Experiment #1
Determining the Frequency Response Function of a Speaker
by Your Name and John Judge1
Partner: Somebody Else
ME 392 – Dynamics Laboratory
Instructor: Dr. Joseph Vignola
The Catholic University of America
02/??/2009
Include my name since you’re basing the report on the template I wrote. In the future,
you will write your lab reports entirely yourself.
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Abstract
The Frequency Response Function (FRF) of a Somebrand Somemodel speaker was
obtained experimentally. The speaker was driven through a Otherbrand Othermodel
power amplifier with broadband white noise of amplitude ??? V, and the acoustic
response ??? m directly in front of the speaker cone was recorded using a Differentbrand
Another model microphone. Measured data was filtered using a 2-pole active lowpass
filter with a ??? Hz cutoff frequency for anti-aliasing prior to analog to digital
conversion. The FRF was calculated as the ratio of the frequency spectrum of the
measured acoustic pressure over the input electrical signal. Results of ??? measurements
lasting ??? seconds each were averaged to obtain a clean final result, which showed that
the speaker has strong response between ?? and ??? Hz and had blah blah blah other
distinct features.
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Table of Contents2
Introduction
?
Experimental Apparatus and Procedure
?
Experimental Results and Discussions
?
Conclusion and Recommendations
?
References
?
Appendix
?
Note that I didn’t include either a “Nomenclature” or a “Theoretical Analysis” section
in this lab report. The nomenclature section is necessary if there are a significant number
of variables and symbols that must be defined for the reader – if there only a few, they
can be described in the text. In general, theoretical analysis is needed for one of two
reasons: (1) to generate theoretical predictions that you expect your experimental
measurements to match, and/or (2) because the raw data is not meaningful by itself and
further analysis must be done, based on some theory, in order to generate meaningful
results. Neither of those is the case for this lab: the only processing applied to the raw
data is a simple calculation of the FRF, which is a well-known procedure that does not
need to be described in great detail.
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1. Introduction
Acoustic sources (speakers) have a variety of applications in research, industry,
and commercial use. A typical speaker converts an electrical input signal into an acoustic
signal in air or some other fluid, at frequencies within the audible range (20-20,000 Hz).
More accurate transduction, especially for higher sound pressure levels, is usually
accomplished by speakers optimized to perform over only a portion of that range, so that
many audio systems are comprised of multiple speaker types (such as subwoofer, woofer,
midrange, and tweeter) in order to accurately span the full audible range. A high quality
acoustic source is one that responds with nearly constant amplitude and phase response to
the electrical input single across a specific frequency range in which the speaker is
designed to operate.
This report describes an experiment to measure the frequency response function
(FRF) of the Somebrand Somemodel speaker. The Somebrand Somemodel speaker is a
??-type speaker designed to produce sound in the frequency range ?? to ?? Hz. Add any
other important description of the speaker here. The experiment entailed measuring the
sound pressure level a fixed distance in front of the speaker cone, and processing the
resulting data to obtain the amplitude ratio and relative phase between the acoustic signal
and the input electrical signal used to drive the speaker, as functions of frequency.
The experiment was controlled using a personal computer with a data-acquisition
card, which generated the input signal used to drive the speaker, recorded the microphone
output, and processed the resulting data. Section ? describes the experimental apparatus
and procedure in detail, including the method for analysis of the measured data. The
results are presented and discussed in Section ?, followed by conclusions about the
effectiveness of the Somebrand Somemodel speaker in Section ?. Details of the custombuilt anti-aliasing filter used in the experiment are provided in an Appendix.
2. Experimental Apparatus and Procedure
A schematic of the experimental setup is shown in Fig. ?3. The system is
controlled by a PC running National Instruments LabVIEW software. A National
Instruments PCI-6221 data acquisition card (DAQ), attached via shielded cable to a
BNC-2120 connector block, allows the computer to pass signals to and from the
experimental apparatus. The signal driving the speaker, which is generated by the PC, is
first passed through a Otherbrand Othermodel power amplifier to provide sufficient
current to the speaker. A Differentbrand Anothermodel microphone is mounted ?? m
directly in front of the speaker cone. The microphone is powered by a PCB brand
Somethingmodel ICP power supply (with unity gain), and the signal is passed through a
custom built lowpass anti-aliasing filter prior to being acquired by the data acquisition
card in the PC.
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Make sure the figures are numbered in order and that any references in the text are to
the correct number. Also, you can make the figures whatever size you like and integrate
them into the text however you like – no need to use my empty boxes as exact size and
placement rules.
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Figure ?: Schematic of the experimental setup
The anti-aliasing filter is a 2-pole Butterworth normalized active low-pass filter
with a cutoff frequency of approximately ?? Hz [1], chosen to be significantly lower than
the Nyquist frequency of the data acquisition system but higher than the expected
response of the speaker. In addition to passive components, the filter includes a single JFET operational amplifier (LF351) powered by the built in power supply on the project
board on which the filter was assembled. A circuit diagram for this filter, as well as
details of its design are provided in the Appendix. Fig. ? shows the measured frequency
spectrum of the filter, showing the cutoff frequency at ?? Hz and a ?? dB/decade rolloff at
higher frequencies.
Figure ?: Frequency response function of the custom-built antialiasing filter:
(a) amplitude, and (b) phase.
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For the results presented in this report, the drive signal delivered by the computer
was uniform white noise with RMS amplitude 0.5 V, with a duration of ?? seconds. The
signal was created digitally at a sample rate of ??? samples/second, and converted to an
analog voltage signal by the output D/A converter of the DAQ. The power amplifier
provides a fixed gain of ???, resulting in ??? VRMS delivered to the speaker (the speaker is
rated for a maximum continuous voltage of ??? VRMS).
The filtered signal from the microphone was digitized by the DAQ at a rate of ???
samples/second for ??? samples. Digitizer voltages were scaled by the microphone
sensitivity of ??? Pa/V. The input and output were triggered from the same digital pulse
so that excitation of the speaker and measurement of the response were synchronized.
The experiment was run repeatedly a total of ?? times. For each iteration, the discrete
Fourier transform (DFT) was taken of both the input and output signals, providing sets of
discrete data describing the frequency spectra of each signal. The frequency response
function (FRF), also known as the sinusoidal transfer function, is the ratio of the
frequency spectrum of the system output to the frequency spectrum of system input, and
is equivalent to the transfer function of the system assuming the response is entirely
steady state and contains no transient behavior [2]. A discrete representation of the
speaker’s FRF was obtained by dividing the DFT of the measured output by the DFT of
the input . The ??? resulting functions were then averaged to obtain a signal result
described the response of the speaker as a function of input frequency.
3. Experimental Results and Discussion
Figure ?? shows the recorded time histories for a single instance of excitation and
measurement. The same data are presented in frequency domain in Fig. ??, after applying
LabView’s built-in FFT algorithm. The excitation amplitude is relatively uniform across
all frequencies in the band of interest, while the measured sound pressure level varies as a
function of frequency. Note that only the amplitude of the frequency domain data is
shown in Fig. ?? (the complex numbers resulting from the discrete Fourier transform are
output by LabView’s FFT algorithm in the form of amplitude and phase data). The
Figure ?: Typical measured time histories of (a) excitation voltage send to
speaker, and (b) sound pressure level recorded by microphone
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corresponding calculated frequency response function is shown in Fig. ?? (both amplitude
and phase of the FRF are shown). Note that the result contains some fluctuations due to
noise.
Figure ?? shows a less noisy representation of the frequency response function of
the speaker, based on averaging the ?? functions for amplitude and phase obtained from
each individual measurement. Due to the averaging, all portions of the measured FRF
which are not coherent from one measurement to the next have been reduced by a factor
of approximately ???. Describe the result in detail here, pointing out any interesting or
important features. Comment on the extent to which you think the result is a pure
representation of the dynamics of the speaker, or includes (unintentionally) dynamics due
to the other components in the system. Justify any claims you make.
Figure ?: Typical frequency spectrum of (a) excitation voltage send to
speaker, and (b) sound pressure level recorded by microphone
Figure ?: Typical frequency response function based on a single iteration of
the experiment: (a) amplitude spectrum, and (b) phase spectrum.
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Figure ?: Frequency response function determined by averaging results from
?? measurements, each of duration ??.
6. Conclusion
The Frequency Response Function of the speaker over the tested frequency
showed a strong response over the frequency range ??? Hz to ??? Hz, and was uniform in
amplitude over that range to within a factor of ???. The response above and below that
frequency range was (describe it). This indicates that the speaker should be used
(describe any relevant conclusions).
The experiment described here provides a measure of the speaker’s FRF using a
minimal set of measurements using a simple laboratory setup. Describe any additional
measurements or analyses that could be used to improve the results, or any
recommendations to a future experimenter for improving the procedure.
References/Bibliography
[1] Scherz, P., Practical Electronics for inventors(1st edition), McGraw-Hill, New York,
p.260, 2000.
[2] Palm, System Dynamics, McGraw-Hill, New York, p. ???, 2005.
Appendix
Include a description of how the antialiasing filter was designed and constructed, with
schematic diagram(s) and/or photograph(s) if necessary.
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