Download COURSE NUMBER: E E 352 Design of a Low

COURSE NUMBER: E E 352
Design of a Low-Pass Audio Filter
By
David Alexander
Vance Drawbaugh
Performed 4/15/13
Submitted 4/18/13
Abstract
The purpose of this lab was to design, simulate and then construct an active low-pass
filter. After construction we demonstrated that it worked by sending an audio signal from a
device through the filter to a low voltage amplifier and speaker.
Introduction
In this lab we will be analyzing an active low-pass filter circuit. We’ll be examining the
theory behind the filter, simulation of the filter, implementation of the filter, and the results. This
lab asked for a pole around 1.25 kHz at 20dB per decade and required an active low-pass filter
with a gain of ten in the pass band.
Theory
It is important to understand how filters work so we know which filter is best suited for
the application. We speculated that the specifications were for a mid-range speaker or a subwoofer. We came to that conclusion because we know that a very generic range for human
hearing starts at 20 Hz and ends at 20 kHz. The pole of our active low pass filter was set for 1.25
kHz which means that the circuit would attenuate or ignore frequencies above the pole. We knew
there was only one pole due to the 20 dB per decade specification. Larger speakers, such as
woofers and sub-woofers, are designed for low frequencies – typically between 20 Hz and 1
kHz. Mid-range speakers tend to stay around 300 Hz to 5 kHz and would only pass frequencies
under the pole. Smaller speakers like tweeters are geared for the higher frequencies, and they
typically have a range of 2 kHz to 20 kHz; this type of speaker would be of no use with this filter
attached.
Implementation
Figure 1- PSPICE simulation circuit
We began with theoretical calculations to find values for the capacitor and resistors of the
op amp filter, taking into account available standard values for capacitors (See Appendix A).
With these calculations we simulated the µA741 amplifier stage of the circuit with PSPICE
according to the circuit in Figure 1. The load resistor was chosen to be 50 kΩ to simulate the
input impedance of the LM386 amplifier (see Figure 3). Following the PSPICE simulation, the
circuit was constructed according to Figure 2. A 10 kΩ potentiometer was added between the
µA741 and LM386 stages to serve as a makeshift volume control mechanism for protecting the
speaker from excessively high voltages. Due to significant interference and noise in the circuit,
coupling capacitors were added from the V+ and V- pins of the µA741 to ground. These
capacitors were a necessity because they filtered the environmental noise from the signal. A 100
Hz signal was applied to the input and the frequency response was recorded from 100 Hz up
through 10,000 Hz. The input signal was set at 1 VP-P (instead of 2 VP-P) in order to protect the
speaker from being damaged. The cutoff frequency was found by observing the point at which
the gain fell 3 dB from the mid-band gain.
Figure 2- implemented circuit
Figure 3- characteristics of LM386 amplifier
Figure 4- characteristics of µA741 operational amplifier
Results
Table 1- cutoff frequencies
Expected Cutoff Frequency (Simulated)
Measured Cutoff Frequency (PSPICE)
Percent Error
Expected Cutoff Frequency (Experimental)
Measured Cutoff Frequency
Percent Error
1250 Hz
≈ 1250 Hz
0%
1294 Hz
1330 Hz
2.78%
Table 1 summarizes the cutoff frequencies found in this experiment. The results of PSPICE
simulation are shown below in Figure 3. Using a trace function within PSPICE, a gain close to
the gain of the 3 dB frequency (7.071) was found to indicate that the simulated cutoff frequency
is approximately 1250 Hz. The measured frequency response data can be found in Table 2 and
its corresponding Bode plot is shown in Figure 4, where the red point represents the recorded
cutoff frequency of 1330 Hz. The calculations used for deriving these values can be found in
Appendix A.
Figure 5- frequency response of PSPICE simulation
Frequency Response of Audio Amplifier Circuit
25
Gain (dB)
20
15
10
5
0
100
1000
Frequency (Hz)
Cutoff Frequency (red) = 1330 Hz
Figure 6- frequency response graph
10000
Table 2- data for active filter
Frequency
VOUT
Gain
Gain
(Hz)
VIN (V) (V)
(V/V)
(dB)
100
1.00
7.20
7.20 17.14665
200
1.00
8.72
8.72 18.81033
300
1.00
9.40
9.40 19.46256
400
1.00
9.28
9.28 19.35096
500
1.00
8.72
8.72 18.81033
600
1.00
8.64
8.64 18.73027
700
1.00
8.40
8.40 18.48559
800
1.00
8.16
8.16
18.2338
900
1.00
7.84
7.84 17.88632
1000
1.00
7.60
7.60 17.61627
2000
1.00
5.12
5.12
14.1854
3000
1.00
3.84
3.84 11.68662
4000
1.00
2.96
2.96 9.425834
5000
1.00
2.44
2.44 7.747797
6000
1.00
2.08
2.08 6.361267
7000
1.00
1.84
1.84 5.296356
8000
1.00
1.64
1.64 4.296877
9000
1.00
1.48
1.48 3.405234
10000
1.00
1.36
1.36 2.670778
Conclusion
The data collected in this experiment generally agreed with our expectations, as the
experimental error stayed within an acceptable range, though the error encountered still merits
discussion. Our recorded cutoff frequency was ultimately 80 Hz greater than the specification.
This may be attributable in part to implementing resistor values slightly below the calculated
resistances. In general for filters of this type, greater resistance translates to poles at lower
frequencies. Moreover, the potentiometer inserted as a volume control placed limits on the gain
achievable by the circuit. Throughout the execution of the experiment the quality of the audio
speaker was questionable, which led to the decision to sacrifice some gain to protect it from
being damaged. The µA741 filter we designed clearly functioned as a low-pass filter and its
effect on the input signal was easily observable when an iPod was connected. The sound
produced by the circuit was not great in quality, but the upper frequencies were clearly filtered
out of the signal.
Appendix A
1. Calculations for Resistor and Capacitor Values:
Inverting Amplifier AV = -Z2/Z1
Z1 = R1
𝑅2
Z2 = R2||1/(sC) = 𝑠𝑅 𝐶+1
-Z2/Z1 = −
𝑅2
𝑠𝑅2 𝐶+1
𝑅1
2
= − 𝑠𝑅
𝑅2
𝑅1
2 𝐶+1
Pole at ωC= 1/(R2C)
1250 Hz = 7854 rad/s
7854 = 1/(R2C)
Let C = 15 nF
1
R2 = (15𝑛𝐹)∗(7854𝑟𝑎𝑑⁄ = 8488 Ω
For AV = 10 V/V,
𝑅2
𝑅1
𝑠)
= 10, so R1 = 848.8 Ω
2. For cutoff frequency of experimental data:
1
Expected Cutoff Frequency (Experimental) = 2𝜋∗(8200Ω)∗(15𝑛𝐹) = 1294 𝐻𝑧
AV (midband)
19.46 dB
AV (cutoff/3dB
frequency)
16.46 dB
fPOLE (experimental)
1330 Hz
3. Signature of Eric Wasatonic, verifying operation of amplifier:
You may contact Eric for further verification.