161 lines
6.0 KiB
Org Mode
161 lines
6.0 KiB
Org Mode
#+TITLE: Measurement of Loudspeaker
|
|
:DRAWER:
|
|
#+LANGUAGE: en
|
|
#+EMAIL: dehaeze.thomas@gmail.com
|
|
#+AUTHOR: Dehaeze Thomas
|
|
|
|
#+HTML_LINK_HOME: ../index.html
|
|
#+HTML_LINK_UP: ../index.html
|
|
|
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
|
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
|
|
|
#+BIND: org-latex-image-default-option "scale=1"
|
|
#+BIND: org-latex-image-default-width ""
|
|
|
|
#+LaTeX_CLASS: scrreprt
|
|
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
|
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
|
|
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
|
#+PROPERTY: header-args:matlab+ :comments org
|
|
#+PROPERTY: header-args:matlab+ :exports both
|
|
#+PROPERTY: header-args:matlab+ :results none
|
|
#+PROPERTY: header-args:matlab+ :eval no-export
|
|
#+PROPERTY: header-args:matlab+ :noweb yes
|
|
#+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
|