Download Laboratory 1 Ohm`s Law

Laboratory 1
Ohm's Law
Key Concepts:
• Measuring resistance, DC voltage and DC current
• Investigating Ohmic (I = V/R) and non-Ohmic components
Equipment Needed:
• Digital Multimeter (2)
• Variable DC power supply
• 9 v battery
• Connections
Components Needed:
(2) 1kΩ Resistors, 5% tolerance
(2) 10 kΩ Resistors, 5% tolerance
(1) 10 kΩ Resistor, 10% tolerance
(1) 1N914 or 1N4148 Diode
Overview:
In this laboratory you will become familiar with measuring voltage, current and
resistance using a digital multimeter (DMM) on simple circuits you build. The laboratory
has four parts:
Part A: Using a multimeter to measure resistance
Part B: Connecting a resistor to a battery and measuring the voltage and current.
Part C: Connecting a resistor to a power supply and measuring the resistor's voltagecurrent characteristic.
Part D: Connecting a diode to a power supply and measuring the diode's voltage-current
characteristic.
Caution:
The two most common ways to destroy a digital multimeter are:
• In current measuring mode, place the meter in parallel with a power supply (that is,
touching the two probes to the two terminals of the power supply) as if measuring
voltage. The usual result is a blown fuse.
• In voltage measuring mode, exceeding the voltage rating of the meter (usually around
2000 V). The usual result is the destruction of the meter. Do not attempt to measure
the potential of a Van de Graaff generator or Tesla coil with a digital multimeter!
The multimeters are much more susceptible to damage in their current-measuring configuration.
As a matter of practice, when you remove a DMM from a circuit, you should always put it back
to the voltage-measuring configuration right away.
1-1
Procedure
Part A:
Use the resistor code to determine which resistors are which. Use the multimeter to
measure the resistance of each resistor in this experiment. Calculate the percent deviation from
the marked value. (Use: [(marked - actual)/actual] x 100%)
a.
b.
c.
d.
e.
1 kΩ (5%)
1 kΩ (5%)
10 kΩ (5%)
10 kΩ (5%)
10 kΩ (10%)
Question: Are the resistance values measured by the multimeter within the tolerance limits
specified by the manufacturer?
Try to determine the inherent accuracy of the meter. How does this affect your results?
Part B:
Connect the following circuit. Notice that the ammeter and voltmeter in the diagram are DMMs
set to measure either current or potential.
A
9v
1 kΩ
V
Measure the current through the circuit using the ammeter.
Measure the voltage across the resistor using the voltmeter.
Measure the voltage across the terminals of the battery using the voltmeter.
Question: Are the two voltages the same? Should they be? Explain.
1-2
Calculate the resistance of the resistor by using Ohm's law and the values you found for the
current and the voltage across the resistor.
Question: How does this value compare to the resistance values from the markings and from
direct measurement? Which do you think is closest to the real value? Explain.
Part C:
Replace the 9v battery in the circuit with a variable DC power supply. Start with the
power supply voltage at about 0.5 v, and measure the voltage across the resistor and the current
in the circuit as before. Increase the power supply in 0.5 v increments, and repeat the
measurements, making a table of your results.
Resistor Voltage (V)
Resistor Current (A)
Plot V vs I and calculate the slope of the line. (Note that while the independent variable is V, it
should go on the vertical axis here instead of the usual horizontal axis.)
1-3
Slope = ∆V / ∆I = ________________________
Question: The equation for a straight line is given by y = mx + b. Given your graph above,
discuss whether or not you have verified that the resistor is an Ohmic device -- that is, whether it
satisfies Ohm's law. (Hint: Think about the mathematical form of Ohm's law.)
Question: You now have a fourth value for the resistance of the resistor, from the slope of the
graph. Briefly discuss how the four values compare, and which you think is closest to the true
value (and why).
1-4
Part D:
Replace the resistor in the circuit with a 10 kΩ resistor, and insert a diode as shown. Note that
unlike the resistor, a diode has a specific direction associated with it. Be sure you insert the
diode correctly.
A
10 kΩ
V
Actual Device
Schematic
The resistor must be included to limit the current through the circuit. Begin with the power
supply at 0 v, measure the voltage drop across the diode and the current in the circuit, as the
voltage increases to 1.0 v in 0.1 v increments. Record the data and graph the voltage versus
current as before.
Diode Voltage (V)
Diode Current (A)
1-5
Question: Given the graph of V versus I, is the diode Ohmic? Explain.
Question: If the resistor were not included in the circuit, could you predict the current through
the diode if 1.0 v were placed across it? Why or why not?
1-6
Laboratory 2
Kirchoff's Laws
Key Concepts:
• Kirchoff's junction and loop laws
• Equivalent resistance
• Voltage dividers
Equipment Needed:
• Digital Multimeter (2)
• 12 v DC power supply
• Breadboard
Components Needed:
(1) 270 Ω Resistors
(1) 2.7 kΩ Resistors
(1) 10 kΩ Resistor
(2) 1 kΩ Resistors
(1) 5.1 kΩ Resistor
(1) 270 kΩ Resistor
Overview:
In this laboratory you will practice using Kirchoff's Laws and gain understanding of how
they apply to circuits. The laboratory has four parts:
Part A: Resistors in series
Part B: Resistors in parallel
Part C: Resistors in series and parallel and Kirchoff's Laws
Part D: Voltage divider
Note:
For the most part, it is not necessary to measure the exact resistance of all components.
Unless asked otherwise, it is acceptable to use the resistance value marked on the
components. But keep in mind that these values may not be precisely correct.
Procedure
Part A:
Before constructing the circuit, calculate the equivalent resistance of R1 and R2 in series. Also
calculate the expected current at points A, B and C in the circuit and the voltage drops across
each resistor.
2-1
Calculated values:
Requivalent = ____________________
A
IA = ______________________
R1
1 kΩ
IC = ______________________
B
12 v
IB = ______________________
VR1 = _____________________
R2
2.7 kΩ
VR2 = _____________________
VPower = ________12 v________
C
Connect R1 and R2 together in series (without the power supply) and measure the equivalent
resistance with the DMM. Then connect the whole circuit and measure the currents and voltages
calculated above.
Requivalent = _____________________
IA = ______________________
VR1 = _____________________
IB = ______________________
VR2 = _____________________
IC = ______________________
VPower = ____________________
Question: How do the measured values compare with the calculated values? Discuss
possibilities for discrepancy.
2-2
Question: Show that Ohm's law holds for each component by calculating the potential drop
across each resistor using the measured currents.
VR1 = IAR1 = __________________________ VR1 measured = __________________________
VR2 = IBR2 = __________________________ VR2 measured = __________________________
Discuss any differences.
Part B:
Before constructing the circuit, calculate the equivalent resistance of R1 and R2 in
parallel. Also calculate the current at points A, B, C and D in the circuit and the voltage drops
across each resistor.
Calculated Values
Requivalent = ____________________
IA = ______________________
A
B
12 v
R1
2.7 kΩ
C
R2
1.0 kΩ
IB = ______________________
IC = ______________________
ID = ______________________
VR1 = _____________________
D
VR2 = _____________________
VPower = ________12 v________
2-3
Connect R1 and R2 together in parallel and measure the equivalent resistance with the DMM.
Then connect the whole circuit and measure the currents and voltages calculated above.
Requivalent = _____________________
IA = ______________________
VR1 = _____________________
IB = ______________________
VR2 = _____________________
IC = ______________________
VPower = ____________________
ID = ______________________
Question: How do the measured values compare with the calculated values? Discuss
possibilities for discrepancy.
Question: Show that Ohm's law holds for each component by calculating the potential drop
across each resistor using the measured currents.
VR1 = IBR1 = __________________________ VR1 measured = __________________________
VR2 = ICR2 = __________________________ VR2 measured = __________________________
Discuss any differences.
2-4
Part C:
Hopefully you have shown that within resistor tolerances and meter accuracies, that the
current through a resistor can be calculated by I = V/R so a direct measurement of current is not
necessary. Construct the following circuit and measure the voltage drop across each resistor.
Given these values, calculate the current through each resistor and show that for each node
Kirchoff's current law holds true and for each loop that Kirchoff's voltage law holds true.
R1
1.0 kΩ
12 v
VR1 = __________________
A
R2
2.7 kΩ
VR2 = __________________
R3
1.0 kΩ
VR3 = __________________
IR1 = ___________________
IR2 = ___________________
B
IR3 = ___________________
Show that Kirchoff's current law (∑I = 0) holds for node A:
Show that Kirchoff's current law holds for node B:
Show that Kirchoff's voltage law (∑V = 0) holds for the loop: [power supply, R3, R2]
Show that Kirchoff's voltage law holds for the loop: [power supply, R3, R1]
Show that Kirchoff's voltage law holds for the loop: [R1, R2]
Question: Most likely the currents and voltages do not add to exactly zero in all the cases above.
Discuss discrepancies. Are they acceptable?
2-5
Part D:
Construct the voltage divider circuit shown below. Measure VB (that is, from the point B
to ground) and verify that it is the same as the voltage found using the voltage divider equation
(1-17) from the text:
 R2 

VB = Vpower 
 R1 + R 2 
R1
5.1 kΩ
12 v
B
VB(calculated) = ________________
VB(measured) = ________________
R2
10 kΩ
Now let's say we need the voltage divider above to supply VB to a load. (A "load resistor" or just
plain "load" is a component or device that the circuit is designed to drive or operate.) Connect a
270 kΩ load resistor from point B to ground and measure the voltage drop VL across it. Now
replace the 270 kΩ load resistor with a 270 Ω load resistor and measure the voltage drop VL
across it. Are the measured values equal to VB, the voltage value of the unloaded circuit?
VL (270 kΩ) = ____________________
VL(270 Ω) = ________________________
Question: Explain the differences between VB and the two measured values for VL.
Question: Discuss the limitations of the voltage divider circuit. Design a rule of thumb on loads
placed on the voltage divider circuit, given that the loaded voltage should be within 10% of the
unloaded voltage. (Hint: Draw a diagram of the loaded circuit and use concepts from all of this
lab to answer the question.)
2-6
Laboratory 3
Thevenin's Theorem
Key Concepts:
• Thevenin's Theorem
• Equivalent resistance and voltage
Equipment Needed:
• Digital Multimeter (2)
• Protoboard
Components Needed:
(2) 100 Ω, 10 kΩ Resistors
(1) 2.7 kΩ Resistors
(1) 1 kΩ, 100 kΩ, 1 MΩ, 10 MΩ Resistors
(1) Variable resistor
Overview:
In this laboratory you will practice using Thevenin's Theorem and gain understanding of
how it applies to circuits. The laboratory has four parts:
Part A: Theoretical Calculations
Part B: Thevenin Equivalent circuit
Part C: Applying Thevenin's Theorem
Part D: Application of Thevenin's Theroem
Procedure
Part A:
Before constructing the circuit, calculate the Thevenin equivalent resistance of RTH and the
Thevenin voltage VTH as seen by the load resistor RL.
Calculated values:
R1
10 kΩ
VTH = ______________________
A
RTH = ______________________
15 v
R2
10 kΩ
RL
2.7 kΩ
IL = ________________________
B
3-1
Now measure the voltage across the load resistor and the current through it.
Measured Values:
VRL = _____________________
IRL = _____________________
Question: How do the currents compare? How does the measured voltage compare to the
Thevenin equivalent voltage? Why should this be?
Part B
Construct the Thevenin equivalent circuit using the voltage and resistance calculated above.
Measure the voltage across the load resistor and the current through it.
Measured Values
RTH
A
VL = ________________________
RL
2.7 kΩ
VTH
IL = _________________________
B
Question: How do the measured current and voltage compare to the calculated Thevenin values
and to the values measured above?
3-2
Part C
Construct the circuit below, using a 1 kΩ resistor as RL. Measure the current IL through RL.
Record the resistance and current values in the table, and repeat the measurements with values of
10 kΩ, 100 kΩ, 1 MΩ for RL.
R
10 MΩ
Resistance RL (Ω)
Current IL (A)
A
5v
RL
B
Question: What can we say about IL as long as RL« R? In other words, the 5 v power supply and
R act like a constant ________ source? Why is this?
Question: As far as RL is concerned, is there any difference between your original circuit in Part
A and your Thevenin equivalent circuit in Part B? Explain.
Question: In terms of VTH and RTH in Part B, what is the open-circuit voltage (Voc) between A
and B? (That is, the voltage between A and B as RL → ∞.)
Question: In terms of VTH and RTH in Part B, what is the short-circuit current (Isc)? (That is, the
current at A as RL → 0.)
Question: How is RTH related to Voc and Isc?
3-3
Part D:
Construct the circuit below. R2 should be a variable resistor, and R4 is the unknown.
R1
R3
B
A
R2
R4
Question: Use the results of Thevenin's Theorem applied to this circuit to show how R4 may be
determined.
Determine the value of R4 using your results from above:
R4 = ________________________
Use the DMM to measure the value of R4 directly:
R4 = ________________________
Question: How do the two values compare? Which do you think is a better estimate? Why?
3-4
Laboratory 4
Test Instruments
Key Concepts:
• Digital Multimeters (DMM)
• Oscilloscopes
• AC Signals
Equipment Needed:
• Digital Multimeter (2)
• Oscilloscope
• Protoboard
Components Needed:
(2) 10 MΩ Resistors
(1) Resistor Substitution Box
(3) 10 kΩ Resistors
Overview:
In this laboratory you will practice using test equipment to make measurements, and see
what effects the instruments themselves have on circuits. The laboratory has three parts:
Part A: DMM Input Resistance
Part B: Use of Oscilloscope
Part C: Frequency Limit of the DMM
Procedure
Part A:
Construct the circuit shown and measure the voltage across the power supply, and across R1 and
R2 .
R1
10 MΩ
Measured values:
VPS = ______________________
VR1 = ______________________
12 v
R2
10 MΩ
VR2 = ______________________
4-1
Question: Kirchoff's voltage law says that VPS - VR1 - VR2 = 0, or that VPS = VR1 + VR2. Does
this law hold true for the data? Why?
The DMM as a voltmeter is not perfect -- that is, it represents a resistive load across the points in
a circuit in which it is placed. The resistive load of the meter is referred to as the input
resistance. If we replace the DMM by a perfect voltmeter (one which represents no load) in
parallel with a resistor Rin, that represents the input resistance of the meter, we can re-draw the
circuit with the meter connected to measure VR2.
Given the data above, calculate Rin for your
DMM.
R1
12 v
R2
Rin
V
Rin = ____________________________
A simple way to measure the input resistance of a voltmeter is to connect the meter in series with
a resistor substitution box and power supply. In other words, connect it like an ammeter. To
obtain Rin one simply varies Rsubstitution until the meter reads half of the power supply voltage. In
that case Rin = Rsubstitution. Set up such a circuit and measure Rin. How does it compare with the
value calculated above?
Rin = ____________________________
4-2
Part B
Connect the A channel probe of the oscilloscope to the output of the function generator
on the protoboard; connect the oscilloscope ground to the protoboard ground. Turn on the
oscilloscope and set it to read channel A. Set the function generator to produce a sine wave.
There are three basic levels of control on the oscilloscope: Setting the basic appearance
(focus and intensity), setting the triggering (level, slope, AC/GND/DC), and setting the scale and
offset of the axes (x-pos, y-pos, volts/div, sec/div). In general the controls are adjusted in the
order listed here.
First set channel A to read GND. You should see a straight line trace. (If you cannot
find the trace, push the "beam find" button, and adjust the x-pos and y-pos knobs to center the
trace.) Adjust the focus and intensity knobs till you have a focused, reasonably intense (but not
overly bright) trace. You should not have to adjust these controls again.
Next set channel A to read AC. You should see some curving on the trace. If an AC
trace is not "stable", then you need to adjust the triggering controls. First adjust the slope control
to +, so that the trace begins when the signal is moving upward. Next adjust the triggering level
until the trace stabilizes. If this knob is set too high, then a small signal will not cause the
oscilloscope to begin its trace at the proper time, and the signal will "move" across the screen.
Now with a stable signal, most of the adjustments on the oscilloscope are done with the
x-pos and y-pos knobs (which shift the trace horiztonally and vertically), and with the volts/div
and sec/div knobs (which adjust the vertical and horizontal scales of the trace). Set channel A to
GND, and use the x-pos and y-pos knobs to center the horizontal trace. Next adjust the volts/div
knob so the sine wave shape nearly fills the screen. Finally, adjust the sec/div knob so that you
can see one or two complete waves.
To practice using the oscilloscope to measure and control signals, use the volts/div and
sec/div knobs and the function generator controls to produce a sine wave with the following
characteristcs:
Period:
5 ms
Frequency (Hz):
Time Scale (s/div):
# Major Divisions (Horizontal):
Peak-to-Peak Voltage:
2.0 v
Voltage scale (v/div):
# Major Divisions (Vertical):
4-3
Repeat the exercise above with a sine wave with different characteristics:
Period:
0.02 ms
Frequency (Hz):
Peak-to-Peak Voltage:
4.5 v
Voltage scale (v/div):
Time Scale (s/div):
# Major Divisions (Horizontal):
# Major Divisions (Vertical):
Input Resistance
Like a DMM, an oscilloscope has an input resistance. With the oscilloscope in the DC
setting, measure its input resistance as you did in the first part of Part A above. (Attach the
probe to the positive end of the resistor and the ground wire to the negative end.)
Oscilloscope Input Resistance = _____________________________
Grounding
The oscilloscope acts like a DMM for time-varying signals, but one way in which it
differs is the way in which it sees ground. The DMM measures voltage between its two probes.
The oscilloscope measures voltage between its probe and the ground provided by the third prong
of its electrical cord. This is a fairly simple concept, but one which can lead to much confusion.
Construct the three resistor circuit shown. (Note that the positive power supply comes from the
function generator, and the negative goes to the ground line on the protoboard.)
Function Generator
1 kHz, 5 Vpp
A
R1
10 kΩ
B
R2
10 kΩ
C
R3
10 kΩ
D
4-4
Question: Calculate the peak-to-peak voltages across each of the resistors in the circuit.
VR1 = ___________________
VR2 = ___________________
VR3 = ___________________
Now use the oscilloscope to measure the peak-to-peak voltages across each resistor. For
instance, to measure VR1 place the probe at A and the ground wire at B.
VR1 = ___________________
VR2 = ___________________
VR3 = ___________________
Question: Do the calculated voltages equal the measured ones? Explain why or why not.
Question: Is it possible to measure directly the voltage across R2 using an oscilloscope?
Explain.
Part C:
While the oscilloscope may cause confusion due to its grounding, it is better at measuring
time-varying signals than the DMM. To explore the DMM's limitations in measuring timevarying signals, use the oscilloscope to set the function generator to produce a 10 volt peak-topeak sine wave with a frequency of 60 Hz. Measure the AC voltage using the DMM.
Voscilloscope = ___________________
VDMM = _______________________
Question: Are the oscilloscope and DMM readings what you expected? Explain.
4-5
Vary the frequency of the signal from 1 Hz to 100 kHz in decade steps (1, 10, 100, …) keeping
the amplitude of the signal as shown on the oscilloscope at 10 v peak-to-peak. (Some adjustment
may be necessary at higher frequencies.) Directly graph VDMM vs frequency on the graph.
Frequency (Hz)
DMM Voltage (v)
10
8
6
4
2
1
10
100
1k
10 k
100 k
Question: What can you say about the frequency limitations of the DMM?
4-6
Laboratory 5
Transient RC Circuits
Key Concepts:
• Transient signals
• Exponential charging and discharging
• Time Constant
• Differentiation and integration of signals
Components Needed:
(1) 10 kΩ Resistor
(1) 0.01 µF Capacitor
Equipment Needed:
• Oscilloscope
• Protoboard
Overview:
Resistor-Capacitor (or RC) circuits serve many purposes in modern electronics. They are
widely used for timing and signal shaping. Understanding the use of these circuits is
essential to doing electronics. The laboratory has four parts:
Part A: RC Circuit Transients
Part B: Signal Differentiation
Part C: CR Circuit Transients
Part D: Signal Differentiation
Procedure
Part A:
Most transients that occur in electrical circuits are very fast, making the DMM fairly useless in
analyzing circuit behavior. For this reason we use an oscilloscope to measure how voltage in a
component varies in time. In this way we can get an immediate picture of the behavior, rather
than individual readings from a DMM.
Consider the battery-driven circuit shown below. When the switch is set to A the battery charges
the capacitor. When the switch is set to B the capacitor discharges to ground. It would be
extremely difficult to move the switch between A and B quickly enough to see this happen, even
with an oscilloscope. For that reason we will use a function generator to drive our transient
circuits.
A
B
V out
5-1
Question: With a battery voltage of 5 V, sketch the output voltage measured as a function of
time, if the switch is toggled between A and B in 1 ms increments.
Voltage
(V)
5
4
3
2
1
0
0
1
2
3
4
5
6
Time (ms)
Question: What differences, if any, are there between a square wave of 500 Hz and the situation
described in the question above?
Construct the following circuit using a 0.01 µF capacitor and a 10 kΩ resistor. Drive the circuit
using a 1 kHz square wave with a peak-to-peak amplitude of 5 V.
Question: Does it matter for this circuit that the voltage varies between -2.5 V and +2.5 V,
instead of between 0 V and +5 V as above? Explain.
V in
V out
Obtain a stable trace and note Vout,
which is measuring the potential
across the capacitor. Sketch what
you see for one square wave period
and label the half-time t1/2 and the
time constant τ. Measure these
accurately and record their values.
t1/2 = __________________
τ = ____________________
5-2
Voltage vs Time
Voltage
(V)
Time
Question: Derive expressions for t1/2 and for τ in terms of R and C.
Question: Calculate the theoretical values of t1/2 and τ using the values of R and C in the circuit.
Compare those values to the ones you measured from the oscilloscope and explain any
differences.
Question: In words, describe what is happening in the above circuit during the first half of the
square wave and what is happening during the second half, in terms of current flow, the voltage
across the resistor and the voltage across the capacitor. Write down two equations (first and
second half) which describe VC(t). Write down two equations that describe VR(t).
5-3
Part B:
Using the same circuit, change the driving frequency and verify that for RC >> the period of the
signal, Tsignal, that the circuit is an integrator. Switch the generator to produce a sine wave.
Sketch Vout and Vin below.
Square Wave Input
Voltage
Time
Sine Wave Input
Voltage
Time
Question: Why is the circuit above called an integrator?
5-4
Part C:
Switch the resistor and capacitor in your previous circuit and measure Vout across the resistor.
As in Part A, drive the circuit with a 1 kHz, 5 V peak-to-peak square wave. Sketch Vout and Vin
below.
V in
V out
Voltage
Time
Question: Describe in words what is happening in the above circuit in terms of current flow and
voltage across R and C as a function of time.
5-5
Part D:
Using the same circuit, change the driving frequency and verify that for RC << the period of the
signal Tsignal, that the circuit is a differentiator. Switch the generator to produce a sine wave.
Sketch Vout and Vin for each case below.
Square Wave Input
Voltage
Time
Sine Wave Input
Voltage
Time
Question: Why is the circuit above called a differentiator?
5-6
Laboratory 6
AC Circuits and Filters
Key Concepts:
• Voltage and Phase Relations in AC Circuits
• Low-pass, High-pass and Bandpass filters
Components Needed:
(2) 10 kΩ Resistor
(1) 2.7 kΩ Resistor
(2) 0.01 µF Capacitor
(1) 1 µF Capacitor
Equipment Needed:
• Digital Multimeter
• Oscilloscope
• Protoboard
Overview:
We have seen how resistors and capacitors may be used to shape waveforms. Here we
will explore RC circuits in their use as filters. The laboratory has four parts:
Part A: Measuring AC voltages in RC circuits
Part B: Low Pass filters
Part C: High Pass filters
Part D: Bandpass filters
Procedure
Part A:
Construct the circuit shown below, with R = 2.7 kΩ and C = 1 µF. Set the function generator to
produce a 10 Hz sine wave of 5 V peak-to-peak. Using the DMM as a voltmeter, measure Vin,
the voltage across the resistor (VR) and the voltage across the capacitor (VC).
Vin = _______________________
V in
V out
VR = _______________________
VC = _______________________
Question: Is Vin what you expected? Explain.
6-1
Question: According to Kirchoff's Voltage Law, Vin = VR + VC. Does this hold true for the
DMM data? Why or why not?
Change the driving frequency to 1000 Hz and measure Vin, VR and VC again using the DMM.
Vin = ___________________
VR = ___________________
VC = ___________________
Question: If your data are different for the 120 Hz signal explain what is happening.
Part B:
Construct a low pass filter using the same circuit as above, with R = 10 kΩ and C = 0.01 µF.
Use the oscilloscope to measure Vout, the peak voltage. Vary the driving sine-wave frequency
from 10 Hz to 100,000 Hz in decade intervals (10, 100, 1000, etc). Also measure the phase
angle between Vin and Vout for each frequency. Plot your results on the graphs below.
Voltage
10
100
1000
10,000
100,000
Frequency (Hz)
6-2
90
45
Phase
(Degrees)
0
-45
-90 10
100
1000
10,000
Frequency (Hz)
100,000
Question: The break-point frequency is given by fB = 1/(2πRC). For this circuit, calculate the
theoretical break-point frequency.
fB = ___________________
From your graph above, estimate the actual break-point frequency.
fB = ___________________
Keeping in mind oscilloscope accuracy (about 5%), resistor tolerance (5%) and capacitor
tolerance (about 20%), how does the theoretical value of fB compare with the actual value?
Question: In terms of current flow in the circuit, describe why the phase angle between Vin and
Vout changes as a function of frequency.
Question: Why is this circuit called a low pass filter?
6-3
Part C:
Construct a high pass filter by switching the resistor and capacitor in the previous circuit. As
before, vary the driving sine-wave frequency from 10 Hz to 100 kHz in decade intervals and
measure the peak voltage of Vout and phase angle between Vin and Vout. Graph the results.
Voltage
10
100
1000
10,000
100,000
Frequency (Hz)
90
45
Phase
(Degrees)
0
-45
-90 10
100
1000
10,000
Frequency (Hz)
100,000
Question: The break-point frequency is given by fB = 1/(2πRC). For this circuit, calculate the
theoretical break-point frequency.
fB = ___________________
From your graph above, estimate the actual break-point frequency.
fB = ___________________
6-4
Keeping in mind oscilloscope accuracy (about 5%), resistor tolerance (5%) and capacitor
tolerance (about 20%), how does the theoretical value of fB compare with the actual value?
Question: In terms of current flow in the circuit, describe why the phase angle between Vin and
Vout changes as a function of frequency.
Question: Why is this circuit called a low pass filter?
Part D:
We have constructed a low pass filter that filters out high frequencies and a high pass filter that
filters out low frequencies. Often a filter is required which filters out both high and low
frequencies but allows frequencies within a certain range to pass. This is a bandpass filter. It is
basically a high pass filter added on to the output of a low pass filter.
V out
V in
R1
10 kΩ
C1
0.01 µF
C2
0.01 µF
R2
10 kΩ
6-5
Once again vary the driving frequency from 10 Hz to 100 kHz in decades and measure Vout and
the phase angle. Graph on the two graphs below.
Voltage
10
100
1000
10,000
100,000
Frequency (Hz)
90
45
Phase
(Degrees)
0
-45
-90 10
100
1000
10,000
Frequency (Hz)
100,000
Question: Describe quantitatively how would the Vout vs. frequency graph change if R2 were
decreased to 1 kΩ? How would the graph change if C1 were increased to 0.1 µF?
6-6
Laboratory 7
RLC Circuits
Key Concepts:
• RLC Transients
• Bandpass Filter and Quality Factor
Equipment Needed:
• Digital Multimeter
• Oscilloscope
Components Needed:
(1) 100 Ω, 1 kΩ Resistors
(1) 1 mH Inductor
(1) 0.47 nF Capacitor
(1) 22 µF Capacitor
Overview:
While inductors are not used extensively in modern electronics, except in some high
frequency applications, there are some instances where they are useful, especially in
filters. In addition, many electronic components may have an inductance, and it is useful
to see its effect. The laboratory has three parts:
Part A: RLC Transients -- Ringing
Part B: RLC Bandpass filter
Part C: RLC Notch filter
Procedure
Part A:
Cables, loops of wire, and other elements on a circuit board can induce stray (unwanted)
inductances and capacitances in a circuit. Their presence is usually spotted by a ringing, or a
damped oscillation, at sharp signal transitions. Sometimes we want a circuit to ring, as in the
case of oscillator circuits. In this circuit we will cause it to ring by driving it with a square wave.
Construct the circuit shown below, with L = 1 mH, R = 1 kΩ and C = 0.47 nF.
V in
V out
7-1
The natural oscillation frequency is given by: fo =
1
2π LC
Calculate the natural oscillation frequency and the period of this oscillation for this circuit.
fo (calculated) = ________________
To (calculated) = ___________________
Drive the circuit with a square wave of 100 kHz frequency, 2 V peak-to-peak. Sketch the signal
response. Also adjust the oscilloscope to be able to measure the period of the ringing signal.
Calculate the frequency of the ringing signal.
Voltage
Time
fo (measured) = ________________
To (measured) = ___________________
Question: How do the calculated and measured values compare? Explain any discrepancies.
Question: Theoretically, the "envelope" outlining the amplitude of the ringing should decay as
e-(R/2L) . Qualitatively, does this appear to be the case?
7-2
Question: Explain qualitatively what is happening in the RLC circuit in terms of current, charge
and voltage in each element as a function of time.
Change the driving frequency to 10 kHz and sketch the results.
Voltage
Time
Question: Why does this signal differ from the result at 100 kHz? Explain mathematically and
in terms of current and voltage in the elements.
7-3
Part B:
In Lab 6 we analyzed an RC bandpass filter. Here we look at a passive RLC bandpass filter.
Construct the same circuit as before, now with L = 1 mH, C = 22 µF and R = 100 Ω.
Question: The resonant, or natural frequency of the circuit is: fo =
1
2π LC
Calculate the resonant frequency for the circuit.
fo (calculated) = ____________________
Drive the circuit with a sine-wave signal with a peak-to-peak voltage of 2 V. Starting at 10 Hz,
measure Vout as a function of frequency as you vary the frequency in decade steps up to 100 kHz.
You should take more readings around the resonant frequency. Plot the values on the graph.
Also measure the phase angle of Vout with respect to Vin and plot it on the graph.
Note: The circuit itself will affect the input voltage. You must adjust the input voltage at
each frequency to ensure that the driving voltage is 2 V peak-to-peak.
Voltage
10
100
1000
10,000
100,000
-90 10
100
1000
10,000
100,000
90
45
Phase
(Degrees)
0
-45
7-4
Question: From your graph, determine fo. How does it compare with the calculated value.
Explain any discrepancies.
fo (measured) = _________________________
Question: The quality factor Q describes the sharpness and steepness of the frequency response.
The value of Q is given by:
ω L 2πfo L
Q= o =
R
R
Calculate the Q value for the circuit.
Q = ___________________________
Question: Explain qualitatively how the bandpass filter works.
Part C:
Sometimes a filter is necessary which passes all but a given range of frequencies, called a notch
filter. Construct the notch filter below, with the same components as the bandpass filter.
V in
V out
7-5
Question: The notch frequency for the above circuit (the frequency which is most attenuated) is
1
calculated with the same formula as for the bandpass filter: fo =
. Calculate the notch
2π LC
frequency.
fo = _______________________
Drive the circuit with a sine wave signal of 2 V as before. (Remember to check the input voltage
at each frequency.) Measure the voltage at each frequency from 10 Hz to 100 kHz in decade
steps and record it on the graph. Also measure the phase angle at each frequency and record it.
Voltage
10
100
1000
10,000
100,000
-90 10
100
1000
10,000
100,000
90
45
Phase
(Degrees)
0
-45
Question: From your graph, determine fo. How does it compare with the calculated value?
Explain any discrepancies.
fo (measured) = _________________________
7-6
Laboratory 8
Diodes: Rectification & Filtering
Key Concepts:
• Signal Rectification
• Filtering
Equipment Needed:
• Protoboard
• Oscilloscope
Components Needed:
(2) 1 kΩ Resistors
(1) 10 kΩ Resistor
(1) 1N914 Diode or Equivalent
(1) 1 µF Capacitor
(1) 0.01 µF Capacitor
Overview:
Up to this point we have used linear components -- ones where current is proportional to
voltage. We brushed up against the non-linear behavior of diodes in Lab 1; now we look
at them and their uses in more depth. The laboratory has two parts:
Part A: Single Diode Rectification
Part B: Filtering
Procedure
Part A:
One of the main uses of diodes is in the rectification of an AC signal to produce a DC signal.
Construct the half-wave rectifier shown below. Note that the diode is directional, as shown.
Actual
Device
V in
V out
Schematic
Use a 1 kΩ resistor, and drive the circuit with a 5 V peak-to-peak sine wave with a frequency of
1 kHz. Note that the output is a rectified sine wave with amplitude a bit less than the input
signal. Sketch both input and output signals below. Repeat with a square wave.
8-1
Sine Wave
Voltage
Time
Square Wave
Voltage
Time
8-2
Question: Do your readings support the rule of thumb that a diode has a forward rectification
voltage drop of about 0.6 V? Explain.
Question: Return to a sine wave and reduce the amplitude of the signal. Reverse the direction of
the diode. Is the output as expected?
Question: Using a sine wave signal, begin with a peak-to-peak value of 5 V and slowly reduce
the amplitude. At what input voltage does the output voltage go to zero volts over all time?
Explain.
Vnon-conduction = ______________________
Construct the following rectified differentiator circuit with 1 kΩ resistors and a 0.01 µF capacitor
and drive it with a 10 kHz square wave of 10 V peak-to-peak amplitude. Sketch the input and
output signals on the graph.
+
V in
V out
8-3
Rectified Square Wave
Voltage
Time
Question: Explain how the circuit above works, and why it produces the signal it does.
Question: Reverse the direction of the diode. Is the output as expected? Explain.
8-4
Part B:
The half wave rectifier you constructed converts AC to DC but in general the DC voltage is not
∆V
.
very useful in powering circuitry since it has 100% ripple as defined by the equation r =
VDC
One way to smooth the ripple is to add a filter capacitor as shown in the circuit below.
V in
+
V out
Construct the circuit using a capacitor C = 1 µF (Note the polarization of the capacitor.) and R =
10 kΩ, and drive it with a sine wave with a peak-to-peak voltage of 20 V and a frequency of 1
kHz. Measure the AC ripple voltage (∆V) as defined in Figure 5.12 of your text and compare it
to the expected theoretical value of
I
V
∆V =
where I = DC .
Cf
R
∆V
Calculate the ripple factor r =
.
VDC
∆V = ___________________
VDC = ___________________
C = ____________________
f = _____________________
I = _____________________
r = _____________________
∆V(theoretical) = _____________________
Question: The equation ∆V = I / (Cf) is an approximate one. Does it give a good rough
prediction of the ripple voltage for the above situation? Explain.
8-5
Vary the driving frequency in decade increments from 10 Hz to 100 kHz and complete the
following table.
f
∆V
VDC
∆V = I/(Cf)
r = ∆V/VDC
10 Hz
100 Hz
1 kHz
10 kHz
100 kHz
Question: Discuss how well or poorly the equation ∆V = I / (Cf) describes the ripple voltage as
it varies with frequency.
8-6
Laboratory 9
Zener Diodes
Key Concepts:
• Signal Rectification
• Power Dissipation
Equipment Needed:
• Protoboard
• Oscilloscope
• (2) DMM
Components Needed:
(1) 1 kΩ Resistor
(1) 100 Ω Resistor
(2) Zener Diodes
Overview:
A zener (or regulator) diode is designed to be run “backwards” (with reverse polarity)
and acts to regulate the voltage across its terminals against variation in either the
unregulated input voltage or the load current. For forward bias (where it is generally
never run) it acts like an ordinary diode. For reverse bias it conducts very little current
until the reverse voltage reaches a specific value VZ (the “zener voltage”), at which point
it draws current in the reverse direction to keep the voltage across the diode at almost
exactly VZ. In other words, with an input voltage above the zener voltage, while the
current may vary, the voltage across the diode remains equal to the zener voltage.
Each zener diode is rated for a maximum DC power dissipation Pmax = Iz maxVZ. With
more current than this passing through the diode, the diode will burn out. So for a zener
diode with an input voltage of at least –VZ, ~ 1 mA < | IZ | < Iz max.
The laboratory has two parts:
Part A: Diode Voltage Curves
Part B: Regulating
Procedure
Part A:
Construct the circuit shown, using a 1 kΩ resistor, and with the zenner diode in reverse bias.
9-1
Use two DMMs to measure Vinput and VZ (the voltage across the diode). Vary Vinput from 0 to 15
v in 0.5 v intervals, and graph the results. Explain why the graph looks as it does.
15
14
13
12
11
10
9
Zenner
Voltage 8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Input Voltage
Question: Explain why the graph looks the way it does.
9-2
Use two DMMs to measure Vinput and VR (the voltage across the resistor). Vary Vinput from 0 to
15 v in 0.5 v intervals, and graph the results. Explain why the graph looks as it does.
15
14
13
12
11
10
Resistor 9
Voltage 8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Input Voltage
Question: Explain why the graph looks the way it does.
9-3
Use two DMMs to measure IZ and VZ. Vary Vinput from -5 to 10 v in 0.5 v intervals, and graph
the values of IZ and VZ. Explain why the graph looks as it does.
10
9
8
7
6
5
4
Zenner
Current 3
(mA)
2
1
0
-1
-2
-3
-4
-5
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Zener Voltage
Question: Explain why the graph looks the way it does.
9-4
Part B:
Construct the circuit shown below. Use two different Zenner diodes and a 100 Ω resistor.
Vinput
Voutput
D1
D2
Drive the circuit using a 10 Vp sine wave at 1000 Hz. Use the oscilloscope and sketch the input
signal and the output signal. Be sure the Channel 1 and 2 traces are centered at the same level
using the "GROUND" setting.
Voltage
Time
Question: Determine the Zenner Voltage of each diode. Explain how you did it.
9-5
Question: Drive the circuit with a 5 volt peak signal. Does the output change? Explain.
In the circuit, turn D2 around and sketch the input and output signals with a 10 Volt peak signal.
Voltage
Time
Question: Why does the signal look the way it does?
Question: What is the purpose of the resistor in this circuit?
9-6
Laboratory 10
Transistors
Key Concepts:
• Current Amplification
• Follower
• Voltage Amplification
Equipment Needed:
• Protoboard
• Oscilloscope
• Resistor Substitution Box
• (2) DMM
Components Needed:
(1) 1 kΩ Resistors
(1) each 270 Ω, 2.7 kΩ, 470 Ω, 10 kΩ Resistors
(1) Resistor Substitution Box
(1) 2N3904 Transistor
Overview:
The advent of the transistor marked a turning point in modern electronics. However,
today the use of discrete transistor circuits is limited, although nearly every integrated
circuit is composed of transistors. The use of bipolar transistors as discrete devices will
be explored in this lab. The laboratory has four parts:
Part A: Current Amplification
Part B: Transistor Switches
Part C: Voltage Follower
Procedure
Part A:
What makes a transistor so useful? The answer is that the transistor is a current amplifier -- it
uses a small current to regulate a large current. The figure below shows an NPN transistor, the
2N3904, connected to measure the current into its base (B) and its collector (C). By varying R
with the resistor substitution box, we can vary the current into the base, IB, and measure the
current that flows into the collector, IC. The current that flows out of the emitter, IE, go ground
it, by Kirchoff's Current Law, equal to the sum of IB and IC. The gain of the circuit, β, is the ratio
of the collector current to the base current: β = IC/IB. The gain measure the current amplification
of the transistor -- how much larger current (IC) can be controlled by the small base current (IB).
10-1
Construct the following circuit and use DMMs to measure the current into the base and into the
collector, and calculate the gain. Vary the resistor substitution box (R) from 1 kΩ to 10 MΩ in
increments listed. Caution: Make certain that R never falls below 1 kΩ or the transistor will
+12 V
be destroyed.
A
1 kΩ
C
R
A
+12 V
R
2N3904
B
E
IB
IC
β
1 kΩ
5 kΩ
10 kΩ
50 kΩ
100 kΩ
500 kΩ
1 MΩ
5 MΩ
10 MΩ
10-2
Question: Is the current gain β constant over the range of IB used? Explain.
Part B:
One of the main uses of a discrete transistor is that of a switch. Often one needs to control a
large current source from a small current source. In other words, a high impedance source needs
to drive a low impedance circuit. As a current amplifier the transistor is suited to this task.
Consider the circuit shown below. Here a high impedance source is simulated with a 10 V peakto-peak square wave fed through a 10 kΩ resistor. The maximum current input to the transistor
is thus 5 V / 10 kΩ or 0.5 mA. A light emitting diode (LED) requires more than 0.5 mA to light.
To light the diode we use a transistor switch which turns the diode on and off. When current is
fed into the base of the transistor, the transistor conducts and is said to be ON. The LED lights.
When the base receives no current the transistor is non-conducting and now current flows from
collector to base.
+12 V
LED
470 Ω
C
10 k Ω
+12 V
Construct the circuit and drive it with a 10 V
peak-to-peak square wave with a frequency
less than 1 Hz. Using an oscilloscope or a
DMM, note when the LED is on and when it
is off (VC high or low).
2N3904
B
E
10-3
Question: Explain the operation of the circuit -- especially why the LED turns on when it does,
and what is the purpose of the 470 Ω resistor?
Part C:
In Part B we looked at how the transistor can be used to amplify current in digital (ON or OFF)
situations. The transistor can also amplify the current of analog signals. The circuit shown
below does just that. The input impedance of the circuit is much larger than the output
impedance and thus the driving signal is buffered (not loaded down) by whatever output circuitry
is connected to the output. This circuit is useful when a feeble signal must drive some device
that requires more current than the signal itself can produce.
+12 V
V in
Question: What could be a common
situation where this sort of circuit
would be helpful?
C
270 Ω
2N3904
B
V out
E
2.7 k Ω
Construct the circuit and drive it with a 5 V peak-to-peak sine wave with frequency 1 kHz.
Sketch the input and output on the graph below.
10-4
Voltage
Time
Question: Is there a phase change between the input and output signals?
Question: Does the output signal replicate the input signal? Explain why or why not in terms of
the transistor's function.
10-5
Remove the ground connection and connect it instead to -12 V. Use the same input signal and
sketch the input and output below.
Voltage
Time
Question: Explain why changing the voltage on the emitter changes the output of the emitter
follower.
10-6
Laboratory 11
Digital Gates I
Key Concepts:
• Wiring Digital Gates into Circuits
• Relation between voltage and logic
• Relation between various gates
Equipment Needed:
• Protoboard
Components Needed:
(1) each 7400 (NAND), 7402 (NOR), 7408 (AND),
7432 (OR), 7486 (XOR) gate chips
Overview:
The integrated chip (IC) combines several transistor and resistor elements to put a
number (for this lab, four) digital logic gates onto one chip. Logic gates perform the
mathematical operations of logic on digital signals, where "high" voltage (usually +5
volts) stands for "true" and "low" voltage (ground) stands for "false". In this lab you will
verify the truth tables for several logic gates, investigate the voltage requirements
defining "high" and "low" voltage, and build more complicated gates from simpler ones.
The laboratory has three parts:
Part A: Logic Gate truth tables
Part B: Voltage Requirements
Part C: Logic devices as Gates
Procedure
Part A:
A TTL logic chip has eight pins which must be connected correctly. The chip is designed to
plug into the protoboard across the vertical "gulley" running through the center of the work
areas. The 7400 NAND gate has the following pin configuration:
Vcc
14
13
12
11
10
9
8
Individual NAND
gate
1
2
3
4
5
6
7
GND
11-1
Hook up a 7400 NAND gate. Pay careful attention to the pin assignments, especially power and
ground. Make sure the notch in the IC is on the side of the chip toward the top of the board.
Connect the output of one NAND gate to one of the logic indicator LED's.
Connect one input to power. Connect the other to power, then to ground.
Question: What is the state of a NAND with one input high?
Connect one input to ground. Connect the other to power, then to ground.
Question: What is the state of a NAND with one input low?
Measure and record a complete truth table for all possible input combinations.
Repeat for 7402 NOR, 7408 AND, 7432 OR, 7486 XOR gates.
11-2
Part B:
Design a configuration that negates the input (an inverter), using the 7400 only. Draw a sketch
of the circuit.
Connect the 7400 as an inverter. Connect the two ends of the 10 kΩ potentiometer to +5 v and
ground, and connect the wiper (the middle part) as input to the inverter. Connect the output of
the inverter to the logic indicator LED. Raise the input voltage from 0 v until the output changes
state.
Question: At what voltage does the output change state with a rising voltage? Record this
voltage threshold limit.
Now repeat the process, except start with the input at +5v and slowly reduce the voltage till the
output changes state.
Question: At what voltage does the output change state with a falling voltage? Record this
voltage threshold limit.
Now connect the input to the inverter to +5v, and hook the other input to the potentiometer.
Slowly reduce this input from +5v toward 0 until the output changes state.
Question: At what voltage does this cause the inverter to change state?
Question: Are there any differences in the voltage at which the gate changes state? Explain.
11-3
Part D:
Logic elements are usually called "gates", because they can be used to control the passage of
information (current) based on conditions relative to a clock signal (which is a regular square
wave). Set the TTL function generator output to about 1-100 Hz, and use this as one input to a
gate. For the other input, use either a 1 or 0 (+5 v or ground). Connect both the input (clock)
and output signal to LED's, and compare the results. Sketch the output for a 7400 (NAND),
7408 (AND), 7432 (OR) and 7402 (NOR). Explain why the signals are the way they are.
Results
Signal
(For all cases)
NAND
Signal
Input
High
Input
Low
AND
High
Low
OR
High
Low
NOR
High
Low
11-4
Vcc
14
13
12
11
10
9
8
7400 NAND
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7402 NOR
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7408 AND
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7432 OR
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7486 XOR
1
2
3
4
5
6
7
GND
11-5
Laboratory 12
Digital Gates II
Key Concepts:
• Boolean Logic
• Combining logic gates
Equipment Needed:
• Protoboard
Components Needed:
(1) each 7400 (NAND), 7402 (NOR), 7408 (AND),
7432 (OR), 7486 (XOR) gate chips
Overview:
Logic gates can be combined to make useful logical (Boolean) statements. Converting
action statements to logic allows the statements to be wired up electronically, so the
process of wiring a digital circuit often begins with translating the desired action into a
Boolean expression.
Procedure
Part A:
Logic gates can be strung together to make complex logic statements. To gain experience at this,
wire the logic statements found in Table 11.7 in your text (p. 249). Construct each side of the
statement separately, then send each output to an LED. The inputs should be moveable, so that
you can vary A and B and see if the two sides of the statement give the same result. Construct
five statements from the table, beginning with statement 7. Draw a schematic for the wiring
construction, using the symbol for AND, NAND, NOR and OR gates.
12-1
Part B:
Design and test at least two gate circuits which carry out electronically a logic statement
originally expressed verbally. Sketch the circuit. Some examples might be:
"You can't have your cake and eat it too."
"You can fool some of the people all of the time or all of the people some of the time, but
you can't fool all of the people all of the time."
"With today's lunch special, you can get soup or a salad, plus main dish, and either coffee
or dessert"
Part C:
Using only 7400's, (NAND), try to design and build an AND, OR and NOR gate. Draw sketches
of the circuits. Wire up the circuits and record their truth tables.
If there is time, design and build an XOR or a NXOR gate and sketch the circuit.
12-2
Vcc
14
13
12
11
10
9
8
7400 NAND
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7402 NOR
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7408 AND
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7432 OR
1
2
3
4
5
6
7
GND
Vcc
14
13
12
11
10
9
8
7486 XOR
1
2
3
4
5
6
7
GND
12-3