Laboratory 1 Ohm's Law - Concordia University Nebraskaestrada.cune.edu/facweb/robert.hermann/Portfolio/Phys 371...1-1 Laboratory 1 Ohm's Law Key Concepts: • Measuring resistance,

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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: Components Needed:

• Digital Multimeter (2) (2) 1kΩ Resistors, 5% tolerance

• Variable DC power supply (2) 10 kΩ Resistors, 5% tolerance

• 9 v battery (1) 10 kΩ Resistor, 10% tolerance

• Connections (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 voltage-

current 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.

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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. 1 kΩ (5%)

b. 1 kΩ (5%)

c. 10 kΩ (5%)

d. 10 kΩ (5%)

e. 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.

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.

A

V 9v 1 kΩ

1-3

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.)

1-4

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).

1-5

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.

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)

A

V

10 kΩ

1-6

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?

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Laboratory 2 Kirchoff's Laws

Key Concepts:

• Kirchoff's junction and loop laws

• Equivalent resistance

• Voltage dividers


• Digital Multimeter (2) (1) 270 Ω Resistors

• 12 v DC power supply (1) 2.7 kΩ Resistors

• Breadboard (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.

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Calculated values:

Requivalent = ____________________

IA = ______________________

IB = ______________________

IC = ______________________

VR1 = _____________________

VR2 = _____________________

VPower = ________12 v________

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.

R2

2.7 kΩ

12 v

R1

1 kΩ

A

B

C

2-3

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 = ______________________

IB = ______________________

IC = ______________________

ID = ______________________

VR1 = _____________________

VR2 = _____________________

VPower = ________12 v________

A

R2

1.0 kΩ 12 v

R1

2.7 kΩ

D

B C

2-4

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.

2-5

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.

VR1 = __________________

VR2 = __________________

VR3 = __________________

IR1 = ___________________

IR2 = ___________________

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?

A

R3

1.0 kΩ 12 v

R2

2.7 kΩ

B

R1

1.0 kΩ

2-6

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:

VB = Vpower

R2

R1 + R2

VB(calculated) = ________________

VB(measured) = ________________

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.)

R2

10 kΩ

12 v

R1

5.1 kΩ

B

3-1

Laboratory 3 Thevenin's Theorem

Key Concepts:

• Thevenin's Theorem

• Equivalent resistance and voltage


• Digital Multimeter (2) (2) 100 Ω, 10 kΩ Resistors

• Protoboard (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:

VTH = ______________________

RTH = ______________________

IL = ________________________

RL

2.7 kΩ

15 v

R1

10 kΩ

A

B

R2

10 kΩ

3-2

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

VL = ________________________

IL = _________________________

Question: How do the measured current and voltage compare to the calculated Thevenin values

and to the values measured above?

A

RL

2.7 kΩ VTH

B

RTH

3-3

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.

Resistance RL (Ω) Current IL (A)

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?

A

RL

5 v

B

R

10 MΩ

3-4

Part D:

Construct the circuit below. R2 should be a variable resistor, and R4 is the unknown.

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?

A B

R1 R3

R2 R4

4-1

Laboratory 4 Test Instruments

Key Concepts:

• Digital Multimeters (DMM)

• Oscilloscopes

• AC Signals


• Digital Multimeter (2)

• Oscilloscope (2) 10 MΩ Resistors

• Protoboard (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 .

Measured values:

VPS = ______________________

VR1 = ______________________

VR2 = ______________________

12 v

R1

10 MΩ

R2

10 MΩ

4-2

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.

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 = ____________________________

Rin

12 v

R1

R2 V

4-3

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): Peak-to-Peak Voltage: 2.0 v

Time Scale (s/div): Voltage scale (v/div):

# Major Divisions (Horizontal): # Major Divisions (Vertical):

4-4

Repeat the exercise above with a sine wave with different characteristics:

Period: 0.02 ms Frequency (Hz): Peak-to-Peak Voltage: 4.5 v

Time Scale (s/div): Voltage scale (v/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

R1

10 kΩ

R2

10 kΩ

R3

10 kΩ

A B C D

4-5

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 time-

varying signals, use the oscilloscope to set the function generator to produce a 10 volt peak-to-

peak 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.

4-6

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 1 k 10 k 100 k

Question: What can you say about the frequency limitations of the DMM?

5-1

Laboratory 5

Transient RC Circuits

Key Concepts:

• Transient signals

• Exponential charging and discharging

• Time Constant

• Differentiation and integration of signals


• Oscilloscope (1) 10 kΩ Resistor

• Protoboard (1) 0.01 µF Capacitor

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

5-2

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.

5

4

3

2

1

0

0 1 2 3 4 5 6

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.

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 = ____________________

Time (ms)

Voltage

(V)

V in

V out

5-3

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).

Voltage

(V)

Time

Voltage vs Time

5-4

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.

Question: Why is the circuit above called an integrator?

Square Wave Input

Voltage

Time

Sine Wave Input

Voltage

Time

5-5

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.

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.

V in

V out

Voltage

Time

5-6

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.

Question: Why is the circuit above called a differentiator?

Square Wave Input

Voltage

Time

Sine Wave Input

Voltage

Time

6-1

Laboratory 6

AC Circuits and Filters

Key Concepts:

• Voltage and Phase Relations in AC Circuits

• Low-pass, High-pass and Bandpass filters


• Digital Multimeter (2) 10 kΩ Resistor

• Oscilloscope (1) 2.7 kΩ Resistor

• Protoboard (2) 0.01 µF Capacitor

(1) 1 µF Capacitor

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 = _______________________

VR = _______________________

VC = _______________________

Question: Is Vin what you expected? Explain.

V in

V out

6-2

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.

10 100 1000 10,000 100,000

Frequency (Hz)

Voltage

6-3

90

45

0

-45

-90 10 100 1000 10,000 100,000

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?

Phase

(Degrees)

Frequency (Hz)

6-4

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.

10 100 1000 10,000 100,000

90

45

0

-45

-90 10 100 1000 10,000 100,000

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 = ___________________

Frequency (Hz)

Voltage

Phase

(Degrees)

Frequency (Hz)

6-5

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 in

V out R1

10 kΩ R2

10 kΩ

C1

0.01 µF

C2

0.01 µF

6-6

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.

10 100 1000 10,000 100,000

90

45

0

-45

-90 10 100 1000 10,000 100,000

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?

Frequency (Hz)

Voltage

Phase

(Degrees)

Frequency (Hz)

7-1

Laboratory 7 RLC Circuits

Key Concepts:

• RLC Transients

• Bandpass Filter and Quality Factor


• Digital Multimeter (1) 100 Ω, 1 kΩ Resistors

• Oscilloscope (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

7-2

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.

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?

Voltage

Time

7-3

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.

Question: Why does this signal differ from the result at 100 kHz? Explain mathematically and

in terms of current and voltage in the elements.

Voltage

Time

7-4

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.

10 100 1000 10,000 100,000

90

45

0

-45

-90 10 100 1000 10,000 100,000

Phase

(Degrees)

Voltage

7-5

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:

Q =ωoL

R=

2πfo L

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

7-6

Question: The notch frequency for the above circuit (the frequency which is most attenuated) is

calculated with the same formula as for the bandpass filter: fo =1

2π LC. Calculate the notch

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.

10 100 1000 10,000 100,000

90

45

0

-45

-90 10 100 1000 10,000 100,000

Question: From your graph, determine fo. How does it compare with the calculated value?

Explain any discrepancies.

fo (measured) = _________________________

Phase

(Degrees)

Voltage

8-1

Laboratory 8 Diodes: Rectification & Filtering

Key Concepts:

• Signal Rectification

• Filtering


• Protoboard (2) 1 kΩ Resistors

• Oscilloscope (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.

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.

V in V out

Actual

Device

Schematic

8-2

Voltage

Time

Sine Wave

Voltage

Time

Square Wave

8-3

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

+

8-4

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.

Voltage

Time

Rectified Square Wave

8-5

Part B:

The half wave rectifier you constructed converts AC to DC but in general the DC voltage is not

very useful in powering circuitry since it has 100% ripple as defined by the equation r =∆V

VDC

.

One way to smooth the ripple is to add a filter capacitor as shown in the circuit below.

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

∆V =I

Cf where I =

VDC

R.

Calculate the ripple factor r =∆V

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.

V in V out

+

8-6

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.

9-1

Laboratory 9

Zener Diodes

Key Concepts:

• Signal Rectification

• Power Dissipation


• Protoboard (1) 1 kΩ Resistor

• Oscilloscope (1) 100 Ω Resistor

• (2) DMM (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.

9-2

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

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

Question: Explain why the graph looks the way it does.

Zenner

Voltage

Input Voltage

9-3

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

9

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


Resistor

Voltage

Input Voltage

9-4

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

3

2

1

0

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10


Zenner

Current

(mA)

Zener Voltage

9-5

Part B:

Construct the circuit shown below. Use two different Zenner diodes and a 100 Ω resistor.

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.

Question: Determine the Zenner Voltage of each diode. Explain how you did it.

Voltage

Time

Vinput Voutput

D1

D2

9-6

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.

Question: Why does the signal look the way it does?

Question: What is the purpose of the resistor in this circuit?

Voltage

Time

10-1

Laboratory 10 Transistors

Key Concepts:

• Current Amplification

• Follower

• Voltage Amplification


• Protoboard (1) 1 kΩ Resistors

• Oscilloscope (1) each 270 Ω, 2.7 kΩ, 470 Ω, 10 kΩ Resistors

• Resistor Substitution Box (1) Resistor Substitution Box

• (2) DMM (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).

10-2

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 kΩΩΩΩ or the transistor will

be destroyed.

R IB IC β

1 kΩ

5 kΩ

10 kΩ

50 kΩ

100 kΩ

500 kΩ

1 MΩ

5 MΩ

10 MΩ

A B

C

E

A

R

1 kΩ

+12 V

+12 V

2N3904

10-3

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 peak-

to-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.

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).

B

C

E

470 Ω

10 k Ω

+12 V

+12 V

2N3904

LED

10-4

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.

Question: What could be a common

situation where this sort of circuit

would be helpful?

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.

B

C

E

2.7 k Ω

270 Ω

V in

+12 V

2N3904

V out

10-5

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.

Voltage

Time

10-6

Remove the ground connection and connect it instead to -12 V. Use the same input signal and

sketch the input and output below.

Question: Explain why changing the voltage on the emitter changes the output of the emitter

follower.

Voltage

Time

11-1

Laboratory 11 Digital Gates I

Key Concepts:

• Wiring Digital Gates into Circuits

• Relation between voltage and logic

• Relation between various gates


• Protoboard (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:

14 13 12 11 10 9

1 2

8

3 4 5 6 7

Vcc

GND

Individual NAND

gate

11-2

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.

11-3

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.

11-4

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 Input

Signal High

Input

Low

AND

High

Low

OR

High

Low

NOR

High

Low

11-5

14 13 12 11 10 9

1 2

8

3 4 5 6 7

Vcc

GND

Vcc

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

14 13 12 11 10 9

1 2

8

3 4 5 6 7

Vcc

GND

7400 NAND

7402 NOR

7408 AND

7432 OR

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

Vcc

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

Vcc

7486 XOR

12-1

Laboratory 12 Digital Gates II

Key Concepts:

• Boolean Logic

• Combining logic gates


• Protoboard (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.

12-2

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.

12-3

14 13 12 11 10 9

1 2

8

3 4 5 6 7

Vcc

GND

Vcc

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

14 13 12 11 10 9

1 2

8

3 4 5 6 7

Vcc

GND

7400 NAND

7402 NOR

7408 AND

7432 OR

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

Vcc

14 13 12 11 10 9

1 2

8

3 4 5 6 7

GND

Vcc

7486 XOR

Laboratory 1 Ohm's Law - Concordia University Nebraskaestrada.cune.edu/facweb/robert.hermann/Portfolio/Phys 371...1-1 Laboratory 1 Ohm's Law Key Concepts: • Measuring resistance,

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