speaker-measurement/speaker-measurement.org

#+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"/>
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#+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