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Transient Response of RC Circuits

EECE 2201/2203

Experiment #6

Transient Response of R-C Circuits

Objective: This lab will familiarize the student with the step response of an R-C circuit and with the characteristics and application of operational amplifiers.

Preparation
Problems:

1. Calculate the time constant for the values in Table 1. (Thinking about this can save you some work.) Using MATLAB®, generate a Vo vs Time graph response as you vary the capacitance and resistance found in the two left hand columns of Table 1 for the circuit in Figure 1.
2. What is the minimum value for PW (Pulse Width) to assure the measurement of a true step response of the circuit in Figure 1, where R = 1kΩ, and C = 0.1 μF? (See Figure #2) (Hint: 5 time constants is approximatey infinity)

R C R C
0.5k Ω 0.1 μ F 2 k Ω 0.01 μ F
1 k Ω 0.1 μ F 2 k Ω 0.05 μ F
2 k Ω 0.1 μ F 2k Ω 0.1 μ F
3 k Ω 0.1 μ F 2 k Ω 0.15μ F
4 k Ω 0.1 μ F 2 k Ω 0.2μ F

Table 1
Equipment: 1 Tektronix TDS1000/2000B oscilloscope
1 wave form generator
1 decade resistor box
1 decade capacitor box

Note: Each team should supply a flash drive, preferably small than 4GB.

Experimental
Procedure: (1) Turn on the oscilloscope and adjust the display if necessary to indicate zero volts for channels 1 and 2. Turn on the waveform generator.
(2) Assemble the circuit shown in Figure #1, using a decade resistance box for R1 and a decade capacitor box for C1. Adjust the waveform generator to an initial value of 1 Volt in amplitude with T = 0.001, using the oscilloscope.
(3) Capture Vout on your removable drive for five values of R1 and C1, using Table #1 as a reference. Record the values for R1 and C1.
(4) Determine the answers to the following questions by manipulating the appropriate values:
a. What happens if you increase the value of R4?
b. What happens if you increase the value of C1?
c. What happens if you decrease T of the input?
d. What happens if you increase PW of the input?
(5) Refer to figure 4. Considering the largest value of Tc calculated in preparation problem #1, what value of t in this expression:
v(t) = {1 – e-t/Tc}Vm, will generate an output voltage, v(t), which is 80% of Vm?

Figure #1

Report: Write a standard laboratory report and fully answer and include the preparation problems and all questions from the procedure. Compare the predicted rise times and the acutal rise times. Explain any discrepancies.

Figure #2
Waveform Parameters


Laboratory Report Format
EECE 2201/2203
1. TITLE PAGE – This should follow the format provided on eCourseware. Change the appropriate dates, experiment number and experiment title. Failure to do so will result in the report being returned to you for correction. The report will not by graded until all the corrections are made.
2. OBJECTIVE – A brief but complete statement of what you intend to find out or verify in the experiment should head the entry in your report. While it is mainly for your readers’ benefit, you will also find that it is a great help in clarifying the problem in your mind.
3. EQUIPMENT – Include a list of the actual instruments, meters, etc. that were used during your experiment.
4. PROCEDURE – For all lab reports, lengthy explanations of procedures are unnecessary. Original commentaries which adequately describe what was done are sufficient. Circuit diagrams should be included in this part. Any discrepancies or anomalies in the procedures should be noted in this section.
5. RESULTS – One of the primary objectives of student laboratory work is to compare the predicted outcomes (preparation problems) and the observed results. As clearly and thoroughly as possible, explain the discrepancies. It is strongly advised to include this error analysis in the tables of data. It is not necessary to show the actual error calculation of every entry in the data table; however a sample calculation for each type must be done. Data tables must be labeled such that it is obvious what circuit measurement yielded what data. Each column of data should be headed with the proper descriptor and units (i.e. volts, amps, etc.)
6. CONCLUSIONS – The conclusion section of the report is for interpreting the results. Reasons for the discrepancies between predicted and actual experimental results should be given. Be brief but complete in this section.
7. PREPARATION PROBLEMS – Attached the preparation problems at the end of the report.

Transient Response of RC Circuits
EECE 2201 (or 2203)
Section XXX
Experiment # 6
Transient Response of RC Circuits
Date Performed
12th April 2017
Your Name in Boldface
Student #
Lab Partner’s Name(s)
Station #
Circuit Wired By:

Title: Transient Response of RC circuits.
Objectives:
To familiarize oneself with the step response of an R-C circuit.
To learn the characteristics and applications of operational amplifiers.
Procedure:
The circuit was assembled as shown using a decade resistor R1 and a decade capacitor C1:

Different values of Tc were recorded for five values of R1 and C1 as shown in the table:
R C Tc R C
0.5k Ω 0.1 μ F 0.05mS 2 k Ω 0.01 μ F
1 k Ω 0.1 μ F 0.1mS 2 k Ω 0.05 μ F
2 k Ω 0.1 μ F 0.2mS 2k Ω 0.1 μ F
3 k Ω 0.1 μ F 0.3mS 2 k Ω 0.15μ F
4 k Ω 0.1 μ F 0.4mS 2 k Ω 0.2μ F

Observations:
Increasing the value of the resistance increases the time constant and as such the cut-off frequency is lower for a higher value of R1. It also leads to a drop in Vout.
Increasing the value of C1 reduces the capacitive reactance which results in a drop in Vout.
Decreasing the period of the input results in a higher input frequency. This reduces the capacitive reactance which in turn reduces Vout. The circuit acts as a Low Pass filter.
Increasing the pulse width results in a lower input frequency. A lower frequency will have a higher capacitive reactance and therefore a higher output voltage Vout.
A plot of Vo against Tc yields the following graph:

Discussion:
v(t)={1-e^((-τ)⁄T_c )}V_m
0.8V_m={1-e^((-τ)⁄0.0004)}V_m
e^((-τ)⁄0.0004)=0.2
ln⁡{e^((-τ)⁄0.0004)}=ln⁡{0.2}
-2500τ= -1.609
τ= 0.64mS
For t = 0.64mS, the output voltage v(t) will be 80% of Vm
Due to component tolerances and faults, the actual output may be higher or lower than the theoretical values. A resistor with a gold tolerance (+ 5%) would yield values closes to the theoretical.
Conclusion:
The step response of an RC circuit varies depending on the values of R and C. The time constant of the circuit also varies. Component tolerance largely affects how close the actual response will be to the theoretical response. Actual rise time is higher than theoretical rise time.

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