221 lines
7.9 KiB
HTML
221 lines
7.9 KiB
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<!-- 2021-05-17 lun. 23:57 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Measurement of Loudspeaker</title>
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<meta name="author" content="Dehaeze Thomas" />
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tags: "ams",
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Measurement of Loudspeaker</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgb7dcd56">1. Equipment</a></li>
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<li><a href="#orga8b11ea">2. Semi-Anechoic Outdoor measurement</a></li>
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<li><a href="#org5f8fade">3. Ground Plane Technique</a></li>
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<li><a href="#orgd4ac4d2">4. In room measurement</a></li>
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</ul>
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</div>
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</div>
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<hr>
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<p>This report is also available as a <a href="./speaker-measurement.pdf">pdf</a>.</p>
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<hr>
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<p>
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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.
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</p>
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<ul class="org-ul">
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<li>Section <a href="#orge26b894">1</a>: the tools used for the measurements are listed</li>
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<li>Section <a href="#orge527a4d">2</a>: the high frequency behavior of the speaker is measured with a semi-anechoic measurement performed outdoors</li>
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<li>Section <a href="#orga1313c1">3</a>: the low frequency behavior of the speaker is measured using the “ground plane technique”</li>
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<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>
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</ul>
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<div id="outline-container-orgb7dcd56" class="outline-2">
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<h2 id="orgb7dcd56"><span class="section-number-2">1</span> Equipment</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orge26b894"></a>
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</p>
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<ul class="org-ul">
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<li>REW software (<a href="https://www.roomeqwizard.com/">link</a>)</li>
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<li>Audiobox USB (<a href="https://www.presonus.com/products/audiobox-usb">link</a>)</li>
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<li>Behringer ECM 8000 Measuring microphone</li>
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<li>TOPPING D70 DAC</li>
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<li>Power amplifier: Amplifier</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orga8b11ea" class="outline-2">
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<h2 id="orga8b11ea"><span class="section-number-2">2</span> Semi-Anechoic Outdoor measurement</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="orge527a4d"></a>
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</p>
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<p>
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The frequency resolution is limited by the time difference between the direct sound and the first reflection.
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</p>
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<p>
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If we note \(\tau\) this time difference, the frequency resolution \(\delta f\) is:
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</p>
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\begin{equation}
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\delta f = \frac{1}{\tau}
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\end{equation}
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<p>
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with \(\delta f\) in hertz and \(\tau\) in seconds.
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</p>
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<p>
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A schematic of the setup is shown in Figure <a href="#orgd15c0ba">1</a>.
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</p>
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<div id="orgd15c0ba" class="figure">
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<p><img src="figs/outside_meas_setup.png" alt="outside_meas_setup.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Schematic of the setup</p>
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</div>
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<p>
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We usually want to measure the speaker with a resonable distance.
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Let’s take \(L = 2\,m\).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">L = 2; <span class="org-comment">% Distance speaker/microphone [m]</span>
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v = 340; <span class="org-comment">% Speed of sound [m/s]</span>
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</pre>
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</div>
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<p>
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We can then compute the time delay \(\tau\) between the direct sound and reflected sound as a function of the height \(H\).
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Similarly, we can compute the frequency resolution \(\delta f\) as a function of \(H\).
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Both are shown in Figure <a href="#org70c02e3">2</a>.
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</p>
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<div class="org-src-container">
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<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>
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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>
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tau = (D <span class="org-type">-</span> L)<span class="org-type">/</span>v; <span class="org-comment">% [s]</span>
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</pre>
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</div>
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<div id="org70c02e3" class="figure">
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<p><img src="figs/required_height_wanted_reflection_delay.png" alt="required_height_wanted_reflection_delay.png" />
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</p>
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<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>
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</div>
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<div class="important" id="orge571119">
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<p>
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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 (\(\delta f \approx 70\,Hz\)).
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However, it is much sufficient for high frequency characterisation of the speaker (say above 500Hz).
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</p>
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</div>
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<p>
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The speaker can then be tilted horizontally and vertically as shown in Figure <a href="#orgd7a99c8">3</a> and <a href="#org98fec49">4</a>.
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</p>
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<div id="orgd7a99c8" class="figure">
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<p><img src="figs/outside_meas_setup_tilt_vert.png" alt="outside_meas_setup_tilt_vert.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Tilting the speaker around a vertical axis</p>
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</div>
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<div id="org98fec49" class="figure">
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<p><img src="figs/outside_meas_setup_tilt_hor.png" alt="outside_meas_setup_tilt_hor.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Tilting the speaker around a horizontal axis</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org5f8fade" class="outline-2">
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<h2 id="org5f8fade"><span class="section-number-2">3</span> Ground Plane Technique</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="orga1313c1"></a>
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</p>
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<p>
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The idea here is to put both the microphone and the speaker on the ground.
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</p>
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<p>
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The ground must be relatively stiff.
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</p>
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<div id="org69a3268" class="figure">
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<p><img src="figs/ground_plane_meas_setup.png" alt="ground_plane_meas_setup.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Schematic of the measurement setup</p>
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</div>
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<p>
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It is then possible to use very large gate windows in order to identify the low frequency behavior of the speaker.
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</p>
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<p>
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It is here not useful to perform any off-axis measurements as at the frequencies, the speaker is perfectly omnidirectionnal.
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</p>
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</div>
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</div>
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<div id="outline-container-orgd4ac4d2" class="outline-2">
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<h2 id="orgd4ac4d2"><span class="section-number-2">4</span> In room measurement</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="org44863a6"></a>
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</p>
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<ul class="org-ul">
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<li class="off"><code>[ ]</code> Estimated response</li>
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<li class="off"><code>[ ]</code> Correlation with measurement</li>
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</ul>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-05-17 lun. 23:57</p>
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</div>
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</body>
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</html>
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