See my files and make a report for this experience based on the sampe
abdlla19
sample_lab_report.pdf
Tennessee State University College of Engineering, Technology, and Computer Science
Department of Electrical and Computer Engineering
ENGR 2001 CIRCUITS I LAB
Section 01
Lab 1 Low Pass/High Pass Filters Transient and AC Analysis
Beyonce Smith Lab Partner: Will Knowles
Instructor: Dr. Carlotta A. Berry
Lab Performed: October 16, 2000 Report Submitted: October 23, 2000
2
ABSTRACT
The purpose of this experiment was to design a high pass and low pass filter that attenuates a 1 kHz signal by 20 db. Test and evaluate this circuit built in a laboratory to determine how closely actual values correlate to theoretical values. Part of this analysis will include observing the transient and AC characteristics by using an oscilloscope, digital multimeter and function generator. The theory used to design this filter included Ohm’s law, the voltage divider rule and Laplace transforms. The results were shown to correlate closely with the theoretical values and therefore were assumed to be significant.
3
TABLE OF CONTENTS
Abstract
I. Objective
II. Theory
III. Equipment
IV. Apparatus
V. Circuits
VI. Procedure
VII. Graphs
VIII. Results, Conclusions, and Recommendations
Appendix A Data Appendix B Formulas and Sample Calculations Appendix C References and Laboratory Instruction Sheet
4
I. Objective: The purpose of this experiment was to explore the behavior of a low pass filter and high pass filter over a range of frequencies with a given break frequency. II. Theory: A filter is a device that attenuates a range of frequencies and passes a range of frequencies. There are several types of filters including low pass, high pass, band pass and band reject. The range of frequencies that are passed by a filter are called the pass band. The frequency where the relationship between input and output is equal to .707 is called the break frequency or half power point. An example of a high pass filter would be a tweeter on a speaker in a car. An example of a low pass filter would be the bass from a speaker in a car. An example of a band pass filter would be the selector for a radio station. In this experiment the low pass and high pass filter will be explored. Equation (1) is the transfer function relationship for the high pass filter. Equation (2) is the low pass transfer function for the low pass filter.
H(S) = sRC
sRC
sV
sV
i
o
1)(
)( (1)
H(s) = sRCsV
sV
i
o
1
1
)(
)( (2)
III. Equipment: Breadboard Wire leads Digital Oscilloscope Digital Multimeter Function Generator Power Supply
Resistors (1 k, 5 k)
Capacitors (.01 F, 1 F) 741 Op-amp IV. Apparatus:
The apparatus used to measure the transient and AC response of a circuit includes the breadboard with the resistor and capacitor positioned for a low pass or high pass filter, oscilloscope, function generator, power supply, and multimeter. The input will be a square wave from the Techtronix function generator. The output will be measured using the Hewlett-Packard digital multimeter across the resistor or capacitor. The characteristics will also be measured across the same component using the Virtual Bench digital oscilloscope. Figure 1 shows the connection of the function generator, oscilloscope, multimeter, and power supply to the circuit on the breadboard.
5
Figure 1: Lab 1 Apparatus
V. Circuits Figure 2 is the circuit for the Low Pass Filter and Figure 3 is the figure for the High Pass Filter.
Figure 2: Low Pass Filter
Figure 3: High Pass Filter
VI. Procedure 1. The circuit shown in Figure 2 was built on the breadboard and connected as
shown on the apparatus. 2. The function generator was set to a 1 V p-p sinusoid with a frequency of 100 Hz. 3. The frequency was varied between100 Hz and 1 MHz and ten readings were
taken for the output voltage and phase angle. 4. For the transient analysis, the input wave form was change to a 1 V p-p square
wave with a frequency of 100 Hz.
Techtronix
Function Generator
TAG #54
Serial #3
Hewlett-Packard
DMM
TAG # A54
Serial #4
VirtualBench
Digital
Oscilloscope
TAG #52
Serial #3
BREADBOARD
(resistors, capacitors)
Techtronix
Power Supply
TAG #54
Serial #3
6
5. The output signal was measured to find the time constant and the first four multiples of this value.
6. The frequency of the ringing was also measured for the output waveform. 7. Finally, the measured data was compared to the theoretical value and an error
analysis was performed. VII. Graphs Figure 4 is the transient analysis graph for the high pass filter it shows the theoretical and measured values on the curve. Figure 5 is the ac analysis graph for the high pass filter and it also shows the measured and theoretical values.
High Pass Filter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.001 0.002 0.003 0.004 0.005 0.006
time (s)
vo(t) [theor] vo(t) [meas]
Figure 4: High Pass Filter – Transient Analysis
High Pass Filter
0
0.2
0.4
0.6
0.8
1
1.2
100 1000 10000 100000
Frequency (Hz)
G a in
( V
o /V
i)
Actual Theoretical
fo
Figure 5: High Pass Filter – AC Analysis VIII. Results, Conclusions and Recommendations The implementation of the high pass filter with real world components worked rather well. The highest error in the evaluation was 21 % and this occurred at 5 kHz. A
7
possible source of error could be the inaccuracy in reading frequencies and gains off of an oscilloscope at very high and very low frequencies. Another source of error could be the accuracy of the input voltage from the function generator. Finally, all real world components have accuracy and sensitivity ratings and this would attribute to the values not correlating exactly with the theoretical hand calculations. In order to improve this experiment it may be necessary to account for the internal resistance of the leads of the function generator. The PSpice simulations for the low pass filter are given below. These were found by performing an AC sweep on the low pass filter from 100 to 10000 Hz. Figures 6 and 7 illustrate the PSpice output for the low pass and high pass filters, respectively. These results were found to correlate closely with those found in the laboratory.
Figure 6: Low Pass Filter – PSpice Results
Figure 7: High Pass Filter – PSpice Results
8
APPENDIX A Data
Table 1: Part 1 Data – Transient Analysis
Frequency (Hz)
Vin (Vp-p)
Vout (Vp-p)
Gain
100 1 .050 .05
1000 1 .201 .201
5000 1 .670 .670
10000 1 .981 .981
15000 1 .992 .992
25000 1 .992 .992
50000 1 .995 .995
75000 1 .9998 .9998
100000 1 .9999 .9999
Table 2: Part 1 Data – AC Analysis
Vin (Vp-p) time (s) vo(t), V
1 0.0005 0.606531
1 0.001 0.367879
1 0.0015 0.22313
1 0.002 0.135335
1 0.0025 0.082085
1 0.003 0.049787
1 0.0035 0.030197
1 0.004 0.018316
1 0.0045 0.011109
1 0.005 0.006738
1 0.0055 0.004087
Table 3: Part 1 Data – AC Analysis, cont.
Frequency
(Hz) Vin
(Vp-p) Vout
(Vp-p) Gain Theoretical
(V) Error (%)
100 1 .050 .05 .05 0
1000 1 .201 .201 .1 10
5000 1 .670 .670 .85 21
10000 1 .981 .981 .996 1.5
15000 1 .992 .992 .995 .3
25000 1 .992 .992 .995 .3
50000 1 .995 .995 1 .5
75000 1 .9998 .9998 1 .02
100000 1 .9999 .9999 1 .01
9
APPENDIX B Formulas, Sample Calculations and Error Analysis
Formulas:
%error: 100* theor
actualtheor
gain for high pass filter: RCjsRCsV
sV
i
o
1
1
1
1
)(
)(
magnitude of gain for a high pass filter : V
V
o
i
f f
f f
c
c
1
2 ( )
time constant: = RC
critical frequency (rad/s): c=1/
critical frequency (Hz): fc = /(2) Calculations: To determine the critical frequency: 1. -20 = 20 log10(Vo/Vi) 2. (Vout/Vin) = 10-1 = 0.1
3. V
V
o
i
f f
f f
c
c
1
2 ( )
4. V
V
o
i
f
f
c
c
0 1 1
1000
1000 2 .
( )
5. fc = 480 Hz critical frequency To determine the component values:
1. Let C = .01 F
2. R = 1/(2(.01 )(480)) = 33.157 k To determine the effect on a 10 kHz signal:
1. V
V
o
i
10000 480
10000 480
2 1 ( )
2. |Vo/Vi| = .9988 3. .11% attenuation of 10 kHz signal 4. 20 log10(.9988) = .01 dB
% error = %88.100* 99.
9988.99.
10
APPENDIX C References
Alexander, Charles K. and Matthew Sadiku, Fundamentals of Electric Circuits, 2nd Edition,
McGraw Hill, 2004.
Irwin, J.David, Basic Engineering Circuit Analysis, 7th Edition, John Wiley & Sons, 2001. ISBN:
0471407402
Johnson, David, E., Johnson, J.R., Hilburn, J.L. and Peter Scott, Basic Electric Circuit Analysis,
5th Edition, John Wiley & Sons, 1999. IBSN: 0471365831
Laboratory Instruction Sheet
Nahvi, Mahmood and Joseph Edminster, Schaums’s Outline of Electric Circuits, 4th Edition,
McGraw-Hill, 2002. ISBN: 0071393072
Nilsson, James W. and Susan A. Riedel, Electric Circuits, 6th Edition, Prentice Hall, 2000. ISBN:
0130321206
Smith, Ralph J. and Richard C. Dorf, Circuits, Devices and Systems: A First Course in Electrical
Engineering, 5th Edition, John Wiley & Sons, 1992. ISBN: 0471839442.
