From 730fea51160e685cce62cb767b976fa8cdbb3d5f Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 2 Feb 2021 18:50:47 +0100 Subject: [PATCH] Rename files --- index.html | 941 +---------------------------- index.pdf | Bin 644689 -> 0 bytes test-bench-pd200.html | 943 ++++++++++++++++++++++++++++++ index.org => test-bench-pd200.org | 7 + test-bench-pd200.pdf | Bin 0 -> 3761363 bytes 5 files changed, 951 insertions(+), 940 deletions(-) mode change 100644 => 120000 index.html delete mode 100644 index.pdf create mode 100644 test-bench-pd200.html rename index.org => test-bench-pd200.org (99%) create mode 100644 test-bench-pd200.pdf diff --git a/index.html b/index.html deleted file mode 100644 index be2572d..0000000 --- a/index.html +++ /dev/null @@ -1,940 +0,0 @@ - - - - - - -Voltage Amplifier PD200 - Test Bench - - - - - - - - -
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Voltage Amplifier PD200 - Test Bench

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1 Introduction

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-The goal of this test bench is to characterize the Voltage amplifier PD200 from PiezoDrive. -

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-The documentation of the PD200 is accessible here. -

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amplifier_PD200.png -

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Figure 1: Picture of the PD200 Voltage Amplifier

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2 Voltage Amplifier Requirements

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Table 1: Requirements for the Voltage Amplifier
 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]
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3 PD200 Expected characteristics

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Table 2: Characteristics of the PD200
CharacteristicsManualSpecification
Input Voltage Range+/- 10 [V]+/- 10 [V]
Output Voltage Range-50/150 [V]-20/150 [V]
Gain20 [V/V] 
Maximum RMS current0.9 [A]> 50 [mA]
Maximum Pulse current10 [A] 
Slew Rate150 [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] 
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-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). -

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pd200_expected_small_signal_bandwidth.png -

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Figure 2: Expected small signal bandwidth

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pd200_expected_noise.png -

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Figure 3: Expected Low frequency noise from 0.03Hz to 20Hz

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4 Voltage Amplifier Model

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-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. -

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-It is also characterized by its output noise \(n\). -This noise is described by its Power Spectral Density. -

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-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. -

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-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. -

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pd200-model-schematic.png -

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Figure 4: Model of the voltage amplifier

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5 Noise measurement

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5.1 Setup

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-Here are the documentation of the equipment used for this test bench: -

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-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. -

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-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. -

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setup-noise-measurement.png -

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Figure 5: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)

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-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. -

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5.2 Model of the setup

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-As shown in Figure 6, there are 4 equipment involved in the measurement: -

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  • a Digital to Analog Convert (DAC)
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  • the Voltage amplifier to be measured with a gain of 20 (PD200)
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  • a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters
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  • an Analog to Digital Converter (ADC)
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-Each of these equipment has some noise: -

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  • \(q_{da}\): quantization noise of the DAC
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  • \(n_{da}\): output noise of the DAC
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  • \(n_p\): output noise of the PD200 (what we wish to characterize)
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  • \(n_a\): input noise of the pre amplifier
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  • \(q_{ad}\): quantization noise of the ADC
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noise_meas_procedure.png -

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Figure 6: Sources of noise in the experimental setup

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5.3 Quantization Noise

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-The quantization noise is something that can be predicted. -The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to: -

-\begin{equation} -\Gamma_q(\omega) = \frac{q}{\sqrt{12 f_s}} -\end{equation} -

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  • \(q = \frac{\Delta V}{2^n}\) the quantization in [V], which is the corresponding value in [V] of the least significant bit
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  • \(\Delta V\) is the full range of the ADC in [V]
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  • \(n\) is the number of bits
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  • \(f_s\) is the sample frequency in [Hz]
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adc = struct();
-adc.Delta_V = 20; % [V]
-adc.n = 16; % number of bits
-adc.Fs = 20e3; % [Hz]
-adc.Gamma_q = adc.Delta_V/2^adc.n/sqrt(12*adc.Fs); % [V/sqrt(Hz)]
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-The obtained Amplitude Spectral Density is 6.2294e-07 \(V/\sqrt{Hz}\). -

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5.4 Pre Amplifier noise measurement

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-First, we wish to measure the noise of the pre-amplifier. -To do so, the input of the pre-amplifier is shunted such that there is 0V at its inputs. -Then, the gain of the amplifier is increase until the measured signal on the ADC is much larger than the quantization noise. -

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-The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal \(n\) is computed. -Finally, the Amplitude Spectral Density of \(n_a\) can be computed taking into account the gain of the pre-amplifier: -

-\begin{equation} -\Gamma_{n_a}(\omega) \approx \frac{\Gamma_n(\omega)}{|G_a(\omega)|} -\end{equation} - -

-This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible. -

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noise_measure_setup_preamp.png -

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Figure 7: Sources of noise in the experimental setup

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-The gain of the low noise amplifier is set to 50000. -

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% Hanning window
-win = hanning(ceil(0.5/Ts));
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-% Power Spectral Density
-[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs);
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-% Save the results inside the struct
-preamp.pxx = pxx;
-preamp.f = f;
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-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. -

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asd_preamp.png -

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Figure 8: Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier

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5.5 PD200 noise measurement

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-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: -

-\begin{equation} -\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_a(\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} -\end{equation} - - -
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noise_measure_setup_pd200.png -

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Figure 9: Sources of noise in the experimental setup

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-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. -

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Figure 10: Measured low frequency noise of the PD200 from 0.01Hz to 20Hz

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-The obtained RMS and peak to peak values of the measured noises are shown in Table 3. -

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Table 3: RMS and Peak to Peak measured low frequency noise (0.01Hz to 20Hz)
 RMS [uV]Peak to Peak [mV]
Specification [10uF]714.04.3
PD200_1565.13.7
PD200_2767.63.5
PD200_3479.93.0
PD200_4615.73.5
PD200_5651.02.4
PD200_6473.22.7
PD200_7423.12.3
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-The Amplitude Spectral Density of the measured noise is now computed and shown in Figure 11. -

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asd_noise_3uF_warmup.png -

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Figure 11: Amplitude Spectral Density of the measured noise

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5.6 DAC noise measurement

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-In order not to have any quantization noise, we impose the DAC to output a zero voltage. -The gain of the low noise amplifier is adjusted to -

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-The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed. -The Amplitude Spectral Density of \(n_{da}\) can be computed taking into account the gain of the pre-amplifier: -

-\begin{equation} -\Gamma_{n_{da}}(\omega) = \frac{\Gamma_m(\omega)}{|G_a(\omega)|} -\end{equation} - -

-And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\): -

-\begin{equation} -\Gamma_{n_{da}} \gg \Gamma_{n_a} -\end{equation} - - -
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Figure 12: Sources of noise in the experimental setup

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asd_noise_dac.png -

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5.7 Total noise measurement

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-Let’s now analyze the measurement of the setup in Figure 6. -

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-The PSD of the measured noise is computed and the ASD is shown in Figure 14. -

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win = hanning(ceil(0.5/Ts));
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-    [pxx, f] = pwelch(pd200dac{i}.Vn, win, [], [], Fs);
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-    pd200dac{i}.pxx = pxx;
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Figure 14: Amplitude Spectral Density of the measured noise and of the individual sources of noise

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-The output noise of the PD200 amplifier is limited by the noise of the DAC. -Having a DAC with lower noise could lower the output noise of the PD200. -SSI2V DACs will be used to verify that. -

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5.8 20bits DAC noise measurement

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- -Let’s now measure the noise of another DAC called the “SSI2V” (doc). -It is a 20bits DAC with an output of +/-10.48 V and a very low noise. -

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-The measurement setup is the same as the one in Figure 12. -

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win = hanning(ceil(0.5/Ts));
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-[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
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-The obtained noise of the SSI2V DAC is shown in Figure 15 and compared with the noise of the 16bits DAC. -It is shown to be much smaller (~1 order of magnitude). -

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Figure 15: Amplitude Spectral Density of the SSI2V DAC’s noise

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-Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC. -The limiting factor should then be the noise of the PD200 itself. -

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6 Transfer Function measurement

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6.1 Setup

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-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 16 is used. -

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-Here are the documentation of the equipment used for this test bench: -

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

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Figure 16: Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)

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6.2 Maximum Frequency/Voltage to not overload the amplifier

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-The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave. -

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-The impedance of the capacitance is: -\[ Z_C(\omega) = \frac{1}{jC\omega} \] -

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-Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\): -\[ V_{out} = \frac{1}{C\omega} I_{out} \] -

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-Moreover, there is a gain of 20 between the input voltage and the output voltage: -\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \] -

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-For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is: -\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \] -

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-\(\omega_max\) as a function of \(V_{in}\) is shown in Figure 17. -

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Figure 17: Maximum frequency as a function of the excitation voltage amplitude

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6.3 Obtained Transfer Functions

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-Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V. -

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Figure 18: Transfer function for the PD200 amplitude between \(V_{in}\) and \(V_{out}\) for multiple voltage amplitudes

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Gp = 19.95/(1 + s/2/pi/35e3);
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Figure 19: Comparison of the model transfer function and the measured frequency response function

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7 Conclusion

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Table 4: Measured characteristics, Manual characterstics and specified ones
CharacteristicsMeasurementManualSpecification
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]-
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Author: Dehaeze Thomas

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Created: 2021-01-23 sam. 15:40

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+

Voltage Amplifier PD200 - Test Bench

+ +
+

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. +

+ + +
+

amplifier_PD200.png +

+

Figure 1: Picture of the PD200 Voltage Amplifier

+
+
+
+ +
+

2 Voltage Amplifier Requirements

+
+ + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 1: Requirements for the Voltage Amplifier
 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

+
+ + + +++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 2: Characteristics of the PD200
CharacteristicsManualSpecification
Input Voltage Range+/- 10 [V]+/- 10 [V]
Output Voltage Range-50/150 [V]-20/150 [V]
Gain20 [V/V] 
Maximum RMS current0.9 [A]> 50 [mA]
Maximum Pulse current10 [A] 
Slew Rate150 [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 2) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure 3). +

+ + +
+

pd200_expected_small_signal_bandwidth.png +

+

Figure 2: Expected small signal bandwidth

+
+ + +
+

pd200_expected_noise.png +

+

Figure 3: Expected Low frequency noise from 0.03Hz to 20Hz

+
+
+
+ +
+

4 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. +

+ +

+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. +

+ +

+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. +

+ + +
+

pd200-model-schematic.png +

+

Figure 4: Model of the voltage amplifier

+
+
+
+ +
+

5 Noise measurement

+
+ +
+ +
+

5.1 Setup

+
+

+ +

+ +
+

+Here are the documentation of the equipment used for this test bench: +

+ + +
+ +

+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. +

+ + +
+

setup-noise-measurement.png +

+

Figure 5: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)

+
+ +

+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. +

+
+
+ +
+

5.2 Model of the setup

+
+

+ +

+ +

+As shown in Figure 6, there are 4 equipment involved in the measurement: +

+
    +
  • a Digital to Analog Convert (DAC)
  • +
  • the Voltage amplifier to be measured with a gain of 20 (PD200)
  • +
  • a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters
  • +
  • an Analog to Digital Converter (ADC)
  • +
+ +

+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)
  • +
  • \(n_a\): input noise of the pre amplifier
  • +
  • \(q_{ad}\): quantization noise of the ADC
  • +
+ + +
+

noise_meas_procedure.png +

+

Figure 6: Sources of noise in the experimental setup

+
+
+
+ +
+

5.3 Quantization Noise

+
+

+ +

+ +

+The quantization noise is something that can be predicted. +The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to: +

+\begin{equation} +\Gamma_q(\omega) = \frac{q}{\sqrt{12 f_s}} +\end{equation} +

+with: +

+
    +
  • \(q = \frac{\Delta V}{2^n}\) the quantization in [V], which is the corresponding value in [V] of the least significant bit
  • +
  • \(\Delta V\) is the full range of the ADC in [V]
  • +
  • \(n\) is the number of bits
  • +
  • \(f_s\) is the sample frequency in [Hz]
  • +
+ +
+
adc = struct();
+adc.Delta_V = 20; % [V]
+adc.n = 16; % number of bits
+adc.Fs = 20e3; % [Hz]
+adc.Gamma_q = adc.Delta_V/2^adc.n/sqrt(12*adc.Fs); % [V/sqrt(Hz)]
+
+
+ +

+The obtained Amplitude Spectral Density is 6.2294e-07 \(V/\sqrt{Hz}\). +

+
+
+ +
+

5.4 Pre Amplifier noise measurement

+
+

+ +

+ +

+First, we wish to measure the noise of the pre-amplifier. +To do so, the input of the pre-amplifier is shunted such that there is 0V at its inputs. +Then, the gain of the amplifier is increase until the measured signal on the ADC is much larger than the quantization noise. +

+ +

+The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal \(n\) is computed. +Finally, the Amplitude Spectral Density of \(n_a\) can be computed taking into account the gain of the pre-amplifier: +

+\begin{equation} +\Gamma_{n_a}(\omega) \approx \frac{\Gamma_n(\omega)}{|G_a(\omega)|} +\end{equation} + +

+This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible. +

+ + +
+

noise_measure_setup_preamp.png +

+

Figure 7: Sources of noise in the experimental setup

+
+ +

+The gain of the low noise amplifier is set to 50000. +

+ +
+
% Hanning window
+win = hanning(ceil(0.5/Ts));
+
+% Power Spectral Density
+[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs);
+
+% Save the results inside the struct
+preamp.pxx = pxx;
+preamp.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. +

+ + +
+

asd_preamp.png +

+

Figure 8: Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier

+
+
+
+ +
+

5.5 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: +

+\begin{equation} +\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_a(\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} +\end{equation} + + +
+

noise_measure_setup_pd200.png +

+

Figure 9: 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. +

+ +
+

pd200_noise_time_lpf.png +

+

Figure 10: 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. +

+ + + +++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 3: RMS and Peak to Peak measured low frequency noise (0.01Hz to 20Hz)
 RMS [uV]Peak to Peak [mV]
Specification [10uF]714.04.3
PD200_1565.13.7
PD200_2767.63.5
PD200_3479.93.0
PD200_4615.73.5
PD200_5651.02.4
PD200_6473.22.7
PD200_7423.12.3
+ +

+The Amplitude Spectral Density of the measured noise is now computed and shown in Figure 11. +

+ +
+

asd_noise_3uF_warmup.png +

+

Figure 11: Amplitude Spectral Density of the measured noise

+
+
+
+ +
+

5.6 DAC noise measurement

+
+

+ +

+ +

+In order not to have any quantization noise, we impose the DAC to output a zero voltage. +The gain of the low noise amplifier is adjusted to +

+ +

+The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed. +The Amplitude Spectral Density of \(n_{da}\) can be computed taking into account the gain of the pre-amplifier: +

+\begin{equation} +\Gamma_{n_{da}}(\omega) = \frac{\Gamma_m(\omega)}{|G_a(\omega)|} +\end{equation} + +

+And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\): +

+\begin{equation} +\Gamma_{n_{da}} \gg \Gamma_{n_a} +\end{equation} + + +
+

noise_measure_setup_dac.png +

+

Figure 12: Sources of noise in the experimental setup

+
+ + +
+

asd_noise_dac.png +

+
+
+
+ +
+

5.7 Total noise measurement

+
+

+ +

+ +

+Let’s now analyze the measurement of the setup in Figure 6. +

+ +

+The PSD of the measured noise is computed and the ASD is shown in Figure 14. +

+
+
win = hanning(ceil(0.5/Ts));
+
+for i = 1:7
+    [pxx, f] = pwelch(pd200dac{i}.Vn, win, [], [], Fs);
+    pd200dac{i}.f = f;
+    pd200dac{i}.pxx = pxx;
+end
+
+
+ + +
+

asd_noise_tot.png +

+

Figure 14: Amplitude Spectral Density of the measured noise and of the individual sources of noise

+
+ +
+

+The output noise of the PD200 amplifier is limited by the noise of the DAC. +Having a DAC with lower noise could lower the output noise of the PD200. +SSI2V DACs will be used to verify that. +

+ +
+
+
+ +
+

5.8 20bits DAC noise measurement

+
+

+ +Let’s now measure the noise of another DAC called the “SSI2V” (doc). +It is a 20bits DAC with an output of +/-10.48 V and a very low noise. +

+ +

+The measurement setup is the same as the one in Figure 12. +

+ +
+
win = hanning(ceil(0.5/Ts));
+
+[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
+ssi2v.pxx = pxx;
+ssi2v.f = f;
+
+
+ +

+The obtained noise of the SSI2V DAC is shown in Figure 15 and compared with the noise of the 16bits DAC. +It is shown to be much smaller (~1 order of magnitude). +

+ + +
+

asd_ssi2v_noise.png +

+

Figure 15: Amplitude Spectral Density of the SSI2V DAC’s noise

+
+ +
+

+Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC. +The limiting factor should then be the noise of the PD200 itself. +

+ +
+
+
+
+ +
+

6 Transfer Function measurement

+
+
+
+

6.1 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 16 is used. +

+ +
+

+Here are the documentation of the equipment used for this test bench: +

+ + +
+ +

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

+ + +
+

setup-dynamics-measurement.png +

+

Figure 16: Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)

+
+
+
+ +
+

6.2 Maximum Frequency/Voltage to not overload the amplifier

+
+

+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: +\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \] +

+ +

+\(\omega_max\) as a function of \(V_{in}\) is shown in Figure 17. +

+ + +
+

max_frequency_voltage.png +

+

Figure 17: Maximum frequency as a function of the excitation voltage amplitude

+
+
+
+ +
+

6.3 Obtained Transfer Functions

+
+

+Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V. +

+ +

+The obtained frequency response functions are shown in Figure 18. +As the input voltage increases, the voltage drop is increasing. +

+ + +
+

pd200_tf_voltage.png +

+

Figure 18: Transfer function for the PD200 amplitude between \(V_{in}\) and \(V_{out}\) for multiple voltage amplitudes

+
+ +

+The small signal transfer function of the amplifier can be approximated by a first order low pass filter. +

+ +
+
Gp = 19.95/(1 + s/2/pi/35e3);
+
+
+ +

+The comparison from the model and measurements are shown in Figure 19. +

+ + +
+

tf_pd200_model.png +

+

Figure 19: Comparison of the model transfer function and the measured frequency response function

+
+
+
+
+ +
+

7 Conclusion

+
+ + + +++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 4: Measured characteristics, Manual characterstics and specified ones
CharacteristicsMeasurementManualSpecification
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]-
+
+
+
+
+

Author: Dehaeze Thomas

+

Created: 2021-02-02 mar. 18:47

+
+ + diff --git a/index.org b/test-bench-pd200.org similarity index 99% rename from index.org rename to test-bench-pd200.org index 63435f9..9226223 100644 --- a/index.org +++ b/test-bench-pd200.org @@ -16,6 +16,7 @@ #+LaTeX_CLASS: scrreprt #+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full] #+LaTeX_HEADER_EXTRA: \input{preamble.tex} +#+EXPORT_FILE_NAME: test-bench-pd200.tex #+PROPERTY: header-args:matlab :session *MATLAB* #+PROPERTY: header-args:matlab+ :comments org @@ -40,6 +41,12 @@ #+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") :END: +#+begin_export html +
+

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. diff --git a/test-bench-pd200.pdf b/test-bench-pd200.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4b97682bc57944b97c129d62c7f8010664ceb7bc GIT binary patch literal 3761363 zcmce6WmKEN)^6|++@ZL82_9UFTY(~_#kIJ*yHlXWtx%wX6xvdtK!Uq#ffB5^yCk{v zeCNCC+;#6=>-%#~vXZ=++3)Ok&z`;K+0PnwJ!KVs!N;N?_VMYSd5{Pbn91Gx6-Zhd zBw!fmVaFt3qHF!i&c+8MVBl-*^N$u4cQ03vfTE&%0FxQ`L0%C2kIzexz~7#K+$9JS z(6;jNa(a*ue2{qP|NH$Qp>OBy?(1b^=glPg(4r3#(6V!L@Nr}k6lMD7>tPfp7auz> zCIJ-}D<3;$I~#XfJCLj_$lJ%u&dL=O@N0@_RF7*Ejt;;+=7M9|VQ|ZASd(7L(w=Z8Zt~_3?kk6GDHT{%=`M zLc;$!BmO4Ae~%Gj|2ZT6uH1i*5&yaDB>Zp7PQw4W>?Hhe%TB`oxtI|Cx5b3;Um)Z&myi;32$Q3^Kd4oelM~6_!qQrxH_|9 z!9d}0Hm<%=q|jytK4BHYEm9+140}qErT6udfL$Td(VQQft3PUYCUx5de8TV)z2B#X z-1rVoNLc9<{Fx(tl0D)s*lAoj2O&OawbTtfJNJShjcng)wt;=ZF05dCI!>hFfM?76SPuH3di 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