CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 1 Colorado Technical University EE 331 – Circuit Analysis II Lab 3: Capacitor Charging and Discharging November 2009 Loren Karl Schwappach Student #06B7050651 This lab report was completed as a course requirement to obtain full course credit in EE331 Circuit Analysis II at ColoradoTechnical University. This lab report investigates the time constant calculations and charging/discharging equations for simple andcomplex RC circuits. Thevenin’s theorem is further utilized to simplify and solve complex RC circuits. Hand calculations are verifiedusing P-Spice schematic calculations to determine viability of design prior to the physical build. P-Spice diagrams and calculations arethen verified by physically modeling the design on a bread board and taking measurements for observation. The results were thenverified by the course instructor. If you have any questions or concerns in regards to this laboratory assignment, this laboratoryreport, the process used in designing the indicated circuitry, or the final conclusions and recommendations derived, please send anemail to LSchwappach@yahoo.com. All computer drawn figures and pictures used in this report are my own and of original andauthentic content. I authorize the use of any and all content included in this report for academic use. the capacitor to measure voltage change and a 20V power supply was connected while the circuit was connected in the I. INTRODUCTION discharge position to allow the capacitor to fully discharge. Next with the power applied the circuit was connected in theT HE time constant of a simple and complex RC circuit can be found by the equation . Where is the charging position while the students recorded how long it took for the capacitor to reach 63.2% of its final voltage (time constant with the SI unit of seconds, is the equivalent = 12.6V). This is one charging time constant, tau. Tau iscircuit resistance in Ohms and is the capacitance in Farads. computed using . For the R=10kΩ circuit one In this lab this equation was verified by comparing theresults after doubling the value of a known resistor in a simple tae = = 4.7s. Next with the capacitorRC circuit. fully charged the circuit was connected in the discharge Next a complex RC circuit is built and converted into its position and this time the students recorded how long it tookThevenin equivalents with respect to charge and discharge. for the capacitor to reach 36.8% of its final voltage (The of these equivalent circuits are then verified by = 7.4V).building the complex circuit on a bread board and taking Next the RC circuit was modified using a 20kΩ resistorreadings with respect to the circuit charged and the as a replacement. The multimeter was again connected acrossdischarging. the capacitor to measure voltage change and a 20V power supply was connected while the circuit was connected in the discharge position to allow the capacitor to fully discharge. II. COMPONENTS Next with the power applied the circuit was connected in the charging position and discharging positions respectively as The following is a list of components that were used. completed previously to determine the if the time constant A DC power supply capable of 25V. would change double as required by . The A digital multimeter for measuring circuit voltage, students again recorded how long it took for the capacitor to circuit current, resistance, and capacitance. reach 63.2% of its final charging voltage ( = A oscilloscope for viewing the input and output 12.6V) and 36.8% of its final discharging voltage ( waveforms of a simple RC circuit with a 1kHz = 7.4V). A table of results obtained follows... square wave input. A signal generator capable of delivering 5V amplitude 1kHz square waves. 10kΩ, 20kΩ, 39kΩ, 47 kΩ, and two 100 kΩ resistors. 1nF, and two 470 F capacitors. Bread board with wires. III. PROCEDURES AND ANALYSIS Table 1: Results from charging/discharging a simple RC First a simple RC circuit was built using a 10kΩ resistor circuit with a 10kΩ and then 20kΩ respectively.and 470 F capacitor. The multimeter was connected across
CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 2 These results closely approximated the results expectedby . A large percentage error was expected dueto the instrumentation used in timing the charge and discharge(counting) times and because of the large variances in resistors(+/- 1% to +/- 20%) and capacitors (+/-50%). A P-Spicemodel and simulation of this stage and expected resultsconfirmed our expectations and follows... Figure 4: P-Spice model of RC with 20kΩ resistor. Figure 2: P-Spice model of RC with 10kΩ resistor. Figure 5: P-Spice charging simulation of 20kΩ resistor RC circuit. Figure 2: P-Spice charging simulation of 10kΩ resistor RC circuit. Figure 6: P-Spice discharging simulation of 20kΩ resistor RC circuit. Next an the multimeter was placed in series between the resistor and the capacitor and the current was checked so the current from the resistor to the capacitor read as positive current. The circuit was again charged and discharged so an observation could be made about the change in direction of current in each case. The results follow.Figure 3: P-Spice discharging simulation of 10kΩ resistor RC circuit.
CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 3 Figure 7: Current direction during capacitor charge and Figure 10: Circuit 2 (discharging): Original circuit discharge. connected through R3 to ground and reduced to Thevenin equivalent. The next stage in the lab was to build the complex circuitshown below and then reduce and redraw the circuit using its With the modeled charging and discharging circuitsThevenin equivalent. With the reduced model circuits the reduced to their Thevenin equivalents the time constants werecharging and discharging time constant could be determined obtained using as indicated by the previoususing . respective figures. These time constants were then verified after measuring the actual capacitor charge and discharge times. The results of and percentage error was much lower this time closer to our expected values and are shown in the table below. Figure 8: Original unreduced RC circuit. Table 2: Results from charging/discharging a complex RC The above circuit was then reduced to two Thevenin circuit.equivalent circuits (One with the circuit connected to power Finally one last simple RC circuit was built. The originaland one with the circuit connected through R3 to ground). The R value had to be modified from 10kΩ to 100kΩ and thecalculations used are included in the figures below. original C value had to be modified from 10nF to 1nF due to capacitor availability in lab room. By scaling the capacitor down a factor of ten and the resistor up a factor of ten the time constant was preserved by . This RC circuit was driven by a 5 V, 1 kHz square wave as illustrated by the completed P-Spice schematic below.Figure 9: Circuit 1 (charging): Original circuit connected to power and reduced to Thevenin equivalent. Figure 31: P-Spice model of simple RC with 100kΩ resistor.
CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 4 This circuit was then simulated in P-Spice and signalwaveform measurements were taken using an oscilloscope. The oscilloscope clearly showed the input step functionsbeing integrated into ramp functions due to the charging anddischarging of the capacitor while the resistor was also slightlyattenuating the signal. The attenuation also hinted that thecircuit was behaving like a low band pass filter. With theseobservations the input frequency was increase by a factor often to allow a better picture of the integration and attenuationtaking place. Results of both experiments follow. Figure 14: Oscillator results taken by camera of input and output signals for input of 1kHz and 10kHz. The top and bottom oscillator voltage scales are 2V/div. The top oscillator time scale is at .2 ms/div (5 div = 1 period). The bottom oscillator time scale is at 20 s/div (5 div = 1 period). IV. HAND CALCULATIONS All hand calculations were illustrated in previous figures.Figure 12: P-Spice simulation of 1kHz input square wave V. CONCLUSION (red) and output triangle wave (green). Also illustrates capacitor charge and discharge. This lab was a success and proved that the time constant of a simple and complex RC circuit can be found through the equation . Comparing the results after doubling the value of the known resistors in a simple RC circuit confirmed this hypothesis. It was further successful in proving that the charging and disharging time constants for a complex circuit can be dirived by transforming the circuits into their respective Thevenin equivalents. Finally, by analyzing the input 1kHz square wave against the output attenuated triangle wave this lab demonstrated the selective frequency passing and signal reshaping posibilities capable of a simple RC circuit. REFERENCES  R. E. Thomas, A. J. Rosa, and G. J. Toussaint, “The Analysis & Design of Linear Circuits, sixth edition” John Wiley & Sons, Inc. Hoboken, NJ, pp. 309, 2009.Figure 13: P-Spice simulation of 10kHz input square wave(red) and output triangle wave (green). Also illustrates the integration and attenuation of higher high frequency signals.