Mobile Studio Activity 7 Report

Transcript

Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Introduction RL and RC Filters are first order linear circuits that respond to alternating current signals. The response of these filters to different frequencies depends on the inductance/capacitance and resistance used in the circuit. At certain determinable frequencies, the filter will attenuate the signal. These are the filter’s cutoff frequencies. Procedure The protoboard configuration for this lab is show to the left. The blue cylindrical device shown is a 100mH inductor. The Mobile Studio Desktop software is used to take voltage readings across the 1kΩ resistor and the 100mH inductor at 100Hz, 1kHz and 10kHz, and then the two devices are switched around and readings are taken again. The same procedure is carried out for a 22mH inductor and a 1mH inductor. Afterwards, a 100µF is connected in series with a 1kΩ resistor. Voltage readings are taken, and then the two are swapped. Repeat this for a 1µF and a 0.1µF capacitor. All readings are taken for both sinusoidal and square wave responses. Analysis RC and RL Filters respond to alternating current at different frequencies in different ways depending on whether a capacitor or an inductor is used. Either way, the resistor and inductor/capacitor both have impedance that acts in AC circuits just like resistance does in DC circuits. The voltage across the resistor is the AC version of a DC voltage divider, for which impedance is used instead. The same is true for the capacitor or inductor. Smaller capacitors will respond with larger voltage AC signals. The opposite is true for inductors. Also, only certain frequency signals can make it through RC and RL Filters. 𝑅 For RL circuits, the cutoff frequency is 𝑓𝑐 = 2𝜋𝐿 , and any frequency lower than this will not pass through 1 the filter. The cutoff frequency for RC circuits is 𝑓𝑐 = 2𝜋𝑅𝐶 , and any frequency higher than this will not pass through the filter. Conclusion First order transient filters can be used in alternating current circuits to filter out specific frequencies from signals. RL and RC Filters make good examples of high-pass and low-pass filters. They also can be used to change input signals to different desirable peak to peak output voltages. 1 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Application 1. Varying the capacitor in an RC Filter while the resistor is kept at 1kΩ will change the peak to peak voltage of the resistor and capacitor responses. Decreasing capacitance will result in a smaller peak to peak voltage across the resistor. This also results in larger peak to peak voltages 1 across the capacitor. This is because voltage over a capacitor, 𝑣𝐶 𝑡 = 𝑣𝐶 𝑡0 + 𝐶 𝑡 𝑖 𝑡0 𝐶 𝑑𝑡, is inversely proportional to capacitance. Capacitance (µF) 100 1 0.1 VR (mV) 498 479 263 VC (mV) 0.690 79.7 411 2. Varying the inductor in an RL Filter while the resistor is kept at 1kΩ will change the peak to peak voltage of the resistor and inductor responses. Decreasing inductance will result in a larger peak to peak voltage across the resistor. This also results in smaller peak to peak voltages across the inductor. This is because voltage over an inductor, 𝑣𝐿 𝑡 = 𝐿 𝑑𝑖𝐿 𝑡 𝑑𝑡 , is directly proportional to inductance. Inductance (mH) 100 22 1 VR (mV) 414 482 495 VL (mV) 382 67.5 3.15 3. Switching the location of the inductor/capacitor and the resistor in an RC or RL Filter doesn’t change the AC frequency response of the circuit. This is because the impedance of the inductor or capacitor in both configurations of the filter is the same. 4. Connecting a Non-Inverting OpAmp to vL in an RC low-pass filter circuit will amplify the capacitor voltage according to the gain of the OpAmp network. If the gain is 2, the s-Domain output of the 2𝑅 OpAmp network should be 𝑉𝑜𝑢𝑡 𝑠 = 𝑅𝐶𝑠+1 ⋅ 𝑉𝑖𝑛 𝑠 . 𝑍𝑅 𝑠 = 𝑅 𝑍𝐶 𝑠 = 𝑉𝐶 𝑠 = 1 𝐶𝑠 𝑉𝐶 𝑠 = 𝑍𝐶 𝑠 ⋅ 𝑉𝑖𝑛 𝑠 𝑍𝑅 𝑠 + 𝑍𝐶 𝑠 1 𝐶𝑠 𝑅 ⋅𝑉 𝑠 = ⋅𝑉 𝑠 𝑅 + 1 𝐶𝑠 𝑖𝑛 𝑅𝐶𝑠 + 1 𝑖𝑛 𝑉𝑜𝑢𝑡 𝑠 = 2𝑉𝐶 𝑠 𝑉𝑜𝑢𝑡 𝑠 = 𝑍𝐶 𝑠 𝑉𝐶 𝑠 = ⋅ 𝑉𝑖𝑛 𝑠 𝑍𝑅 𝑠 + 𝑍𝐶 𝑠 2 2𝑅 ⋅𝑉 𝑠 𝑅𝐶𝑠 + 1 𝑖𝑛 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 5. RL Filters act as high-pass filters while RC Filters act as low-pass filters. High-pass filters reject frequencies lower than the cutoff frequency, and low-pass filters reject frequencies higher than the cutoff frequency. At the cutoff frequency, the gain of the circuit will be approximately 1 2. Data R1 L1 R1 2 2 100mH 1k V1 VOFF = 0 VAMPL = 1 FREQ = 1k L1 100mH C1 1 1k V1 V1 VOFF = 0 VAMPL = 1 FREQ = 1k R1 1k V1 VOFF = 0 VAMPL = 1 FREQ = 1k C1 100uF 100uF VOFF = 0 VAMPL = 1 FREQ = 1k R1 1k 1 0 0 0 Table 1 - Effective Time Constants for RL and RC Filters Frequency (kHz) 1 1 10 1 0.1 0.1 Capacitance /Inductance 100mH 22mH 1mH 100µF 1µF 0.1µF Experimental (µs) 92.4 18.2 1.47 98.1 988 121 Theoretical (µs) 110 25.3 1.12 -1210 227 Table 2 - Cutoff Frequencies for RL and RC Filters Capacitance /Inductance 100mH 22mH 1mH 100µF 1µF 0.1µF Cutoff Frequency (kHz) 1.592 7.234 159.2 0.001592 0.1592 1.592 3 0 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 1 - Mobile Studio: 1kΩ/100mH RL Filter at 100Hz Figure 2 - Mobile Studio: 100mH/1kΩ LR Filter at 100Hz Figure 3 - Mobile Studio: 1kΩ/100mH RL Filter at 1kHz Figure 4 - Mobile Studio: 100mH/1kΩ LR Filter at 1kHz Figure 5 - Mobile Studio: 1kΩ/100mH RL Filter at 10kHz Figure 6 - Mobile Studio: 100mH/1kΩ LR Filter at 10kHz 4 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 7 - Mobile Studio: 1kΩ/22mH RL Filter at 100Hz Figure 8 - Mobile Studio: 22mH/1kΩ LR Filter at 100Hz Figure 9 - Mobile Studio: 1kΩ/22mH RL Filter at 1kHz Figure 10 - Mobile Studio: 22mH/1kΩ LR Filter at 1kHz Figure 11 - Mobile Studio: 1kΩ/22mH RL Filter at 10kHz 5 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 12 - Mobile Studio: 22mH/1kΩ LR Filter at 10kHz Figure 13 - Mobile Studio: 1kΩ/1mH RL Filter at 100Hz Figure 14 - Mobile Studio: 1mH/1kΩ LR Filter at 100Hz Figure 15 - Mobile Studio: 1kΩ/1mH RL Filter at 1kHz Figure 16 - Mobile Studio: 1mH/1kΩ LR Filter at 1kHz Figure 17 - Mobile Studio: 1kΩ/1mH RL Filter at 10kHz 6 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 18 - Mobile Studio: 1mH/1kΩ LR Filter at 10kHz Figure 19 - Mobile Studio: Effective time constant of 100mH RL Filter at 1kHz Figure 20 - Mobile Studio: Effective time constant of 100mH LR Filter at 1kHz Figure 21 - Mobile Studio: Effective time constant of 22mH RL Filter at 1kHz 7 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 22 - Mobile Studio: Effective time constant of 22mH LR Filter at 1kHz Figure 23 - Mobile Studio: Effective time constant for 1mH RL Filter at 10kHz Figure 24 - Mobile Studio: Effective time constant for 1mH LR Filter at 10kHz Figure 25 - Mobile Studio: Cutoff freq 1.58kHz for 100mH/1kΩ RC Filter 8 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 26 - Mobile Studio: Cutoff freq 4.477kHz for 1kΩ/100mH RL Filter Figure 27 - Mobile Studio: 1kΩ/100μF RC Filter at 100Hz Figure 28 - Mobile Studio: 100μF/1kΩ CR Filter at 100Hz Figure 29 - Mobile Studio: 1kΩ/100µF RC Filter at 1kHz Figure 30 - Mobile Studio: 100µF/1kΩ CR Filter at 1kHz 9 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 31 - Mobile Studio: 1kΩ/100µF RC Filter at 10kHz Figure 32 - Mobile Studio: 100µF/1kΩ CR Filter at 10kHz Figure 33 - Mobile Studio: 1kΩ/1μF RC Filter at 100Hz Figure 34 - Mobile Studio: 1μF/1kΩ CR Filter at 100Hz Figure 35 - Mobile Studio: 1kΩ/1µF RC Filter at 1kHz 10 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 36 - Mobile Studio: 1µF/1kΩ CR Filter at 1kHz Figure 37 - Mobile Studio: 1kΩ/1µF RC Filter at 10kHz Figure 38 - Mobile Studio: 1µF/1kΩ CR Filter at 10kHz Figure 39 - Mobile Studio: 1kΩ/0.1µF RC Filter at 100Hz Figure 40 - Mobile Studio: 0.1µF/1kΩ CR Filter at 100Hz 11 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 41 - Mobile Studio: 1kΩ/0.1µF RC Filter at 1kHz Figure 42 - Mobile Studio: 0.1µF/1kΩ CR Filter at 1kHz Figure 43 - Mobile Studio: 1kΩ/0.1µF RC Filter at 10kHz Figure 44 - Mobile Studio: 0.1µF/1kΩ CR Filter at 10kHz 12 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 45 - Mobile Studio: Effective time constant of 100µF RC Filter at 1kHz Figure 46 - Mobile Studio: Effective time constant of 100µF CR Filter at 1kHz Figure 47 - Mobile Studio: Effective time constant for 1μF RC Filter at 100Hz Figure 48 - Mobile Studio: Effective time constant for 1μF CR Filter at 100Hz 13 Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 49 - Mobile Studio: Effective time constant for 0.1µF RC Filter at 100Hz Figure 50 - Mobile Studio: Effective time constant for 0.1µF CR Filter at 100Hz Figure 51 - PSPICE Simulation: Voltage across Potentiometer in RL or LR Filter with 100mH Inductor 300mV (356.804µs, 210.390mV) (1.3168ms, 206.216mV) (356.804µs, 168.957mV) 200mV (476.799µs, 62.236mV) (1.3768ms, 151.911mV) 100mV (1.4968ms, 46.628mV) 0mV -100mV (1.9767ms, -33.049mV) (956.780µs, -23.348mV) R=1kΩ (896.782µs, -151.327mV) (1.9167ms, -151.047mV) R=500Ω -200mV (1.8567ms, -207.372mV) (836.785µs, -208.415mV) R=100Ω -300mV 0s 0.2ms V(R1:1,L1:1) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms Time 14 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 52 - PSPICE Simulation: Voltage across 100mH Inductor in RL or LR Filter with Potentiometer 300mV 200mV (1.1968ms, 228.476mV) (236.809µs, 213.027mV) (1.1368ms, 193.580mV) (176.812µs, 139.497mV) 100mV (1.0768ms, 132.091mV) (116.814µs, 94.737mV) 0mV -100mV (596.795µs, -132.713mV) (1.6168ms, -130.740mV) (656.792µs, -198.076mV) R=100Ω -200mV (1.6168ms, -191.796mV) (716.790µs, -262.424mV) (1.7368ms, -250.140mV) R=500Ω R=1kΩ -300mV 0s 0.2ms V(L1:1) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms 2.8ms 3.0ms Time Figure 53 - PSPICE Simulation: Voltage across Potentiometer in RL or LR Filter with 22mH Inductor 300mV (286.245µs, 242.292mV) (1.2462ms, 240.019mV) (286.245µs, 237.759mV) (1.3062ms, 237.217mV) 200mV (406.240µs, 163.532mV) (1.4262ms, 143.409mV) 100mV 0mV -100mV (886.221µs, -142.290mV) (1.9062ms, -144.920mV) R=1kΩ R=500Ω -200mV (1.7862ms, -237.713mV) (766.226µs, -234.468mV) R=100Ω (1.7862ms, -242.300mV) (766.226µs, -243.076mV) -300mV 0s 0.2ms V(V1:+,L1:1) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms Time 15 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 54 - PSPICE Simulation: Voltage across 22mH Inductor in RL or LR Filter with Potentiometer 300mV (1.1262ms, 199.653mV) 200mV (166.250µs, 146.222mV) (1.0662ms, 65.906mV) (110.482µs, 54.886mV) 100mV (1.0062ms, 33.857mV) (75.552µs, 31.221mV) 0mV (1.5462ms, -33.640mV) (526.236µs, -34.017mV) -100mV R=100Ω (1.5462ms, -66.570mV) (526.236µs, -66.185mV) -200mV R=500Ω R=1kΩ (1.6662ms, -202.021mV) (646.231µs, -208.955mV) -300mV 0s 0.2ms V(L1:1) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms Time Figure 55 - PSPICE Simulation: Voltage across Potentiometer in RL or LR Filter with 1mH Inductor 300mV (256.998µs, 248.339mV) (256.998µs, 249.197mV) (256.998µs, 247.870mV) 200mV 100mV 0mV -100mV R=100Ω R=500Ω R=1kΩ -200mV (777.030µs, -246.979mV) (737.027µs, -248.211mV) (777.030µs, -246.979mV) -300mV 0s 0.1ms 0.2ms V(R1:1,R1:2) 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms 0.9ms 1.0ms Time 16 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms 1.6ms 1.7ms 1.8ms 1.9ms 2.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 56 - PSPICE Simulation: Voltage across 1mH Inductor in RL or LR Filter with Potentiometer 16mV (1.0196ms, 15.644mV) (49.819µs, 15.125mV) 12mV 8mV (14.203µs, 3.1364mV) 4mV (1.0196ms, 3.1041mV) (5.3739µs, 1.5723mV) (1.0196ms, 1.5672mV) 0V (1.4996ms, -1.5810mV) (479.644µs, -1.5618mV) -4mV (1.4996ms, -3.1229mV) (479.644µs, -3.0924mV) -8mV R=100Ω R=500Ω -12mV R=1kΩ -16mV 0s (1.4996ms, -15.639mV) (539.642µs, -15.401mV) 0.2ms V(L1:1) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms Time Figure 57 - PSPICE Simulation: Voltage across 1k Resistor in RL or LR Filter with 100mH Inductor 300mV (308.342µs, 206.350mV) (1.3025ms, 199.365mV) (2.5900ms, 249.486mV) (47.990µs, 59.665mV) F=100Hz 200mV (445.614µs, 36.311mV) F=1kHz 100mV F=10kHz 0mV (495.465µs,-35.650mV) -100mV -200mV (1.8025ms, -197.224mV) (7.5900ms, -249.486mV) (806.382µs, -200.325mV) -300mV 0s 0.5ms 1.0ms V(R1:1,L1:1) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 17 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 58 - PSPICE Simulation: Voltage across 100mH Inductor in RL or LR Filter 300mV (442.138µs, 15.200mV) (21.252µs, 213.835mV) (1.0240ms, 236.281mV) (1.1240ms, 134.951mV) F=10kHz (181.577µs, 95.155mV) 200mV F=1kHz 100mV F=100Hz 0mV -100mV -200mV (1.0740ms, -235.297mV) (69.514µs, -251.528mV) (5.1240ms, -15.683mV) (1.5990ms, -136.162mV) (654.064µs, -135.265mV) -300mV 0s 0.4ms V(L1:1) 0.8ms 1.2ms 1.6ms 2.0ms 2.4ms 2.8ms 3.2ms 3.6ms 4.0ms 4.4ms 4.8ms 5.2ms 5.6ms 6.0ms Time Figure 59 - PSPICE Simulation: Voltage across 1k Resistor in RL or LR Filter with 22mH Inductor 300mV (249.116µs, 243.489mV) (1.2491ms, 243.308mV) (2.5491ms, 249.936mV) F=1kHz 200mV (36.651µs, 152.633mV) (136.616µs, 128.922mV) 100mV F=10kHz 0mV F=100Hz -100mV (186.616µs, -128.658mV) (86.651µs, -126.445mV) -200mV (749.116µs, -243.311mV) (7.5491ms, -249.936mV) (1.7491ms, -243.308mV) -300mV 0s 0.5ms 1.0ms V(V1:+,L1:1) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 18 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 60 - PSPICE Simulation: Voltage across 22mH Inductor in RL or LR Filter 200mV (215.639µs, 191.169mV) 150mV (18.478µs, 140.660mV) (1.0781ms, 33.400mV) 53.139µs, 3.4444mV) 100mV (0.174µs, 31.159mV) F=10kHz F=1kHz 50mV F=100Hz 0mV -50mV -100mV (65.674µs, -197.381mV) (490.639µs, -34.569mV) (5.0781ms, -3.4546mV) (1.5531ms, -34.958mV) -150mV (265.639µs, -191.176mV) -200mV 0s 0.4ms V(R1:2) 0.8ms 1.2ms 1.6ms 2.0ms 2.4ms 2.8ms 3.2ms 3.6ms 4.0ms 4.4ms 4.8ms 5.2ms 5.6ms 6.0ms Time Figure 61 - PSPICE Simulation: Voltage across 1k Resistor in RL or LR Filter with 1mH Inductor 300mV (20.794µs, 218.062mV) (2.4193ms, 249.664mV) (294.283µs, 236.145mV) 200mV F=100Hz F=1kHz 100mV F=10kHz 0mV -100mV -200mV (794.283µs, -236.147mV) (81.783µs, -218.184mV) (7.4193ms, -249.664mV) -300mV 0s 0.5ms 1.0ms V(V1:+,L1:1) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 19 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 62 - PSPICE Simulation: Voltage across 1mH Inductor in RL or LR Filter 20mV (5.1445µs, 15.140mV) (301.862µs, 16.247mV) 15mV (8.0479µs, 1.5729mV) 10mV (1.0019ms, 1.6396mV) F=10kHz (26.862µs, 157.158µV) 5mV F=1kHz F=100Hz 0V -5mV (526.862µs, -1.6193mV) (1.4894ms, -1.6283mV) (5.0269ms, -157.129µV) -10mV -15mV (351.862µs, -16.246mV) (51.862µs, -16.138mV) -20mV 0s 0.4ms V(R1:2) 0.8ms 1.2ms 1.6ms 2.0ms 2.4ms 2.8ms 3.2ms 3.6ms 4.0ms 4.4ms 4.8ms 5.2ms 5.6ms 6.0ms Time Figure 63 - PSPICE Simulation: Effective Time Constant of RL or LR Filter for 100mH and 22mH 600mV (515.000µs, 462.667mV) (515.000µs, 362.643mV) 400mV (540.316µs, 120.126mV) (625.490µs, 154.548mV) 200mV 0V -200mV -400mV (1.0300ms, -362.643mV) (1.0300ms, -461.476mV) L=22mH -600mV L=100mH -800mV 0s 0.1ms 0.2ms 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms V(L1:1) Time 20 0.9ms 1.0ms 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 64 - PSPICE Simulation: Effective Time Constant of RL or LR Filter for 1mH 300mV (51.500µs, 260.350mV) 200mV (52.620µs, 86.793mV) 100mV (6.8735µs, 18.135µV) 0mV -100mV -200mV (103.000µs, -260.350mV) L=1mH -300mV 0s 10us 20us 30us 40us 50us 60us 70us 80us 90us 100us 110us 120us 130us 140us 150us V(L1:1) Time Figure 65 - PSPICE Simulation: Cutoff Frequency of RL Filter for 100mH 200m V (1.3622ms, 176.231mV) F=1.591kHz 150m V 100m V 50m V 0m V 50mV 100mV 150mV 200mV 0 s V(L1:2 ) 0.5m s 1.0m s 1.5m s 2.0m s 2.5m s Tim e 21 3.0m s 3.5m s 4.0m s 4.5m s 5.0m s Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 66 - PSPICE Simulation: Cutoff Frequency of RL Filter for 22mH 200mV F=7.234kHz (299.603µs, 176.258mV) 150mV 100mV 50mV 0mV -50mV -100mV -150mV -200mV 0s 0.1ms 0.2ms 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms 0.9ms 1.0ms 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms V(L1:2) Time Figure 67 - PSPICE Simulation: Voltage across Potentiometer in RC or CR Filter with 100μF Capacitor 300mV (229.187µs, 244.451mV) (269.190µs, 247.300mV) 200mV (269.190µs, 247.742mV) 100mV 0mV -100mV R=100Ω -200mV (749.219µs, -250.391mV) R=500Ω (749.219µs, -250.778mV) R=1kΩ (749.219µs, -253.626mV) -300mV 0s 0.1ms 0.2ms V(R1:2,C1:2) 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms 0.9ms 1.0ms Time 22 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms 1.6ms 1.7ms 1.8ms 1.9ms 2.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 68 - PSPICE Simulation: Voltage across 100μF Capacitor in RC or CR Filter with Potentiometer 8.0mV R=100Ω (466.289µs, 7.3677mV) R=500Ω R=1kΩ 6.0mV (41.442ms, 3.3846mV) (466.289µs, 1.4994mV) 4.0mV (466.289µs, 751.309µV) 2.0mV 0V (1.0283ms, 43.778µV) -2.0mV (1.0283ms, 60.974µV) (1.0283ms, -27.792µV) (42.013ms, -3.5764mV) -4.0mV 0s 5ms 10ms 15ms 20ms 25ms 30ms 35ms 40ms 45ms 50ms V(C1:2) Time Figure 69 - PSPICE Simulation: Voltage across Potentiometer in RC or CR Filter with 1μF Capacitor 300mV (1.1968ms, 228.476mV) (236.809µs, 213.027mV) (1.1968ms, 228.979mV) 200mV (236.809µs, 185.188mV) (1.0768ms, 132.091mV) (116.814µs, 94.737mV) 100mV 0mV -100mV R=1kΩ -200mV (596.795µs, -132.713mV) R=500Ω (1.6168ms, -130.740mV) (716.790µs, -251.663mV) R=100Ω (1.6768ms, -235.256mV) (716.790µs, -262.424mV) (1.7368ms, -250.140mV) -300mV 0s 0.2ms V(R1:2,C1:2) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms Time 23 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 70 - PSPICE Simulation: Voltage across 1μF Capacitor in RC or CR Filter with Potentiometer 300mV (356.804µs, 210.390mV) (1.3168ms, 206.216mV) 200mV (416.802µs, 103.525mV) (1.4368ms, 77.834mV) 100mV (476.799µs, 62.236mV) (1.4968ms, 46.628mV) 0mV (1.9767ms, -33.049mV) (956.780µs, -23.348mV) -100mV (1.9767ms, -71.821mV) (956.780µs, -63.499mV) R=100Ω -200mV R=500Ω R=1kΩ (1.8567ms, -207.372mV) (836.785µs, -208.415mV) -300mV 0s 0.2ms V(C1:2) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms 2.8ms 3.0ms Time Figure 71 - PSPICE Simulation: Voltage across Potentiometer in RC or CR Filter with 0.1μF Capacitor 150mV (1.0893ms, 131.827mV) (129.698µs, 95.739mV) 100mV (1.0293ms, 73.859mV) (86.577µs, 59.664mV) 50mV (1.0293ms, 15.688mV) (38.322µs, 15.098mV) 0mV (1.5093ms, -15.803mV) (489.323µs, -15.669mV) -50mV R=1kΩ -100mV (549.321µs, -74.426mV) (1.5693ms, -73.819mV) R=500Ω R=100Ω (1.5693ms, -130.694mV) (609.319µs, -131.108mV) -150mV 0s 0.2ms V(R1:2,C1:2) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms Time 24 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 72 - PSPICE Simulation: Voltage across 0.1μF Capacitor in RC or CR Filter with Potentiometer 300mV (249.333µs, 247.960mV) (1.2693ms, 248.113mV) (309.331µs, 233.688mV) (1.2693ms, 230.039mV) 200mV (309.331µs, 208.458mV) (1.3293ms, 206.838mV) 100mV 0mV -100mV (849.309µs, -206.966mV) R=100Ω -200mV R=500Ω (1.8693ms, -203.876mV) (789.311µs, -233.663mV) R=1kΩ (1.8093ms, -233.600mV) (789.311µs, -244.341mV) (1.7493ms, -247.965mV) -300mV 0s 0.2ms V(C1:2) 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms Time Figure 73 - PSPICE Simulation: Voltage across 1k Resistor in RC or CR Filter with 100μF Capacitor 300mV (213.380µs, 241.820mV) (728.146µs, 227.278mV) (2.5407ms, 245.830mV) 200mV F=100Hz F=1kHz 100mV F=10kHz 0mV -100mV -200mV (778.146µs, -227.369mV) (7.5474ms, -253.377mV) (715.646µs, -244.371mV) -300mV 0s 0.5ms 1.0ms V(R1:2,C1:2) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 25 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 74 - PSPICE Simulation: Voltage across 100μF Capacitor in RC or CR Filter 8.0mV (4.6666ms, 7.3660mV) 6.0mV (345.231ms, 3.9077mV) 4.0mV (465.194µs, 750.060µV) 2.0mV 0V F=100Hz -2.0mV F=1kHz F=10kHz (350.229ms, -3.5410mV) -4.0mV 0s 20ms V(C1:2) 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms 220ms 240ms 260ms 280ms 300ms 320ms 340ms 360ms 380ms 400ms Time Figure 75 - PSPICE Simulation: Voltage across 1k Resistor in RC or CR Filter with 1μF Capacitor 300mV (26.033µs, 228.263mV) (1.2119ms, 234.949mV) F=1kHz (220.890µs, 214.150mV) 200mV (1.3563ms, 98.549mV) F=10kHz 100mV F=100Hz 0mV -100mV -200mV (1.7148ms, -251.763mV) (76.033µs, -235.572mV) (5.9443ms, -133.342mV) (715.741µs, -264.807mV) -300mV 0s 0.5ms 1.0ms V(R1:2,C1:2) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 26 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 76 - PSPICE Simulation: Voltage across 1μF Capacitor in RC or CR Filter 300mV (3.3443ms, 215.421mV) 200mV (51.033µs, 7.1541mV) (469.772µs, 60.643mV) 100mV (6.4443ms, 35.995mV) (2.0505ms, 4.7699mV) 0mV (2.1005ms, -2.3083mV) (6.9443ms, -35.715mV) (965.019µs, -22.580mV) -100mV (98.086µs, 54.663µV) -200mV F=100Hz F=1kHz F=10kHz (8.3443ms, -211.458mV) -300mV 0s 0.5ms V(C1:2) 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Time Figure 77 - Simulation: Voltage across 1k Resistor in RC or CR Filter with 0.1μF Capacitor 300mV (3.6181ms, 220.504mV) (26.111µs, 195.510mV) 200mV F=1kHz (113.174µs, 95.366mV) (1.0556ms, 132.826mV) 100mV F=10kHz (498.585µs,15.207mV) 0mV F=100Hz -100mV (5.0931ms, -15.695mV) (1.5556ms, -131.737mV) (561.017µs, -132.829mV) -200mV (76.111µs, -242.426mV) (3.6681ms, -220.504mV) -300mV 0s 0.5ms 1.0ms V(R1:2,C1:2) 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms Time 27 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 78 - PSPICE Simulation: Voltage across 0.1μF Capacitor in RC or CR Filter 300mV (51.111µs, 56.650mV) (2.6931ms, 249.044mV) (298.962µs, 205.756mV) (1.3056ms, 198.942mV) 200mV (1.3431ms, 33.246mV) 100mV 0mV (1.3931ms, -33.287mV) (74µs, -20.295mV) -100mV -200mV F=1kHz F=10kHz F=100Hz (1.7931ms, -198.129mV) (809.503µs, -199.814mV) (7.6931ms, -249.044mV) -300mV 0s 0.5ms V(C1:2) 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms Time Figure 79 - PSPICE Simulation: Effective Time Constant of RC or CR Filter for 1uF and 0.1uF 300mV (10.200ms, 247.149mV) 200mV (5.2265ms, 82.076mV) (6.2106ms, 82.076mV) 100mV 0mV -100mV -200mV C=0.1µF C=1µF (5.0000ms, -248.416mV) -300mV 0s 1ms V(C1:2) 2ms 3ms 4ms 5ms 6ms 7ms 8ms 9ms 10ms Time 28 11ms 12ms 13ms 14ms 15ms 16ms 17ms 18ms 19ms 20ms Mobile Studio Activity #7 Adam Steinberger Electric Circuits Section 2 Figure 80 - PSPICE Simulation: Cutoff Frequency of RC Filter for 100uF 200mV F=1.592Hz (1.5186s, 167.024mV) 150mV 100mV 50mV 0mV -50mV -100mV -150mV -200mV 0s 0.5s 1.0s 1.5s 2.0s 2.5s 3.0s 3.5s 4.0s 4.5s 5.0s 40ms 45ms 50ms V(R1:1) Time Figure 81 - PSPICE Simulation: Cutoff Frequency of RC Filter for 1uF 200mV (15.186ms, 167.012mV) F=159.2Hz 150mV 100mV 50mV 0mV -50mV -100mV -150mV -200mV 0s 5ms 10ms 15ms 20ms 25ms V(R1:1) Time 29 30ms 35ms