensors. Taken from <sup id=\"53230532ada812541a7cd984b3aa2662\"><a href=\"#thurner15_fiber_based_distan_sensin_inter\" title=\"Thurner, Quacquarelli, Braun, Pierre-Fran\ccois, Dal Savio, Karrai \&amp; Khaled, Fiber-Based Distance Sensing Interferometry, {Applied optics}, v(10), 3051--3063 (2015).\">thurner15_fiber_based_distan_sensin_inter</a></sup>" >}}
@@ -65,4 +65,4 @@ Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionp
## Bibliography {#bibliography}
<a id="orgbadb097"></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="org654bd0b"></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>.

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title = "Rotation Stage"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Slip Rings]({{< relref "slip_rings" >}})
: [Slip Rings]({{<relref "slip_rings.md#" >}})
## Manufacturers {#manufacturers}

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title = "Shaker"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
: [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
## Manufacturers {#manufacturers}

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title = "Signal Conditioner"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Sensors]({{< relref "sensors" >}}), [Electronics]({{< relref "electronics" >}})
: [Sensors]({{<relref "sensors.md#" >}}), [Electronics]({{<relref "electronics.md#" >}})
Most sensors needs some signal conditioner electronics before digitize the signal.
Few examples are:
@@ -25,6 +26,6 @@ The signal conditioning electronics can have different functions:
Depending on the electrical quantity that is meaningful for the measurement, different types of amplifiers are used:
- Current to Voltage ([Transimpedance Amplifiers]({{< relref "transimpedance_amplifiers" >}}))
- Charge to Voltage ([Charge Amplifiers]({{< relref "charge_amplifiers" >}}))
- Voltage to Voltage ([Voltage Amplifier]({{< relref "voltage_amplifier" >}}))
- Current to Voltage ([Transimpedance Amplifiers]({{<relref "transimpedance_amplifiers.md#" >}}))
- Charge to Voltage ([Charge Amplifiers]({{<relref "charge_amplifiers.md#" >}}))
- Voltage to Voltage ([Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}))

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title = "Simulink Real Time Target Machines"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
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title = "Slip Rings"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Rotation Stage]({{< relref "rotation_stage" >}})
: [Rotation Stage]({{<relref "rotation_stage.md#" >}})
## Manufacturers {#manufacturers}

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title = "Springs"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@@ -18,5 +19,3 @@ Tags
| [Paulstra](https://www.paulstra-industry.com/en/ranges/metal-mountings/v1210) | France |
| [Norelem](https://www.norelem.com/us/en/Products/Product-overview/Systems-and-components-for-machine-and-plant-construction/26000-Compression-springs-Elastomer-springs-Rubber-buffers-Shock-absorbers-Gas-springs.html) | France |
| [VibraSystems](https://vibrasystems.com/elastomer-and-spring-hangers.html) | USA |
<./biblio/references.bib>

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title = "Tip-Tilt Mirrors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
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title = "Transconductance Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}}), [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
: [Electronics]({{<relref "electronics.md#" >}}), [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
## Description {#description}

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title = "Transimpedance Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Description {#description}

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title = "Voice Coil Actuators"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Actuators]({{< relref "actuators" >}})
: [Actuators]({{<relref "actuators.md#" >}})
## Working Principle {#working-principle}
@@ -16,12 +17,12 @@ Tags
## Model of a Voice Coil Actuator {#model-of-a-voice-coil-actuator}
([Schmidt, Schitter, and Rankers 2014](#orgc4c6d58))
([Schmidt, Schitter, and Rankers 2014](#org173764e))
## Driving Electronics {#driving-electronics}
As the force is proportional to the current, a [Transconductance Amplifiers]({{< relref "transconductance_amplifiers" >}}) (voltage-controller current source) is generally used as the driving electronics.
As the force is proportional to the current, a [Transconductance Amplifiers]({{<relref "transconductance_amplifiers.md#" >}}) (voltage-controller current source) is generally used as the driving electronics.
## Manufacturers {#manufacturers}
@@ -43,4 +44,4 @@ As the force is proportional to the current, a [Transconductance Amplifiers]({{<
## Bibliography {#bibliography}
<a id="orgc4c6d58"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="org173764e"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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title = "Voltage Amplifier"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}), [Electronics]({{< relref "electronics" >}})
: [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}}), [Piezoelectric Actuators]({{<relref "piezoelectric_actuators.md#" >}}), [Electronics]({{<relref "electronics.md#" >}})
## Voltage Amplifiers to drive Capacitive Loads {#voltage-amplifiers-to-drive-capacitive-loads}
@@ -33,9 +34,9 @@ Tags
The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org14569de)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org63f8350)).
<a id="org14569de"></a>
<a id="org63f8350"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@@ -55,7 +56,7 @@ 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](#orga5b5a57).
The maximum voltage as a function of frequency is shown in Figure [2](#orgfbd4a45).
```matlab
Vpkp = 170; % [V]
@@ -69,7 +70,7 @@ The maximum voltage as a function of frequency is shown in Figure [2](#orga5b5a5
56.172
```
<a id="orga5b5a57"></a>
<a id="orgfbd4a45"></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\\)" >}}
@@ -89,7 +90,7 @@ Specifications are usually:
- Maximum Current
- DC Gain (usually around 10)
- Output Noise or [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- Output Noise or [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}})
The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
@@ -105,7 +106,7 @@ This can pose several problems:
### Noise {#noise}
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org8deb271)).
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org2170119)).
Proper enclosures and cabling are necessary to protect the system from capacitive and inductive interferance.
@@ -117,14 +118,14 @@ The **input** impedance of voltage amplifiers are generally set to \\(50 \Omega\
The **output** (or internal) impedance of voltage amplifier is generally wanted small in order to have a small voltage drop when large current are drawn.
However, for stability reasons and to avoid overshoot (due to the internal negative feedback loop), this impedance can be chosen quite large.
This is discussed in ([Spengen 2017](#org22b2168)).
This is discussed in ([Spengen 2017](#org55e5dcc)).
## Bibliography {#bibliography}
<a id="org6dde1c6"></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="org200fc06"></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="org22b2168"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org55e5dcc"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org8deb271"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.
<a id="org2170119"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.