1
Laboratory of the circuits and signals
Laboratory work No.1
RC AND RL SERIES CIRCUIT INVESTIGATION
Objectives:
„ to get acquainted with the circuit simulation package EWB,
„ to get acquainted with voltages and currents parameters measurement technique using voltmeters,
ammeters and oscilloscope,
„ to simulate and investigate frequency responses simple series RC and RL circuits - to measure
voltage changes in the circuits, to find phase changes and compare results of the measurements
with the results of calculations,
„ to analyse properties of the RC and RL circuits in the frequency domain.
Introduction:
Work procedures:
1. Turn on your work place computer, find the EWB icon or program (version 5.0c – educational is
preferable) and load it. Find icon of the program MathCAD and load it also.
a
b
Fig. 1. EWB component menu: Sources (a) Basic
Components (b), Measurement Devices (c)
c
2
2. Using the AC voltage source (take it from
Sources table Fig.1a, four resistors (take them from
the Basic Components table – Fig. 1b), voltmeters
and ammeter (take them from the indicators table –
Fig. 1c) build circuit (voltage divider) shown in the
Fig.2. Values of the source voltage and resistors take
from the table 1.
Fig.2. Simple series resistive circuit – voltage divider
Table 1
Initial data for the investigations
Version
Vin, V
Rs, Ω
R1, Ω
R2, Ω
RL, Ω
1
10
50
100
100
50
2
15
75
150
150
75
3
20
100
200
200
100
4
25
50
300
300
50
5
20
75
400
400
75
6
15
100
500
500
100
7
10
50
600
600
50
8
15
75
700
700
75
9
20
100
800
800
100
10
25
50
900
900
50
11
20
75
1000
1000
75
12
15
100
1200
1200
100
13
10
50
1500
1500
50
Measure voltages of the circuit nodes and current in the load resistor (click Turn On switch in the
right upper corner of the EWB window – Fig. 1c). Measurement results put into table 2.
Table 2
Results
Measurement
Calculation
Vin, V
IL, mA
V1 , V
V2 , V
V3 , V
3. Calculate current and voltages in the circuit and compare with the ammeter and voltmeters
readings. Use of MathCAD is preferable.
4. Rebuild the circuit as shown in Fig.3. Values of
resistances must be the as in the previous
investigation. This circuit is acting as current
divider. Measure circuit input voltage and
currents. Measurement results put into table 3.
Fig.3. Simple parallel resistive circuit – current divider
Results
Measurement
Calculation
Itotal, mA
I1, mA
I2, mA
IL, mA
Table 3
Itotal, mA
4. Calculate voltage and currents in the circuit and compare with the voltmeter and ammeters
readings.
5. Rebuild previous circuit and
change DC voltage source to AC
voltage source (Fig. 4.). Set up
source voltage equal to 1 V and
frequency – 1 kHz. Measure
voltages and currents and compare
Fig.4. Simple series resistive circuit with AC voltage
with the results in the table two (do
source
not forget to set up measurement
3
devices to the AC mode. Also preferable to increase voltmeter’s resistance till 100 MΩ and
decrease ammeter’s resistance till 1 nΩ - see example on the figure 5). If you see difference –
explain reason.
6. Build the new circuit as shown in the figure 6a. Oscilloscope take from the devices menu (last
icon in the components row – Fig.1c.). Adjust the oscilloscope to see the picture as shown in
the figure 6b. Measure amplitude and period of the voltages. Results put into table 4.
Table 4
Input voltage
Ain, V
Voltage on the resistors R2 and
RL
T, ms
A2, V
T2, ms
Fig 5. Voltmeter properties adjustment
a
b
Fig. 6. Measurements using oscilloscope: investigated circuit (a) and results (b)
7. Build RC circuit shown in the figure 7a. Find values of the components in the table 5.Voltage
source amplitude must be equal to 1 V. Adjust oscilloscope to see picture as shown in the
figure 7b.
a
b
Fig. 7. RC circuit (a) and voltages diagrams (b)
4
Table 5
Initial data for the RC and RL networks investigation
Version
Rs, Ω
R, Ω
C, nF
L, mH
1
50
100
200
10
2
75
125
250
12
3
100
150
300
14
4
75
175
350
16
5
50
200
400
18
6
75
225
450
20
7
100
250
500
22
8
75
275
550
24
9
50
300
600
26
10
75
325
650
28
11
100
350
700
30
12
75
375
750
32
13
50
400
800
34
14
75
425
850
36
8. Calculate circuit corner frequencies f C and ω C . Results put into table 6.
Table 6
Value
ω C , krad/s
f C , kHz
9. Measure frequency responses
Calculated
H ( f ) and ϕ ( f ) . Results put
Measured
into table 7.
Table 7
RC circuit frequency responses
Frequency
0
0.2
f0
0.6
f0
0.8
f0
0.9
f0
0.95
f0
f0
1.05
f0
1.1
f0
1.2
f0
1.6
f0
2
f0
3
f0
Value, kHz
Ain, V
Aout, V
H(f)
Meas.
Calc.
ΔT , μ s
ϕ ( f ), Meas.
Calc.
deg
10. Calculate using MathCAD both frequency responses. Put the calculation results into table 7
also.
11. Sketch the graphs of the measured and calculated frequency responses: by hand on the graph
paper or using Excel. Graphs must be presented with grid and marked axis.
12. Build RL circuit shown in the figure 8a. Take values of the components in the table 5. Adjust
source voltage amplitude to 1V and frequency to 1 kHz. Adjust the oscilloscope to see the
picture as shown in the Fig.8b. Calculate corner frequencies of the circuit and put them into
the table 8.
Table 8
Measure and calculate RL circuit
Value
ω C , krad/s
f C , kHz
frequency responses and put results
Calculated
into table 9.
Measured
5
a
b
Fig. 8. RC circuit (a) and voltage responses (b)
Table 9
RL circuit frequency responses
Frequency
0
0.2
f0
0.6
f0
0.8
f0
0.9
f0
0.95
f0
f0
1.05
f0
1.1
f0
1.2
f0
1.6
f0
2
f0
3
f0
Value, kHz
Ain, V
Aout, V
H(f)
Meas.
Calc.
ΔT , μ s
ϕ ( f ), Meas.
Calc.
deg
Plot the graphs of the measured and calculated LR circuit responses.
Report of the work
1. Objectives.
2. Results of the voltage and current divider investigation (investigated circuit diagrams – screenshots
of the EWB diagrams, results tables 2 and 3). Explanation of the difference in measurements using
voltmeter and oscilloscope (compare tables 2 and 4).
3. Results of the series RC network investigation (circuit diagrams, formulas to calculate corner
frequencies, frequency responses, tables with initial data, tables with the results of the measurements
and calculations of the corner frequencies and frequency responses, graphs of the measured and
calculated magnitude and phase responses).
4. Results of the series RL network investigation (circuit diagrams, formulas to calculate corner
frequencies, frequency responses, tables with initial data, tables with the results of the measurements
and calculations of the corner frequencies and frequency responses, graphs of the measured and
calculated magnitude and phase responses).
5. Conclusions (explanation of the frequency responses measurement technique, properties of the RC
and RL networks in the frequency domain)..
6
Control questions
Explain difference between amplitude, appearance and average values.
Explain voltage and current division in the circuits.
Explain technique of amplitude and phase measurements using oscilloscope.
What is RC and RL circuit primary and secondary parameters?
Explain what is frequency responses of the circuit. Derive formulas to calculate frequency
responses of RC and RL type series circuits.
6. What is time constant? Explain its physical mean and influence to circuit frequency and transient
responses.
1.
2.
3.
4.
5.