CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging

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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 Colorado

Technical University. This lab report investigates the time constant calculations and charging/discharging equations for simple and

complex RC circuits. Thevenin’s theorem is further utilized to simplify and solve complex RC circuits. Hand calculations are verified

using P-Spice schematic calculations to determine viability of design prior to the physical build. P-Spice diagrams and calculations are

then verified by physically modeling the design on a bread board and taking measurements for observation. The results were then

verified by the course instructor. If you have any questions or concerns in regards to this laboratory assignment, this laboratory

report, the process used in designing the indicated circuitry, or the final conclusions and recommendations derived, please send an

email to LSchwappach@yahoo.com. All computer drawn figures and pictures used in this report are my own and of original and

authentic content. I authorize the use of any and all content included in this report for academic use.

I. INTRODUCTION

HE time constant of a simple and complex RC circuit can

be found by the equation . Where is the

time constant with the SI unit of seconds, is the equivalent

circuit resistance in Ohms and is the capacitance in Farads.

In this lab this equation was verified by comparing the results after doubling the value of a known resistor in a simple

RC circuit.

Next a complex RC circuit is built and converted into its

Thevenin equivalents with respect to charge and discharge.

The of these equivalent circuits are then verified by

building the complex circuit on a bread board and taking

readings with respect to the circuit charged and the

discharging.

II. COMPONENTS

The following is a list of components that were used.

A DC power supply capable of 25V.

A digital multimeter for measuring circuit voltage,

circuit current, resistance, and capacitance.

A oscilloscope for viewing the input and output

waveforms of a simple RC circuit with a 1kHz

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

First a simple RC circuit was built using a 10kΩ resistor

and 470 F capacitor. The multimeter was connected across

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.

Next with the power applied the circuit was connected in the

charging position while the students recorded how long it took

for the capacitor to reach 63.2% of its final voltage ( = 12.6V). This is one charging time constant, tau. Tau is

computed using . For the R=10kΩ circuit one

tae = = 4.7s. Next with the capacitor

fully charged the circuit was connected in the discharge

position and this time the students recorded how long it took

for the capacitor to reach 36.8% of its final voltage ( = 7.4V).

Next the RC circuit was modified using a 20kΩ resistor

as a replacement. The multimeter was again connected across

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.

Next with the power applied the circuit was connected in the

charging position and discharging positions respectively as

completed previously to determine the if the time constant

would change double as required by . The

students again recorded how long it took for the capacitor to

reach 63.2% of its final charging voltage ( =

12.6V) and 36.8% of its final discharging voltage ( = 7.4V). A table of results obtained follows...

Table 1: Results from charging/discharging a simple RC

circuit with a 10kΩ and then 20kΩ respectively.

T

CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging

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These results closely approximated the results expected

by . A large percentage error was expected due

to 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-Spice

model and simulation of this stage and expected results

confirmed our expectations and follows...

Figure 2: P-Spice model of RC with 10kΩ resistor.

Figure 2: P-Spice charging simulation of 10kΩ resistor

RC circuit.

Figure 3: P-Spice discharging simulation of 10kΩ resistor

RC circuit.

Figure 4: P-Spice model of RC with 20kΩ resistor.

Figure 5: P-Spice charging simulation of 20kΩ 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.

CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging

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Figure 7: Current direction during capacitor charge and

discharge.

The next stage in the lab was to build the complex circuit

shown below and then reduce and redraw the circuit using its

Thevenin equivalent. With the reduced model circuits the

charging and discharging time constant could be determined

using .

Figure 8: Original unreduced RC circuit.

The above circuit was then reduced to two Thevenin

equivalent circuits (One with the circuit connected to power

and one with the circuit connected through R3 to ground). The

calculations used are included in the figures below.

Figure 9: Circuit 1 (charging): Original circuit connected

to power and reduced to Thevenin equivalent.

Figure 10: Circuit 2 (discharging): Original circuit

connected through R3 to ground and reduced to Thevenin

equivalent.

With the modeled charging and discharging circuits

reduced to their Thevenin equivalents the time constants were

obtained using as indicated by the previous

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.

Table 2: Results from charging/discharging a complex RC

circuit.

Finally one last simple RC circuit was built. The original

R value had to be modified from 10kΩ to 100kΩ and the

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 31: P-Spice model of simple RC with 100kΩ

resistor.

CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging

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This circuit was then simulated in P-Spice and signal

waveform measurements were taken using an oscilloscope.

The oscilloscope clearly showed the input step functions

being integrated into ramp functions due to the charging and

discharging of the capacitor while the resistor was also slightly

attenuating the signal. The attenuation also hinted that the

circuit was behaving like a low band pass filter. With these

observations the input frequency was increase by a factor of

ten to allow a better picture of the integration and attenuation

taking place. Results of both experiments follow.

Figure 12: P-Spice simulation of 1kHz input square wave

(red) and output triangle wave (green). Also illustrates

capacitor charge and discharge.

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.

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.

V. CONCLUSION

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

[1] 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.