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< h1 class = "title" > Voltage Amplifier PD200 - Test Bench< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#orgc43f0fc" > 1. Requirements PD200 Expected characteristics< / a > < / li >
< li > < a href = "#org9e1f8da" > 2. Voltage Amplifier Model< / a > < / li >
< li > < a href = "#org58651b6" > 3. Transfer Function measurement< / a >
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< ul >
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< li > < a href = "#org304a75d" > 3.1. Setup< / a > < / li >
< li > < a href = "#org02635e8" > 3.2. Maximum Frequency/Voltage to not overload the amplifier< / a > < / li >
< li > < a href = "#orgc7c2c23" > 3.3. Small Signal Bandwidth< / a > < / li >
< li > < a href = "#org1d1072a" > 3.4. Bandwidth for multiple excitation signals< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgff95d7c" > 4. Noise measurement< / a >
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< ul >
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< li > < a href = "#orgc596a2b" > 4.1. Measurement Setup< / a > < / li >
< li > < a href = "#org09a7143" > 4.2. Model of the setup< / a > < / li >
< li > < a href = "#org38f7579" > 4.3. Quantization Noise< / a > < / li >
< li > < a href = "#orgc755c39" > 4.4. EG& G - Amplifier noise measurement< / a > < / li >
< li > < a href = "#orgc16dd7a" > 4.5. Femto - Amplifier noise measurement< / a > < / li >
< li > < a href = "#org32350ff" > 4.6. PD200 noise measurement< / a > < / li >
< li > < a href = "#orgea9aca9" > 4.7. DAC noise measurement< / a > < / li >
< li > < a href = "#org71ad511" > 4.8. Total noise measurement< / a > < / li >
< li > < a href = "#org8d4a13f" > 4.9. 20bits DAC noise measurement< / a > < / li >
< li > < a href = "#org8e194b0" > 4.10. PD200 Amplifier noise model< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org63b40e4" > 5. Comparison to other commercial amplifiers< / a >
< ul >
< li > < a href = "#orgb2b3b03" > 5.1. Transfer functions< / a > < / li >
< li > < a href = "#org3779171" > 5.2. Noise Characteristics< / a > < / li >
< / ul >
< / li >
< li > < a href = "#org61f0483" > 6. Conclusion< / a > < / li >
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< / ul >
< / div >
< / div >
< hr >
< p > This report is also available as a < a href = "./test-bench-pd200.pdf" > pdf< / a > .< / p >
< hr >
< p >
The goal of this test bench is to characterize the Voltage amplifier < a href = "https://www.piezodrive.com/drivers/pd200-60-watt-voltage-amplifier/" > PD200< / a > from PiezoDrive.
< / p >
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< div class = "note" id = "org51a8585" >
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< p >
The documentation of the PD200 is accessible < a href = "doc/PD200-V7-R1.pdf" > here< / a > .
< / p >
< / div >
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< p >
This document is organized as follows:
< / p >
< ul class = "org-ul" >
< li > Section < a href = "#org0690faf" > 1< / a > : the requirements for the amplifiers and the characteristics of the PD200 amplifiers as advertise in the datasheet are listed.< / li >
< li > Section < a href = "#org2496dac" > 2< / a > : a very simple amplifier model consisting of a transfer function and a noise source is described.< / li >
< li > Section < a href = "#org3f48045" > 3< / a > : the transfer function from input voltage to output voltage is identified.< / li >
< li > Section < a href = "#orgf21cb12" > 4< / a > : the power spectral density of the amplifier’ s noise is measured< / li >
< li > Section < a href = "#org0768992" > 5< / a > : the characteristics of the PD200 amplifier are compared to the E.505 amplifier from PI and to the LA75 from cedrat< / li >
< li > Section < a href = "#org3f6c507" > 6< / a > : the measured characteristics of the PD200 amplifier are compared with the requirements< / li >
< / ul >
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< div id = "outline-container-orgc43f0fc" class = "outline-2" >
< h2 id = "orgc43f0fc" > < span class = "section-number-2" > 1< / span > Requirements PD200 Expected characteristics< / h2 >
< div class = "outline-text-2" id = "text-1" >
< p >
< a id = "org0690faf" > < / a >
< / p >
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< p >
A picture of the PD200 amplifier is shown in Figure < a href = "#orgf059e11" > 1< / a > .
< / p >
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< div id = "orgf059e11" class = "figure" >
< p > < img src = "figs/amplifier_PD200.png" alt = "amplifier_PD200.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Picture of the PD200 Voltage Amplifier< / p >
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< / div >
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< p >
The specifications as well as the amplifier characteristics as shown in the datasheet are summarized in Table < a href = "#org53168ab" > 1< / a > .
< / p >
< table id = "org53168ab" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Characteristics of the PD200 compared with the specifications< / caption >
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< colgroup >
< col class = "org-left" / >
< col class = "org-center" / >
< col class = "org-center" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > < b > Characteristics< / b > < / th >
< th scope = "col" class = "org-center" > < b > Manual< / b > < / th >
< th scope = "col" class = "org-center" > < b > Specification< / b > < / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Input Voltage Range< / td >
< td class = "org-center" > +/- 10 [V]< / td >
< td class = "org-center" > +/- 10 [V]< / td >
< / tr >
< tr >
< td class = "org-left" > Output Voltage Range< / td >
< td class = "org-center" > -50/150 [V]< / td >
< td class = "org-center" > -20/150 [V]< / td >
< / tr >
< tr >
< td class = "org-left" > Gain< / td >
< td class = "org-center" > 20 [V/V]< / td >
< td class = "org-center" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Maximum RMS current< / td >
< td class = "org-center" > 0.9 [A]< / td >
< td class = "org-center" > > 50 [mA]< / td >
< / tr >
< tr >
< td class = "org-left" > Maximum Pulse current< / td >
< td class = "org-center" > 10 [A]< / td >
< td class = "org-center" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Slew Rate< / td >
< td class = "org-center" > 150 [V/us]< / td >
< td class = "org-center" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Noise (10uF load)< / td >
< td class = "org-center" > 0.7 [mV RMS]< / td >
< td class = "org-center" > < 2 [mV rms]< / td >
< / tr >
< tr >
< td class = "org-left" > Small Signal Bandwidth (10uF load)< / td >
< td class = "org-center" > 7.4 [kHz]< / td >
< td class = "org-center" > > 5 [kHz]< / td >
< / tr >
< tr >
< td class = "org-left" > Large Signal Bandwidth (150V, 10uF)< / td >
< td class = "org-center" > 300 [Hz]< / td >
< td class = "org-center" >   < / td >
< / tr >
< / tbody >
< / table >
< p >
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The most important characteristics are the large (small signal) bandwidth > 5 [kHz] and the small noise (< 2 [mV RMS]).
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< / p >
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< p >
For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure < a href = "#orgee79c85" > 2< / a > ) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure < a href = "#org5bb9d30" > 3< / a > ).
< / p >
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< p >
These two characteristics are respectively measured in Section < a href = "#org3f48045" > 3< / a > and Section < a href = "#orgf21cb12" > 4< / a > .
< / p >
< div id = "orgee79c85" class = "figure" >
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< p > < img src = "./figs/pd200_expected_small_signal_bandwidth.png" alt = "pd200_expected_small_signal_bandwidth.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Expected small signal bandwidth< / p >
< / div >
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< div id = "org5bb9d30" class = "figure" >
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< p > < img src = "figs/pd200_expected_noise.png" alt = "pd200_expected_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Expected Low frequency noise from 0.03Hz to 20Hz< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org9e1f8da" class = "outline-2" >
< h2 id = "org9e1f8da" > < span class = "section-number-2" > 2< / span > Voltage Amplifier Model< / h2 >
< div class = "outline-text-2" id = "text-2" >
< p >
< a id = "org2496dac" > < / a >
< / p >
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< p >
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.
< / p >
< p >
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It is also characterized by its < b > input< / b > noise \(n\).
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< / p >
< p >
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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 input noise.
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< / p >
< p >
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As \(G_p\) depends on the load capacitance, it should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
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< / p >
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< div id = "org3d926d5" class = "figure" >
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< p > < img src = "figs/pd200-model-schematic.png" alt = "pd200-model-schematic.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Model of the voltage amplifier< / p >
< / div >
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< p >
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 < a href = "#org93c8310" > 6< / a > .
< / p >
< p >
The Amplitude Spectral Density \(\Gamma_n\) is then:
< / p >
\begin{equation}
\Gamma_n(\omega) = |G_n(j\omega)| \Gamma_{\tilde{n}}(\omega)
\end{equation}
< p >
with \(\Gamma_{\tilde{n}}(\omega) = 1\).
< / p >
< div id = "org64a2245" class = "figure" >
< p > < img src = "figs/pd200-model-schematic-normalized.png" alt = "pd200-model-schematic-normalized.png" / >
< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org58651b6" class = "outline-2" >
< h2 id = "org58651b6" > < span class = "section-number-2" > 3< / span > Transfer Function measurement< / h2 >
< div class = "outline-text-2" id = "text-3" >
< p >
< a id = "org3f48045" > < / a >
< / p >
< p >
In this section, the transfer function of the PD200 amplifier is measured:
< / p >
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< ul class = "org-ul" >
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< li > Section < a href = "#orgaa5a588" > 3.1< / a > : the measurement setup is described< / li >
< li > Section < a href = "#org04fcc9e" > 3.2< / a > : the maximum sinusoidal excitation frequency is estimated in order to not overload the amplifier< / li >
< li > Section < a href = "#org5972a0a" > 3.3< / a > : the small signal bandwidth measurement results are shown< / li >
< li > Section < a href = "#orgad0b3ab" > 3.4< / a > : the amplifier’ s transfer function is estimated for several input amplitudes< / li >
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< / ul >
< / div >
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< div id = "outline-container-org304a75d" class = "outline-3" >
< h3 id = "org304a75d" > < span class = "section-number-3" > 3.1< / span > Setup< / h3 >
< div class = "outline-text-3" id = "text-3-1" >
< p >
< a id = "orgaa5a588" > < / a >
< / p >
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< p >
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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 < a href = "#org93c8310" > 6< / a > is used.
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< / p >
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< div class = "note" id = "org3919fdc" >
< p >
Here are the documentation of the equipment used for this test bench:
< / p >
< ul class = "org-ul" >
< li > Voltage Amplifier: < a href = "doc/PD200-V7-R1.pdf" > PD200< / a > < / li >
< li > Load Capacitor: < a href = "doc/KEM_F3040_C4G_AXIAL-1104248.pdf" > Film Capacitors 600V 10uF 5%< / a > < / li >
< li > DAC/ADC: < a href = "doc/IO131-OEM-Datasheet.pdf" > IO313 Speedgoat Interface< / a > < / li >
< / ul >
< / div >
< p >
For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.
< / p >
< div id = "org93c8310" class = "figure" >
< p > < img src = "figs/setup-dynamics-measurement.png" alt = "setup-dynamics-measurement.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-org02635e8" class = "outline-3" >
< h3 id = "org02635e8" > < span class = "section-number-3" > 3.2< / span > Maximum Frequency/Voltage to not overload the amplifier< / h3 >
< div class = "outline-text-3" id = "text-3-2" >
< p >
< a id = "org04fcc9e" > < / a >
< / p >
< p >
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.
< / p >
< p >
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
< / p >
< p >
The impedance of the capacitance is:
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
< / p >
< p >
Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\):
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
< / p >
< p >
Moreover, there is a gain of 20 between the input voltage and the output voltage:
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
< / p >
< p >
For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:
< / p >
\begin{equation}
\boxed{\omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}}}
\end{equation}
< p >
with:
< / p >
< ul class = "org-ul" >
< li > \(\omega_{\text{max}}\) the maximum input sinusoidal frequency in Radians per seconds< / li >
< li > \(C\) the load capacitance in Farads< / li >
< li > \(V_{in}\) the input voltage sinusoidal amplitude in Volts< / li >
< li > \(I_{out,\text{max}}\) the specified maximum output current in Amperes< / li >
< / ul >
< p >
\(\omega_{\text{max}}/2\pi\) as a function of \(V_{in}\) is shown in Figure < a href = "#org3e7ecd4" > 7< / a > .
< / p >
< div id = "org3e7ecd4" class = "figure" >
< p > < img src = "figs/max_frequency_voltage.png" alt = "max_frequency_voltage.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Maximum frequency as a function of the excitation voltage amplitude< / p >
< / div >
< p >
When doing sweep sine excitation, we make sure not to reach this maximum excitation frequency.
< / p >
< / div >
< / div >
< div id = "outline-container-orgc7c2c23" class = "outline-3" >
< h3 id = "orgc7c2c23" > < span class = "section-number-3" > 3.3< / span > Small Signal Bandwidth< / h3 >
< div class = "outline-text-3" id = "text-3-3" >
< p >
< a id = "org5972a0a" > < / a >
Load Data
< / p >
< p >
Compute Transfer Functions
< / p >
< p >
Compare
< / p >
< p >
Model
< / p >
< p >
Save Model
< / p >
< / div >
< / div >
< div id = "outline-container-org1d1072a" class = "outline-3" >
< h3 id = "org1d1072a" > < span class = "section-number-3" > 3.4< / span > Bandwidth for multiple excitation signals< / h3 >
< div class = "outline-text-3" id = "text-3-4" >
< p >
< a id = "orgad0b3ab" > < / a >
< / p >
< p >
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Iout_max = 0.57; < span class = "org-comment" > % Maximum output current [A]< / span >
C = 10e< span class = "org-type" > -< / span > 6; < span class = "org-comment" > % Load Capacitance [F]< / span >
V_in = [0.1, 0.5, 1, 2, 4];
f_max = 0.8< span class = "org-type" > *< / span > Iout_max< span class = "org-type" > ./< / span > (20< span class = "org-type" > *< / span > C< span class = "org-type" > *< / span > V_in< span class = "org-type" > /< / span > sqrt(2))< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > ;
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > 1:length(Vin_ampl)< / span >
pd200{< span class = "org-constant" > i< / span > }.notes.pd200.f_max = f_max(< span class = "org-constant" > i< / span > );
pd200{< span class = "org-constant" > i< / span > }.notes.pd200.Vin = V_in(< span class = "org-constant" > i< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
< / div >
< div id = "outline-container-orgff95d7c" class = "outline-2" >
< h2 id = "orgff95d7c" > < span class = "section-number-2" > 4< / span > Noise measurement< / h2 >
< div class = "outline-text-2" id = "text-4" >
< p >
< a id = "orgf21cb12" > < / a >
< / p >
< p >
In section < a href = "#org22a9e3d" > 4.1< / a > , the measurement setup is described and a model (block diagram) of the setup is given in section < a href = "#org7b1d1b0" > 4.2< / a > .
< / p >
< p >
Then, the noise contribution of each element is measured:
< / p >
< ul class = "org-ul" >
< li > Section < a href = "#org118a1be" > 4.3< / a > : the quantization noise of the ADC is estimated< / li >
< li > Sections < a href = "#org80f2aac" > 4.4< / a > and < a href = "#orgd77aed9" > 4.5< / a > : the noise of the low-noise amplifiers are estimated< / li >
< li > Section < a href = "#org5f12bbc" > 4.6< / a > : the input voltage noise of the PD200 amplifier is estimated< / li >
< li > Section < a href = "#org50df610" > 4.7< / a > : the output noise of the DAC is measured< / li >
< li > Section < a href = "#orgd1ca5a0" > 4.8< / a > : 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< / li >
< li > Section < a href = "#org6a7ec65" > 4.9< / a > : the noise of an 20bits DAC is measured and it is shown if it could lowering the overall noise of the setup< / li >
< / ul >
< p >
Finally in section < a href = "#org3c4edcc" > 4.10< / a > , a model of the PD200 amplifier’ s noise is developed.
< / p >
< / div >
< div id = "outline-container-orgc596a2b" class = "outline-3" >
< h3 id = "orgc596a2b" > < span class = "section-number-3" > 4.1< / span > Measurement Setup< / h3 >
< div class = "outline-text-3" id = "text-4-1" >
< p >
< a id = "org22a9e3d" > < / a >
< / p >
< div class = "note" id = "org6c9ffc6" >
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< p >
Here are the documentation of the equipment used for this test bench:
< / p >
< ul class = "org-ul" >
< li > Voltage Amplifier < a href = "doc/PD200-V7-R1.pdf" > PD200< / a > < / li >
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< li > Load Capacitor: < a href = "doc/KEM_F3040_C4G_AXIAL-1104248.pdf" > Film Capacitors 600V 10uF 5%< / a > < / li >
< li > Low Noise Voltage Amplifiers < a href = "doc/egg-5113-preamplifier.pdf" > EG& G 5113< / a > and < a href = "doc/de-dlpva-100-b.pdf" > Femto DLPVA< / a > < / li >
< li > ADC: < a href = "doc/IO131-OEM-Datasheet.pdf" > IO313 Speedgoat card< / a > < / li >
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< / ul >
< / div >
< p >
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:
< / p >
\begin{equation}
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\Gamma_{n}(\omega) \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
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\end{equation}
< p >
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The RMS noise being very small compare to the ADC resolution, we must amplify this noise before digitizing the signal.
< / p >
< p >
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The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200.
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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.
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< / p >
< p >
The gain of the low-noise amplifier can be increased until the full range of the ADC is used.
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This gain should be around 1000 (60dB).
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< / p >
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< div id = "orgdae3c58" class = "figure" >
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< p > < img src = "figs/setup-noise-measurement.png" alt = "setup-noise-measurement.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)< / p >
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< / div >
< p >
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.
< / p >
< / div >
< / div >
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< div id = "outline-container-org09a7143" class = "outline-3" >
< h3 id = "org09a7143" > < span class = "section-number-3" > 4.2< / span > Model of the setup< / h3 >
< div class = "outline-text-3" id = "text-4-2" >
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< p >
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< a id = "org7b1d1b0" > < / a >
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< / p >
< p >
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As shown in Figure < a href = "#org7a80897" > 9< / a > , there are 4 equipment involved in the measurement:
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< / p >
< ul class = "org-ul" >
< li > a Digital to Analog Convert (DAC)< / li >
< li > the Voltage amplifier to be measured with a gain of 20 (PD200)< / li >
< li > a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters< / li >
< li > an Analog to Digital Converter (ADC)< / li >
< / ul >
< p >
Each of these equipment has some noise:
< / p >
< ul class = "org-ul" >
< li > \(q_{da}\): quantization noise of the DAC< / li >
< li > \(n_{da}\): output noise of the DAC< / li >
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< li > \(n_p\): input noise of the PD200 (what we wish to characterize)< / li >
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< li > \(n_a\): input noise of the pre amplifier< / li >
< li > \(q_{ad}\): quantization noise of the ADC< / li >
< / ul >
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< div id = "org7a80897" class = "figure" >
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< p > < img src = "figs/noise_meas_procedure.png" alt = "noise_meas_procedure.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 9: < / span > Sources of noise in the experimental setup< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org38f7579" class = "outline-3" >
< h3 id = "org38f7579" > < span class = "section-number-3" > 4.3< / span > Quantization Noise< / h3 >
< div class = "outline-text-3" id = "text-4-3" >
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< p >
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< a id = "org118a1be" > < / a >
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< / p >
< p >
The quantization noise is something that can be predicted.
The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to:
< / p >
\begin{equation}
\Gamma_q(\omega) = \frac{q}{\sqrt{12 f_s}}
\end{equation}
< p >
with:
< / p >
< ul class = "org-ul" >
< li > \(q = \frac{\Delta V}{2^n}\) the quantization in [V], which is the corresponding value in [V] of the least significant bit< / li >
< li > \(\Delta V\) is the full range of the ADC in [V]< / li >
< li > \(n\) is the number of bits< / li >
< li > \(f_s\) is the sample frequency in [Hz]< / li >
< / ul >
< div class = "org-src-container" >
< pre class = "src src-matlab" > adc = struct();
adc.Delta_V = 20; < span class = "org-comment" > % [V]< / span >
adc.n = 16; < span class = "org-comment" > % number of bits< / span >
adc.Fs = 20e3; < span class = "org-comment" > % [Hz]< / span >
adc.Gamma_q = adc.Delta_V< span class = "org-type" > /< / span > 2< span class = "org-type" > ^< / span > adc.n< span class = "org-type" > /< / span > sqrt(12< span class = "org-type" > *< / span > adc.Fs); < span class = "org-comment" > % [V/sqrt(Hz)]< / span >
< / pre >
< / div >
< p >
The obtained Amplitude Spectral Density is < code > 6.2294e-07< / code > \(V/\sqrt{Hz}\).
< / p >
< / div >
< / div >
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< div id = "outline-container-orgc755c39" class = "outline-3" >
< h3 id = "orgc755c39" > < span class = "section-number-3" > 4.4< / span > EG& G - Amplifier noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-4" >
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< p >
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< a id = "org80f2aac" > < / a >
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< / p >
< p >
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.
< / p >
< p >
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:
< / p >
\begin{equation}
\Gamma_{n_a}(\omega) \approx \frac{\Gamma_n(\omega)}{|G_a(\omega)|}
\end{equation}
< p >
This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
< / p >
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< div id = "org04b4812" class = "figure" >
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< p > < img src = "figs/noise_measure_setup_preamp.png" alt = "noise_measure_setup_preamp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 10: < / span > Sources of noise in the experimental setup< / p >
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< / div >
< p >
The gain of the low noise amplifier is set to < code > 50000< / code > .
< / p >
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< p >
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure < a href = "#org6a8e4a8" > 11< / a > .
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
< / p >
< div id = "org6a8e4a8" class = "figure" >
< p > < img src = "figs/asd_egg.png" alt = "asd_egg.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > Obtained Amplitude Spectral Density of the EG& G Low Noise Voltage Amplifier< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-orgc16dd7a" class = "outline-3" >
< h3 id = "orgc16dd7a" > < span class = "section-number-3" > 4.5< / span > Femto - Amplifier noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-5" >
< p >
< a id = "orgd77aed9" > < / a >
< / p >
< p >
Similarly to Section < a href = "#org80f2aac" > 4.4< / a > , the noise of the Femto amplifier is identified.
< / p >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-comment" > % Hanning window< / span >
win = hanning(ceil(0.5< span class = "org-type" > /< / span > Ts));
< span class = "org-comment" > % Power Spectral Density< / span >
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[pxx, f] = pwelch(femto.Vout, win, [], [], Fs);
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< span class = "org-comment" > % Save the results inside the struct< / span >
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femto.pxx = pxx;
femto.f = f;
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< / pre >
< / div >
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< div id = "orgd6ec0a3" class = "figure" >
< p > < img src = "figs/asd_femto.png" alt = "asd_femto.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > Obtained Amplitude Spectral Density of the Femto Low Noise Voltage Amplifier< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org32350ff" class = "outline-3" >
< h3 id = "org32350ff" > < span class = "section-number-3" > 4.6< / span > PD200 noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-6" >
< p >
< a id = "org5f12bbc" > < / a >
< / p >
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< p >
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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.
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< / p >
< p >
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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:
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< / p >
\begin{equation}
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\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_p(j\omega) G_a(j\omega)|}
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\end{equation}
< p >
And we verify that this is indeed the noise of the PD200 and not the noise of the pre-amplifier by checking that:
< / p >
\begin{equation}
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\Gamma_{n_p}(\omega) |G_p(j\omega)| \ll \Gamma_{n_a}
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\end{equation}
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< div id = "orgef32d0c" class = "figure" >
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< p > < img src = "figs/noise_measure_setup_pd200.png" alt = "noise_measure_setup_pd200.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > Sources of noise in the experimental setup< / p >
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< / div >
< p >
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The measured low frequency < b > output< / b > noise of one of the PD200 amplifiers is shown in Figure < a href = "#org37538d1" > 14< / a > .
It is very similar to the one specified in the datasheet in Figure < a href = "#org5bb9d30" > 3< / a > .
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< / p >
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< div id = "org37538d1" class = "figure" >
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< p > < img src = "figs/pd200_noise_time_lpf.png" alt = "pd200_noise_time_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Measured low frequency noise of the PD200 from 0.01Hz to 20Hz< / p >
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< / div >
< p >
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The obtained RMS and peak to peak values of the measured < b > output< / b > noise are shown in Table < a href = "#orgbddbe0f" > 2< / a > .
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< / p >
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< table id = "orgbddbe0f" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > RMS and Peak to Peak measured low frequency output noise (0.01Hz to 20Hz)< / caption >
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< colgroup >
< col class = "org-left" / >
< col class = "org-right" / >
< col class = "org-right" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" >   < / th >
< th scope = "col" class = "org-right" > < b > RMS [uV]< / b > < / th >
< th scope = "col" class = "org-right" > < b > Peak to Peak [mV]< / b > < / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Specification [10uF]< / td >
< td class = "org-right" > 714.0< / td >
< td class = "org-right" > 4.3< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_1< / td >
< td class = "org-right" > 565.1< / td >
< td class = "org-right" > 3.7< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_2< / td >
< td class = "org-right" > 767.6< / td >
< td class = "org-right" > 3.5< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_3< / td >
< td class = "org-right" > 479.9< / td >
< td class = "org-right" > 3.0< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_4< / td >
< td class = "org-right" > 615.7< / td >
< td class = "org-right" > 3.5< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_5< / td >
< td class = "org-right" > 651.0< / td >
< td class = "org-right" > 2.4< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_6< / td >
< td class = "org-right" > 473.2< / td >
< td class = "org-right" > 2.7< / td >
< / tr >
< tr >
< td class = "org-left" > PD200_7< / td >
< td class = "org-right" > 423.1< / td >
< td class = "org-right" > 2.3< / td >
< / tr >
< / tbody >
< / table >
< p >
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The Amplitude Spectral Density of the measured < b > input< / b > noise is computed and shown in Figure < a href = "#org8143da2" > 15< / a > .
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< / p >
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< p >
The contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise.
< / p >
< div id = "org8143da2" class = "figure" >
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< p > < img src = "figs/asd_noise_3uF_warmup.png" alt = "asd_noise_3uF_warmup.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 15: < / span > Amplitude Spectral Density of the measured noise< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgea9aca9" class = "outline-3" >
< h3 id = "orgea9aca9" > < span class = "section-number-3" > 4.7< / span > DAC noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-7" >
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< p >
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< a id = "org50df610" > < / a >
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< / p >
< p >
In order not to have any quantization noise, we impose the DAC to output a zero voltage.
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The gain of the low noise amplifier is adjusted in order to have sufficient voltage going to the ADC.
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< / p >
< p >
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:
< / p >
\begin{equation}
\Gamma_{n_{da}}(\omega) = \frac{\Gamma_m(\omega)}{|G_a(\omega)|}
\end{equation}
< p >
And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\):
< / p >
\begin{equation}
\Gamma_{n_{da}} \gg \Gamma_{n_a}
\end{equation}
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< div id = "orgf6bcfdf" class = "figure" >
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< p > < img src = "figs/noise_measure_setup_dac.png" alt = "noise_measure_setup_dac.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 16: < / span > Sources of noise in the experimental setup< / p >
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< / div >
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< div id = "org5bf4a01" class = "figure" >
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< p > < img src = "figs/asd_noise_dac.png" alt = "asd_noise_dac.png" / >
< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org71ad511" class = "outline-3" >
< h3 id = "org71ad511" > < span class = "section-number-3" > 4.8< / span > Total noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-8" >
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< p >
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< a id = "orgd1ca5a0" > < / a >
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< / p >
< p >
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Let’ s now analyze the measurement of the setup in Figure < a href = "#org1480d92" > 18< / a > .
< / p >
< div id = "org1480d92" class = "figure" >
< p > < img src = "figs/noise_meas_procedure.png" alt = "noise_meas_procedure.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 18: < / span > Sources of noise in the experimental setup< / p >
< / div >
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< p >
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The PSD of the measured noise is computed and the ASD is shown in Figure < a href = "#orgc059f95" > 19< / a > .
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(0.5< span class = "org-type" > /< / span > Ts));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > 1:7< / span >
[pxx, f] = pwelch(pd200dac{< span class = "org-constant" > i< / span > }.Vn, win, [], [], Fs);
pd200dac{< span class = "org-constant" > i< / span > }.f = f;
pd200dac{< span class = "org-constant" > i< / span > }.pxx = pxx;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "orgc059f95" class = "figure" >
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< p > < img src = "figs/asd_noise_tot.png" alt = "asd_noise_tot.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 19: < / span > Amplitude Spectral Density of the measured noise and of the individual sources of noise< / p >
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< / div >
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< div class = "important" id = "orgd4a443e" >
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< p >
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.
< / p >
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< div id = "outline-container-org8d4a13f" class = "outline-3" >
< h3 id = "org8d4a13f" > < span class = "section-number-3" > 4.9< / span > 20bits DAC noise measurement< / h3 >
< div class = "outline-text-3" id = "text-4-9" >
< p >
< a id = "org6a7ec65" > < / a >
< / p >
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< p >
Let’ s now measure the noise of another DAC called the “ SSI2V” (< a href = "doc/[SSI2V]Datasheet.pdf" > doc< / a > ).
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It is a 20bits DAC with an output of +/-10.48 V and a very low output noise.
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< / p >
< p >
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The measurement setup is the same as the one in Figure < a href = "#orgf6bcfdf" > 16< / a > .
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(0.5< span class = "org-type" > /< / span > Ts));
[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
ssi2v.pxx = pxx;
ssi2v.f = f;
< / pre >
< / div >
< p >
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The obtained noise of the SSI2V DAC is shown in Figure < a href = "#orge8679e1" > 20< / a > and compared with the noise of the 16bits DAC.
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It is shown to be much smaller (~1 order of magnitude).
< / p >
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< div id = "orge8679e1" class = "figure" >
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< p > < img src = "figs/asd_ssi2v_noise.png" alt = "asd_ssi2v_noise.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 20: < / span > Amplitude Spectral Density of the SSI2V DAC’ s noise< / p >
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< / div >
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< div class = "important" id = "org83f9d60" >
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< p >
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.
< / p >
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< div id = "outline-container-org8e194b0" class = "outline-3" >
< h3 id = "org8e194b0" > < span class = "section-number-3" > 4.10< / span > PD200 Amplifier noise model< / h3 >
< div class = "outline-text-3" id = "text-4-10" >
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< p >
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< a id = "org3c4edcc" > < / a >
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< / p >
< p >
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Let’ s design a transfer function whose norm represent the Amplitude Spectral Density of the input voltage noise of the PD200 amplifier.
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< / p >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > Gn = 2.5e< span class = "org-type" > -< / span > 5 < span class = "org-type" > *< / span > ((1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > 30)< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > 2))< span class = "org-type" > ^< / span > 2 < span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > 5e3);
< / pre >
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< / div >
< p >
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The comparison between the measured ASD of the modeled ASD is done in Figure
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< / p >
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< div id = "org046b04a" class = "figure" >
< p > < img src = "figs/pd200_asd_noise_model.png" alt = "pd200_asd_noise_model.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 21: < / span > ASD of the measured input voltage noise and modeled noise using \(G_n(s)\)< / p >
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< / div >
< p >
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Let’ s now compute the Cumulative Amplitude Spectrum corresponding to the measurement and the model and compare them.
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< / p >
< p >
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The integration from low to high frequency and from high to low frequency are both shown in Figure
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< / p >
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< div id = "orgf7b2ac4" class = "figure" >
< p > < img src = "figs/pd200_cas_noise_model.png" alt = "pd200_cas_noise_model.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 22: < / span > Cumulative Amplitude Spectrum of the measured input voltage noise and modeled noise using \(G_n(s)\)< / p >
< / div >
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< p >
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The obtained RMS noise of the model is < code > 650.77< / code > uV RMS which is the same as advertise.
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< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org63b40e4" class = "outline-2" >
< h2 id = "org63b40e4" > < span class = "section-number-2" > 5< / span > Comparison to other commercial amplifiers< / h2 >
< div class = "outline-text-2" id = "text-5" >
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< p >
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< a id = "org0768992" > < / a >
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< / p >
< / div >
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< div id = "outline-container-orgb2b3b03" class = "outline-3" >
< h3 id = "orgb2b3b03" > < span class = "section-number-3" > 5.1< / span > Transfer functions< / h3 >
< / div >
< div id = "outline-container-org3779171" class = "outline-3" >
< h3 id = "org3779171" > < span class = "section-number-3" > 5.2< / span > Noise Characteristics< / h3 >
< div class = "outline-text-3" id = "text-5-2" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > pd200.Vout = pd200.Vout< span class = "org-type" > /< / span > pd200.notes.pre_amp.gain;
la75.Vout = la75.Vout< span class = "org-type" > /< / span > la75.notes.pre_amp.gain;
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< / pre >
< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(pd200.t, 1e3< span class = "org-type" > *< / span > pd200.Vout)
plot(la75.t, 1e3< span class = "org-type" > *< / span > la75.Vout)
hold off;
xlabel(< span class = "org-string" > 'Time [s]'< / span > );
ylabel(< span class = "org-string" > 'Voltage [mV]'< / span > );
< span class = "org-comment" > % ylim([-3, 3]);< / span >
< / pre >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org61f0483" class = "outline-2" >
< h2 id = "org61f0483" > < span class = "section-number-2" > 6< / span > Conclusion< / h2 >
< div class = "outline-text-2" id = "text-6" >
< p >
< a id = "org3f6c507" > < / a >
< / p >
< table id = "orgca48cbf" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< caption class = "t-above" > < span class = "table-number" > Table 3:< / span > Measured characteristics, Manual characterstics and specified ones< / caption >
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< colgroup >
< col class = "org-left" / >
< col class = "org-center" / >
< col class = "org-center" / >
< col class = "org-center" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > < b > Characteristics< / b > < / th >
< th scope = "col" class = "org-center" > < b > Measurement< / b > < / th >
< th scope = "col" class = "org-center" > < b > Manual< / b > < / th >
< th scope = "col" class = "org-center" > < b > Specification< / b > < / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Input Voltage Range< / td >
< td class = "org-center" > -< / td >
< td class = "org-center" > +/- 10 [V]< / td >
< td class = "org-center" > +/- 10 [V]< / td >
< / tr >
< tr >
< td class = "org-left" > Output Voltage Range< / td >
< td class = "org-center" > -< / td >
< td class = "org-center" > -50/150 [V]< / td >
< td class = "org-center" > -20/150 [V]< / td >
< / tr >
< tr >
< td class = "org-left" > Gain< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 20 [V/V]< / td >
< td class = "org-center" > -< / td >
< / tr >
< tr >
< td class = "org-left" > Maximum RMS current< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 0.9 [A]< / td >
< td class = "org-center" > > 50 [mA]< / td >
< / tr >
< tr >
< td class = "org-left" > Maximum Pulse current< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 10 [A]< / td >
< td class = "org-center" > -< / td >
< / tr >
< tr >
< td class = "org-left" > Slew Rate< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 150 [V/us]< / td >
< td class = "org-center" > -< / td >
< / tr >
< tr >
< td class = "org-left" > Noise (10uF load)< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 0.7 [mV RMS]< / td >
< td class = "org-center" > < 2 [mV rms]< / td >
< / tr >
< tr >
< td class = "org-left" > Small Signal Bandwidth (10uF load)< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 7.4 [kHz]< / td >
< td class = "org-center" > > 5 [kHz]< / td >
< / tr >
< tr >
< td class = "org-left" > Large Signal Bandwidth (150V, 10uF)< / td >
< td class = "org-center" >   < / td >
< td class = "org-center" > 300 [Hz]< / td >
< td class = "org-center" > -< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-02-10 mer. 16:16< / p >
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< / div >
< / body >
< / html >
