+
This report is also available as a pdf.
++#+end_export + +* 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 +|
Table of Contents
-
-
- 1. Introduction -
- 2. Voltage Amplifier Requirements -
- 3. PD200 Expected characteristics -
- 4. Voltage Amplifier Model -
- 5. Noise measurement +
- 1. Requirements PD200 Expected characteristics +
- 2. Voltage Amplifier Model +
- 3. Transfer Function measurement
-
-
- 5.1. Setup -
- 5.2. Model of the setup -
- 5.3. Quantization Noise -
- 5.4. Pre Amplifier noise measurement -
- 5.5. PD200 noise measurement -
- 5.6. DAC noise measurement -
- 5.7. Total noise measurement -
- 5.8. 20bits DAC noise measurement +
- 3.1. Setup +
- 3.2. Maximum Frequency/Voltage to not overload the amplifier +
- 3.3. Small Signal Bandwidth +
- 3.4. Bandwidth for multiple excitation signals
- - 6. Transfer Function measurement +
- 4. Noise measurement
-
-
- 6.1. Setup -
- 6.2. Maximum Frequency/Voltage to not overload the amplifier -
- 6.3. Obtained Transfer Functions +
- 4.1. Measurement Setup +
- 4.2. Model of the setup +
- 4.3. Quantization Noise +
- 4.4. EG&G - Amplifier noise measurement +
- 4.5. Femto - Amplifier noise measurement +
- 4.6. PD200 noise measurement +
- 4.7. DAC noise measurement +
- 4.8. Total noise measurement +
- 4.9. 20bits DAC noise measurement +
- 4.10. PD200 Amplifier noise model
- - 7. Conclusion +
- 5. Comparison to other commercial amplifiers + + +
- 6. Conclusion
This report is also available as a pdf.
-
-
-
1 Introduction
-The goal of this test bench is to characterize the Voltage amplifier PD200 from PiezoDrive.
+The documentation of the PD200 is accessible here.
+
+
+This document is organized as follows: +
+-
+
- Section 1: the requirements for the amplifiers and the characteristics of the PD200 amplifiers as advertise in the datasheet are listed. +
- Section 2: a very simple amplifier model consisting of a transfer function and a noise source is described. +
- Section 3: the transfer function from input voltage to output voltage is identified. +
- Section 4: the power spectral density of the amplifier’s noise is measured +
- Section 5: the characteristics of the PD200 amplifier are compared to the E.505 amplifier from PI and to the LA75 from cedrat +
- Section 6: the measured characteristics of the PD200 amplifier are compared with the requirements +
+
-1 Requirements PD200 Expected characteristics
+
+
+
+
-
-+A picture of the PD200 amplifier is shown in Figure 1. +
+ + +
Figure 1: Picture of the PD200 Voltage Amplifier
-
-
-2 Voltage Amplifier Requirements
-
-
-
-
-| - | 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] | -
-
3 PD200 Expected characteristics
-
-
-
+
-For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure 2) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure 3). +The most important characteristics are the large (small signal) bandwidth > 5 [kHz] and the small noise (< 2 [mV RMS]). +
+ ++For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure 2) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure 3). +
+ ++These two characteristics are respectively measured in Section 3 and Section 4.
-
+
-
Figure 2: Expected small signal bandwidth
+
-
Figure 3: Expected Low frequency noise from 0.03Hz to 20Hz
@@ -234,67 +224,274 @@ For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(
-
4 Voltage Amplifier Model
-
+
+
2 Voltage Amplifier Model
+
+
+
-The Amplifier is characterized by its dynamics \(G_p(s)\) 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. +It is also characterized by its input noise \(n\).
-The objective is therefore to determine the transfer function \(G_p(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise. +The objective is therefore to determine the transfer function \(G_p(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier input noise.
-As both \(G_p\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(10\,\mu F\) capacitor. +As \(G_p\) depends on the load capacitance, it should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
-
+
+
+
+
Figure 4: Model of the voltage amplifier
+The input noise of the amplifier \(n\) can be further modeled by shaping a white noise with unitary PSD \(\tilde{n}\) with a transfer function \(G_n(s)\) as shown in Figure 6. +
+ ++The Amplitude Spectral Density \(\Gamma_n\) is then: +
+\begin{equation} +\Gamma_n(\omega) = |G_n(j\omega)| \Gamma_{\tilde{n}}(\omega) +\end{equation} ++with \(\Gamma_{\tilde{n}}(\omega) = 1\). +
+ + + +
+
+
-
5 Noise measurement
-
+
+
3 Transfer Function measurement
+
+
+
-+In this section, the transfer function of the PD200 amplifier is measured: +
-
-
- Section 5.1 -
- Section 5.2 -
- Section 5.3 -
- Section 5.4 -
- Section 5.5 -
- Section 5.6 -
- Section 5.7 -
- Section 5.8 +
- Section 3.1: the measurement setup is described +
- Section 3.2: the maximum sinusoidal excitation frequency is estimated in order to not overload the amplifier +
- Section 3.3: the small signal bandwidth measurement results are shown +
- Section 3.4: the amplifier’s transfer function is estimated for several input amplitudes
-
5.1 Setup
-
+
+
+
+3.1 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 6 is used. +
+ +
+
+
++Here are the documentation of the equipment used for this test bench: +
+-
+
- Voltage Amplifier: PD200 +
- Load Capacitor: Film Capacitors 600V 10uF 5% +
- DAC/ADC: IO313 Speedgoat Interface +
+For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible. +
+ + +
+
+
+
Figure 6: Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)
+
+
+
+3.2 Maximum Frequency/Voltage to not overload the amplifier
+
+
+
+
++Then the maximum output current of the amplifier is reached, the amplifier automatically shuts down itself. +We should then make sure that the output current does not reach this maximum specified current. +
+ ++The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave. +
+ ++The impedance of the capacitance is: +\[ Z_C(\omega) = \frac{1}{jC\omega} \] +
+ ++Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\): +\[ V_{out} = \frac{1}{C\omega} I_{out} \] +
+ ++Moreover, there is a gain of 20 between the input voltage and the output voltage: +\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \] +
+ ++For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is: +
+\begin{equation} +\boxed{\omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}}} +\end{equation} ++with: +
+-
+
- \(\omega_{\text{max}}\) the maximum input sinusoidal frequency in Radians per seconds +
- \(C\) the load capacitance in Farads +
- \(V_{in}\) the input voltage sinusoidal amplitude in Volts +
- \(I_{out,\text{max}}\) the specified maximum output current in Amperes +
+\(\omega_{\text{max}}/2\pi\) as a function of \(V_{in}\) is shown in Figure 7. +
+ + +
+
+
+
+
Figure 7: Maximum frequency as a function of the excitation voltage amplitude
++When doing sweep sine excitation, we make sure not to reach this maximum excitation frequency. +
+
+
+
+3.3 Small Signal Bandwidth
+ +
+
+3.4 Bandwidth for multiple excitation signals
+
+
+
+
++Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V. +
+ +
+
+Iout_max = 0.57; % Maximum output current [A] +C = 10e-6; % Load Capacitance [F] + +V_in = [0.1, 0.5, 1, 2, 4]; +f_max = 0.8*Iout_max./(20*C*V_in/sqrt(2))/2/pi; +for i = 1:length(Vin_ampl) + pd200{i}.notes.pd200.f_max = f_max(i); + pd200{i}.notes.pd200.Vin = V_in(i); +end ++
+
4 Noise measurement
+
+
+
+
++In section 4.1, the measurement setup is described and a model (block diagram) of the setup is given in section 4.2. +
+ ++Then, the noise contribution of each element is measured: +
+-
+
- Section 4.3: the quantization noise of the ADC is estimated +
- Sections 4.4 and 4.5: the noise of the low-noise amplifiers are estimated +
- Section 4.6: the input voltage noise of the PD200 amplifier is estimated +
- Section 4.7: the output noise of the DAC is measured +
- Section 4.8: the noise of the full measurement chain (DAC to PD200 to pre-amplifier to ADC) is measured and it is found that the DAC is the main source of noise +
- Section 4.9: the noise of an 20bits DAC is measured and it is shown if it could lowering the overall noise of the setup +
+Finally in section 4.10, a model of the PD200 amplifier’s noise is developed. +
+
+
4.1 Measurement Setup
+
+
+
+
@@ -304,25 +501,28 @@ The output noise of the voltage amplifier PD200 is foreseen to be around 1mV rms
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}}
+ \Gamma_{n}(\omega) \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
\end{equation}
-Here are the documentation of the equipment used for this test bench:
- Voltage Amplifier PD200 -
- Load Capacitor EPCOS 10uF Multilayer Ceramic Capacitor -
- Low Noise Voltage Amplifier EG&G 5113 -
- Speedgoat ADC IO313 +
- Load Capacitor: Film Capacitors 600V 10uF 5% +
- Low Noise Voltage Amplifiers EG&G 5113 and Femto DLPVA +
- ADC: IO313 Speedgoat card
-The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal. +The RMS noise being very small compare to the ADC resolution, we must amplify this 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. +We use either 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. +This gain should be around 1000 (60dB).
-
+
Figure 5: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)
+Figure 8: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)
@@ -332,15 +532,15 @@ An high pass filter at low frequency can be added if there is a problem of large
-
5.2 Model of the setup
-
+
+
-
4.2 Model of the setup
+-As shown in Figure 6, there are 4 equipment involved in the measurement: +As shown in Figure 9, there are 4 equipment involved in the measurement:
- a Digital to Analog Convert (DAC) @@ -355,25 +555,25 @@ Each of these equipment has some noise:
- \(q_{da}\): quantization noise of the DAC
- \(n_{da}\): output noise of the DAC -
- \(n_p\): output noise of the PD200 (what we wish to characterize) +
- \(n_p\): input noise of the PD200 (what we wish to characterize)
- \(n_a\): input noise of the pre amplifier
- \(q_{ad}\): quantization noise of the ADC
+
Figure 6: Sources of noise in the experimental setup
+Figure 9: Sources of noise in the experimental setup
-
5.3 Quantization Noise
-
+
+
-4.3 Quantization Noise
+
-
5.4 Pre Amplifier noise measurement
-
+
+
+
+
4.4 EG&G - Amplifier noise measurement
+@@ -434,90 +634,113 @@ This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
-
+
+
Figure 7: Sources of noise in the experimental setup
+Figure 10: Sources of noise in the experimental setup
The gain of the low noise amplifier is set to 50000.
+The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure 11. +The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ. +
+ + +
+
+
+
Figure 11: Obtained Amplitude Spectral Density of the EG&G Low Noise Voltage Amplifier
+
+
4.5 Femto - Amplifier noise measurement
+
+
+
+
-
-+Similarly to Section 4.4, the noise of the Femto amplifier is identified. +
+% Hanning window win = hanning(ceil(0.5/Ts)); % Power Spectral Density -[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs); +[pxx, f] = pwelch(femto.Vout, win, [], [], Fs); % Save the results inside the struct -preamp.pxx = pxx; -preamp.f = f; +femto.pxx = pxx; +femto.f = f;
-The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure 8. -The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ. -
- -
-
+
+
Figure 8: Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier
+Figure 12: Obtained Amplitude Spectral Density of the Femto Low Noise Voltage Amplifier
-
5.5 PD200 noise measurement
-
+
+
4.6 PD200 noise measurement
+-The input of the PD200 amplifier is shunted such that there is 0V between its inputs. -Then the gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC. -We compute the Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\). -The Amplitude Spectral Density of \(n_p\) can be computed taking into account the gain of the pre-amplifier: +The input of the PD200 amplifier is shunted with a 50 Ohm resistor. +The gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC. +
+ ++The Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\) is computed. +The Amplitude Spectral Density of \(n_p\) is then computed taking into account the gain of the pre-amplifier and the can of the PD200 amplifier:
\begin{equation} -\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_a(\omega)|} +\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_p(j\omega) G_a(j\omega)|} \end{equation}And we verify that this is indeed the noise of the PD200 and not the noise of the pre-amplifier by checking that:
\begin{equation} -\Gamma_{n_p} \ll \Gamma_{n_a} +\Gamma_{n_p}(\omega) |G_p(j\omega)| \ll \Gamma_{n_a} \end{equation} -
+
Figure 9: Sources of noise in the experimental setup
+Figure 13: Sources of noise in the experimental setup
-The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure 10. -It is very similar to the one specified in the datasheet in Figure 3. +The measured low frequency output noise of one of the PD200 amplifiers is shown in Figure 14. +It is very similar to the one specified in the datasheet in Figure 3.
-
+
Figure 10: Measured low frequency noise of the PD200 from 0.01Hz to 20Hz
+Figure 14: Measured low frequency noise of the PD200 from 0.01Hz to 20Hz
-The obtained RMS and peak to peak values of the measured noises are shown in Table 3. +The obtained RMS and peak to peak values of the measured output noise are shown in Table 2.
-
-
+
+