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Download COURSE NUMBER: E E 352 Design of a Low
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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.