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Thomas Dehaeze 2021-05-17 23:57:47 +02:00
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<!-- 2021-05-17 lun. 23:57 -->
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<title>Measurement of Loudspeaker</title>
<meta name="author" content="Dehaeze Thomas" />
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</div><div id="content">
<h1 class="title">Measurement of Loudspeaker</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgb7dcd56">1. Equipment</a></li>
<li><a href="#orga8b11ea">2. Semi-Anechoic Outdoor measurement</a></li>
<li><a href="#org5f8fade">3. Ground Plane Technique</a></li>
<li><a href="#orgd4ac4d2">4. In room measurement</a></li>
</ul>
</div>
</div>
<hr>
<p>This report is also available as a <a href="./speaker-measurement.pdf">pdf</a>.</p>
<hr>
<p>
Because of the lack of a large anechoic room or a near field scanner system (e.g. the <a href="http://www.klippel.de/products/rd-system/modules/nfs-near-field-scanner.html#:~:text=The%20Near-Field%20Scanner%203D,move%20during%20the%20scanning%20process.">Klippel NFS</a>), the low frequency and high frequency response of the speaker have to be measured separately.
</p>
<ul class="org-ul">
<li>Section <a href="#orge26b894">1</a>: the tools used for the measurements are listed</li>
<li>Section <a href="#orge527a4d">2</a>: the high frequency behavior of the speaker is measured with a semi-anechoic measurement performed outdoors</li>
<li>Section <a href="#orga1313c1">3</a>: the low frequency behavior of the speaker is measured using the &ldquo;ground plane technique&rdquo;</li>
<li>Section <a href="#org44863a6">4</a>: the response of the speaker in a typical room is estimated from the two above measurements and compare with in-room measurements</li>
</ul>
<div id="outline-container-orgb7dcd56" class="outline-2">
<h2 id="orgb7dcd56"><span class="section-number-2">1</span> Equipment</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orge26b894"></a>
</p>
<ul class="org-ul">
<li>REW software (<a href="https://www.roomeqwizard.com/">link</a>)</li>
<li>Audiobox USB (<a href="https://www.presonus.com/products/audiobox-usb">link</a>)</li>
<li>Behringer ECM 8000 Measuring microphone</li>
<li>TOPPING D70 DAC</li>
<li>Power amplifier: Amplifier</li>
</ul>
</div>
</div>
<div id="outline-container-orga8b11ea" class="outline-2">
<h2 id="orga8b11ea"><span class="section-number-2">2</span> Semi-Anechoic Outdoor measurement</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orge527a4d"></a>
</p>
<p>
The frequency resolution is limited by the time difference between the direct sound and the first reflection.
</p>
<p>
If we note \(\tau\) this time difference, the frequency resolution \(\delta f\) is:
</p>
\begin{equation}
\delta f = \frac{1}{\tau}
\end{equation}
<p>
with \(\delta f\) in hertz and \(\tau\) in seconds.
</p>
<p>
A schematic of the setup is shown in Figure <a href="#orgd15c0ba">1</a>.
</p>
<div id="orgd15c0ba" class="figure">
<p><img src="figs/outside_meas_setup.png" alt="outside_meas_setup.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Schematic of the setup</p>
</div>
<p>
We usually want to measure the speaker with a resonable distance.
Let&rsquo;s take \(L = 2\,m\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">L = 2; <span class="org-comment">% Distance speaker/microphone [m]</span>
v = 340; <span class="org-comment">% Speed of sound [m/s]</span>
</pre>
</div>
<p>
We can then compute the time delay \(\tau\) between the direct sound and reflected sound as a function of the height \(H\).
Similarly, we can compute the frequency resolution \(\delta f\) as a function of \(H\).
Both are shown in Figure <a href="#org70c02e3">2</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">H = [0<span class="org-type">:</span>0.01<span class="org-type">:</span>4]; <span class="org-comment">% [m]</span>
D = 2<span class="org-type">*</span>sqrt(H<span class="org-type">.^</span>2 <span class="org-type">+</span> L<span class="org-type">^</span>2<span class="org-type">/</span>4); <span class="org-comment">% [m]</span>
tau = (D <span class="org-type">-</span> L)<span class="org-type">/</span>v; <span class="org-comment">% [s]</span>
</pre>
</div>
<div id="org70c02e3" class="figure">
<p><img src="figs/required_height_wanted_reflection_delay.png" alt="required_height_wanted_reflection_delay.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Time delay \(\tau\) between the direct sound and (first) reflected sound as a function of the height \(H\). The resulting frequency resolution \(\delta f\) is also shown.</p>
</div>
<div class="important" id="orge571119">
<p>
It is shown than even for high heights (\(H = 3\,m\)), the frequency resolution will be quite poor for low frequency characterisation of the speaker (\(\delta f \approx 70\,Hz\)).
However, it is much sufficient for high frequency characterisation of the speaker (say above 500Hz).
</p>
</div>
<p>
The speaker can then be tilted horizontally and vertically as shown in Figure <a href="#orgd7a99c8">3</a> and <a href="#org98fec49">4</a>.
</p>
<div id="orgd7a99c8" class="figure">
<p><img src="figs/outside_meas_setup_tilt_vert.png" alt="outside_meas_setup_tilt_vert.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Tilting the speaker around a vertical axis</p>
</div>
<div id="org98fec49" class="figure">
<p><img src="figs/outside_meas_setup_tilt_hor.png" alt="outside_meas_setup_tilt_hor.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Tilting the speaker around a horizontal axis</p>
</div>
</div>
</div>
<div id="outline-container-org5f8fade" class="outline-2">
<h2 id="org5f8fade"><span class="section-number-2">3</span> Ground Plane Technique</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orga1313c1"></a>
</p>
<p>
The idea here is to put both the microphone and the speaker on the ground.
</p>
<p>
The ground must be relatively stiff.
</p>
<div id="org69a3268" class="figure">
<p><img src="figs/ground_plane_meas_setup.png" alt="ground_plane_meas_setup.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Schematic of the measurement setup</p>
</div>
<p>
It is then possible to use very large gate windows in order to identify the low frequency behavior of the speaker.
</p>
<p>
It is here not useful to perform any off-axis measurements as at the frequencies, the speaker is perfectly omnidirectionnal.
</p>
</div>
</div>
<div id="outline-container-orgd4ac4d2" class="outline-2">
<h2 id="orgd4ac4d2"><span class="section-number-2">4</span> In room measurement</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org44863a6"></a>
</p>
<ul class="org-ul">
<li class="off"><code>[&#xa0;]</code> Estimated response</li>
<li class="off"><code>[&#xa0;]</code> Correlation with measurement</li>
</ul>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-05-17 lun. 23:57</p>
</div>
</body>
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#+TITLE: Measurement of Loudspeaker
:DRAWER:
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#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_UP: ../index.html
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#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:
#+begin_export html
<hr>
<p>This report is also available as a <a href="./speaker-measurement.pdf">pdf</a>.</p>
<hr>
#+end_export
* Introduction :ignore:
Because of the lack of a large anechoic room or a near field scanner system (e.g. the [[http://www.klippel.de/products/rd-system/modules/nfs-near-field-scanner.html#:~:text=The%20Near-Field%20Scanner%203D,move%20during%20the%20scanning%20process.][Klippel NFS]]), the low frequency and high frequency response of the speaker have to be measured separately.
- Section [[sec:equipment]]: the tools used for the measurements are listed
- Section [[sec:outdoor_meas]]: the high frequency behavior of the speaker is measured with a semi-anechoic measurement performed outdoors
- Section [[sec:ground_plane_meas]]: the low frequency behavior of the speaker is measured using the "ground plane technique"
- Section [[sec:in_room_meas]]: the response of the speaker in a typical room is estimated from the two above measurements and compare with in-room measurements
* Equipment
<<sec:equipment>>
- REW software ([[https://www.roomeqwizard.com/][link]])
- Audiobox USB ([[https://www.presonus.com/products/audiobox-usb][link]])
- Behringer ECM 8000 Measuring microphone
- TOPPING D70 DAC
- Power amplifier: Amplifier
* Semi-Anechoic Outdoor measurement
<<sec:outdoor_meas>>
** Introduction :ignore:
The frequency resolution is limited by the time difference between the direct sound and the first reflection.
If we note $\tau$ this time difference, the frequency resolution $\delta f$ is:
\begin{equation}
\delta f = \frac{1}{\tau}
\end{equation}
with $\delta f$ in hertz and $\tau$ in seconds.
A schematic of the setup is shown in Figure [[fig:outside_meas_setup]].
#+name: fig:outside_meas_setup
#+caption: Schematic of the setup
[[file:figs/outside_meas_setup.png]]
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Analysis :ignore:
We usually want to measure the speaker with a resonable distance.
Let's take $L = 2\,m$.
#+begin_src matlab
L = 2; % Distance speaker/microphone [m]
v = 340; % Speed of sound [m/s]
#+end_src
We can then compute the time delay $\tau$ between the direct sound and reflected sound as a function of the height $H$.
Similarly, we can compute the frequency resolution $\delta f$ as a function of $H$.
Both are shown in Figure [[fig:required_height_wanted_reflection_delay]].
#+begin_src matlab
H = [0:0.01:4]; % [m]
D = 2*sqrt(H.^2 + L^2/4); % [m]
tau = (D - L)/v; % [s]
#+end_src
#+begin_src matlab :exports none
figure;
yyaxis left
plot(H, 1000*tau)
ylabel('Reflection Time $\tau$ [ms]');
yyaxis right
plot(H, 1./tau);
ylabel('Frequency Resolution $\delta f$ [Hz]');
set(gca, 'yscale', 'log');
ylim([1e1, 1e3]);
xlabel('Height $H$ [m]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/required_height_wanted_reflection_delay.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:required_height_wanted_reflection_delay
#+caption: Time delay $\tau$ between the direct sound and (first) reflected sound as a function of the height $H$. The resulting frequency resolution $\delta f$ is also shown.
#+RESULTS:
[[file:figs/required_height_wanted_reflection_delay.png]]
#+begin_important
It is shown than even for high heights ($H = 3\,m$), the frequency resolution will be quite poor for low frequency characterisation of the speaker ($\delta f \approx 70\,Hz$).
However, it is much sufficient for high frequency characterisation of the speaker (say above 500Hz).
#+end_important
The speaker can then be tilted horizontally and vertically as shown in Figure [[fig:outside_meas_setup_tilt_vert]] and [[fig:outside_meas_setup_tilt_hor]].
#+name: fig:outside_meas_setup_tilt_vert
#+caption: Tilting the speaker around a vertical axis
[[file:figs/outside_meas_setup_tilt_vert.png]]
#+name: fig:outside_meas_setup_tilt_hor
#+caption: Tilting the speaker around a horizontal axis
[[file:figs/outside_meas_setup_tilt_hor.png]]
* Ground Plane Technique
<<sec:ground_plane_meas>>
** Introduction :ignore:
The idea here is to put both the microphone and the speaker on the ground.
The ground must be relatively stiff.
#+name: fig:ground_plane_meas_setup
#+caption: Schematic of the measurement setup
[[file:figs/ground_plane_meas_setup.png]]
It is then possible to use very large gate windows in order to identify the low frequency behavior of the speaker.
It is here not useful to perform any off-axis measurements as at the frequencies, the speaker is perfectly omnidirectionnal.
* In room measurement
<<sec:in_room_meas>>
- [ ] Estimated response
- [ ] Correlation with measurement

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