SAN FRANCISCO STATE UNIVERSITY
ELECTRICAL ENGINEERING
Experiment #4 Circuit Analysis and Equivalent Circuits
Objectives
To verify nodal and loop analysis techniques and to investigate Thevenin and Norton
equivalent circuits.
Introduction
The nodal and loop analysis techniques are the most important circuit analysis tools.
Before coming to the lab, find the voltage across and current through each of the
branches of the circuit shown in Fig. 1, using first nodal analysis and then loop
analysis techniques. (Be especially alert to the polarities of the power sources.) Attach
your work as an appendix to the report.
R1
2.2k
R2
R3
1k
10k
V1
10Vdc
R4
V2
15Vdc
22k
0
Fig. 1. Circuit for nodal and loop analyses.
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Experiment #4
Circuit Analysis and Equivalent Circuits
The Thevenin's theorem states that any one-port circuit (circuit with just one pair of
terminals) with linear sources and resistances can be represented by an equivalent circuit
consisting of a resistor, RTH, in series with a voltage source, VTH (see Fig. 2(a)).
Likewise, the Norton's equivalent circuit is consisted of a resistor, RTH, in parallel with a
current source, INO (see Fig. 2(b)).
Before coming to the lab, find the Thevenin and Norton equivalents of the circuit shown
in Fig. 3. Attach your calculations as an appendix to the report.
RTH
VTH
RNO
INO
Fig. 2. (a) Thevenin’s equivalent circuit
R1
Fig. 2. (b) Norton’s equivalent circuit
R3
A
V1
15Vdc
1k
1k
R2
1k
B
Fig. 3. A linear one-port circuit
27
Experiment #4
Circuit Analysis and Equivalent Circuits
Your work station contains a dual power supply. A brief description of its front panel
controls and connectors is given in Appendix G.
There are four power supply options:
o 0 to +6 volts using the COM terminal and the +6V terminal.
o 0 to +20 volts using the COM terminal and the +20V terminal
o 0 to ±20 volts with fixed tracking ratio using the COM terminal, the +20V
terminal, and the –20V terminal. Tracking ratio is set to FIXED. Fixed Tracking
Ratio means that the plus voltage will be equal to the minus voltage but will have
opposite polarities.
o 0 to ±20 volts with unfixed tracking ratio using the COM terminal, the +20V
terminal, and the –20V terminal. Tracking ratio is NOT set to FIXED. This
means that the plus voltage can be different from the minus voltage (using the
tracking ratio knob.)
THE CONCEPT OF GROUND AND WHY THERE IS CONFUSION
Electrical (Equipment) Ground
In the electrical industry, all electrical devices that have metal parts must be “grounded”
when in operation. It is called an equipment ground. That is why modern wall plugs
have three holes. The small round hole in the wall plug is the equipment ground. That
ground is connected to all other metal equipment and eventually to the earth, (usually a
metal rod buried in the earth.) The symbol that is generally used looks the same as the
Electronic Circuit Ground, but it is not the same. On the lower right-hand side of the
laboratory equipment power supply is a ground symbol. That ground is an electrical
equipment ground and is not referenced to the voltage outputs. Do not use that ground
for your experiments when you see the ground symbol in the schematic.
Electronic Circuit Ground
0
In electronic circuits, the name “ground” is also used, although it is different. In addition,
the same symbol is used as for the equipment ground. The equipment and circuit grounds
are, for the most part, completely different and should not be intermingled. (That is why
in PSpice the ground symbol is designated with a “0” to show that it is a power supply
zero voltage reference.) On the laboratory equipment power supply, the 0 voltage
reference which relates to electronic circuits is the COM terminal. The parts of the
circuit diagram with ground symbols must be connected to the COM only.
28
Experiment #4
Circuit Analysis and Equivalent Circuits
Laboratory Work
1) Construct the circuit shown in Fig. 1. The two voltage sources are obtained from the
dual power supply in the non-fixed tracking mode. Measure voltage across and
current through each of the circuit branches using the DMM and record them in a data
table. Compare the measured values with the calculated values. Explain any possible
differences. Does KCL hold for every node? Does KVL hold for every loop?
2) Since the circuit of Fig. 1 is a linear circuit, predict (without going through circuit
analysis again) the expected voltage values across the four resistors if the two source
voltages are reduced to 50 % of their original values. Without altering the Tracking
Ratio knob on the dual power supply and, with the help of a voltmeter, adjust the +
output of the dual power supply to 1/2 of its original value by turning the ±20V knob.
Now measure and record the voltage at the negative output. Is it what you
expected? Why? Now measure and record voltages across each resistor and
compare with those predicted.
3) Construct the circuit of Fig. 3. Measure the open circuit voltage (VOC) and short
circuit current (ISC) and find VTH, INO, and RTH. Note: Do not attempt to measure
RTH directly with the ohmmeter. Why? Since the i-v characteristics (current on
vertical axis, voltage on horizontal axis) of a linear circuit is a straight line, it can be
defined by two points. In this case, (i,v) = (0, VOC) and (i,v) = (ISC, 0). Using graph
paper or Excel, construct the i-v characteristic.
4) Connect a 510 Ω resistor to the output terminals and measure the resulting voltage
across and current through the 510 Ω resistor. Do the same for a 4.7 k Ω resistor.
Plot these two (i,v) points on you i-v graph. Do they fit the characteristic? Discuss.
5) Leave the circuit of Fig. 3 in place and construct its Thevenin equivalent circuit on
another part of your circuit board. Find VOC and ISC for this circuit. Do they agree
with those for the original circuit?
6) Repeat step 4 for the Thevenin equivalent circuit. How closely do the resulting (i,v)
values correspond to those of the original circuit?
7) The maximum power transfer principle states that RL will receive a maximum
amount of power if RL = RTH. Consider the decade box as the RL, measure the
voltage, VL, across the decade box with the following RL values:
a) RL = 0.2 RTH, 0.5 RTH, 0.9 RTH, 1.0 RTH, 1.1 RTH, 2 RTH, and 5 RTH.
V2
8) Calculate the power PL = L delivered to the load at the above RL values. Plot PL
RL
vs. RL. From the graph, find the RL value corresponding to the maximum power
point. Does it agree with the theoretically predicted value? Explain reasons for
possible discrepancies.
Experiment #4
29
Circuit Analysis and Equivalent Circuits