ECE 231 Laboratory Manual 090112 (Word 10)

8/10/2019 ECE 231 Laboratory Manual 090112 (Word 10)

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ECE 231 Elements of Electrical Engineering

Laboratory Manual

Prepared by R. Frank Smith

California State Polytechnic University, Pomona

Reference TextStudent Reference Manual for Instrumentation Laboratories, Wolf and Smith, Prentice Hall, 2004

Revised 09/01/12


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R. Frank Smith, California State Polytechnic University, Pomona, 2012 Page i

Table of Contents

Exercise 1 - Ohm's Law 1

Exercise 2 - Kirchhoff's Laws 7

Exercise 3 - Oscilloscope/Function Generator Operation 11

Exercise 4 - Thvenin's and Norton Theorems 16

Exercise 5A - Diode Characteristics 22

Exercise 5B - Diode Characteristics 28

Exercise 5C - Diode Characteristics 32

Exercise 6Frequency/Time Response of RL and RC Circuits 35

Exercise 7 - Resonant Circuits

Exercise 8Time Domain Response of 2nd

Order Circuits

42

47


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ECE 231 Laboratory Exercise 1

Ohms Law

R. Frank Smith, California State Polytechnic University, Pomona, 2012 Page 1

ECE 231 Laboratory Exercise 1Ohms Law

Laboratory Group (Names) _______________ ______________ _______________

OBJECTIVES

Verify Ohms Law

Learn to read resistor color codes

Learn to use ohmmeter, voltmeter, and ammeter

Learn to calculate power loss in resistors

EQUIPMENT REQUIRED

ECE 231 Circuit Board (In Stock room)

One banana cable

One lot of clip leads (students must supply their own clip leads)

DMM (digital multimeter)

DC power supply

BACKGROUND

Resistors are used for many purposes such as electric heaters, voltage, and current dividing elements, and

current-limiting devices. As such, their resistance values and tolerances vary widely. Resistance tolerances mayrange from +0.001 to +20%. The most common types of resistors are carbon composition, wire wound, metal

film, carbon film, steel, and liquid. Their ratings can range from microwatts to megawatts. Variable resistors are

called either potentiometers or rheostats. When used as a potentiometer their output is a variable voltage.

When used as a rheostat they are used to control current. A good reference source is

http://en.wikipedia.org/wiki/Electronic_color_code. Review this website before you come to the laboratory.

Many types of resistors do not have a color code such as resistors made to military specifications and surface

mount resistors. You might remember the following mnemonic to remember the color versus number code:

Bad (0) Boys (1) Race (2) Our(3) Young (4) Girls (5) But (6) Violet(7) Generally (8) Wins (9).

Black Brown Red Orange Yellow Green Blue Violet Grey White

Most resistors use either 4 or 5 bands of colors. The 5 band color is usually used for 1% and 0.1 % resistors.

This band represents 5% if gold, 1% if brown, and fire resistant if yellow.

When you observe a resistor it is not always possible to predict its wattage by just observing its size. There are

many variables that affect a resistors wattage. Some such parameters are size, mounting, encapsulation, and

cooling. There are three ways you can calculate the power being dissipated in a resistor in this laboratory. See


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Ohms Law


Eq.1. In a thermodynamics' laboratory you could measure the rise in temperature of water in a calorimeter to

determine the power being dissipated by a resistor. Consider the following design problem. What size (ohms

and wattage) resistor would you use for the heating element in a coffee maker or toaster? Assume 120 VAC and

300 watts.

(1)

The resistance of a resistor can be approximated by equation (2):

Resistance (R)= (2)

Where resistivity of the material; L = length of material; and A is the area of the material. The material maybe solid, liquid, or gaseous. Each of these parameters is often functions of temperature and stress. Liquid isoften used for low resistances rated in the megawatts.

Part 1. There are 7 resistors and one potentiometer on the BOARD. Determine and record the values of the 7

resistors and the potentiometer and their associated color code if appropriate. See your text or the internet for

the color code. Measure each resistor with an ohmmeter then see how that relates to the color code. We will

assume the color code is the Theoretical Value. See Figure 1.

Figure 1. Experimental board for ECE 231 experiments.


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Ohms Law


Table 1. Resistor color codes

Measured

Value

Color Code Theoretical

Value (Color Code)

% error

Experimental

Discrepancy

Part 2. Connect a variable voltage supply to threedifferent resistors and vary the voltage from 0 to 10 volts. See

Figure 2. If the overload light is illuminated you may have tripped the overload protective device. Press the red

reset button to reset the overload device.

Figure 2. Variable voltage supply. Use cable with banana plug. Notch side goes to black.

Plot the current versus the voltage in Figure 4 for each resistor. Label each curve with its resistance value.

There is both a Fluke and Beckman multimeter that can be used to measure the current. See Figure 3. How does

the plot verify Ohms Law? What can you say about the slope of the plots? Calculate the slopes and show that

they are equal to 1/R.


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Ohms Law


Hint: All of the curves go through zero so only one additional point for each resistor is required to generate the

Ohms Law curve. Simply set the voltage supply at one voltage (for example 10 volts) for all the resistors and

then measure the current in each resistor. Verify the current using Ohms Law.

Figure 3. Laboratory bench equipment.

Figure 4. Plot for verifying Ohm's Law,


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Ohms Law


How does the plot verify Ohms Law? What can you say about the slope of the plots? Calculate the slopes and

show that they are equal to 1/R.

What are the possible ways to measure the current through a resistor? There are several ways. How do you

calculate the current through a resistor under test without using an ammeter? For a circuit board with surface

mounted resistors you would usually use the calculation method. Calculation of the measure of uncertainty for

each method is different. A good reference source for error analysis is the Reference text or

http://www.lhup.edu/~dsimanek/errors.htm.

Part 3. Connect a small resistor (less than 100 ohms) to the variable power supply. Gradually increase the

voltage and feel, using your finger, the increase in the temperature of the resistor. Only increase the voltage so

that the wattage lost in the resistor is less than 1/2 watt. What voltage created a watt loss? At what wattage

does the resistor get too hot to touch? Comment on how hot the resistor gets when it is dissipating 1/4, 1/3, and

1/2 watt. Hint: Power = V2/R. Resistors are available on the 5th floor in the student work area and stock room.

CAUTION

Going beyond watt can cause the resistor to explode or ignite. A 100 ohm resistor will dissipate watt at 5

volts. You will usually see smoke or fire at watt. Do NOT exceed 7 volts for a 100 ohm resistor.

Table 2. Wattage versus resistor temperature

Measured Test Value Temperature

Check appropriate box

Comments

Resistance Voltage Wattage Ambient Warm Hot

1/4

1/3

1/2

Voltage


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Ohms Law


Part 4. Write a professional comprehensive laboratory report using a word processor. Show your

results, calculations, error analysis, and include a comprehensive conclusion. There are lots of sample

lab reports on the internet. Every figure must be sequentially numbered and referenced in the

preceding text. Your calculations may be handwritten and attached to the report if properly

referenced in the text. Number all pages.

On the cover page of your laboratory report include the number and tile of the experiment, date

performed, and laboratory partners.

Conclusion or comments.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________


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Oscilloscope/Function Generator Operation


ECE 231 Laboratory Exercise 2Kirchhoffs Laws


OBJECTIVE

Verify Kirchhoffs voltage law

Verify Kirchhoffs current law

Gain experience in using both an ammeter and voltmeter

Construct two (2) circuits as shown in Figure 1 and Figure 2.

Figure 1. Schematics for verifying Kirchhoff's Laws

EQUIPMENT REQUIRED


Two banana cables (one for DC power supply and one for DMM)

One lot of clip leads (students must supply their own clip leads)


DC power supply

BACKGROUND

Gustav Kirchhoff first described his laws in 1845. His first law KCL simply stated is that current into a

node must equal the current leaving a node where a node is the point where two or more components

are connected together. In Figure 1 above, the three currents I1, I2, and I3 leave the top node and go

through the three resistors and then merge on the ground circuit. The voltage across any parallel

resistors is always the same. Current through any resistor can be determined by using Ohm's law.

R1

R2

R3

R3R2R1

V110Vdc

V110Vdc

0

0

Ammeter

Ammeter

I

Parallel Circuit

Series Circuit

1 2I

3I

BA

E

D

C


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or by measuring the current through each resistor using an ammeter.

Kirchhoff's Current Law (KCL)

where is the n is the number of branches at a node.

Kirchhoff's Voltage Law (KVL) where is the n is the number of components (resistorsand voltage sources) in a loop.

Kirchhoff's second law is like going on a hike from your car around a mountain (independent of path).

When you get back to your car, your net change in potential energy is zero. No matter how you

measure voltages around a circuit, when you return to your starting point the change in voltage is zero.

Figure 2. Protoboard connection for the series circuit

PROCEDURE

Part 1

Select three adjacent resistors and connect them in SERIES with your power supply. Now measure the

voltage at each node (A thru E) in your circuit.


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1. Measure the voltages at all of the nodes relative to the power supply ground. Show that the

sum of the voltages ACROSS all of the components in a loop complies with Kirchhoffs voltage

law. Complete Table 1.

Table 1. Voltages across each component and current through each resistor

VEA VAB VBC VCD VDE

Calculated IR1= Calculated IR2= Calculated IR3=

Measured IR1= Measured IR2= Measured IR3=

Power Power Power Power Power

2. Now measure the node voltages relative to node C. For example, Vca = -Vac which says that

the voltage from c to a = minus the voltage from a to c. The voltages at the nodes relative to

ground will not add to zero to prove Kirchhoffs voltage law. It is the sum of the voltages across

each component in a series that add to zero NOT the sum of the node voltages. Remember, the

reference node in a circuit can be anywhere you want in a real circuit.

Table 2. Node voltages relative to node C (i.e. C is connect to the black meter lead)

VCA VCB VCC VCD VCE

0

NOTE Remember, the reference node in a circuit can be anywhere you want in a real

circuit; therefore the voltage at a node will most likely change depending upon your

reference.

3.

Calculate the power delivered by the power supply. Show that it is equal to the power

consumed by the resistors. Enter the power into Table 1.


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CAUTION

Never connect an ammeter in parallel with the component you are trying to measure the current

through. The ammeter is in essence a short circuit and must be in series with the components through

which current is being measured. An error in the connection could seriously damage the ammeter and

other circuit components.

Part 2.

Select three resistors and connect them in PARALLEL with your power supply. Now measure the

current from the power supply. This procedure is NOT shown in Figure 2. It is up to you to figure out

the connection scheme since only the power supply ammeter connection is shown in Figure 1. You

only have one ammeter. Therefore, rewire each branch circuit with the ammeter in SERIES with the

branch circuit resistor. Verify the ammeter reading using the calculation method and a voltmeter.

1. Measure the source current and the branch currents I1, I2, and I3. Show that the currents

comply with Kirchhoffs current law. If you read any negative currents with your ammeter,

what did you do wrong?

2. Calculate the power delivered by the power supply. Show that it is equal to the power

consumed by the three resistors.

Table 3. Currents in the parallel circuit of Figure 1.

I Source= I1+I2+I3 I1 I2 I3

Measured = Measured= Measured= Measured=

Calculated= Calculated= Calculated=

Power= Power= Power= Power=

Write a professional comprehensive lab report using a word processor. Show your results and

include a comprehensive conclusion. There are lots of sample lab reports on the internet.

Conclusion

_______________________________________________________________________

________________________________________________________________________

_______________________________________________________________________


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ECE 231 Laboratory Exercise 3Oscilloscope/Function Generator Operation


OBJECTIVES

Gain experience in using an oscilloscope to measure time varying signals.

Gain experience in using a signal generator to create time varying test signals.

Gain experience in properly using an oscilloscopes controlsand soft keys.

Learn the frequency limitations of instruments.

EQUIPMENTREQUIRED

One banana cable

Three BNC cables

One lot of clip leads and/or jumper wires


Use the DC offset in signal generator for the DC power supply

Signal generator

BACKGROUND

The oscilloscope is primarily a voltmeter forobserving time varying signals. It has a fairly low inputimpedance of one megohm (1M ) so it cannot be used when a load impedance of this size woulddistort the signal being measured. It is an excellent tool for measuring transient phenomenon such as

impact forces on a load cell. Modern oscilloscopes can operate in both a digital mode and analog

mode. They also have built-in computers for doing signal analysis such as Fourier transforms on the

incoming signal. This type of measurement and analysis would be very useful in measuring impact

response of a suspension system.

It is important that you do not indiscriminately turn the controls especially if you have not been

instructed in their use and function. This can prevent the oscilloscope from being able to properly

display an incoming signal.

An ideal meter will not disturb the circuit when taking measurements. Multimeters and oscilloscopes

are not ideal instruments. You can determine the root-mean-square (rms) value of a sine wave

displayed on an oscilloscope by the following equation:


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If you are using one of the new digital oscilloscopes, you can read waveform parameters on the lower

menu which displays Vrms, Vp-p, and frequency. and phase The voltage from a household outlet is 120

VAC. This is the rms value. The peak value is 1.414 *120= 169.7 voltages. The heating value of 120

VAC rms is exactly equal to a 120 VDC voltage source such as a photovoltaic panel.

PROCEDUREPart 1

1. Connect channel 1 of the oscilloscope to the signal generator and to the digital multimeter (set

to voltage). See Figure 1. Make sure that the ground on the oscilloscope and signal generator

are connected together. Both are internally grounded to the building ground system.

2.

Set the signal generator to 1 KHz, 5 V pk-to-pk for each of the following waveforms: sine wave,

triangle wave, and square wave. Increase the frequency to 10 kHz, and then 100 kHz. Connect

a BNC cable to both the signal generator and the oscilloscope channel 1 (two cables required).

Connect the red clip leads together. Plug your banana cable into the multimeter then connect

the red clip to the red clip leads going to channel 1 and the signal generator. See Figure 1. The

instruments are internally connected to the black lead so you shouldnt have to do anything

with the black lead. You can connect them all together if you want. The black lead should be at

earth ground potential. Make sure the trigger is set to channel 1.

3. Plot what you see on the oscilloscope screen. in Figure 2. You can copy the signal seen on the

oscilloscope and paste it into your lab report so that you dont have to draw it by hand.

4. Compare the readings on the multimeter with what you see on the oscilloscope. Place the

results in Table 1. Add dc offset to your input signal and describe what happens on the

oscilloscope. Try to read just the offset using the multimeters and the oscilloscope. Change the

oscilloscope Vertical Mode from GND, to AC, and then to DC. On the dc setting you see both the

dc and ac signal. In the ac setting you only see the ac waveform. Describe what happens to

the waveform displayed on the oscilloscope with and without DC offset. The multimeter should

not be able to read the voltage as accurately as the oscilloscope. Record your readings in Table

1. The oscilloscope will automatically display the signals voltage value and frequency

automatically. Use the soft keys to select voltage and time measurements.


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Figure 1. Test Setup

Time (sec.,msec., sec.)

Figure 2. Oscilloscope Display


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Table 1. Measured and calculated results

Waveform Oscilloscope

reading Vp-p

Multimeter

reading

Frequency Calculated RMS

voltage

Sine wave 1 k Hz

Sine wave +5dc 1 k HZ

Triangular 1 kHz

Square 1 kHz

Sine wave 10 kHzSine wave +5dc 10 kHz

Triangular 10 kHz

Square 10 kHz

Sine wave 100 kHz

Sine wave +5dc 100 kHz

Triangular 100 kHz

Square 100 kHz

5.

Now slowly increase the frequency of the function generator until the multimeter has an error of at

least 10%. The voltmeter reading will be less than the oscilloscope reading.

6.

What is the frequency limitation of the multimeter. ______________ Hertz. Sine wave

7.

What is the frequency limitation of the multimeter. ______________ Hertz. Square wave

8. What is the frequency limitation of the multimeter. ______________ Hertz. Saw tooth wave

Notes: If the amount of heat (joules) generated by a DC source ( ) is equal to the heat generatedby an ac source over the same period T ,( . Equating the energies and solving results in . The following are equations for common waveforms:Sine wave ; square wave ; triangle wave


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(Hz) = 9. Describe how you measure the frequency of a waveform from the oscilloscope display if you

didnt have soft keys to measure it automatically

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

10.Why does the multimeter reading decrease as the frequency increases?

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Hint: See Exercise 6. The input circuit topology to many analog voltmeters is usually a low pass filter.

Write a professional comprehensive lab report using a word processor. Show your results and include

a comprehensive conclusion. There are lots of sample lab reports on the internet.

Conclusion

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________


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Thvenin and Norton Theorems


ECE 231 Laboratory Exercise 4Thveninand Norton Theorems


OBJECTIVES

Learn various ways to measure Thvenin's voltage and resistance.

Validate the maximum power theorem.

EQUIPMENTREQUIRED





One DC power supply

Four or more resistors (available in bins adjacent to stock room, 5thfloor). Select various sizes

Potentiometer for variable load10K or larger. It should be twice as big as your largest resistor

BACKGROUND

Thvenin's Theorem (1883) states that any linear circuit can be replaced by a single voltage source and a

single series resistance. In 1926 Nortons Theoremwas shown to be equal to Thvenins Theorem, see

Figure 1. You might wonder why the 43 year delay between the two theorems. Batteries were easy to

construct and incorporate into a circuit. No one knew how to make a good constant current source.

We do not have current sources available in the lab to verify Norton's theorem, but it can be calculated

using Ohms Law. Constructing constant current sources is beyond the scope of this course.

Thvenin's

Voltage

Source

Thvenin's

Resistance

Vout Norton

Current

Source

Thvenin's

Resistance

Vout

=

Figure 1. Thvenin's and Nortons equivalent circuits for a Linear Circuit

Procedure for Finding the Thvenin Equivalent Circuit Mathematically

A.

Circuits with independent sources only. No Dependent sources.

Step 1. Find RThvenin


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1.

Deactivate all of the independent sources by shorting all batteries or DC supplies and opening all current

sources.

2. The equivalent resistance between the terminals for which you would like to know the Thvenin

resistance is found by combining all of the resisters into one equivalent resistance between the

appropriate terminals. These are usually designated a and b.

3.

A load resistor which is equivalent to the Thvenin resistance will result in maximum power beingdissipated in the load resistor and of the input voltage will be across the load.

2

maximum

4

th

th

VPower

R

Step 2. Find V Thveninbetween terminals a and b.

1.

Use the original circuit and nodal analysis to find the voltage between terminals "a" and "b."

B.

Circuits with independent and dependent sources.


1.

Deactivate all of the independent sources by shorting all batteries or DC supplies and opening all current

sources.

2.

Connect a 1 amp your current source between terminals "a" and "b."

3.

Find the voltage between terminals "a" and "b using nodal analysis. This voltage will be the Thvenin

resistance by the use of Ohm's law.

Resistance1

abab Thevenin

VVoltageR R

Current

Step 2. Find V Thveninbetween terminals a and b.

1.

Use the original circuit and nodal analysis to find the voltage between terminals "a" and "b."

C.

Circuits with dependent sources only. No independent sources.

These circuits cannot output any power as such they reduce to a Thvenin resistance only.



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1.

Connect a 1 amp your current source between terminals "a" and "b."

2.

Find the voltage between terminals "a" and "b. This voltage will be the Thvenin resistance by the use

of Ohm's law.

Resistance1

ab

ab

Voltage

Current

VV

3.

Find this voltage using nodal analysis.

Thvenin's and Nortons Theorems are expressed mathematically by equation 1.

(1)Measuring Vopen circuitjustrequires a single voltmeter measurement by definition.

CAUTION

Do not attempt to measure I short circuitby shorting your circuit under test. This can be hazardous to

both you and the circuit, especially when testing industrial power circuits.

Determining the short circuit current is extremely important in the design of power distribution

systems. When you examine the circuit breakers on your home power panel you will notice that the

manufacturer has the Short Circuit capacity prominently displayed on the circuit breaker. It will be

either 5000 A or 10,000 A. For industrial plants it can go as high as 200,000 A. Installing a circuit

breaker with a smaller short circuit rating than that which can be supplied by the utility company can

result in an explosion and fire. The short circuit capacity of a circuit determines the fuse size you use to

protect electronic circuits.

Small current sources are frequently used in many electronic circuits and integrated circuits; however,

they are rarely used in industrial power circuits. They are also commonly used to drive light emitting

diodes (LEDs).

The maximum power theorem states that the maximum power will be delivered to a load when the

load resistance is equal to the Thvenin's resistance.This is the basis for selecting the resistance of a

speaker system for a stereo. This assures that in the design stereo systems that maximize the power

will be delivered from the amplifier to the speakers.


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PROCEDURE

Part 1

1. Choose three resistors for R1, R2, and R3. Measure their resistance values using the

multimeter. Do not use the color code to determine the resistance value. Choose three

resistors that are reasonably close in value. Do not pick, for example, 10K, 300, and 100 ohms.

The 10 K resistor will make it difficult to get good experimental results. You should realize by

now that the resistor color codes are not an accurate way to determine resistor values.

2. Construct the circuit shown in Figure 1 on the protoboard. Use either a 5 V or 10 V source.

Using a multimeter, measure the voltage between points a and b with NO LOAD connected.

Record your measurement in column 6. This is Thveninby definition.

3. Remove the Vdc power source and connect a jumper between 1 and 2. This is the same as

shorting the supply voltage mathematically. Now measure the resistance between a and b

using your multimeter. By definition this is RThvenin. Record this value in Table 1. Column 1.

4.

Calculate RThveninby combining the series and parallel resistors with the source disabled

(shorted). Record this value in Table 1. Column 2. Now compare your measured value and

calculated values in order to perform an error analysis. Enter this value in column 3.

Figure 1. Linear resistor circuit.

5. We are now going to determine RTheveninin another way. Connect a load to your circuit

constructed in step 2. For best results the load resistance should be in the same range as your

estimated RThevenin.

6. Now measure the output voltage between a and b in order to make the appropriate

calculation. Divide this voltage by Rload. This will be the current going through the Thvenin

equivalent circuit.

7. Simply apply Ohms Law to find rThevenin..

(2)8. How does this RThevenin compare to the value determined in column 2. Calculate % difference

between columns 2 and 4 then enter this value in Table 1, column 5.

0 "b""2"

R1

R3

V1

10 Vdc

"1"R2

"a"

Rload


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Table 1. Measured and calculated data.

1 2 3 4 5 6 7 8

RTheveninMeasured

with sources

removed

(shorted)

RTheveninCalculated 1

with sources

removed

% Error

between

measured

and

calculated

RTheveninCalculated 2

using Ohms

Law and an

Rload

% Difference

between

calculated 1

and

calculated 2

VabMeasured

VabCalculated

% Error

Thveninvoltage

measuredand

calculated

Part 2

1. Now construct the circuit shown in Figure 1, but replace Rloadwith a potentiometer

connected between a and b. The equivalent circuit is shown in Figure 2. We will now

determine rThvenin using the potentiometer.

2.

Measure the voltage between a and b as the potentiometer is adjusted.

3. Adjust the potentiometer wiper until the voltmeter reads VThvenin/2 NOT Vsource/2. The

potentiometer is now set at the maximum power load which is equal to rThvenin

4. Calculate the maximum power delivered to the load using equation (3).

5. Measure the value of the potentiometer and determine how close it is to the value of

rThvenin determined above.

(3)

Figure 2. Maximum power circuit.

6.

Now prove that this is the load for maximum power. There are resistor values above andbelow the maximum power point resistor that have equal powers since the solution to the

maximum power equation is a quadratic equation. Prove it by measuring the voltage Vab

across the potentiometer after the potentiometer is rotated 1 turn CW. Then measure the

potentiometer resistance at this position. Calculate the power delivered to the

potentiometer using equation (3).

0

Rload

0

V1

VPotentiometer

Wiper

Thevenin

V1

TheveninVRload

Thevenin

Thevenin

R R


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( ) (3)7. Repeat step 4, but this time rotate the potentiometer 2 turns CCW (1 turn to get back to the

maximum power resistance then one additional turn). Calculate the power delivered to the

potentiometer using equation (3). Compare results.

P1 turn CW= __________ Pmax= _________ P2turns CCW= ___________

This value must be less than Pmax This value must be less than Pmax

Conclusion

____________________________________________________________________________________

____________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________


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ECE 231 Laboratory Exercise 5A

Diode Characteristics


ECE 231 Laboratory Exercise 5ADiode Characteristics

The preferred Exercise is shown in Exercises 5B or 5C.

Laboratory Group (Names) ____________________ ___________________ __________________

OBJECTIVES

Validate the Schottky diode equation.

Calculate the dc and dynamic (ac) resistance of a diode.

Observe the rectifying characteristics of a diode.

EQUIPMENTREQUIRED



One lot of clip leads and/or jumper wires DMM (digital multimeter)

One DC power supply

One diode

Four or more resistors (available in bins adjacent to the 5thfloor stock

BACKGROUND

The Schottky diode equation (1) is a very good approximation of how an actual diode behaves in the

laboratory. The plot of this equation is shown in Figure 1. The experiment will be to investigate theproperties of a diode in quadrant I and III. Most diodes if operated in the breakdown region (far left)

will be destroyed. There are however diodes made to operate in this region, and they are called zener

diodes. The next region (center) is the reverse region. This is the normal region when a diode is

reverse biased. The next region, quadrant I, is the normal forward biased region.

( )Some definitions

Isis the reverse saturation current and is approximately equal to 10-12

A. It is sometimes referred to as

Ioor Ir. This current is proportional to the area of the diode. We will not measure this current in this

experiment.

VD= diode voltage, nis approximately 1 to 2. Use 1 for this lab. VTis 26 mV at 300oK.

VDshould be in the range of 0.6 to 0.75 V for silicon diodes and 0.3 V for germanium diodes.is usually

taken as 1.


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Some industrial diodes can be several inches in diameter. Common ones used by students are shown

in Figure 2. The ones used on circuit boards with surface mounted components are only about 1 or 2

mm across. See Figure 3 for typical electronic schematic symbols for diodes. Photodiodes may receive

light or output light (Light Emitting Diode LED). Zener diodes are designed to operate in the

breakdown region. There breakdown voltage can range from several volts to tens of volts.

Figure 1. Plot of diode characteristic equation. Source: Wikimedia Commons
http://upload.wikimedia.org/wikipedia/commons/a/a5/Diode-IV-Curve.svg


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Figure 2. An assortment of typical diodes.

Anode

Anode Cathode

Cathode+

+ -

-

General purpose diode

Zener diode

Photodiode or LED

Figure 3. Electronic symbols for diodes.

PROCEDURE

Part 1

1. Construct the circuit shown in Figure 4 on the protoboard. Identify three resistors on the

protoboards with values of 100, 1K, and 10K. Measure the resistor values using the

multimeter. Do not use the color code to determine the resistance value. You are going to

construct three circuits using these resistors.


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2. Measure and calculate the voltages, currents , and rac for Table 1.

Figure 4. Linear resistor network.

Table 1. Diode Data

Vs = 10

Plot data in Figure 5

I diode=

V1/R1

V diode=

Vs-V1rac

R1 I = V1/R1 Vdiode =

Vs-V1

Vs = 8

R1 = 1000

100 Vs = 12

R1 = 1000

1000 r ac =

10000

3. Plot the diode curve in Figure 5. Alternatively, you can copy the oscilloscope display and

paste it in your lab report when performing experiments 5B or 5C.4. Connect the circuit shown in Figure 4, but replace the DC sources with a 1 KHz, 5 V sine

wave and replace the multimeter with the oscilloscope. Set R1 = 1000 ohms. Draw your

results in Figure 6.

R1 = 100

R1 = 1000

R1 = 10000

0

V1D1

DIODEV1

10Vdc R1

Vs

Multimeter(volts)

10


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Diode Voltage X 10-1

Figure 5. Diode Characteristic Curve

Time

Figure 6. Wave rectifier oscilloscope trace

1 2 3 4 5 9876 10

0

0

1

2

3

4

5

6

7

8

9

urrent-

-5

0 1 2 3 4 5 6 7 8 9 10

olta

e

-4

-3

-2

-1

0

1

2

3

4

5


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1. Write a professional comprehensive lab report using a word processor. Show your results

and include a comprehensive conclusion. There are lots of sample lab reports on the

internet.

Conclusion

_____________________________________________________________________________


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ECE 231 Laboratory Exercise 5B



ECE 231 Laboratory Exercise 5B -Diode Characteristics

OBJECTIVES

Validate the Schottky diode equation. Calculate the dc and dynamic (ac) resistance of a diode.

Observe the rectifying characteristics of a diode.

EQUIPMENTREQUIRED


Three BNC cables



One AC power supply

Diode circuit (two diodes and two resistors) supplied by instructor or you can construct your own.

Oscilloscope with XY Mode capability

BACKGROUND

See experiment 5A.

This is an alternate method of measuring a diode characteristic using an oscilloscope. This is a much better

method and gives good results so long as the two diodes are reasonably matched. If you need better results

then use a commercial Curve Tracer. The method described in 5A is very labor intensive and is not

recommended. This method also allows the student to experiment with -wave rectification and ripple filtering.

A diode has two types of resistance, dc and ac.

at a specific point on the curve. This value varies depending on the operating point that you selectbut it should be in the neighborhood of 100 ohms. The diode curve may look like a straight line, but it is not. It

is an exponential curve.

This is referred to as a diodes dynamic resistance. It should be less than 10 ohms.


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Figure 1. Oscilloscope in X- Y Mode . Horizontal axis is diode voltage drop and the vertical axis is the diode

current (i=V/750). This analysis is done using National Instruments Multisim software.


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Figure 2. Diode used as a halfwave rectifier. Connect the largest capacitor across the resistor and see what

happens. This is called filtering. If you increase the frequency to 100 KHz and you will see that the capacitor

changes the pulses into a DC voltage with a small ripple voltage. Increasing either the frequency or the capacitor

size will reduce the ripple.

Use the original Exercise 5A for a theoretical background. Your lab report should discuss what you did and what

you observed. Diodes act like one way check valves in many electronic circuits. They allow current to go only

one way in a wire.


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Figure 3. Halfwave rectifier with filter capacitor. The input is a 10 sinewave (CH 2) and the output (CH 1) is a DC

value with about a 10% ripple.

As you increase the frequency, the ripple become less because the capacitor has to discharge for a shorter

period. You can also reduce the ripple by installing a larger capacitor. The minimum size capacitor is

(1)This is a typical power supply design calculation.2. Write a professional comprehensive lab report using a word processor. Show your results


internet.


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ECE 231 Laboratory Exercise 5C



at a specific point on the curve. This value varies depending on the operating point that you selectbut it should be in the neighborhood of 100 ohms. The diode curve may look like a straight line, but it is not. It

is an exponential curve.

This is referred to as a diodes dynamic resistance. It should be less than 10 ohms.


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ECE 231 Laboratory Exercise 5C



Figure 1. Experimental determination of a diodes operating characteristic with the oscilloscope in XY mode.

The 5 ohm resistor is used as a current sensor.

Determine both the dc and ac resistance of the diode using the oscilloscope cure.

You can download the diode curve into Microsoft word and paste it in your lab report.

A diode has two types of resistance, dc and ac.

at a specific point on the curve. This value varies depending on the operating point that you select.The diode curve may look like a straight line, but it is not. It is an exponential curve.

This is referred to as a diodes dynamic resistance

Rdc= ________________ Rac= _______________

Perform the 1/2wave rectifier experiment described in Experiment 5B.



internet.


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Frequency Response of RL and RC Circuits


ECE 231 Laboratory Exercise 6Frequency / Time Response of RL and RC Circuits

Laboratory Group (Names)____________________ ___________________ __________________

OBJECTIVES

Observe and calculate the response of first-order low pass and high pass filters. Gain experience in plotting Bode plots and calculating decibels.

Test your ability to design and properly test a circuit.

EQUIPMENTREQUIRED


Three BNC cables (one for input ac voltage and two for input/ output voltage to oscilloscope)


Two-channel Oscilloscope

BACKGROUND

Both capacitors and inductors have reactances that are frequency dependent. (1)When measuring the capacitance and inductance of a component it is very important that you know

the frequency at which the measuring instrument is using. All components R, C, and L consist of all

three. The frequency at which they are operating is a predictor of which ones can be ignored in

calculations. This laboratory experiment will not examine these characteristics of R,C , and L.

Capacitors and inductors as received from manufacturers usually have high tolerances. For example itis not uncommon for a capacitor to have a tolerance of + 20%.; therefore, measure the values of your

components on the protoboards using an RLC meter.

The voltage transfer function (voltage gain) of a filter is expressed as eq. (2) (2)The method used to calculate Vout is the voltage divider rule. The only difference is that resistances are

replaced by reactances which are complex vectors. Complex impedance is shown in equation (3).

(3)The transfer function will have to be plotted on semi log paper with the vertical axis in dB and the

horizontal axis in a logarithmic scale. The definition of dB is shown in eq. (4). (4)


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The corner frequency of the filters occurs when R=XL or XC. This is also called the -3dB corner

frequency, or power frequency, eq. (5).

(5)A negative slope on a Bode plot also functions as an integrator and a positive slope also

functions as a differentiator. This makes these circuits useful in signal conditioning as

well as filtering.

PROCEDURE

1. Construct the four circuits shown in Figure 1. Select components for a corner frequency

between 1 KHz and 5 KHz. Show all of your calculations. That is, design four circuits that

operate within the capabilities of the equipment in the laboratory.

Figure 1. Low Pass and Hi Pass filter schematics. These same circuits can function as integrators or

differentiators.

The circuit simulations for low-pass and hi-pass circuits are shown in Figures 2 and 4. Notice that the

corner frequencies are approximately 1591 Hz.

Note

You cannot view the waveforms shown in Figures 2 and 4. You have to plot these by hand or with the

assistance of Excel. You can see the waveform shown in Figures 3 and 5 when the same circuits are

functioning as integrators and differentiators.

L1

1 2

V1

10 Vac

R1

0

V1

10 Vac

L1

1

2

V1

10 Vac

Hi Pass Filters

C1

V1

10 Vac

R1

0

C1

Low Pass Filters

R1

R1

0

0


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Figure 2. Low Pass circuit simulation using National Instruments Multisim Software. At frequencies

above the corner frequency the circuit behaves as an integrator. Input a high frequency square wave

and you should see a triangular wave on the oscilloscope.


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Figure 3 is a plot of an integrator where the input square wave frequency is about 10 times the corner

frequency.

Figure 3. Low-Pass circuit functioning as an integrator.when the input frequency is above the corner

frequency. Input is 10 KHz square wave and output is a triangular wave.

2. Connect your signal generator to the input and channel 1 of the oscilloscope. Select a

reasonable input such as 5 volts peak. Sweep the frequency from about two decades below

the corner frequency to two decades above the corner frequency. You will know you are at

the corner frequency when the voltage output is 0.707 (-3 dB) lower than the input voltage.

Observe the output on channel 2 of the oscilloscope. Plot the output seen on channel 2 as

the input frequency is varied. We do not have Bode plotters as shown in Figure 2 in the lab

so the plots must be performed by hand. Record and tabulate all of your settings and

readings. The low-pass and hi-pass curves cannot be observed on the oscilloscope as shownin Figures 2 and 4. The phase shift between the input and output can be read on the

oscilloscope using the soft keys.

3. Make plots of each low-pass filter shown in Figure 1. One plot with a capacitor/resistor and

one with an inductor/resistor. You can plot the phase shift on the same Bode plot by

adding a separate vertical scale for the phase.


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4. While one of the low-pass filters (you choose) is still connected change the input (channel 1)

to a high frequency square wave and observe that the output (channel 2) is a triangular

wave. The circuit is now functioning as an integrator. See Figure 3.

5. Make plots of each hi-pass filter shown in Figure 4.

6. While one of the hi-pass filters is still connected change the input (channel 1) to a low

frequency triangular wave and observe the output (channel 2) is a square wave. The circuit

is now functioning as a differentiator. The slope of the triangular wave is proportional to the

height of the square wave. See Figure 5. You can copy your oscilloscope trace and paste it

in your report.

Draw the schematic of the circuit used for your curves. Make sure the reader can tell which

schematic goes with which curve.

The Bode Plots of your data for the low-pass and hi-pass filters must be plotted on semi-log

graph paper. The vertical axis shall be in dBs and the horizontal axis shall be log frequency. You

can download semi log graph paper off the internet or buy it at the bookstore. Use two vertical

scales. One for dBs and one for phase.


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Figure 4. Hi Pass circuit simulation using National Instruments Multisim Software. At frequencies

below the corner frequency the circuit behaves as a differentiator. Input a low frequency triangular

wave and you should see a square wave on the oscilloscope.


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Figure 5. Hi-pass filter acting as an integrator. The input is a low frequency (100 Hz ) triangular wave

and the output is a square wave.

7.

Write a professional comprehensive lab report using a word processor. Show your results


internet.




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Resonant Circuits


ECE 231 Laboratory Exercise 7- Resonant Circuits


OBJECTIVES

Observe and calculate the response of a resonant circuit.

Gain experience in plotting series and parallel resonant circuit response.

Gain experience in varying the bandwidth of a resonant circuit.

EQUIPMENTREQUIRED

ECE 231 Circuit Board (In Stock room) Use capacitors and resistors on board.



10 mH Inductor box from stockroom (provided by instructor) Oscilloscope

BACKGROUND

Resonant circuits are used in many applications such as computer circuits, high voltage generators, and

communications devices such as radios. In this laboratory experiment you will construct and measure

the performance of both a series and parallel resonant circuits.

For a series resonant circuit the voltage of the voltage across the resistor will be the same as thesource voltage; however, the voltage across the inductors L and capacitor C will be considerably higher

depending upon the quality factor Q of the circuit. The series circuit is often called a bandpass circuit.

It usually provides voltage gain.

For a parallel circuit, just the opposite is true. The voltage across the inductor and capacitor will equal

the source voltage and the voltage across the resistor will approach zero. This type of circuit is often

called a notch filter. They are often used to drive induction heaters and welders. This circuit usually

provides current gain.

Use the inductor as the output load for the series circuit. If you use the capacitor and you are able tobuild a circuit with a very high Q you could damage the capacitor. The series circuit you will construct

is shown in Figure 1. It has a resonant frequency of about 5 KHz.


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Resonant Circuits



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Resonant Circuits


Figure 1. Series RLC Resonance circuit simulation using National Instruments Multisim software

Equations that predict the behavior of resonant circuits are as follows:

Vomaxoccurs at o(center frequency ) = where XL= Xc = 2 fCutoff frequency (1) Cutoff frequency (2) =

Where radian/secondThe bandwidth is defined at the frequencies where Voutdrops to 0.707 Vsourceor3dB.

That is bandwidth cc R/L (Series Ckt.) and = 1/RC (Parallel Ckt.)

Quality factor = (Series Ckt.) and oRC (Parallel Ckt.)

PROCEDURE

1. Construct the circuit shown in Figure 1.

2. Connect your signal generator to the input. Select a reasonable input such as 5 volts peak.

Sweep the frequency from about two decades below the resonant frequency to two

decades above the resonant frequency. Observe the output on the oscilloscope. Record

and tabulate all of your settings and readings. You CANNOT see the curves shown in Figure


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Resonant Circuits


1 on the oscilloscope. These curves were generated using computer simulation and a Bode

Plotter. Therefore, you have to make the plots by hand.

3. Plot your results on semi log graph paper.

4. Construct the parallel resonant circuit shown in Figure 2.

Phase Angle


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Resonant Circuits


Magnitude

Figure 2. Parallel RLC Resonance circuit simulation using National Instruments Multisim software

5. Connect your signal generator to the input. Select a reasonable input such as 5 volts peak.

Sweep the frequency from about two decades below the resonant frequency to two

decades above the resonant frequency. Observe the output on the oscilloscope. Recordand tabulate all of your settings and readings.



internet.

Show your calculations and compare them to your measurements for fo,f1,f2, , and Q.

What kind of errors did you get between what you calculated and what you measured?

Draw the schematic of the circuit used for your curves. Make sure the reader can tell which

schematic goes with which curve.

The plots of your data for resonant circuits must be plotted on semi-log graph paper. Thevertical axis shall be in dBs and the horizontal axis shall be log frequency. You can download

semi log graph paper off the internet or buy it at the bookstore. Use two vertical scales.

One for dBs and one for phase.




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Time Domain Response 2ndOrder Circuits


ECE 231 Laboratory Exercise 8. Time Domain Response 2nd Order Circuits


OBJECTIVES Observe and calculate the time domain response of a 2nd order circuit.

Gain experience in plotting circuit response.

Gain experience in observing the time domain response of a 2nd order circuit on an

oscilloscope.

EQUIPMENTREQUIRED

ECE 231 Circuit Board (In Stock room)use potentiometer and 0.1 f capacitor on board



400 mH inductor box (stockroom)

Signal generator Use square wave output for channel 1 input.

Two channel oscilloscope. Channel 1 input and channel 2 output (voltage across the capacitor).

BACKGROUND

The time domain response of a circuit is important to understanding the transient behavior of a circuit.

There are three cases that will be examined in this laboratory experiment. They are the under

damped, critically damped, and over damped cases. You will be using a series circuit similar to the one

used when determining the resonance behavior of a circuit (frequency response). Equations (6), (9),and (12) show the basic form of the circuit behavior for the three cases. These equations are derived

beginning with a loop equation of the circuit shown in Figure 1. By knowing the boundary conditions

(initial and final values), the coefficients of the defining equations can be determined. The experiment

will determine the response of the circuit to a step input. This can be done by applying a square wave

to the circuit and observing the response on an analog oscilloscope or by apply in a step input voltage

to the circuit and observing the response on a digital storage oscilloscope. When applying a square

wave to the circuit the frequency of the square wave must be lower in frequency (longer in time) than

the time response you are trying to observe.

This experiment is similar to driving a car over a speed bump and observing the response of the shock

absorber system. An elevator control system is an example of a critical or over damped controlsystem. All structural systems are under damped and so are most mechanical systems. A mechanical

scale is designed to be critically damped. This is often accomplished by using an eddy current brake.

The pneumatic closure on a door is normally over damped. The damping ratio is defined as the

cosine of the angle between the natural frequency vector,n, and the real axis in the complex plain

such that n= and where and n . See Figure 1.


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(source: MIT Dept. of Mechanical Engineering)

Figure 1. Complex Plane where is the dampening coefficient.

You will need to construct the circuit shown in Figure 2 for this exercise.

Figure 2. Circuit that you will construct to demonstrate 2ndorder system operation.

The simulation results of an underdamped case is shown on the oscilloscope.


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The theoretical derivations of the equations that predict the behavior of a series RLC circuit are shown

below.

Write the general differential loop equation for the series (not a parallel) circuit is shown in Fig. 2. Start

by writing a loop (mesh) equation using Kirchhoffs voltage law around the loop. The result is equation

(1). Voltage rises are negative and drops are positive. (1)Take the derivative of (1) and rearrange it.

(2)

Transfer to the frequency domain using the Laplace Transform where

(3)Where (refer to Figure 1)

(4)Roots of the general solution are

(5)

The time domain solutions to the Laplacian Equation has three solutions we are interested in.

Over Damped solution 1 (two non-equal real roots)

(6) (7) (8)

The time domain simulation of the over damped solution is shown in Figure 3.


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Figure 3 Circuit simulation of overdamped case using National Instruments Multisim software R = 10K

Critically Dampedsolution 2 (two equal real roots)

(9) (10) (11)

The time domain simulation of the critically damped solution is shown in Figure 4.

Figure 4 Circuit simulation of critically damped case using National Instruments Multisim software R = 4K


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Under Damped solution 3 ( two complex conjugate roots)

(12) (13)

(14)where

(15)The time domain simulation of the underdamped solution is shown in Figure 5.

Figure 5 Circuit simulation of overdamped case using National Instruments Multisim software R =1K

Notice that the peak output voltage is 4 times the peak voltage of the input square wave.

PROCEDURE

1. Construct the circuit shown in Figure 1. You are going to vary the value of R1 (the

potentiometer) from 10 K (overdamped case- two real roots) to 4 K (critically damped case- twoequal roots) to 1K (underdamped case- complex conjugate roots). Verify these numbers by

solving equation (5). The oscilloscope curve shown in Figure 3 is for R1= 10 K.

2. Connect your signal generator (set to a square wave output) to the input of your circuit. Select

a reasonable input such as 5 volts. Adjust the frequency of the square wave until you can

observe the response of the circuit. Observe the output on the oscilloscope by connecting the

oscilloscope across the capacitor. Record and tabulate all of your settings and readings. For


54/54



good characterization of the circuit behavior, the square wave pulse width must be sufficiently long in

order for the circuit to approximately reach a steady state condition. For this circuit a 200 Hz pulse

width square wave would be a good starting point. Set the oscilloscope vertical sensitivity to 5V per

division and the horizontal sensitivity to 1 ms per division.

3. Plot your results on linear graph paper. Estimate the damped frequency of oscillation. Compare

it to the value calculated using equation (15) or copy oscilloscope display using computersoftware routine in Microsoft Word and paste into your lab report.

4. Write a professional comprehensive lab report using a word processor. Show your results and


What kind of errors did you get between what you calculated and what you measured?

What is the comparison between the oscillations observed when R1was set to 1k and n as

calculated using equation (4)?

How does this exercise translate to the behavior of mechanical systems?

Documents

ECE 231 Laboratory Manual 090112 (Word 10)