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EN 52 Lab1- Frequency Response
Sheldon Provost
Napster.com (partner)
February 8,2001
what’s a ground??
Must have
silly
picture
Disclaimer: This should give you a rough idea of what I‟m looking for in lab reports. The data here is not
representative of what you should‟ve gotten. Data is just data. It should correspond with theory, but if it
does not, then you should be able to explain why. Remember, you cannot redo a lab outside scheduled lab
times, therefore you won‟t be graded harshly for correctness of data. This was pieced together quickly, so
there is probably a bunch of errors. Hope it helps.
Abstract
An Abstract is a The frequency responses of an RCA integrated Stereo Amplifier and an Optimus STS 1000 woofer class
concise overview of speaker were characterized using sinusoids of frequency range 50Hz to 25 kHz. The tests were carried out
the lab. Someone in standard lab conditions where instruments and measurements were subject to noise and interference. The
should be able to speaker response was characterized using a microphone with an assumed „ideal‟ frequency response. The
know exactly hat you amplifier performed optimally outside the voice range 200Hz to 8kHhz and that of the speaker was 100Hz
did and what results to 1kHz. The phase variance of the amplifier was 13% and 41% for the speaker. The Total Harmonic
you got from the Distortion of the amplifier was found to be .00233% and for the speaker was .00162%.
abstract.
Background Information and Motivation
Motivation: must do lab for grade.
Back in my day, we had to walk uphill for miles to get to school. It was uphill going home too.
We had no amplifiers, we had to improvise. We used a megaphone. Using such crude methods,
our hearing deteriorated rapidly. To test the performance of our amplifier we had to use man‟s
best friend to measure the frequency response. Why do you think RCA, the amplifier maker, has a dog on
their logo? Blah blah blah… (you get the idea)
Theory
Background info and Frequency Response of LTI Systems
motivation is an Given a Linear Time Invariant System comprised of R‟s, C‟s and L‟s with independent and dependent
introduction to the
voltage and current sources, if a input of sin(t ) is applied, then A( ) sin(t ( )) is the output
lab.
(HFS 12). The frequency response, as its name suggests, characterizes a device with respect to frequency. It
is a measure of how much the output differs from the input in terms of Gain and Phase Shift. The gain
response is the ration of the output and input amplitudes and the phase response is the variation of the phase
shift with respect to frequency. The frequency response is usually plotted on a logarithmic scale known as
Bode Plots (named in honour of HW Bode).
Spectrum Analysis/Fourier Transform and Harmonic Distortion
Fourier analysis shows that any periodic signal is comprised of a linear combination of sinusoids as shown
The Theory section in equation 1 (Dorf, et. al 689). A harmonic is defined as an integer multiple of a fundamental frequency
should contain all o and is a term in a Fourier Series. The Fourier Transform gives a frequency representation of an
equations and funda-
mental concepts used aperiodic time signal. Also, the coefficients for the Fourier Series can be obtained from the Fourier
Transform of a periodic signal (equation 1). Equation
in the analysis of the
Numbers
results.
f (t ) an cos(n 0t ) bn sin(n o t ) (1)
0
In an ideal amplifier system, the input signal should be the same as the output with only a change in
amplitude. In practical systems distortions result from using non-linear loads i.e. C‟s and L‟s.
The same analogy can be applied to music theory. Figure 1 shows the characteristics of an ideal tuning fork
for Middle C and the waveforms 2 instruments. The harmonic distortions in music define the characteristics
of different instruments.
Note Typeface ratios. The total harmonic distortion (THD) of a signal is defined as the percentage of the sum of the squares all
Also, double space is harmonic frequencies to square of the fundamental frequency.
optional.
2
hn
THD 100 (2)
2
h0
Page
Numbers
-2-
Middle C- 523 Hz Trumpet-1 Harmonic
1 2 Middle C- 523 Hz Guitar-1 Harmonic
1 2
0.5 1
0.5 1
0 0
0 0
-0.5 -1
-0.5 -1
-1 -2 -1 -2
0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6
Time -3 Time -3
Time -3 Time -3
x 10 x 10 x 10 x 10
Trumpet-2 Harmonics Trumpet-3 Harmonics Guitar-2 Harmonics Guitar-3 Harmonics
4 4 2 2
2 2
Figure 1 1
0 0 Numbers0 0
-2 -2 -1 -1
-4 -4 -2 -2
0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6
Time -3 Time -3 Time -3 Time -3
x 10 x 10 x 10 x 10
Figure 1.Harmonic Distortions of a trumpet and guitar.
Amplifier and Speaker Design
An ideal amplifier and speaker will have constant gain and phase responses. For practical purposes,
amplifiers and speakers are concerned only with the frequency ranges of speech and hearing. The typical
range of speech is 200Hz to 8kHz. Complementary, the range of hearing is 80 Hz to 25 kHz. The hearing
range consideration is obvious; the speech range however, is not as intuitive. Some systems have separate
amplifiers for microphones to accentuate singing/voice. Also, people place more emphasis on the lower
frequency ranges, the “feel” of a bass-line. With this in mind, a cheap amplifier will only be concerned with
lower music range.
Procedure
With a mid range frequency (8kHz) as input, the volume of the amplifier was adjusted. The value chosen
was about 25%.
The Procedure should The tone control on the amplifier was set to HIGH.
contain an outline of
the steps taken in Frequency Response and Harmonic Distortion of Speaker
performing the ex-
periment.
Sometimes
you can go
Figure 2.Speaker Response Setup. too far…
The frequency response of the speaker was measured using a function generator and an amplifier line out
channel as input and a microphone as an output as shown in Figure 2. The frequency range was 50Hz to
25 kHz at increments of 5 points per decade (multiples of 10.2 ). The Spectrum of the output was measured
using the FFT(Fast Fourier Transform) function on the oscilloscope. Choosing a frequency from the range
500Hz to 1 KHz (747 Hz) and using 5 of its harmonics, the THD was calculated from the FFT data. The
results are shown in Figures 7 and 8 and Tables 1 and 3.
output
gain( ) 20 log( ) (3)
dB input
( ) f t 360 (4)
deg
-3-
Frequency Response and Harmonic Distortion of Amplifier
Figure 3.Amplifier Response Setup.
The procedure is similar to above except the function generator is the input and the line-out channel of the
amplifier with an 8Ω load (to simulate the speaker) is the output as shown in Figure 3. The results are
shown in Figures 4 and 6 and Tables 2 and 3.
2
5 hn
THD 100 (5)
n1 h 2
0
The oscilloscope‟s probe was impotent when it came to giving some good data. The probe setting should
correspond with the probe type.
Don‟t rely on
autocorrect, proof read.
“probe was important”
Regular
Results/Analysis
intervals, not
The Analysis section data points
is a discussion of the
Amplifier Frequency Response - Gain
results obtained based
on the theory from 10 100 1000 10000 100000
above. 0
Bode
Plot
Label -5 Gridlines
Axes
Gain (dB)
-10
-15
Don‟t just say “I -20
took data, here it
is.” Comment on it
-25
Frequency (Hz)
Figure 4.Amplifier Frequency Response – Gain (original data)
Figure 4 shows the Gain response of the amplifier. The curve is not consistent with theoretical analysis.
The data shows all dB values < 0 which implies attenuation rather than amplification. This means that the
volume chosen was too low on the amplifier. The basic equation for a frequency response is
output
k , k is the amplifier volume.
input
Using a log scale (dB) 20 log(k gain) 20 log(k ) 20 log( gain) , therefore a low volume should correspond
to a downward shift in the plot and not affect the shape of the curve. Figure 5 shows the frequency response
at a higher volume and clearly both plots have the same basic shape. The frequencies of most attenuation
seem to be in the voice range. The amplifier seems to amplify music over voice. The area of best
amplification is in the low range implying best performance is with sub woofers. The tonal control was set
-4-
to HIGH implying that the high range should have higher amplification. Since the shape of the curve
without tonal control isn‟t known, a poor high range frequency response can be assumed. Blah Blah…
Amplifier Frequency Response - Gain
10 100 1000 10000 100000
14
12
10
8
Gain (dB)
6
Sometimes you 4
have to REDO 2
and experiment 0
-2
-4
-6
-8
Frequency (Hz)
Figure 5.Amplifier Frequency Response – Gain (data at higher volume)
Amplifier Frequency Response - Phase
10 100 1000 10000 100000
400
350
300
Phase (Degrees)
250
200
150
100
50
0
-50
Frequency (Hz)
Figure 6.a. Amplifier Frequency Response – Phase
Figure 6, above, shows the phase response of the amplifier. Assuming a there are no jump discontinuities as
above, negative phase(180) is considered and is plotted below. This shows a relatively small phase
variance 13%.
Am plifier Frequency Response - Phase
10 100 1000 10000 100000
60
40
Phase (Degrees)
20
0
-20
-40
Frequency (Hz)
-5-
Figure 6.b. Amplifier Frequency Response – Phase
Speaker Frequency Response - Gain
10 100 1000 10000 100000
0
-5
-10
Gain (dB)
-15
-20
-25
-30
Frequency (Hz)
Figure 7.Speaker Frequency Response - Gain
Figure 7 shows the speaker frequency response. The range 200Hz to 10kHz is where the most amplification
occurs1. This corresponds with the fact that the speaker is of woofer class. The plot also shows significant
attenuation in the voice range. In the higher ranges the attenuation is still considerable in comparison to the
low range.
Speaker Frequency Response - Phase
10 100 1000 10000 100000
350
300
Phase (Degrees)
250
200
150
100
50
0
Frequency (Hz)
Figure 8.a. Speaker Frequency Response – Phase
The phase response of the speaker seems to be very erratic. The most obvious source of error is the
microphone placement. There is added phase variance based on the position of the microphone. Using the
1
speed of sound as 331.45ms and the approximate microphone position as 30 cm, the time taken for the
signal to reach the microphone is t 0.0001 s. The phase variance would then be t MOD2 T, where T is the
period of the sine wave.
sin( o t ( ) V ( )) (6)
Using the same argument as with the amplifier, Figure 8.b shows a variance in phase of 41%.
1
Although it is negative dB, the analysis of the volume control shows that it can still be considered as
amplification.
2
The MODulous operator gives the remainder after division. Example (11 mod 2) =1
-6-
Speaker Frequency Response - Phase
10 100 1000 10000 100000
200
150
Phase (Degrees)
100
50
0
-50
-100
-150
-200
Frequency (Hz)
Figure 8.b. Speaker Frequency Response – Phase
Questions Don‟t rely on spell
check, proof read. “The
Which speaker are you using? big bass speaker”
The big ass speaker.
What is the significance of the phase response for the entire system?
The phase is a measure of
Would you purchase the amplifier for your home stereo system? Why or why not?
I live in a hole in Miller Hall, therefore a cheap amplifier is ideal. It would go very well with the Miller
ambiance. Considering that my neighbours love to watch tv at a high volume, the amplifier has a good
frequency response at low frequencies. Attending the number 5 party school in the country for undergrad,
tit‟s common knowledge that bass travels well through walls and floorboards. The phase response is decent,
however a property of hearing is that the phase of a signal does not affect recognition of what is heard.
Even with a terrible phase response, this amplifier would suit my need for vengeance.
What is the effect of the distance between the speaker and microphone on the amplitude response and
the phase response?
The amplitude would decrease based on the inverse square law. The attenuation is the same for all
frequencies, therefore the shape of the Bode plot is preserved. The effect of the phase is based on the
modulus of the period of the frequency and the time delay. (SEE Analysis).
Would you purchase the speaker for your home stereo system? Why or why not?
The speaker is designed for one thing only-bass. The frequency response verifies this claim. Depending on
my need for bass, that would determine if it is worth it.
What is the Harmonic distortion factor for the amplifier and speaker?
The Total Harmonic Distortion of the amplifier is 0.00233% and for the speaker is 0.00162%.
Our amplifier is a pretty inexpensive model. Conclude from your measurements, whether if you had
some extra money to spend, should you spend it on a fancier amplifier or better speakers?
The performance of the speaker is inconclusive, therefore it is hard to comment .
Conclusion
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The Lab TA‟s are wonderful. If I had extra money to spend on audio equipment, I would rather give it to
the TA‟s.
The lab was a good introduction to test and measurement equipment as well as frequency response of an
LTI system. The speaker response is not too accurate. It was subject to interference as well as microphone
position issues. The amplitude response does seem to correspond with theory-performing better in the low
frequency range. The phase is inconclusive. The Amplifier response, however, is relatively accurate. It is
not subject to the same interference. The performance is interesting. It works well in the low frequency
range. Depending on the application, either device could be suitable. Blah Blah…
References
The Reference sec-
tion is a works cited
page. Copying the
Your Almighty TA‟s
work of one person is
plagerism, copying Bahar, R. Iris and H.F. Silverman. “Introductory Notes for EN 52”
many is research! Dorf, Richard C and Svodoba, James A. “Introduction to Electric Circuits”, 5 th edition. John Wiley and
Sons, NY 2001
University of Minnesota "EE Tutorials”
http://www.ee.umn.edu/resources/toolbox/ee/tutorials/indext.html
(2 Aug. 1999).
-8-
Keep the
Appedix same # of
decimal
Speaker Frequency Response places Amplifier Frequency Response
(Hz) Vo(mV) Vi(mV) Gain(dB) t(ms) (deg) (Hz) Vo(mV) Vi(mV) Gain(dB) t(ms) (deg)
50.000 13.000 110.000 -18.549 1.400 25.200 50.000 119.000 210.000 -4.933 0.003 0.054
79.245 31.000 90.000 -9.258 2.000 57.056 79.245 107.000 206.000 -5.690 1.000 28.528
125.594 21.000 51.800 -7.842 2.900 131.120 125.594 88.000 206.000 -7.388 1.000 45.214
199.054 26.000 37.000 -3.065 2.120 151.918 199.054 75.000 206.000 -8.776 0.760 54.461
315.479 26.000 37.000 -3.065 2.160 245.316 315.479 36.000 199.000 -14.851 0.340 38.615
500.000 18.000 28.000 -3.838 0.280 50.400 500.000 27.000 199.000 -17.350 0.200 36.000
792.447 16.000 24.000 -3.522 0.400 114.112 792.447 23.000 199.000 -18.743 0.110 31.381
1255.943 1.360 20.000 -23.350 0.100 45.214 1255.943 21.000 199.000 -19.533 0.020 9.043
1990.536 1.710 20.000 -21.361 0.416 298.103 1990.536 20.000 199.000 -19.956 0.000 0.000
3154.787 1.050 21.000 -26.021 0.208 236.230 3154.787 22.000 201.000 -19.215 0.304 345.260
5000.000 6.720 25.000 -11.411 0.154 277.200 5000.000 25.000 201.000 -18.105 0.187 336.600
7924.466 12.000 31.000 -8.244 0.083 236.783 7924.466 32.000 201.000 -15.961 0.115 328.073
12559.432 10.000 41.000 -12.256 0.072 325.540 12559.432 42.000 201.000 -13.599 0.075 339.105
19905.359 11.400 52.100 -13.199 0.026 186.314 19905.359 54.000 201.000 -11.416 0.048 343.965
25000.000 2.870 56.500 -25.883 0.000 0.000 25000.000 58.000 201.000 -10.795 0.040 360.000
Table 1:Speaker Frequency Response Table 2: Amplifier Frequency Response
Total Harmonic Distortion@747Hz
Amplifier Speaker V
o
(Hz) Gain(dB) Gain Gain(dB) Gain gain( ) 20 log( )
dB V
747 -26.87 4.53E-02 -26.60 4.68E-02 i
1494 -73.75 2.05E-04 -81.87 8.06E-05
2241 -85.63 5.23E-05 -84.38 6.04E-05 ( ) f t 360
deg
2988 -88.12 3.93E-05 -76.88 1.43E-04
2
3735 -89.38 3.40E-05 -86.88 4.53E-05 5 hn
THD 100
4482 -95.00 1.78E-05 -85.63 5.23E-05 n1 h 2
THD=2.33E-03% THD=1.62E-03% 0
Table 3: Total Harmonic Distortion
-9-
