Update Content - 2022-08-24

content/phdthesis/jabben07_mechat.md

@@ -43,9 +43,9 @@ This approach allows frequency dependent error budgeting, which is why it is ref
 #### Ground vibrations {#ground-vibrations}
 
 
-#### Electronic Noise {#electronic-noise}
+#### [Electronic Noise]({{< relref "electronic_noise.md" >}}) {#electronic-noise--electronic-noise-dot-md}
 
-**Thermal Noise** (or Johson noise).
+**Thermal Noise** (or Johnson noise).
 This noise can be modeled as a voltage source in series with the system impedance.
 The noise source has a PSD given by:
 \\[ S\_T(f) = 4 k T \text{Re}(Z(f)) \ [V^2/Hz] \\]
@@ -65,7 +65,7 @@ with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\\, [C]\\)), \\(i\_{
 
 <div class="exampl">
 
-An averable current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\\,[A]\\) from zero up to one kHz.
+A current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\\,[A]\\) from zero up to one kHz.
 
 </div>
 

content/zettels/brushless_dc_motor.md

@@ -0,0 +1,20 @@
++++
+title = "Brushless DC Motor"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+
+## Manufacturers {#manufacturers}
+
+-   <https://www.maxongroup.com/maxon/view/content/Overview-brushless-DC-motors>
+-   <https://www.faulhaber.com/en/products/brushless-dc-motors/>
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+</div>

content/zettels/charge_amplifiers.md

@@ -45,7 +45,7 @@ The gain of the charge amplified (Figure [1](#figure--fig:charge-amplifier-circu
 | [DJB](https://www.djbinstruments.com/products/instrumentation/view/9-Channel-Charge-Voltage-Amplifier-IEPE-Signal-Conditioning-Rack-Mounted) | UK      |
 | [MTI Instruments](https://www.mtiinstruments.com/products/turbine-balancing-vibration-analysis/charge-amplifiers/ca1800/)                    | USA     |
 | [Sinocera](http://www.china-yec.net/instruments/signal-conditioner/multi-channels-charge-amplifier.html)                                     | China   |
-| [L-Card](https://en.lcard.ru/products/accesories/le-41)                                                                                      | Rusia   |
+| [Physimetron](http://www.physimetron.de/produkte_en.html)                                                                                    | Germany |
 
 
 ## Bibliography {#bibliography}

content/zettels/discrete_transfer_functions.md

@@ -8,6 +8,100 @@ Tags
 : [Digital Filters]({{< relref "digital_filters.md" >}})
 
 
+## Continuous to discrete transfer function {#continuous-to-discrete-transfer-function}
+
+In order to convert an analog filter (Laplace domain) to a digital filter (z-domain), the `c2d` command can be used ([doc](https://fr.mathworks.com/help/control/ref/lti.c2d.html)).
+
+<div class="exampl">
+
+Let's define a simple first order low pass filter in the Laplace domain:
+
+```matlab
+s = tf('s');
+G = 1/(1 + s/(2*pi*10));
+```
+
+To obtain the equivalent digital filter:
+
+```matlab
+Ts = 1e-3; % Sampling Time [s]
+Gz = c2d(G, Ts, 'tustin');
+```
+
+</div>
+
+There are several methods to go from the analog to the digital domain, `Tustin` is the one I use the most as it ensures the stability of the digital filter provided that the analog filter is stable.
+
+
+## Obtaining analytical formula of filter {#obtaining-analytical-formula-of-filter}
+
+The Matlab [Symbolic Toolbox](https://fr.mathworks.com/help/symbolic/) can be used to obtain analytical formula for discrete transfer functions.
+
+Let's consider a notch filter:
+
+\begin{equation}
+  G(s) = \frac{s^2 + 2 g\_c \xi \omega\_n s + \omega\_n^2}{s^2 + 2 \xi \omega\_n s + \omega\_n^2}
+\end{equation}
+
+with:
+
+-   \\(\omega\_n\\): frequency of the notch
+-   \\(g\_c\\): gain at the notch frequency
+-   \\(\xi\\): damping ratio (notch width)
+
+First the symbolic variables are declared (`Ts` is the sampling time, `s` the Laplace variable and `z` the "z-transform" variable).
+
+```matlab
+%% Declaration of the symbolic variables
+syms gc wn xi Ts s z
+```
+
+The symbolic formula of the notch filter is defined:
+
+```matlab
+%% Notch Filter - Symbolic representation
+Ga = (s^2 + 2*xi*gc*s*wn + wn^2)/(s^2 + 2*xi*s*wn + wn^2);
+```
+
+Then the bi-linear transformation is performed to go from continuous to discrete:
+
+```matlab
+%% Bilinear Transform
+s = 2/Ts*(z - 1)/(z + 1);
+```
+
+Finally, the numerator and denominator coefficients can be extracted:
+
+```matlab
+%% Get numerator and denominator
+[N,D] = numden(Ga);
+
+%% Extract coefficients (from z^0 to z^n)
+num = coeffs(N, z);
+den = coeffs(D, z);
+```
+
+```text
+num = (Ts^2*wn^2 - 4*Ts*gc*wn*xi + 4) + (2*Ts^2*wn^2 - 8) * z + (Ts^2*wn^2 + 4*Ts*gc*wn*xi + 4) * z^2
+```
+
+```text
+den = (Ts^2*wn^2 - 4*Ts*wn*xi + 4) + (2*Ts^2*wn^2 - 8) * z + (Ts^2*wn^2 + 4*Ts*wn*xi + 4) * z^2
+```
+
+
+## Variable Discrete Filter {#variable-discrete-filter}
+
+Once the analytical formula of a discrete transfer function is obtained, it is possible to vary some parameters in real time.
+
+This is easily done in Simulink (see Figure [1](#figure--fig:variable-controller-simulink)) where a `Discrete Varying Transfer Function` block is used.
+The coefficients are simply computed with a Matlab function.
+
+<a id="figure--fig:variable-controller-simulink"></a>
+
+{{< figure src="/ox-hugo/variable_controller_simulink.png" caption="<span class=\"figure-number\">Figure 1: </span>Variable Discrete Filter in Simulink" >}}
+
+
 ## Typical Transfer functions {#typical-transfer-functions}
 
 

content/zettels/electronic_noise.md

@@ -0,0 +1,77 @@
++++
+title = "Electronic Noise"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+: [Electronics]({{< relref "electronics.md" >}}), [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio.md" >}})
+
+
+## Thermal (Johnson) Noise {#thermal--johnson--noise}
+
+Thermal noise is generated by the thermal agitation of the electrons inside the electrical conductor.
+Its Power Spectral Density is equal to:
+
+\begin{equation}
+S\_T \approx 4 k T \text{Re}(Z(f)) \quad [V^2/Hz]
+\end{equation}
+
+with:
+with \\(k = 1.38 \cdot 10^{-23} \\,[J/K]\\) the Boltzmann's constant, \\(T\\) the temperature [K] and \\(Z(f)\\) the frequency dependent impedance of the system.
+
+This noise can be modeled as a voltage source in series with the system impedance.
+
+| Resistance      | PSD \\([V^2 / Hz]\\)     | ASD \\([V/\sqrt{Hz}]\\)  | RMS (1kHz) | RMS (10kHz) |
+|-----------------|--------------------------|--------------------------|------------|-------------|
+| \\(1 \Omega\\)  | \\(1.6 \cdot 10^{-20}\\) | \\(1.2 \cdot 10^{-10}\\) | 4nV        | 130nV       |
+| \\(1 k\Omega\\) | \\(1.6 \cdot 10^{-17}\\) | \\(4 \cdot 10^{-9}\\)    | 130nV      | 4uV         |
+| \\(1 M\Omega\\) | \\(1.6 \cdot 10^{-14}\\) | \\(1.2 \cdot 10^{-7}\\)  | 4uV        | 130uV       |
+
+
+## Shot Noise {#shot-noise}
+
+Seen with junctions in a transistor.
+It has a white spectral density:
+
+\begin{equation}
+S\_S = 2 q\_e i\_{dc} \ [A^2/Hz]
+\end{equation}
+
+with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\\, [C]\\)), \\(i\_{dc}\\) the average current [A].
+
+<div class="exampl">
+
+A current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\\,[A]\\) from zero up to one kHz.
+
+</div>
+
+
+## Excess Noise (or \\(1/f\\) noise) {#excess-noise--or-1-f-noise}
+
+It results from fluctuating conductivity due to imperfect contact between two materials.
+The PSD of excess noise increases when the frequency decreases:
+\\[ S\_E = \frac{K\_f}{f^\alpha}\ [V^2/Hz] \\]
+where \\(K\_f\\) is dependent on the average voltage drop over the resistor and the index \\(\alpha\\) is usually between 0.8 and 1.4, and often set to unity for approximate calculation.
+
+
+## Noise of Amplifiers {#noise-of-amplifiers}
+
+The noise of amplifiers can be modelled as shown in Figure [1](#figure--fig:electronic-amplifier-noise).
+
+<a id="figure--fig:electronic-amplifier-noise"></a>
+
+{{< figure src="/ox-hugo/electronic_amplifier_noise.png" caption="<span class=\"figure-number\">Figure 1: </span>Amplifier noise model" >}}
+
+The identification of this noise is a two steps process:
+
+1.  The amplifier input is short-circuited such that only \\(V^2(f)\\) has an impact on the output.
+    The output noise is measured and \\(V^2\\) in \\([V^2/Hz]\\) is identified
+2.  The amplifier input is open-circuited such that only \\(I^2(f)\\) has an impact on the output.
+    The output noise is measured and \\(I^2(f)\\) in \\([A^2/Hz]\\) is identified.
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+</div>

content/zettels/encoders.md

@@ -11,7 +11,10 @@ Tags
 There are two main types of encoders: optical encoders, and magnetic encoders.
 
 
-## Manufacturers {#manufacturers}
+## Linear Encoders {#linear-encoders}
+
+
+### Manufacturers {#manufacturers}
 
 | Manufacturers                                                                   | Country |
 |---------------------------------------------------------------------------------|---------|
@@ -20,6 +23,14 @@ There are two main types of encoders: optical encoders, and magnetic encoders.
 | [Renishaw](https://www.renishaw.com/en/browse-encoder-range--6440)              | UK      |
 | [Celera Motion](https://www.celeramotion.com/microe/)                           | USA     |
 
+<https://www.posic.com/EN/>
+<https://www.rls.si/eng/products/rotary-magnetic-encoders>
+
+
+## Angular Encoders {#angular-encoders}
+
+<https://www.maxongroup.com/maxon/view/category/sensor>
+
 
 ## Bibliography {#bibliography}
 

content/zettels/gravity_compensation.md

@@ -0,0 +1,34 @@
++++
+title = "Gravity Compensation"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+
+## Counterweight {#counterweight}
+
+(<a href="#citeproc_bib_item_2">Yoshioka et al. 2017</a>)
+
+
+## Magnetic {#magnetic}
+
+(<a href="#citeproc_bib_item_1">Hol, Lomonova, and Vandenput 2006</a>)
+
+
+## Constant force spring {#constant-force-spring}
+
+
+## Variable Gravity Compensation {#variable-gravity-compensation}
+
+As the mass / position of the load may change during operation, a variable gravity compensation mechanism is very useful.
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Hol, S.A.J., E. Lomonova, and A.J.A. Vandenput. 2006. “Design of a Magnetic Gravity Compensation System.” <i>Precision Engineering</i> 30 (3): 265–73. doi:<a href="https://doi.org/10.1016/j.precisioneng.2005.09.005">10.1016/j.precisioneng.2005.09.005</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Yoshioka, Hayato, Hidenori Shinno, Jiang Zhu, and Manabu Uchiumi. 2017. “A Newly Developed Zero-Gravity Vertical Motion Mechanism for Precision Machining.” <i>Cirp Annals</i> 66 (1): 389–92. doi:<a href="https://doi.org/10.1016/j.cirp.2017.04.057">10.1016/j.cirp.2017.04.057</a>.</div>
+</div>

content/zettels/lock_in_amplifier.md

@@ -0,0 +1,32 @@
++++
+title = "Lock-in Amplifier"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+
+## Synchronous Detection {#synchronous-detection}
+
+(<a href="#citeproc_bib_item_1">Francais 2003</a>)
+(<a href="#citeproc_bib_item_3">Zurich 2016</a>)
+(<a href="#citeproc_bib_item_2">Horowitz 2015</a>)
+
+
+## Manufacturers {#manufacturers}
+
+| Manufacturers                                                             | Country |
+|---------------------------------------------------------------------------|---------|
+| [Femto](https://www.femto.de/en/products/lock-in-amplifiers.html)         | Germany |
+| [Zurick Instruments](https://www.zhinst.com/europe/en/lock-in-amplifiers) | Swiss   |
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Francais, Olivier. 2003. “Detection Synchrone.”</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Horowitz, Paul. 2015. <i>The Art of Electronics - Third Edition</i>. New York, NY, USA: Cambridge University Press.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_3"></a>Zurich, Instruments. 2016. “Principles of Lock-in Detection and the State of the Art.” Zurich Instruments.</div>
+</div>

content/zettels/motors.md

@@ -0,0 +1,37 @@
++++
+title = "Motors"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+Reviews:
+
+-   (<a href="#citeproc_bib_item_1">Murugesan 1981</a>)
+
+
+## Linear Motors {#linear-motors}
+
+
+### Short Stroke {#short-stroke}
+
+[Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}})
+
+
+### Long Stroke {#long-stroke}
+
+[Voice Coil Actuators]({{< relref "voice_coil_actuators.md" >}})
+
+
+## Angular Motors {#angular-motors}
+
+[Stepper Motor]({{< relref "stepper_motor.md" >}})
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Murugesan, S. 1981. “An Overview of Electric Motors for Space Applications.” <i>Ieee Transactions on Industrial Electronics and Control Instrumentation</i> IECI-28 (4): 260–65. doi:<a href="https://doi.org/10.1109/TIECI.1981.351050">10.1109/TIECI.1981.351050</a>.</div>
+</div>

content/zettels/stepper_motor.md

@@ -9,18 +9,91 @@ Tags
 :
 
 
-## Errors between steps (micro-stepping) {#errors-between-steps--micro-stepping}
+## Types of Stepper motors {#types-of-stepper-motors}
 
-For a two phase stepper motor, there are (typically) **200 steps per revolution** (i.e. 1.8% per step).
+<https://blog.orientalmotor.com/stepper-motor-basics-pm-vs-vr-vs-hybrid>
+
+-   Permanent Magnet
+-   Variable Reluctance
+-   Hybrid
+
+<a id="figure--fig:stepper-two-phase-hybrid-stepper"></a>
+
+{{< figure src="/ox-hugo/stepper_two_phase_hybrid_stepper.png" caption="<span class=\"figure-number\">Figure 1: </span>Interior of a two phase hybrid stepper motor. This motor has eight windings and 50 roto teeth" >}}
+
+<a id="figure--fig:stepper-hybrid-schematic"></a>
+
+{{< figure src="/ox-hugo/stepper_hybrid_schematic.png" caption="<span class=\"figure-number\">Figure 2: </span>Schematic of a two phase hybrid stepper motor. This motor has four windings and 15 pole pairs" >}}
+
+
+## Micro Stepping {#micro-stepping}
+
+From (<a href="#citeproc_bib_item_2">Ronquist and Winroth 2016</a>):
+
+> By varying the magnitude and direction of the winding currents, the rotor is continuously attracted in the desired direction.
+> A "step" occurs whenever a rotor tooth moves slightly to align itself to an electromagnet tooth.
+>
+> It is possible to decrease the step size of the hybrid stepper motor by using a control logic called **microstepping**.
+> As opposed to fully exciting each phase in turn, as described previously, microstepping involves transitioning between each phase shift.
+> That is, the current references are defined by sinusoidal signals displaced 90 electrical degrees from each other.
+> For most time instances, then, both phases are excited to a certain degree.
+> The result is that the electric position vector can be placed between two teeth.
+> The resolution of the motor has therefore been increased.
+
+From (<a href="#citeproc_bib_item_1">Condit 2004</a>):
+
+> There are several factors that affect the linearity of microstepping in real motors.
+> The first limitation is static friction in the system.
+>
+> [...]
+>
+> Another limitation is the fact that the torque versus position curve is not perfectly sinusoidal.
+> The toothed shape of the motor and other physical characteristics of the motor contribute to this.
+> Figure [3](#figure--fig:stepper-real-pos-vs-actual-pos) shows a plot of actual position vs expected position for a typical motor.
+
+<a id="figure--fig:stepper-real-pos-vs-actual-pos"></a>
+
+{{< figure src="/ox-hugo/stepper_real_pos_vs_actual_pos.png" caption="<span class=\"figure-number\">Figure 3: </span>Real vs actuator rotor position" >}}
+
+
+## Open Loop errors {#open-loop-errors}
+
+Nice references:
+
+-   (<a href="#citeproc_bib_item_3">Vyas, Patel, and Shah 2015</a>)
+-   (<a href="#citeproc_bib_item_2">Ronquist and Winroth 2016</a>)
+
+<div class="seealso">
+
+References about these errors can be search for using "torque ripple", "Cogging torque" and "load dependent error" keywords.
+
+</div>
+
+
+### Error with period equal to one **turn** {#error-with-period-equal-to-one-turn}
+
+A stepper motor has a position error with a period equal to a full turn.
+
+An example is shown in Figure [4](#figure--fig:stepper-error-one-turn-period) (from (<a href="#citeproc_bib_item_2">Ronquist and Winroth 2016</a>)).
+The high frequency errors that can be observed have a period of one step (i.e. 200 periods each turn).
+
+<a id="figure--fig:stepper-error-one-turn-period"></a>
+
+{{< figure src="/ox-hugo/stepper_error_one_turn_period.png" caption="<span class=\"figure-number\">Figure 4: </span>Angle error of the stepper motor during a 100rpm (i.e. 0.6s per turn)" >}}
+
+
+### Error with period equal to one **step** {#error-with-period-equal-to-one-step}
+
+For a two phase stepper motor, there are (typically) **200 steps per revolution** (i.e. 1.8 degrees per step).
 
 Between each step, even when using some micro-stepping, there are some position errors that are due to non-perfect magnetic and electromagnetic fields.
 
 The period of this error is corresponding to 200 period/revolution.
 
-Then scanning, this can lead to high frequency vibrations.
+Then scanning, this can lead to **high frequency vibrations**.
 
 This is what is typically limiting the accuracy of the stepper motor (usually specified in between 3% and 5% of the step increment).
-This is approximately corresponding to **1mrad**.
+This is approximately corresponding to **1mrad** and can be around 0.1mrad for best stepper motors.
 
 <div class="exampl">
 
@@ -31,12 +104,23 @@ A rotation of 1 turn per second will induce vibrations at 200Hz with an amplitud
 
 Note that this error is not a pure sine, it also has some harmonics with corresponding periods of 1/100 revolution and 1/50 revolution.
 
-This error should repeat every turn and can be calibrated provided it is repeatable over time.
-
 One way to reduce these errors is to use a ball-screw mechanism with a smaller pitch.
 The price to pay is smaller velocity.
 
 
+### Load Dependent Error {#load-dependent-error}
+
+If the electromagnetic torque would be the only torque acting on the system, the electrical angle generated by the control system would correspond directly to the reference angle.
+
+The position error is to a large degree due to the so called load angle when the motor is positioned by an open-loop controller.
+The load angle results from applying an external torque to the stepper motor, **causing the magnetic rotor to be out of phase with the electrical field**.
+
+The most common way to limit these errors is to always operate the motor with its rated winding currents.
+This results in significant energy losses and heating of the motor which deprive the motor of its efficiency.
+
+Another option is to use a position sensor such as an encoder with a feedback controller.
+
+
 ## Manufacturers {#manufacturers}
 
 | Manufacturers                                                            | Country        |
@@ -53,4 +137,7 @@ The price to pay is smaller velocity.
 ## Bibliography {#bibliography}
 
 <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Condit, Reston. 2004. “Stepping Motors Fundamentals.” Microchip Technology.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Ronquist, Anton, and Birger Winroth. 2016. “Estimation and Compensation of Load-Dependent Position Error in a Hybrid Stepper Motor.” Linköping University, Automatic Control; Linköping University, Automatic Control.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_3"></a>Vyas, Darshit C, Jinesh G Patel, and Mrs Heli A Shah. 2015. “Microstepping of Stepper Motor and Sources of Errors in Microstepping System.” <i>Int. Journal of Engineering Research and General Science</i> 3 (2).</div>
 </div>

content/zettels/tuned_mass_damper.md

@@ -7,7 +7,7 @@ draft = false
 Tags
 : [Passive Damping]({{< relref "passive_damping.md" >}})
 
-Review: (<a href="#citeproc_bib_item_1">Elias and Matsagar 2017</a>)
+Review: (<a href="#citeproc_bib_item_1">Elias and Matsagar 2017</a>), (<a href="#citeproc_bib_item_2">Verbaan 2015</a>)
 
 
 ## Working Principle {#working-principle}
@@ -69,7 +69,7 @@ c2 = 2*xi*sqrt(k2*m2);
 ```
 
 <div class="table-caption">
-  <span class="table-number">Table 1</span>:
+  <span class="table-number">Table 1:</span>
   Obtained parameters of the TMD
 </div>
 
@@ -128,8 +128,7 @@ Possible damping sources:
 -   Magnetic (eddy current)
 -   Viscous
 
-## References
-
 <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
   <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Elias, Said, and Vasant Matsagar. 2017. “Research Developments in Vibration Control of Structures Using Passive Tuned Mass Dampers.” <i>Annual Reviews in Control</i> 44 (nil): 129–56. doi:<a href="https://doi.org/10.1016/j.arcontrol.2017.09.015">10.1016/j.arcontrol.2017.09.015</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Verbaan, C.A.M. 2015. “Robust mass damper design for bandwidth increase of motion stages.” Mechanical Engineering; Technische Universiteit Eindhoven.</div>
 </div>

content/zettels/voltage_amplifier.md

@@ -121,6 +121,25 @@ However, for stability reasons and to avoid overshoot (due to the internal negat
 This is discussed in (<a href="#citeproc_bib_item_2">Van Spengen 2017</a>).
 
 
+## Small Signal Voltage Amplifier {#small-signal-voltage-amplifier}
+
+Input is usually BNC.
+Output voltage is to up +/-10V.
+It has high input impedance.
+
+| Model                                                                                          | Channel | LPF            | HPF            | Gains     | Shape     | Noise | Price |
+|------------------------------------------------------------------------------------------------|---------|----------------|----------------|-----------|-----------|-------|-------|
+| [7008](https://www.krohn-hite.com/html/preamps.html)                                           | 8       | 100kHz         | AC or DC       | 1 to 1k   | 19" Rack  | 7nV   |       |
+| [MCVA5](https://www.specs-group.com/nc/nanonis/products/detail/mcva5-preamplifier/)            | 4       |                | AC or DC       | 1 to 1k   | Large     | 4nV   |       |
+| [DP-314](https://www.warneronline.com/4-channel-differential-amplifier-with-active-headstages) | 4       | 100Hz to 50kHz | 0.1Hz to 300Hz | 10 to 10k | 19" Rack  |       |       |
+| [ee701](https://www.ee-quipment.com/products/differential-preamplifier?variant=35410631368)    | 1       | 10Hz to 1MHz   | x              | 1 to 1k   | Small     |       | 400   |
+| [LNA 10](https://www.priggen.com/LNA-10-Low-Noise-Differential-Preamplifier-for-Oscilloscopes) | 1       | 1Hz to 1MHz    | x              | 10 to 1k  | Small     |       | 700   |
+| [Koheron](https://www.koheron.com/photonics/amp200-amplifier)                                  | 1       |                | AC or DC       | 5 to 500  | Small PCB | 2.4nV | 225   |
+| [5307](https://www.nfcorp.co.jp/english/pro/mi/loc/pre/5307/index.html)                        | 1       |                | AC or DC       | 10 to 1k  | Large     | 4nV   |       |
+| [DLPVA](https://www.femto.de/en/products/voltage-amplifiers/variable-gain-100-khz-dlpva.html)  | 1       | 1kHz, 100kHz   | AC or DC       | 10 to 10k | Small     | 2nV   |       |
+| [AMP200](https://www.thorlabs.com/thorproduct.cfm?partnumber=AMP200)                           | 1       |                |                | 10 to 1k  | Small     | 5nV   | 470   |
+
+
 ## Bibliography {#bibliography}
 
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