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California Polytechnic State University, San Luis Obispo *

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Electrical Engineering

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Apr 3, 2024

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Professor: David McDonald EE 242 Section 05 12:10 pm- 3:00 pm Experiment # 5 Low and High Pass RC Filters Group 8 Written By: Kush Patel, Jesus Galindo

Purpose: The purpose of this lab is to take a deeper look into High Pass and Low Pass filters, and observing how they only allow certain frequencies to pass through their filters. A Low Pass filter blocks frequencies above the cutoff frequency and a High Pass filter blocks all frequencies below the cutoff frequenc. The practical use of this can be seen with audio source and how filtering certain frequencies can allow for noise reduction and equalizers. Additionally, the practical use of these filters can be seen in image modification where it can be used to enhance images and reduce noise. LAB EQUIPMENT: 1 Agilent 33120A Function Generator (FG) 1 Agilent 34410A Digital Multimeter 1 Agilent 54621A Oscilloscope 1 Resistor Decade Box 1 Capacitor Decade Box 3 BNC-Banana 1 Bag of short leads 2 Banana-Banana leads

Figure 1. Low-Pass Filter Section 1: • Built: Jesus Galindo • Verified: Kush Patel • Worked the first time: Yes Steps: Section 1. Measurement of the magnitude and phase response of RC low-pass and high-pass filters 1. Set up the circuit shown in Figure 1 with C= 0.02 F. For the value of resistor R use 20 K, 50 K,and 100 K. Set the function generator at high-Z output termination and adjust it to provide 8 Vp-p sinusoidal waveform 2. For each value of R, construct a table as shown below. Enter the measured rms values of Vs and Vo, (using the digital multimeter) and the phase difference between Vo and Vs, while setting the frequency of the function generator to the values shown in the table below.

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f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.69897 2.809 2.708 0.964044 -0.5 25 1.39794 2.83 2.722 0.961837 -3 50 1.69897 2.831 2.708 0.956552 -6.6 250 2.39794 2.829 2.342 0.827854 -30 500 2.69897 2.827 1.755 0.620799 -49 2500 3.39794 2.824 0.455 0.161119 -79.3 5000 3.69897 2.824 0.231 0.081799 -84 25000 4.39794 2.826 0.005 0.001769 -82 Fig. 2 Low Pa ss Filter with 20kΩ Resistance f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.698970004 2.808 2.566 0.913817664 -1.4 25 1.397940009 2.83 2.559 0.904240283 -7.7 50 1.698970004 2.83 2.486 0.87844523 -15.2 250 2.397940009 2.829 1.496 0.528808766 -54.6 500 2.698970004 2.828 0.866 0.306223479 -70 2500 3.397940009 2.828 0.185 0.065417256 -84.6 5000 3.698970004 2.8285 0.092 0.032526074 -85 25000 4.397940009 2.8308 0.019 0.006711884 -86.3 Fig. 3 Low Pass Filter with 50kΩ Resistance f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.698970004 2.808 2.36 0.84045584 -2.4 25 1.397940009 2.83 2.3 0.812720848 -14.2 50 1.698970004 2.83 2.108 0.744876325 -27 250 2.397940009 2.83 0.855 0.302120141 -68.4 500 2.698970004 2.8299 0.45 0.15901622 -78.1 2500 3.397940009 2.8298 0.092 0.032511132 -84.5 5000 3.698970004 2.8299 0.046 0.016254991 -83 25000 4.397940009 2.832 0.01 0.003531073 -83.2 Fig. 4 Low Pass Filter with 100kΩ Resistance 3. Plot the magnitude and phase of the transfer function as a function of the frequency for each value of R using the tables you generated in step 2. Use log scale for the frequency and plot the three magnitude responses on one graph and the three phase responses on another.

Fig. 5 Low Pass Frequency(Log 10 ) versus Amplitude for 20kΩ, 50Ω, and 100kΩ Fig. 6 Low Pass Phase Angle versus Frequency (Log 10 ) for 20kΩ, 50Ω, and 100kΩ 4. Obtain the half power frequencies directly from your magnitude plots for each value of the resistor used. Enter your results in the table below.

f c (calculated) f c (measured) Percent difference ((m-c)/c)*100 R = 20kΩ C = 0.02 uF 397.89 Hz 398.11 Hz 0.05% R = 50kΩ C = 0.02 uF 159.15 Hz 158.49 Hz 0.41% R = 100kΩ C = 0.02 uF 78.58 Hz 79.43 Hz 1.12% 5. Repeat steps 1 through using the high-pass filter of Figure 2. f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.698970004 2.808 0.33 0.117521368 89.4 25 1.397940009 2.83 0.167 0.059010601 86.4 50 1.698970004 2.831 0.332 0.117273048 83 250 2.397940009 2.829 1.429 0.505125486 59.1 500 2.698970004 2.827 2.138 0.756278741 40 2500 3.397940009 2.824 2.757 0.976274788 9.6 5000 3.698970004 2.834 2.788 0.983768525 4.9 25000 4.397940009 2.826 2.8 0.990799717 1.1 Fig. 8 High Pass Filter with 20kΩ Resistance f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.698970004 2.807 0.079 0.028143926 88 25 1.397940009 2.83 0.393 0.138869258 82 50 1.698970004 2.831 0.762 0.26916284 74 250 2.397940009 2.829 2.825 0.998586073 35.4 500 2.698970004 2.828 2.64 0.933521924 19.9 2500 3.397940009 2.828 2.798 0.989391796 4.5 5000 3.698970004 2.828 2.803 0.99115983 2.1 25000 4.397940009 2.83 2.806 0.991519435 0.5 Fig. 9 High Pass Filter with 50kΩ Resistance f(Hz) Log10(f) Vs(Vrms) Vo(Vrms) |H(w)| angle(H(w)) 5 0.698970004 2.807 0.148 0.05272533 86.7 25 1.397940009 2.83 0.707 0.249823322 75.4

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50 1.698970004 2.831 1.294 0.457082303 63 250 2.397940009 2.83 2.616 0.924381625 21.1 500 2.698970004 2.8295 2.753 0.972963421 11.1 2500 3.397940009 2.8293 2.803 0.990704415 2.6 5000 3.698970004 2.8296 2.805 0.991306192 1.1 25000 4.397940009 2.832 2.807 0.991172316 0.4 Fig. 10 High Pass Filter with 100kΩ Resistance Fig. 11 High Pass Frequency(Log 10 ) versus Amplitude for 20kΩ, 50Ω, and 100kΩ

Fig. 11 High Pass Phase Angle versus Frequency (Log 10 ) for 20kΩ, 50Ω, and 100kΩ f c (calculated) f c (measured) Percent difference R = 20kΩ C = 0.02 uF 397.89 Hz 398.11 Hz 0.05% R = 50kΩ C = 0.02 uF 159.15 Hz 158.50 Hz 0.41% R = 100kΩ C = 0.02 uF 78.58 Hz 79.43 Hz 1.08% QUESTIONS 1. How well do the calculated magnitude and the phase plots in your prelab compare with the corresponding plots obtained via experimental measurements? Explain the reasons for the difference. They correspond almost perfectly. There is almost no difference 2. Explain the reasons or percent differences between the calculated and measured values of the half power frequencies.

The most likely reason for the differences in calculated versus measured is the small differences in the expected versus actual values of the individual components. 3. Why is f c called ‘half power’ frequency? F c is called the half power frequency. because it’s the frequency where the power of the circuit is at half of the maximum. Take Away Message: Regardless if a filter is high or low pass, it should still have the same f c. Section 2: • Built: Kush Patel • Verified: Jesus Galindo • Worked First Time: No 1. From File Menu open “new Schematic” 2. To select the voltage source, on Edit Menu, select “Component” or F2 3. From the list, select “Voltage”, this is a voltage source. 4. Right click on source and selecting “Advanced” : Select “Small Signal AC Analysis” a. Amplitude = 1. 5. Select R and C either from the Edit Menu or bar menu. Use the values shown in the figure. 6. Right click allows to placing the value of the component (Ohms and uF, etc.) You can use u for micro. 7. After having all components on the board, connect them using “wire” option shown by a pencil. 8. Make sure to connect the source ground.

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9. Under “Simulate: select Run and then select AC Analysis o Linear o 20 o Start 1Hz o Stop 200Hz. o Adjust start and stop frequencies to show LPF or HPF 10. Place the voltage probe at the output of the circuit and left click. Report Requirements: 11. Print the circuit diagrams and the LPF and the HPF characteristics. Figure 12: High-Pass Filter Schematic

Figure 13: High-Pass Filter Behavior Figure 14: Low-Pass Filter Schematic Figure 15: Low-Pass Filter Behavior 12. Determine the cutoff frequencies for LPF and HPF and compare to theoretical values.

The theoretical cutoff frequencies for the LPF were 397.89Hz, 159.15Hz, and 78.58Hz for resistances of 20k Ω , 50 Ω , and 100k Ω respectively. The cutoff frequencies of the simulation were 396.23Hz, 160.21Hz, and 78.12Hz for resistances of 20k Ω , 50 Ω , and 100k Ω respectively. The theoretical cutoff frequencies for the HPF were 397.89Hz, 159.15Hz, and 78.58Hz for resistances of 20k Ω , 50 Ω , and 100k Ω respectively. The cutoff frequencies of the simulation were 397.29Hz, 160.43Hz, and 77.34Hz for resistances of 20k Ω , 50 Ω , and 100k Ω respectively. These measurements were obtained using the built-in cursors in LTSpice. Takeaway Message: It is always important to verify measured values on the equipment by comparing them to simulated values as well as theoretical calculated values. This is a good way to ensure that all parts of a system are working correctly.

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Write in 3rd person. (Avoid “I”, “We”, etc.). Envision customer reading it. Each Section/Procedure: List; “Build: (Initials) and Verified (Initials)”. Swap roles for each section/procedure. The report should be self-contained and should not refer to diagrams or other data in other documents. Don’t refer to the lab manual or other documents. The reader does not have access to these documents The report should flow, covering each circuit or technical topic in order as you likely did the experiment. Include data and calculations with circuit. DO NOT organize the report by Schematics Section, Calculations Section, and Data Section. See how a text book is organized. Use Engineering Notation vs Scientific Notation. (Powers of 3). Example, mA, uA etc. Use the same numbering scheme as in the lab manual. Everything except for text requires a Name, Number and Description. Example: Figure 1.1, Test setup for measuring propagation delay of a CMOS inverter. List Table X.X, Graph X.X, Figure X.X etc. Make questions visible Graphs need axis labels and units. All waveforms need to be labeled on the graph. Don’t let the reader guess or assume. (ex. Vin?, Vout? Axis labels/units?) ANNOTATE all important parts of a waveform. Non-annotated waveforms have no value. Show sample calculations whenever calculations done.

Comment on data that you know or believe is suspect. Be SPECIFIC with example when describing sources of “error” or differences. Make your lab partners read and agree with the report content. The TEST: Could a student or customer just like you perform the experiment and obtain the same data and draw the same conclusions using only your report. Best practice is not to cut and paste schematics from the lab manual. Use YOUR schematics with instruments labeled on the schematic. LTspice works well for this. Scope data captures need to be with all the scope settings, not processed. Align grounds with major grid lines Set /per division to 1, 2, 5, etc on O- Scope. Not “Fine” with 1.263 volts per division Data MUST be yours. Include a “Take Away Message” for each section. 1 -2 sentences. What does the data tell you? What would you want the customer to know?