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21
content/zettels/analog_to_digital_converters.md
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+++
title = "Analog to Digital Converters"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
keywords = ["electronics"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{<relref "electronics.md#" >}})
: [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](#orgbdb61af))
- Delta Sigma <baker11_how_delta_sigma_adcs_work_part>
- Successive Approximation
@ -33,11 +33,11 @@ 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](#org4bd731c)).
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](#figure--fig:probability-density-function-adc)).
<a id="org4bd731c"></a>
<a id="figure--fig:probability-density-function-adc"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="<span class=\"figure-number\">Figure 1: </span>Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
Now, we can calculate the time average power of the quantization noise as
@ -59,13 +59,12 @@ Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we
\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} \\\\\\
\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}
@ -73,7 +72,6 @@ Finally, the Power Spectral Density of the quantization noise of an ADC is equal
</div>
<div class="exampl">
<div></div>
Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz.
@ -87,7 +85,4 @@ The quantization is:
{{< youtube b9lxtOJj3yU >}}
## Bibliography {#bibliography}
<a id="orgbdb61af"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.
## Oversampling {#oversampling}

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content/zettels/decimation.md
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@ -108,6 +108,24 @@ Which is much more efficient that the single stage decimation.
</div>
There are two **practical issues** to consider for two-stage decimation:
- First, if the dual-filter system is required to have a pass-band peak-peak ripple of \\(R\\) dB, then both filters must be designed to have a pass-band peak-peak ripple of no greater than \\(R/2\\) dB.
- Second, the number of multiplications needed to compute each \\(x\_{\text{new}}(m)\\) output sample is much larger than \\(N\_\text{total}\\) because we must compute so many \\(\text{LPF}\_1\\) and \\(\text{LPF}\_2\\) output samples destined to be discarded.
In order to cope with the second issue, an efficient decimation filter implementation scheme called _polyphase decomposition_ can be used.
<summary>The advantages of two stage decimation, over single-stage decimation are:
<ul class="org-ul">
<li>an overall reduction in computation workload</li>
<li>reduced signal and filter coefficient data storage</li>
<li>simpler filter designs</li>
<li>a decrease in the ill effects of finite binary-work-length filter coefficients</li>
</ul>
These advantages become more pronounced as the overall desired decimation factor \(M\) becomes larger.</summary>
## References: {#references}

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content/zettels/integral_force_feedback.md
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title = "Integral Force Feedback"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
+++
Tags
: [Active Damping]({{< relref "active_damping" >}})
: [Active Damping]({{< relref "active_damping.md" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}}), [Force Sensors]({{< relref "force_sensors.md" >}})
## Self-Sensing for perfect collocation {#self-sensing-for-perfect-collocation}
This can be done with a [Voice Coil Actuator]({{< relref "voice_coil_actuators.md" >}}) (see <verma20_perfec_colloc_using_self_sensin_elect_actuat>) or with a [Piezoelectric Actuator]({{< relref "piezoelectric_actuators.md" >}}) (see <jansen19_activ_dampin_dynam_struc_using>).

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content/zettels/piezoelectric_actuators.md
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title = "Piezoelectric Actuators"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
+++
Tags
: [Actuators]({{<relref "actuators.md#" >}}), [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}})
: [Actuators]({{< relref "actuators.md" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}})
## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
@ -18,9 +18,9 @@ Tags
|----------------------------------------------------------------------------------------------------------------------|-----------|
| [Cedrat](http://www.cedrat-technologies.com/) | France |
| [PI](https://www.physikinstrumente.com/en/) | USA |
| [Piezo System](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
| [Piezo System](https://www.piezosystem.com/products/piezo_actuators/stacktypeactuators/) | Germany |
| [Noliac](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA |
| [PiezoDrive](https://www.piezodrive.com/actuators/) | Australia |
| [Mechano Transformer](http://www.mechano-transformer.com/en/products/10.html) | Japan |
| [CoreMorrow](http://www.coremorrow.com/en/pro-9-1.html) | China |
@ -33,7 +33,7 @@ Tags
### Model {#model}
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#" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in <fleming10_nanop_system_with_force_feedb> ([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.
@ -57,25 +57,25 @@ 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](#orgb463c4c)):
The Amplified Piezo Actuators principle is presented in <claeyssen07_amplif_piezoel_actuat>:
> 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](#org2bf81f0)).
A model of an amplified piezoelectric actuator is described in <lucinskis16_dynam_charac>.
<a id="org77a46eb"></a>
<a id="figure--fig:ling16-topology-piezo-mechanism-types"></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>" >}}
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="<span class=\"figure-number\">Figure 1: </span>Topology of several types of compliant mechanisms <ling16_enhan_mathem_model_displ_amplif>" >}}
| Manufacturers | Country |
|----------------------------------------------------------------------------------------------------|-----------|
| [Cedrat](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
| [PiezoDrive](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
| [Dynamic-Structures](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA |
| [Noliac](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
| [Mechano Transformer](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html) | Japan |
| [Mechano Transformer](http://www.mechano-transformer.com/en/products/01a_actuator_5.html) | Japan |
| [CoreMorrow](http://www.coremorrow.com/en/pro-13-1.html) | China |
| [PiezoData](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
@ -99,7 +99,7 @@ Typical specifications of piezoelectric stack actuators are usually in terms of:
The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied without any load.
Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\%\\).
Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\\%\\).
The free displacement \\(\Delta L\_{f}\\) is then related to the length \\(L\\) of piezoelectric stack by:
\begin{equation}
@ -142,72 +142,62 @@ with:
### Resolution {#resolution}
The resolution is limited by the noise in the [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}).
The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}).
Typical [Signal to Noise Ratio]({{<relref "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}
r \approx \frac{L}{10^5}
\end{equation}
For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolution will be \\(\approx 1\,[nm]\\).
For a piezoelectric stack with a displacement of \\(100\\,[\mu m]\\), the resolution will be \\(\approx 1\\,[nm]\\).
### 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](#orgca6870e)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#figure--fig:piezoelectric-capacitance-voltage-max)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[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.
[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="orgca6870e"></a>
<a id="figure--fig:piezoelectric-capacitance-voltage-max"></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" >}}
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="<span class=\"figure-number\">Figure 2: </span>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](#orge05f5e6)).
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](#figure--fig:piezoelectric-mass-load)).
<a id="orge05f5e6"></a>
<a id="figure--fig:piezoelectric-mass-load"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="<span class=\"figure-number\">Figure 3: </span>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](#orgfcd374f)):
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](#figure--fig:piezoelectric-spring-load)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="orgfcd374f"></a>
<a id="figure--fig:piezoelectric-spring-load"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="<span class=\"figure-number\">Figure 4: </span>Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#orgada6c4c)).
For piezo actuators, force and displacement are inversely related (Figure [5](#figure--fig:piezoelectric-force-displ-relation)).
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="orgada6c4c"></a>
<a id="figure--fig:piezoelectric-force-displ-relation"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="<span class=\"figure-number\">Figure 5: </span>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]({{<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="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="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="org2bf81f0"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
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" >}}).

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content/zettels/stepper_motor.md
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@ -17,3 +17,11 @@ Tags
For a two phase stepper motor, there are (typically) 200 steps per revolution.
Errors with a period of 200 period/revolution can be expected.
## Manufacturers {#manufacturers}
| Manufacturers | Country |
|--------------------------------------------------------------------------|----------------|
| [AML](https://arunmicro.com/) | United Kingdom |
| [Sanyo](https://www.sanyodenki.com/catalogs/servo/stepping_systems.html) | |

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