THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01:
ENG237-01
(i) Cathode Ray Oscilloscope (CRO) and (ii) Kirchhoff’s
Laws and Maximum Power Transfer Theorem.
Part (i) Cathode Ray Oscilloscope (CRO)
Objectives
To introduce the control facilities of CRO, and to use CRO to measure DC and AC
voltages.
Apparatus
1.
2.
3.
4.
Oscilloscope: SS-7802A, SS-7804 or GOS-620
DC power supply
Signal generator
Stop watch
Introduction
The CRO is said to be the eyes of electronic engineers, because it is a very useful and
versatile instrument to detect and measure signals in electronic circuits. Basically, the
CRO is a voltmeter and frequency meter with a high speed display mechanism. The
simplified block diagram of CRO is shown in Fig. 1.
Fig. 1
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ENG237-01
It can be seen from the diagram that the CRO will display Y inputs on the vertical axis and
time-base or X input on the horizontal axis on the screen. The commonly used control
facilities of CRO are as follows:
INTENSITY:
FOCUS:
POSITION:
TIME/DIV:
VARIABLE-TIME/DIV:
varies the intensity of traces.
controls the definition of the display.
displaces the trace in the Y axis or X axis manually.
selects sweep speeds.
enables sweep speed t be set at intermediate speeds between
the TIME/DIV settings. Push TIME/DIV button to toggle
between calibrated and variable modes.
VOLTS/DIV:
provides steps of attenuation of each channel's input signal.
VARIABLE-VOLTS/DIV: enables voltage scale to be set at intermediate levels. Push
VOLTS/DIV button to toggle between calibrated and variable
modes.
DC/AC Selector (Model SS-7802A and SS-7804):
switches the input to AC coupled or DC coupled.
GND Button (Model SS-7802A and SS-7804):
switches the input to DC/AC coupled or ground.
AC-GND-DC Selector (Model GOS-620):
switches the input to AC coupled, DC coupled or ground.
TRIGGERING LEVEL: determines the starting level of the stationary trace.
Procedure
(A) Using the CRO only
0. Use the power switch to turn the CRO “ON”.
1. Turn off the times 10 switch by (i) toggling “MAG x10” button until “MAG”
disappear from the bottom line on the screen for models SS-7802A and SS-7804,
or (ii) releasing “x10 MAG” button for model GOS-620.
2. (i) Display Channel 2 only by using buttons CH1, CH2) and press “x-y” button for
models SS-7802A and SS-7804, or (ii) or simply select Channel 1 and X-Y mode
for model GOS-620.
3. Turn “INTEN” knob until one illuminated spot appears. Do not increase intensity
too much. A very bright spot may be harmful to the screen and human eye.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01
4. Adjust “FOCUS” knob to obtain the sharpest spot.
5. Turn the “CH1-POSITION” or “HORIZONTAL-POSITION” knob. The spot shall
move along X axis.
6. Turn the “CH2-POSITION” knob. The spot shall move along Y axis.
7. (i) For models SS-7802A and SS-7804, toggle “TIME/DIV” button to set it at
calibrated mode by pressing “A” button. A “>” sign on the top-left of the screen
shall disappear, or (ii) for model GOS-620, turn the “HORIZONTAL-VAR” knob
to “CAL” position for calibration.
8. Turn “TIME/DIV” knob to set time-base at 500 ms/DIV. The spot shall sweep
across the screen slowly. Use a stop watch to check the speed. Record the results.
Repeat with setting at 100 ms/DIV. Press “TIME/DIV” button to enter variable
mode. Check the speed again.
9. Press “TIME/DIV” to select calibrated mode again. Set the time-base to 500
µs/DIV. The spot will trace a line on the screen. Turn “TIME/DIV” or
“HORIZONATAL-VAR” knob one step at a time to observe the screen.
(B) DC and AC voltage measurements
1. Use channel 1 only. Select GND on the “AC-GND-DC” selector or “CH1-GND”
button to display a grounded trace, i.e. 0 V. By turning the “CH1-POSITION”
knob, the reference 0 V line can be placed anywhere on the screen. Normally the
center line is chosen as the 0 V line.
2. Press “CH1-GND” button or “AC-GND-DC” selector to DC measurement mode.
Switch “CH1-VOLTS/DIV” button or “CH1-VAR” knob to “CAL” to enter
calibrated mode. Connect the input wires of CH1 to the output terminals of a DC
power supply. Increase the power supply voltage to 20 V in steps of 2 volt. At each
step measure the voltage on the scope, change the VOLTS/DIV setting when
needed. Record the results. Switch the DC power supply on and off three times and
observe the trace on the screen.
3. Connect the input wires to the output terminals of a signal generator: the ground
wire to “LO” and the wire to “HI”. Select AC coupled or “AC-GND-DC” selector
to AC.
4. Set the signal generator to “sine wave” at frequency of 500 Hz. Adjust the
amplitude to maximum (attenuator = 0 dB).
(i) Model SS-7802A and SS-7804
Toggle “SOURCE” button until “CH1” shows on the top line.
Toggle “TV” button until there is no “TV” show on the top line.
Toggle “COUPL” until “DC” shows on the top line.
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ENG237-01
Or
(ii) Model GOS-620
Set trigger source to CH1.
Set trigger mode to AUTO.
Then, turn the “TRIG LEVEL” knob to obtain a stationary trace on the screen.
Measure and record the period, frequency, maximum (peak) voltage, and
peak-to-peak voltage as shown in Fig. 2.
5. Repeat procedure 4 with frequency set at 5 kHz, 50 kHz, 500 kHz etc. Adjust the
“TIME/DIV” knob to obtain proper displays.
Comments:
1. Is the CRO a voltmeter and frequency meter with a high speed display mechanism?
Why?
2. Before measuring a voltage or frequency, what do you do with those
“VARIABLE” knobs?
3. Comment on the results obtained from the CRO.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01
Part (ii) Kirchhoff’s Laws and Maximum Power Transfer Theorem
Introduction
The objectives of this experiment are to (1) verify Kirchhoff’s laws and (2) study the maximum
power transfer theorem.
Sign conventions for current
IXY
X
Y
IXY = -IYX
Where IXY is the current flowing from node X to Y.
Sign conventions for potential difference
VXY
Y
X
VXY = -VYX
Where VXY is the voltage across XY and is positive when point X is at a higher potential
than point Y.
Apparatus
1. Power supply
2. Multi-meter
3. Experimental board
1. Kirchhoff’s Laws
1.1 Introduction
The interconnection of circuit elements imposes constraints on the relationship between
the terminal voltages and currents. These constraints are referred to as Kirchhoff’s laws.
The two laws that state the constraints in mathematical form are known as Kirchhoff’s
Current law (KCL) and Kirchhoff’s Voltage law (KVL).
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Department of Electronic and Information Engineering
ENG237-01
Kirchhoff’s Current law (KCL) states that the algebraic sum of the currents at any node
(junction) is zero. In mathematical form, for n branches converging into a node, KCL
states that
I1+I2+…+Ik+…+In = 0
where Ik is the current flowing in the kth branch and its direction is assumed to be pointing
towards the node.
To use Kirchhoff’s current law, an algebraic sign corresponding to a reference direction
must be assigned to every current at a node. Figure 3 shows the conventional notation that
is used to specify the algebraic sign. In general, a positive sign is assigned to a current
entering a node. Conversely, a negative sign is assigned to a current leaving a node. For
example, at node 2 in Figure 3, we have
IA - IB - ID = 0
Figure 3
Kirchhoff's Voltage law (KVL) states that the algebraic sum of the voltages between
successive nodes in a closed path in a circuit is equal to zero. In mathematical form, for a
closed path with successive nodes 1,2, ...n, KVL states that
V1,2+V2,3+…+Vn-1,n+Vn,1 = 0
From Figure 4, we have
V1+V2+V3+V4 = 0
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01
Figure 4
1.2 Procedures
Connect the DC power supply as shown in Figure 5
Figure 5
1.2.1
Kirchhoff's Current Law
(a) Adjust the D.C. supply to keep the voltage across Nodes A and C to 5 V.
(b) Calculate the currents at Node B by measuring the voltages across the branches
that connect to Node B. Complete the following table:
Voltage (V)
Current entering Node B (A)
VAB=
IAB =
VMB =
IMB =
VCB =
ICB =
(c) Calculate IAB + IMB + ICB.
(d) Repeat Step (b) for Node M. Complete the following table:
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THE HONG KONG POLYTECHNIC UNIVERSITY
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Voltage (V)
Current entering Node B (A)
VAM=
IAM =
VCM =
ICM =
VBM =
IBM =
ENG237-01
(e) Calculate IAM + ICM + IBM .
(f) Comment on the results of (c) and (e).
1.2.2
Kirchhoff's Voltage Law
(a) Adjust the voltage across AC to 5 V.
(b) Measure the voltage around loop AMBCA. Complete the following table:
Loop AMBCA
Voltage (V)
VAM
VMB
VBC
VCA
(c) Calculate VAM + VMB + VBC + VCA.
(d) Measure the voltage around loop ABMCA. Complete the following table:
Loop ABMCA
Voltage(V)
VAB
VBM
VMC
VCA
(e) Calculate VAB + VBM + VMC +VCA.
(f) Comment on the results of (c) and (e).
2.
Maximum Power transfer theorem
2.1 Introduction
The maximum power transfer theorem states that in DC circuits, the maximum
possible power that can be delivered to a load occurs when the load resistance (RL)
equals the internal resistance (Ri) of the DC generator.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01
Ri
RL
V
Figure 6
In Figure 6, the power PL dissipated in the load resistor RL can be written as:
2
PL =
VL
RL
where VL is the voltage across the load RL and
VRL
.
VL =
Ri + RL
2.2 Procedures
(a) Connect the circuit as shown in Figure 7 with Ri = 5 k Ω and adjust the power
supply to 5 V DC.
Ri
+
+
DC
VL V
RL
Supply
-
Figure 7
(b) Vary the load RL from l k Ω to l0 k Ω resistances in "small" but "suitable" steps
and record the corresponding values of VL and IL in each step.
Ri = 5 kΩ
VL (V)
IL (mA)
RL (Ω)
PL (mW)
(c) Calculate the relative values of RL.
(d) Plot the power delivered to the load against RL.
(e) From the power curve obtained, find the maximum power dissipated and the
corresponding value of RL.
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THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Electronic and Information Engineering
ENG237-01
(f) Determine the total resistance of the supply section using the condition for
maximum power transfer.
(g) Repeat the above procedures with Ri = 10 k Ω and Ri = 20 k Ω , so as to obtain
families of P-curves.
Ri = 10 kΩ (with RL varying from 5 kΩ to 15 kΩ)
VL (V)
IL (mA)
RL (Ω)
PL (mW)
Ri = 20 kΩ (with RL varying from 15 kΩ to 25 kΩ)
VL (V)
IL (mA)
RL (Ω)
PL (mW)
Discussions
(1) A person accidentally grabs conductors connected to each end of a DC voltage source, one
in each hand.
(a) What is the minimum source voltage that can produce electrical shock sufficient to cause
paralysis, preventing the person from letting go of the conductors? You may assume that
the characteristic resistance of a human arm is 400 Ω and the current level for muscle
paralysis is 50 to 70 mA.
(b) Is there a significant risk of this type of accident occurring while servicing a personal
computer, which has typically 5 V and 12 V sources?
(2) State the criterion for maximum power transfer from a source to a load. If you are free to
select Ri without changing the source voltage, how can you maximize the power delivered to
the load?
(3) Prove the maximum power transfer theorem.
References
1. C.K. Tse, Linear Circuit Analysis, 1st Ed., Addison-Wesley, England, 1998.
2. K. Harry, Electronics, a self-teaching guide, 1st Ed., John Wiley & Sons, USA, 1979.
3. J.W. Nilsson and S. A. Riedel, Electric Circuits, 5th Ed., Addison-Wesley, USA, 1996.
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