#+TITLE: Voltage Amplifier PD200 - Test Bench
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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* Introduction
The goal of this test bench is to characterize the Voltage amplifier [[https://www.piezodrive.com/drivers/pd200-60-watt-voltage-amplifier/][PD200]] from PiezoDrive.

The documentation of the PD200 is accessible [[file:doc/PD200-V7-R1.pdf][here]].

#+name: fig:amplifier_PD200
#+caption: Picture of the PD200 Voltage Amplifier
#+attr_latex: :width 0.8\linewidth
[[file:figs/amplifier_PD200.png]]

* Voltage Amplifier Requirements

#+name: tab:voltage_amplifier_requirements
#+caption: Requirements for the Voltage Amplifier
#+attr_latex: :environment tabularx :width 0.5\linewidth :align lX
#+attr_latex: :center t :booktabs t :float t
| <l>                            |        <c>         |
|                                |  *Specification*   |
|--------------------------------+--------------------|
| Continuous Current             |     > 50 [mA]      |
| Output Voltage Noise (1-200Hz) |    < 2 [mV rms]    |
| Voltage Input Range            |     +/- 10 [V]     |
| Voltage Output Range           | -20 [V] to 150 [V] |
| Small signal bandwidth (-3dB)  |     > 5 [kHz]      |

* PD200 Expected characteristics

#+name: tab:pd200_characteristics
#+caption: Characteristics of the PD200
#+attr_latex: :environment tabularx :width \linewidth :align lXX
#+attr_latex: :center t :booktabs t :float t
| <l>                                 |     <c>      |       <c>       |
| *Characteristics*                   |   *Manual*   | *Specification* |
|-------------------------------------+--------------+-----------------|
| Input Voltage Range                 |  +/- 10 [V]  |   +/- 10 [V]    |
| Output Voltage Range                | -50/150 [V]  |   -20/150 [V]   |
| Gain                                |   20 [V/V]   |                 |
| Maximum RMS current                 |   0.9 [A]    |    > 50 [mA]    |
| Maximum Pulse current               |    10 [A]    |                 |
| Slew Rate                           |  150 [V/us]  |                 |
| Noise (10uF load)                   | 0.7 [mV RMS] |  < 2 [mV rms]   |
| Small Signal Bandwidth (10uF load)  |  7.4 [kHz]   |    > 5 [kHz]    |
| Large Signal Bandwidth (150V, 10uF) |   300 [Hz]   |                 |

For a load capacitance of $10\,\mu F$, the expected $-3\,dB$ bandwidth is $6.4\,kHz$ (Figure [[fig:pd200_expected_small_signal_bandwidth]]) and the low frequency noise is $650\,\mu V\,\text{rms}$ (Figure [[fig:pd200_expected_noise]]).

#+name: fig:pd200_expected_small_signal_bandwidth
#+caption:Expected small signal bandwidth
#+attr_latex: :width 0.8\linewidth
[[file:./figs/pd200_expected_small_signal_bandwidth.png]]

#+name: fig:pd200_expected_noise
#+caption: Expected Low frequency noise from 0.03Hz to 20Hz
#+attr_latex: :width 0.8\linewidth
[[file:figs/pd200_expected_noise.png]]

* Voltage Amplifier Model
The Amplifier is characterized by its dynamics $G_a(s)$ from voltage inputs $V_{in}$ to voltage output $V_{out}$.
Ideally, the gain from $V_{in}$ to $V_{out}$ is constant over a wide frequency band with very small phase drop.

It is also characterized by its output noise $n$.
This noise is described by its Power Spectral Density.

The objective is therefore to determine the transfer function $G_a(s)$ from the input voltage to the output voltage as well as the Power Spectral Density $S_n(\omega)$ of the amplifier output noise.

As both $G_a$ and $S_n$ depends on the load capacitance, they should be measured when loading the amplifier with a $\SI{10}{\micro\farad}$ capacitor.

#+begin_src latex :file pd200-model-schematic.pdf
  \begin{tikzpicture}
    \node[block] (G) at (0,0){$G_a(s)$};
    \node[addb, right=0.8 of G] (add){};

    \draw[<-] (G.west) -- ++(-1.2, 0) node[above right]{$V_{in}$};
    \draw[->] (G.east) -- (add.west);
    \draw[->] (add.east) -- ++(1.2, 0) node[above left]{$V_{out}$};
    \draw[<-] (add.north) -- ++(0, 0.6) node[below right](n){$n$};

    \begin{scope}[on background layer]
      \node[fit={(G.south west) (n.north-|add.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
      \node[below] at (P.north) {PD-200};
    \end{scope}
  \end{tikzpicture}
#+end_src

#+name: fig:pd200-model-schematic
#+caption: Model of the voltage amplifier
#+RESULTS:
[[file:figs/pd200-model-schematic.png]]

* Noise measurement
** Setup
#+begin_note
Here are the documentation of the equipment used for this test bench:
- Voltage Amplifier [[file:doc/PD200-V7-R1.pdf][PD200]]
- Load Capacitor [[file:doc/0900766b815ea422.pdf][EPCOS 10uF Multilayer Ceramic Capacitor]]
- Low Noise Voltage Amplifier [[file:doc/egg-5113-preamplifier.pdf][EG&G 5113]]
- Speedgoat ADC [[file:doc/IO131-OEM-Datasheet.pdf][IO313]]
#+end_note

The output noise of the voltage amplifier PD200 is foreseen to be around 1mV rms in a bandwidth from DC to 1MHz.
If we suppose a white noise, this correspond to an amplitude spectral density:
\begin{equation}
  \phi_{n} \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
\end{equation}

The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal.
The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200.
We use the amplifier EG&G 5113 that has a noise of $\approx 4 nV/\sqrt{Hz}$ referred to its input which is much smaller than the noise induced by the PD200.

The gain of the low-noise amplifier can be increased until the full range of the ADC is used.
This gain should be around 1000.

#+name: fig:setup-noise-measurement
#+caption: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise $n$
#+attr_latex: :width \linewidth
[[file:figs/setup-noise-measurement.png]]

A low pass filter at 10kHz can be included in the EG&G amplifier in order to limit aliasing.
An high pass filter at low frequency can be added if there is a problem of large offset.

** Results

* Transfer Function measurement
** Setup
In order to measure the transfer function from the input voltage $V_{in}$ to the output voltage $V_{out}$, the test bench shown in Figure [[fig:setup-dynamics-measurement]] is used.

#+begin_note
Here are the documentation of the equipment used for this test bench:
- Voltage Amplifier [[file:doc/PD200-V7-R1.pdf][PD200]]
- Load Capacitor [[file:doc/0900766b815ea422.pdf][EPCOS 10uF Multilayer Ceramic Capacitor]]
- Speedgoat DAC/ADC [[file:doc/IO131-OEM-Datasheet.pdf][IO313]]
#+end_note

For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.

#+name: fig:setup-dynamics-measurement
#+caption: Schematic of the test bench to estimate the dynamics from voltage input $V_{in}$ to voltage output $V_{out}$
[[file:figs/setup-dynamics-measurement.png]]

** Results
* Conclusion

#+name: tab:table_name
#+caption: Measured characteristics, Manual characterstics and specified ones
#+attr_latex: :environment tabularx :width \linewidth :align lXXX
#+attr_latex: :center t :booktabs t :float t
| <l>                                 |      <c>      |     <c>      |       <c>       |
| *Characteristics*                   | *Measurement* |   *Manual*   | *Specification* |
|-------------------------------------+---------------+--------------+-----------------|
| Input Voltage Range                 |       -       |  +/- 10 [V]  |   +/- 10 [V]    |
| Output Voltage Range                |       -       | -50/150 [V]  |   -20/150 [V]   |
| Gain                                |               |   20 [V/V]   |        -        |
| Maximum RMS current                 |               |   0.9 [A]    |    > 50 [mA]    |
| Maximum Pulse current               |               |    10 [A]    |        -        |
| Slew Rate                           |               |  150 [V/us]  |        -        |
| Noise (10uF load)                   |               | 0.7 [mV RMS] |  < 2 [mV rms]   |
| Small Signal Bandwidth (10uF load)  |               |  7.4 [kHz]   |    > 5 [kHz]    |
| Large Signal Bandwidth (150V, 10uF) |               |   300 [Hz]   |        -        |