ECE 231 Laboratory M

ECE 231 Elements of Electrical Engineering

Laboratory Manual

Prepared by R. Frank Smith

California State Polytechnic University, Pomona

Reference Text – Student Reference Manual for Instrumentation Laboratories, Wolf and Smith, Prentice Hall, 2004

Revised 09/05/16

Table of Contents

Exercise 1 - Ohm's Law 1

Exercise 2 - Kirchhoff's Laws 7

Exercise 3 - Oscilloscope/Function Generator Operation 11

Exercise 4 - Thévenin's and Norton Theorems 16

Exercise 5A - Diode Characteristics 22

Exercise 5B - Diode Characteristics 28

Exercise 5C - Diode Characteristics 32

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

Exercise 7 - Resonant Circuits

Exercise 8 – Time Domain Response of 2nd Order Circuits

42

47

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

ECE 231 Laboratory Exercise 1Ohm’s Law

ECE 231 Laboratory Exercise 1 – Ohm’s Law

Laboratory Group (Names) _______________ ______________ _______________

OBJECTIVES

Verify Ohm’s 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 may range 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 resistor’s 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 Eq.1. In a thermodynamics' laboratory you could measure the rise in temperature of water in a calorimeter to

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

ECE 231 Laboratory Exercise 1Ohm’s Lawdetermine 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.

P=V 2

R=I 2R=V ∆R IR (1)

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

Resistance (R)= ρLA (2)

Where ρ=¿resistivity of the material; L = length of material; and A is the area of the material. The material may be solid, liquid, or gaseous. Each of these parameters is often functions of temperature and stress. Liquid is often 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.


ECE 231 Laboratory Exercise 1Ohm’s LawFigure 1. Experimental board for ECE 231 experiments.

Table 1. Resistor color codes

MeasuredValue

Color Code TheoreticalValue (Color Code)

% errorExperimental Discrepancy

Part 2. Connect a variable voltage supply to three different 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 Ohm’s Law? What can you say about the slope of the plots? Calculate the slopes and show that they are equal to 1/R.


ECE 231 Laboratory Exercise 1Ohm’s LawHint: All of the curves go through zero so only one additional point for each resistor is required to generate the Ohm’s 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 Ohm’s Law.

Figure 3. Laboratory bench equipment.

Figure 4. Plot for verifying Ohm's Law, ( 1R

= ∆ I∆V )


ECE 231 Laboratory Exercise 1Ohm’s LawHow does the plot verify Ohm’s 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 ¼ 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 ¼ watt can cause the resistor to explode or ignite. A 100 ohm resistor will dissipate ¼ watt at 5 volts. You will usually see smoke or fire at ½ watt. Do NOT exceed 7 volts for a 100 ohm resistor.

Table 2. Wattage versus resistor temperature

Measured Test Value TemperatureCheck appropriate box

Comments

Resistance Voltage Wattage Ambient Warm Hot

1/4 1/3 1/2

Voltage


ECE 231 Laboratory Exercise 1Ohm’s LawPart 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.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________


ECE 231 Laboratory Exercise 2Oscilloscope/Function Generator Operation

ECE 231 Laboratory Exercise 2 – Kirchhoff’s Laws

Laboratory Group (Names) _______________ ______________ _______________OBJECTIVE

Verify Kirchhoff’s voltage law Verify Kirchhoff’s current law Gain experience in using both an ammeter and voltmeter Construct two (2) circuits as shown in Figure 1 and Figure 2.

R1

R2

R3

R3R2R1V110Vdc

V110Vdc

0

0

AmmeterAmmeter

I

Parallel Circuit

Series Circuit

1 2I

3I

BA

E

D

C

Figure 1. Schematics for verifying Kirchhoff's Laws

EQUIPMENT REQUIRED

ECE 231 Circuit Board (In Stock room) Two banana cables (one for DC power supply and one for DMM) One lot of clip leads (students must supply their own clip leads) DMM (digital multimeter) 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.



I=VR

=Voltage acrossa resistorResistance

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

Kirchhoff's Current Law (KCL) ∑k=1

n

I k=0 where is the n is the number of branches at a node.

Kirchhoff's Voltage Law (KVL) ∑k=1

n

V k=0 where is the n is the number of components (resistors and

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.



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 Kirchhoff’s 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 Kirchhoff’s 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.



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 Kirchhoff’s 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 ______________________________________________________________________________________________________________________________________________________________________________________________________________________



ECE 231 Laboratory Exercise 3 – Oscilloscope/Function Generator Operation

Laboratory Group (Names) _______________ ______________ _______________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 oscilloscope’s controls and soft keys. Learn the frequency limitations of instruments.

EQUIPMENT REQUIRED One banana cable Three BNC cables One lot of clip leads and/or jumper wires DMM (digital multimeter) Use the DC offset in signal generator for the DC power supply Signal generator

BACKGROUND

The oscilloscope is primarily a voltmeter for observing time varying signals. It has a fairly low input impedance of one megohm (1M ) so it cannot be used when a load impedance of this size would distort 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: V rms=V p− p

2√22

=0.3535 v p−p=0.707 v p


ECE 231 Laboratory Exercise 3Oscilloscope/Function Generator OperationIf 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 shouldn’t 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 don’t 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 signal’s voltage value and frequency automatically. Use the soft keys to select voltage and time measurements.



Figure 1. Test Setup

Time (sec.,msec., sec.)

Figure 2. Oscilloscope Display



Table 1. Measured and calculated results

Waveform Oscilloscope reading Vp-p

Multimeter reading

Frequency Calculated RMS voltage

Sine wave 1 k HzSine wave +5dc 1 k HZTriangular 1 kHzSquare 1 kHz

Sine wave 10 kHzSine wave +5dc 10 kHzTriangular 10 kHzSquare 10 kHz

Sine wave 100 kHzSine wave +5dc 100 kHzTriangular 100 kHzSquare 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 wave7. What is the frequency limitation of the multimeter. ______________ Hertz. Square wave8. What is the frequency limitation of the multimeter. ______________ Hertz. Saw tooth wave

Notes: If the amount of heat (joules) generated by a DC source (idc2 RT ) is equal to the heat generated

by an ac source over the same period T ,(∫0

T

R∗i2dt ¿. Equating the energies and solving results in

IDC=irms=√ 1T∫0

T

it2 t dt . The following are Vrms equations for common waveforms:

Sine wave V rms=V p−p

2√22

; square wave V rms=V p; triangle wave V rms=Vp−p2√3



1period T of onecycle

=frequency of waveform (Hz) = ωradians / second

2 π

9. Describe how you measure the frequency of a waveform from the oscilloscope display if you didn’t 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.


Conclusion

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


ECE 231 Laboratory Exercise 4Thévenin and Norton Theorems

ECE 231 Laboratory Exercise 4 – Thévenin and Norton Theorems

Laboratory Group (Names) _______________ ______________ _______________

OBJECTIVES

Learn various ways to measure Thévenin's voltage and resistance. Validate the maximum power theorem.

EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Two banana cables (one for DC power supply and one for DMM) One lot of clip leads and/or jumper wires DMM (digital multimeter) One DC power supply Four or more resistors (available in bins adjacent to stock room, 5th floor). Select various sizes Potentiometer for variable load – 10K or larger. It should be twice as big as your largest resistor

BACKGROUND

Thévenin's Theorem (1883) states that any linear circuit can be replaced by a single voltage source and a single series resistance. In 1926 Norton’s Theorem was shown to be equal to Thévenin’s 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 Ohm’s Law. Constructing constant current sources is beyond the scope of this course.

Figure 1. Thévenin's and Norton’s equivalent circuits for a Linear Circuit

Procedure for Finding the Thèvenin Equivalent Circuit Mathematically

A. Circuits with independent sources only. No Dependent sources.

Step 1. Find R Thèvenin



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 Thèvenin 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 Thèvenin resistance will result in maximum power being dissipated in the load resistor and of ½ the input voltage will be across the load.

Step 2. Find V Thèvenin between 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 Thèvenin

resistance by the use of Ohm's law.

Step 2. Find V Thèvenin between 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 Thèvenin resistance only.




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 Thèvenin resistance by the use

of Ohm's law.

3. Find this voltage using nodal analysis.

Thévenin's and Norton’s Theorems are expressed mathematically by equation 1.

rThevenin=v theveniniNorton

=vopencircuitishort circuit

=vopen circuit−¿ vloaded

v loadedRload

=half power load ¿ (1)

Measuring Vopen circuit just requires a single voltmeter measurement by definition.

CAUTION

Do not attempt to measure I short circuit by 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 Thévenin'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.



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 Thévenin by 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 RThèvenin. Record this value in Table 1. Column 1.

4. Calculate RThèvenin by 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.

0 "b""2"

R 1

R 3

V 110 V d c

"1" R 2

"a"

R lo a d

Figure 1. Linear resistor circuit.

5. We are now going to determine RThevenin in 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 Thévenin equivalent circuit.

7. Simply apply Ohm’s Law to find rThevenin..

rThevenin=voltageacross r Thevenin

irThevenin=vopen circuit−¿ vloaded

v loadedRload

¿ (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.

Table 1. Measured and calculated data.

1 2 3 4 5 6 7 8RThevenin Measuredwith sources removed (shorted)

RThevenin Calculated 1with sources removed

% Errorbetween measured and calculated

RThevenin Calculated 2 using Ohm’sLaw and an Rload

% Differencebetween calculated 1 and calculated 2

VabMeasured

VabCalculated

% Error

Thévenin

voltage measured and calculated

Part 2

1. Now construct the circuit shown in Figure 1, but replace Rload with a potentiometer connected between “a” and “b.” The equivalent circuit is shown in Figure 2. We will now determine rThèvenin 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 VThèvenin/2 NOT Vsource/2. The

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

determined above.

Maximum power=(V Thèvenin

2 )2

Rload=

V ab2

Rpotentiometer

(3)

0

R lo ad

0

V 1V Potentiometer

Wiper

Thevenin

V 1

Thevenin VR lo a d

Thevenin

Thevenin

R R

Figure 2. Maximum power circuit.

6. Now prove that this is the load for maximum power. There are resistor values above and below 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).

power=(v potentiometer ) 2

R potentiometer

(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

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


ECE 231 Laboratory Exercise 5ADiode Characteristics

ECE 231 Laboratory Exercise 5A – Diode 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.

EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Two banana cables (one for DC power supply and one for DMM) 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 5th floor stock

BACKGROUNDThe 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 the properties 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.

I diode=I s (eV D/(nV T )−1 )

Some definitionsIs is the reverse saturation current and is approximately equal to 10-12A. It is sometimes referred to as Io or Ir. This current is proportional to the area of the diode. We will not measure this current in this experiment.VD = diode voltage, n is approximately 1 to 2. Use 1 for this lab. VT is 26 mV at 300oK.VD should 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.


ECE 231 Laboratory Exercise 5ADiode CharacteristicsSome 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


Figure 2. An assortment of typical diodes.

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.

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



rac=∆V∆ i

=V diode@12V−V diode@8V

idiode@12V−idiode@8V

R1 = 100R1 = 1000R1 = 10000

0

V1D 1

D I O D EV 1

10V dc R 1

Vs

Multimeter(volts)

Figure 4. Linear resistor network.

Table 1. Diode Data

Vs = 10Plot data in Figure 5

I diode=V1/R1

V diode=Vs-V1

rac

R1 I = V1/R1 Vdiode = Vs-V1

Vs = 8R1 = 1000

100 Vs = 12R1 = 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.


10


Diode Voltage X 10-1

Figure 5. Diode Characteristic Curve


1 2 3 4 5 9876 1000

00

1

2

3

4

5

6

7

8

9

Curr

ent -

mA

-50 1 2 3 4 5 6 7 8 9 10

00

Volta

ge

-4

-3

-2

-1

0

1

2

3

4

5


Time

Figure 6. ½ Wave rectifier oscilloscope trace

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

_____________________________________________________________________________


ECE 231 Laboratory Exercise 5BDiode Characteristics

ECE 231 Laboratory Exercise 5B -Diode Characteristics


EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Three BNC cables One lot of clip leads and/or jumper wires DMM (digital multimeter) 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

BACKGROUNDSee 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 ½-wave rectification and ripple filtering.

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

Rdc=vi at a specific point on the curve. This value varies depending on the operating point that you select

but 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.

Rac=change∈voltageabout aspecific pointchange∈current about a specific point

= ∆v∆ i

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



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 Instrument’s Multisim software.



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.



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

Cminimum=iload∗(discharge timeof capacitor )Ripple voltage peak−¿− peak

(1)

This is a typical power supply design calculation.



ECE 231 Laboratory Exercise 5CDiode Characteristics

ECE 231 Laboratory Exercise 5C -Diode Characteristics


EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Three BNC cables One lot of clip leads and/or jumper wires DMM (digital multimeter) One AC power supply Diode and one resistor (10 ohms or less is best) Oscilloscope with XY Mode capability

BACKGROUNDSee experiment 5A.

This is an alternate method of measuring a diode characteristic using an oscilloscope and only one diode. Again, if you need better results then use a commercial Curve Tracer. The method described in 5B ideally should use two matched diodes. Even if the diodes aren’t perfectly matched, the results are pretty good.

This method requires an oscilloscope that has an XY mode. Most oscilloscopes have this option. Use the soft keys to select the 1X and 2Y for channel 1 and 2. The x-axis is channel 1 and it will display the diode’s forward voltage drop which should be between 0.6 and 0.75 volts. The y-axis is the current passing through the diode.

PROCEDURE

Part 1

Review experiments 5A for a discussion of diode theory and 5B for using diodes for generating a dc voltage from an alternating current (ac) source by using a capacitor on the output of a rectifier circuit.

Construct the circuit shown in Figure 1 then observe the diode’s characteristic curve discussed in exercise 5A.



ECE 231 Laboratory Exercise 5CDiode Characteristics

Rdc=vi at a specific point on the curve. This value varies depending on the operating point that you select

but 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.


= ∆v∆ i

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


ECE 231 Laboratory Exercise 5CDiode CharacteristicsFigure 1. Experimental determination of a diode’s 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.


Rdc=vi 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.


= ∆v∆ i

This is referred to as a diode’s dynamic resistance

Rdc = ________________ Rac= _______________

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



ECE 231 Laboratory Exercise 6Frequency Response of RL and RC CircuitsECE 231 Laboratory Exercise 6—Frequency / 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.

EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Three BNC cables (one for input ac voltage and two for input/ output voltage to oscilloscope) One lot of clip leads and/or jumper wires Two-channel Oscilloscope

BACKGROUNDBoth capacitors and inductors have reactances that are frequency dependent.

X c=1

2 πfC= 1ωC X L=2πfL=ωL (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 it is 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)

Hv ( jω )=V out( jω)

V ¿( jω) (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).

Z=√R2+ (X L−XC )2 arctan ( X L−XC

R ) (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).


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

dB=20 logV out

V ¿ (4)

The corner frequency of the filters occurs when R=XL or XC. This is also called the -3dB corner frequency, or ½ power frequency, eq. (5).

frequencycorner=1

2πRC= R

2 πL (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.

L 11 2

V 11 0 V a c

R 1

0

V 1

1 0 V a c

L 1

1

2V 1

1 0 V a c

Hi Pass Filters

C 1

V 11 0 V a c

R 1

0

C 1

Low Pass Filters

R 1

R 1

0

0

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.



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.



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 shown in 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.



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.



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.



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.




ECE 231 Laboratory Exercise 7Resonant 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.

EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) Use capacitors and resistors on board. Three BNC cables (one for input ac voltage and two for input/ output voltage to oscilloscope) One lot of clip leads and/or jumper wires 10 mH Inductor box from stockroom (provided by instructor) Oscilloscope

BACKGROUNDResonant 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 the source 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 to build 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.



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



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

V o( jω)

V s ( jω)

=ω RL

√( 1LC

−ω2)2

+(ω RL )

2

θ( jω)=90o−tan−1( ω RL

1LC

−ω2)Vomax occurs at o (center frequency ) = √ 1

LC where XL= Xc = 2 f

Cutoff frequency (1) ¿ωc1=−R2 L

+√( R2 L )2

+( 1LC )

Cutoff frequency (2) =¿ωc2=R

2 L+√( R2 L )

2

+( 1LC )

Where ωo=√ωc1∗ωc2 radian/second

The bandwidth is defined at the frequencies where Vout drops to 0.707 Vsource or–3dB.

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

Quality factor ωo

β=

f of 2−f 1

=√ LCR2 =

ωo LR

(Series Ckt.) and (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



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



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. Record and tabulate all of your settings and readings.


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. 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.



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

EQUIPMENT REQUIRED ECE 231 Circuit Board (In Stock room) – use potentiometer and 0.1 f capacitor on board Three BNC cables (one for input ac voltage and two for input/ output voltage to oscilloscope) One lot of clip leads and/or jumper wires 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).

BACKGROUNDThe 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 control system. 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,ωn, and the real axis in the complex plain such that ωn=√α 2+ωd

2 and where α=δωn and ωd= jωn√1−δ 2 . See Figure 1.



(source: MIT Dept. of Mechanical Engineering)Figure 1. Complex Plane where ζ 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 2nd order system operation.

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


ECE 231 Laboratory Exercise 8 Time Domain Response 2nd Order CircuitsThe 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 Kirchhoff’s voltage law around the loop. The result is equation (1). Voltage rises are negative and drops are positive.

−V s+Ri+Ldidt

+ 1Ci=0 (1)

Take the derivative of (1) and rearrange it.

d i2

d t 2 +RLdidt

+ 1LC

i=0 (2)

Transfer to the frequency domain using the Laplace Transform where s=ddt

s2+RLs+ 1LC

=0=s2++2αs+ωn2=0 (3)

Where (refer to Figure 1)

α= R2L

=ζ ωn∧ωn=1

√LC (4)Roots of the general solution are

S1,2=−α±√α2−ωn2 (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)

x(t )=x f+A1' es1 t+A2

' es2 t (6)x(0)=x f+A1

' +A2' (7)

dxdt

(0 )=A1' s1+A2

' s2 (8)The time domain simulation of the over damped solution is shown in Figure 3.R. Frank Smith, California State Polytechnic University, Pomona, 2012 Page 49


Figure 3. Circuit simulation of overdamped case using National Instruments Multisim software R = 10KCritically Damped solution 2 (two equal real roots)

x(t )=x f+D1' t e−αt+D2

' e−αt (9)x(0)=x f+αD2

' (10) dx

dt(0 )=D1

' +αD2' (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 = 4KR. Frank Smith, California State Polytechnic University, Pomona, 2012 Page 50


Under Damped solution 3 ( two complex conjugate roots)

x(t )=x f+(B1' cosωd t+B2

' sinωd t)e−αt (12)

Typeequationhere . x(0)=x f+B1' (13)

dxdt

(0 )=−αB1' +ωd B2

' (14)where ωd=√ωo

2+α 2 (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 =1KNotice 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 R 1 (the potentiometer) from 10 K (overdamped case- two real roots) to 4 K (critically damped case- two equal 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 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 computer software 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 include a comprehensive conclusion. There are lots of sample lab reports on the internet. What kind of errors did you get between what you calculated and what you measured? What is the comparison between the oscillations observed when R1 was 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 M