Lab 3: Circuit Reduction and Voltage-Current Characteristics
Overview
This lab assignment focuses on the voltage-current characteristics of two-terminal
circuits. Ohm’s law is a special case of this: the circuit is simply a single resistor with
two terminals and Ohm’s law provides a relationship between the voltage and the
current at the terminals. In this assignment, this concept is extended to circuits
containing more than just a single resistor.
In Part I of the assignment, a network of multiple resistors is interconnected to create
an equivalent resistance. The network still has only two terminals, and the
equivalent resistance relates the voltage between these terminals to the current into
the network.
In Parts II and III, non-ideal effects of voltage sources and voltmeters are
investigated. These devices have two terminals, and the non-ideal effects can be
modeled by studying the relationship between voltage and current at the terminals.
Finally, in Part IV, a voltage-current relationship for a circuit containing multiple
resistors and a source is obtained. Since the circuit is still linear, the voltage-current
characteristic curve is a straight line (like that of a resistor) but with a non-zero yintercept.
Note:
There is a link to a video that discusses non-ideal sources and materials on
the class web page. You may find it useful when performing parts II and III
of the lab assignment. It also provides information about current limits on
the Analog Discovery – the Discovery shuts down if you attempt to exceed
these limits, to protect the USB drive on your computer.
Symbol Key:
Demo
Analysis
Sim
Data
Demonstrate circuit operation to teaching assistant.
Analysis; include principle results of analysis in laboratory report.
Numerical simulation (using PSPICE or MATLAB as indicated).
Record data in your lab notebook.
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©2015, Tim Hanshaw
Lab 3: Circuit Reduction and Voltage-Current Characteristics
I. Equivalent Resistance
General Discussion:
A network of multiple resistors can be used to implement a desired resistance. It is
common, when prototyping circuits, to use this approach to create a desired
resistance value. In this lab assignment we will design resistive networks, composed
of the available fixed resistors, to provide specified resistances.
Resistors with the following resistance values and tolerances are needed:
1.
800Ω ± 5%
2.
25Ω ± 5%
Since resistors with these values are not included in the parts kit; the available fixed resistors
will be used to construct circuits with the required equivalent resistance.
Pre-lab:
Using only fixed-value resistors available in your analog parts kit, design circuits
which have the equivalent resistances listed above.
Analysis
Lab Procedures:
1. Construct the circuits you designed in the pre-lab. Use an ohmmeter to
measure the equivalent resistance of each of the circuits. Comment on your
results – specifically, whether the design requirements were met.
2. Demonstrate operation of your circuits to the Teaching Assistant Have the
TA initial your lab worksheet.
Note:
As always, measure and record the resistance of the individual resistors
used in your circuits.
II. Non-Ideal Power Sources
Often, theoretical models of electrical circuits assume that power supplies are ideal,
but physical circuits can exhibit non-ideal effects of the power supplies. It is
important to have experience with these effects, so that they can be recognized
when they appear. In this part of the lab assignment, we will measure the voltagecurrent characteristics of non-ideal voltage sources.
General Discussion:
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Data
Analysis
Demo
Lab 3: Circuit Reduction and Voltage-Current Characteristics
The circuit we will implement in this portion of the lab assignment is shown in Figure
1(a). However, in this assignment we will not assume that the voltage source is
ideal. That is, our model of source’s voltage will not be independent of current.
Instead, we will recognize that the voltage source cannot provided unlimited current
and we will adjust our model of the source accordingly. A simple way to model this
effect is to add a resistor in series with an ideal voltage source, as shown in Figure
1(b). Notice that the source model still has two terminals, and that we are
developing a mathematical model of the relationship between voltage and current at
these terminals. We don’t really know1 what the actual circuit is inside the source
(that is still a “black box” that we can’t see inside), we just need an equation that lets
us model the circuit’s behavior.
Notes:
•
•
Source resistances should be “small”. (Ideal sources have zero
resistance.) The effects of the source resistance will therefore be most
obvious when resistance R is also “small”. Since the definition of “small” is
relative, it is important to know the internal resistance of your source so
that you know how much current your source will deliver before non-ideal
effects become significant.
Vout and IS in Figure 1(b) can be measured, but VS and RS can‘t (they are
inside the power supply).
(a) Ideal source circuit
(b) Non-ideal source circuit
Figure 1. Circuit schematics.
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Or in most cases even care.
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©2015, Tim Hanshaw
Lab 3: Circuit Reduction and Voltage-Current Characteristics
Pre-lab:
If R = 20Ω and VS = 1V, analyze the circuit of Figure 1(b) to determine expressions
for the measured voltage Vout, source current IS, and power dissipated by the
resistor, for the cases in which
Analysis
(a) The voltage source is ideal (in this case, your result will be a number) , and
(b) The voltage source is non-ideal, and has an internal resistance RS (in this case, your
result will be a function of RS).
Lab Procedures:
1. Create the circuit of Figure 1(a) R = 20Ω±5%. Measure and record the actual
resistance.
2. Set the voltage VS = 1V. Measure and record the actual value of VS by opencircuiting the waveform generator terminals measuring the voltage across the
terminals. (Under these conditions, there is no current supplied by the
voltage source so that the internal source resistance is not affecting the
voltage measurement.)
3. Connect the resistor to your circuit. Measure the voltage Vout and the source
current IS.
4. Use your results from part (b) of the pre-lab and your measurement of Vout
and the VS to estimate the internal resistance of the voltage source.
Data
Data
Data
Analysis
5. Demonstrate operation of your circuit to the Teaching Assistant Have the TA
initial your lab worksheet.
Demo
6. Repeat your source resistance estimate above with R ≈ 30Ω .
Data
Comment on the consistency between the results for the two different values
of R
III. Non-Ideal Voltage Measurement
Theoretical models of electrical circuits usually don’t take into account the effects of
measuring the voltages and currents in the circuit. In reality, any time we measure a
voltage or current, the circuit’s behavior is altered to some extent – sometimes the
effects of the measurement process can be very significant. In this lab assignment,
we will experimentally explore the effects of non-ideal meters.
General Discussion:
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©2015, Tim Hanshaw
Analysis
Lab 3: Circuit Reduction and Voltage-Current Characteristics
In our circuit, we will measure the voltage Vout as shown in Figure 2(a). Once a
voltmeter is connected in parallel with the resistor R2, we are also – whether we like
it or not – placing the meter’s internal resistance in parallel with the resistor R2 as
shown in Figure 2(b). This can affect the measurement of the voltage Vout.
(a) Ideal circuit
(b) With non-ideal meter
Figure 2. Circuit schematics.
Pre-lab:
Analyze the circuit of Figure 2(b) to determine an expected value for the measured
voltage Vout for the cases in which
(a) The measurement of Vout is determined using an ideal voltmeter (a voltmeter
with infinite internal resistance), and
(b) The measurement of Vout is determined using a voltmeter with internal
resistance RM. (In this case, your result will be a formula which depends
upon RM.)
Notes:
•
Your analysis should show that if R>>RM, Req ≈ R and the measured Vout
will be essentially the same as the Vout indicated in Figure 2(a). If,
however, this condition is not true, the voltmeter’s internal resistance can
have a significant (and generally undesirable) effect on the voltage being
measured. Therefore, “large” meter resistances are generally desirable.
Since the definition of “large” is relative, it is important to know the
internal resistance of your meter so that you know how much effect the
meter will have on your measurements.
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©2015, Tim Hanshaw
Analysis
Analysis
Lab 3: Circuit Reduction and Voltage-Current Characteristics
Lab Procedures:
1. Construct the circuit of Figure 2 with R = 10MΩ. Measure the voltage Vout
using your DMM.
2. Estimate the internal resistance of the voltmeter.
Data
Analysis
3. Demonstrate operation of your circuit to the Teaching Assistant Have the TA
initial your lab worksheet.
Demo
4. Repeat the measurement of part 1 using the Scope instrument on your
Analog Discovery to measure Vout.
Data
Estimate the internal resistance of the Scope instrument.
Note:
You will probably find that the Analog Discover internal resistance is
significantly lower than the internal resistance of your DMM.
Most oscilloscopes will allow you to purchase different probes with
varying resistances. The choice of probes depends on the application;
The Analog Discovery is not intended for applications which require a
high probe resistance.
IV. Voltage-Current Characteristics of Two-Terminal Networks
In this part of the lab, the voltage-current characteristics of a simple circuit containing
a power supply will be measured, and the result compared to analytical expectations.
General Discussion:
This lab assignment concerns the circuit shown in Figure 1 below. (Pay special
attention to the polarity of the 4V source relative to the polarity of Vab!)
Figure 1. Circuit schematic.
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©2015, Tim Hanshaw
Analysis
Lab 3: Circuit Reduction and Voltage-Current Characteristics
Pre-lab:
a) Calculate the functional relationship between the voltage Vab and the current I
for the circuit of Figure 1. Plot the voltage Vab as a function of the current, I
(the plot should have voltage on the vertical axis and current on the horizontal
axis). Calculate the slope of the curve and the y-intercept of the curve.
b) Calculate the expected voltage Vab if the terminals a-b are open-circuited.
Compare this voltage to the y-intercept of the curve you calculated in part (a)
of the pre-lab. Kill the 3V source and determine the equivalent resistance of
the circuit seen across the terminals a-b. Compare this value to the slope of
the curve you calculated in part (a) of the pre-lab.
Analysis
Analysis
Lab Procedures:
1. Build the circuit of Figure 1. Use W1 to apply the 3V voltage source and W2
to apply the voltage Vab. (Please pay attention to the polarity on the 3V
source!) Record the actual resistance values.
2. Record the current, I, resulting from values Vab = -4V, -2V, -1V, -0.5V, -0.2V,
0.2V, 0.5V, 1.0V, 2.0V, and 4.0V. Tabulate the voltage vs. current data. Plot
the data, with current on the x-axis and voltage on the y-axis. Perform a
least-squares curve fit of a straight line to the data and determine the slope
and y-intercept of the line.
Data
Data
Analysis
3. Replace the Vab voltage source with an open-circuit and measure the
resulting voltage Vab.
Data
4. With Vab still open-circuited as in step 4, replace the 3V source with a shortcircuit and use your DMM to measure the resistance seen across terminals ab.
Data
Post-lab exercises:
Summarize the results of your pre-lab analysis and your experimental results. You
should provide, at a minimum:
1. The slope of the voltage-current characteristic estimated from the pre-lab, the
measured slope determined from the best-fit straight line created in part 2 of
the lab procedures, and the measured resistance from part 4 of the lab
procedures. Comment briefly on the differences between the three values.
2. The y-intercept of the voltage-current characteristic estimated from the prelab, the measured y-intercept determined from the best-fit straight line
created in part 2 of the lab procedures, and the measured open-circuit
voltage from part 4 of the lab procedures. Comment briefly on the differences
between the three values.
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©2015, Tim Hanshaw
Analysis