enme350-LabManual Spring 11-2

ENME 350 Electronics and Instrumentation I Lab Manual (draft - Jan 14, 2011) _________________________________________________________________________________________________

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ENME 350

Electronics and Instrumentation I

LABORATORY MANUAL

Department of Mechanical Engineering University of Maryland

College Park


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PREFACE

The laboratory is an integral part of the course. Students must complete the laboratory assignments in order to obtain a passing grade for the course. Students will perform experiments in groups of 2 to 4, or as assigned by the lab instructor. All partners are expected to take an active part in preparation for and execution of each experiment. Each student in a group is responsible for a separate report on each experiment. Lab partners will be rotated every week. Lab reports are not accepted if the student did not attend the associated lab.


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TABLE OF CONTENTS

Lab no. Title Page no.

Laboratory 1 Time-Varying Signals: Generation and Measurement

4

Laboratory 2 Voltage and Current Measurement and Verification of

Basic Circuit Principles

7

Laboratory 3 Thevenin’s Equivalent Circuit, Mesh Analysis, and

Maximum Power Transfer

12

Laboratory 4 Introduction to PSpice 16

Laboratory 5 DC Circuit Analysis Using PSpice 28

Laboratory 6 First Order Circuits: RC and RL Transients Using PSpice 32

Laboratory 7 RC Circuits Transient Response 36

Laboratory 8 RLC Circuits: Sinusoidal Steady-State Analysis, Phasor

Analysis, and Resonace (using PSpice)

39

Laboratory 9 Diodes and Their Applications 42

Laboratory 10 Operational Amplifiers 46

Appendix A Report Writing 49

Appendix B Solderless Breadboards Schematic 54


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Laboratory 1: TIME-VARYING SIGNALS: GENERATION AND

MEASUREMENT

OBJECTIVE

The goal of this experiment is to demonstrate time varying signals (AC signals) and their characteristics. Students will use a function generator to generate various types of time varying signals (also called waveforms). An oscilloscope will be used to view the generated signals and to measure their characteristics.

INSTRUMENTS NEEDED

Power supply (PS) Function generator Oscilloscope (Tektronix TDS 220) Probe Digital multimeter (DMM)

DESCRIPTION

A function generator is an instrument that is used to generate various types of waveforms (sinusoidal, square and triangular waveforms) where the frequency and the amplitude of the waveform can be selected. An oscilloscope (also called a scope for short) is a device that is used to view both DC and AC waveforms and measure their characteristics (such as amplitude for both DC and AC signals and frequency or period for AC signals). The scope has two input channels so that two waveforms can be viewed simultaneously. The waveform to be viewed must be connected to one of the channels of the oscilloscope. Your lab instructor will explain to you how to use both the function generator and the oscilloscope.

GENERATING AND OBSERVING SIGNALS

Step 1: Turn on the oscilloscope. Only channel 1 will be used.

Scope settings (channel 1):

Vertical Mode Horizontal Mode • Set the sensitivity to 1 volt/division • Set the input coupling to DC coupling

• Set the sweep rate to 500ms/division

Connect the probe to channel 1 of the scope and connect the two terminals of the probe together using a wire (i.e., form a short circuit between the two terminals of the probe). The display should show a spot, moving left to right (or a horizontal line). This is called “the trace”. Use channel 1 vertical position


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control to bring the position of the trace to the mid-point of the screen and adjust the horizontal position control so that the trace starts at the left end of the screen. DC VOLTAGE MEASUREMENT USING THE SCOPE

In this part, the oscilloscope will be used to view a DC signal. The voltage to be measured must be connected between the inner conductor of the input terminal and the outer, grounded conductor. You will be making connections to the scope’s input through an “x1 probe.” The probe has an x1/x10 selector. Note that x1 means the probe does not attenuate, or reduce the signal; and x10 means the probe attenuates the input signal by a factor of 10. (For example, if the input signal is 4 V DC, when the probe selector is set to x1, it will be displayed as a 4 V on the scope whereas if the probe selector is set to x10, the signal will be displayed as a 0.4 V signal on the scope.) Connect the probe to the input of channel 1 and set the selector on the probe to x1. Of the two leads of the probe, the flexible one with an alligator clip is the ground terminal.

Step 2: Turn the power supply on, and use a multimeter to set the output voltage of the PS to 2 volts. Connect the scope’s probe to the output of the PS. Observe and record its effect on the vertical position of the trace. Change the output of the PS to 3 volts and record the effect on the vertical position of the trace. Set the selector on the probe to x10 and record the effect on the scope. Disconnect the probe from the PS.

Step 3: Set the output voltage of the PS to 4 volts. Use the multimeter to make sure that the output of the PS is exactly 4 volts. Connect the output of the PS to channel 1 of the scope using the probe. Set the probe selector to x1. Set the sensitivity of channel 1 to 2 volt/division. Setting the sensitivity is like setting the range on a voltmeter.

Measure and record the PS voltage on the scope by observing the vertical displacement of the trace from the zero-reference level as follows:

Voltage (in V) = displacement (in major divisions) × sensitivity (in V/division) Note that displacement upward is taken as positive, whereas displacement downward is taken as negative. Change the voltage of the PS to 6 volts and repeat the measurement. The values measured on the scope should coincide with the PS output values measured by the multimeter.

AC VOLTAGE MEASUREMENT

In this part, the function generator will be used to produce time varying signals or AC signals. The function generator produces time-varying voltages (waveforms), just as the PS produces DC voltages. There are controls on the function generator to choose the type of the output waveform (sinusoid, square, or triangular) and to set the amplitude and frequency of the output waveform. Use the following settings:

Frequency: 500 Hz Amplitude (peak value): 4 V Function type: Sinusoidal DC offset: Off

Set the scope’s vertical sensitivity to 2 V/division and the scope’s sweep rate to 1 ms/division.


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Step 4: Connect the output of the function generator to channel 1 of the scope using a coaxial connector (do not use the probe).

Step 5: Vary the frequency controls on the function generator and the sweep rate control on the scope, in a coordinated fashion, so that each time you can see a few cycles of the waveform on the screen. Observe the effect on the trace. Continue experimenting until you fully understand the function of these controls.

Step 6: (Measuring the frequency of a sinusoid using the scope) Set the function generator output frequency to 500 Hz and the amplitude level to 1 V. Set the sweep rate on the scope to 1 ms/div so that you can observe several periods of the waveform on the screen.

Measure and record the period of the sinusoidal waveform (the period is the time it takes the waveform to repeat itself).

Period (in seconds) = # of divisions it takes the signal to repeat itself × sweep rate (in sec/div)

Frequency (in Hz) = 1Period

Step 7: Use the function generator to produce a square waveform (simply press the button with a square wave symbol on the function generator). Repeat Step 4 through Step 6 for a square wave.

Note: The oscilloscopes in the lab are equipped with built in functions for measurement of

various waveform characteristics (e.g., peak-to-peak value, mean value, frequency).

Experiment with these utilities by using the measure function on the scope. Ask your TA for

help if you have any questions.


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Laboratory 2: VOLTAGE AND CURRENT MEASUREMENT AND VERIFICATION OF

BASIC CIRCUIT PRINCIPLES

OBJECTIVES

• To illustrate how voltages and currents are measured in direct current (DC) circuits and how the voltage-current (v-i) characteristics of a resistor are calculated from voltage and current measurements.

• To verify fundamental circuit properties such as Ohm’s law and to illustrate series and parallel DC resistive circuits.

• To become familiar with potentiometers and the way resistance is measured.

INSTRUMENTS NEEDED

Power supply (PS): is used to power circuits. Digital multimeter (DMM): is used to make measurements of current, voltage and resistance.

PARTS NEEDED

A 1.5 V Battery A Solderless Breadboard A Switch 1 KΩ, 10 KΩ Resistors A Potentiometer (0-1 KΩ)

TESTING CIRCUIT CONNECTIONS

You will use an ohmmeter to test circuit connections. These tests are usually performed after building the circuit. You will practice circuit connection testing on a “single-pole, double-throw” switch (see Figure 2.1). The position of the switch determines which terminals are connected, A-B or A-C. When two terminals of the switch are connected (terminals A-B in Figure 2.1), a short is established between them, with virtually zero resistance. When two terminals of the switch are not connected (terminals A-C in Figure 2.1), an open circuit exists between the terminals, with virtually infinite resistance. Getting familiar with the switch: Mark the terminals of the switch provided to you as A, B, and C. Use an ohmmeter to verify that when terminal A is connected to terminal B, the resistance between A-B is zero and the resistance between A-C is infinite (or very large).

A

C

B

Figure 2.1 A schematic of a switch.


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VOLTAGE MEASUREMENT

The goal is to measure the voltage drop across a resistor. To do that, a voltmeter must be connected across the resistor in parallel. You do not need to break the circuit connections when making voltage measurements. The voltage between two points A and B is measured by connecting the two leads of the voltmeter between A and B (refer to Figure 2.2). Note that the polarity in DC measurements is important. If you want to measure the potential of point A with respect to point B, the red terminal of the voltmeter should be connected to point A and the black terminal to point B.

Step 1: Set up the circuit shown on Figure 2.2 (without the voltmeter). You will be provided with a 1.5 V battery (which will be used as a power source), a switch, and a 1 kΩ resistor. Keep the switch open (off). Set the multimeter as a voltmeter for direct current (DC) measurements (VDC mode). The voltage between two points A and B is measured by connecting the two leads of the voltmeter between point A and point B as in Figure 2.2.

PS

Voltmeter

V

Switch

A

B

R

Figure 2.2 Voltage measurement.

Step 2: Connect the voltmeter across the resistor as shown in Figure 2.2. Set the multimeter to an appropriate measurement range. The maximum of the range should be higher than the voltage to be measured. Measure the voltage across the resistor (the voltage of point A with respect to B), first when the switch is open and then when the switch is closed. Repeat both measurements for the voltage of point B with respect to point A. Relate the readings with the previous ones (i.e., relate VAB to VBA).

CURRENT MEASUREMENT

The goal is to measure the current through the resistor. To do that, an ammeter (a current meter) must be connected in series with the resistor. Note that to connect the ammeter in series in a circuit, you need to break the connection in the circuit and connect the ammeter there. Also, for current measurements in DC circuits, the direction of current is important. In order to measure a current in a given reference direction, the ammeter must be connected such that the current enters the ammeter through the red lead and exits through the black lead. Note that when an ammeter is connected in a circuit, it is (ideally) equivalent to a short circuit (wire), so it does not affect other elements in the circuit (DO NOT CONNECT THE AMMETER IN PARALLEL, DOING SO WILL BURN THE AMMETER). Step 3: Disconnect the multimeter from the circuit of Figure 2.2 and open the switch. Set the multimeter as an ammeter for DC measurements (ADC).


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Connect the ammeter in series between the switch and the resistor as shown in Figure 2.3 (a) and set it to an appropriate measurement range.

R

AmmeterA

i1 i1

Switch

PS

(a)

R

AmmeterA

i2 i2

Switch

PS

(b)

Figuer 2.3 Current measurement.

Close the switch and record the measurement of i1. Repeat the steps above and measure the current i2 in Figure 2.3 (b). Notice that only the reference direction is different in this case. Compare the values of i1 and i2.

MEASURING RESISTANCE AND CALCULATING V-I CHARACTERISTICS

The plot of current versus voltage for a circuit element is called the v-i characteristics. In this experiment, the v-i characteristics of a resistor will be calculated. A voltmeter and an ammeter will be used. You will also use a power supply instead of a battery. Step 4: Connect the circuit of Figure 2.3 (a) with the power supply off and connect the voltmeter across the resistor. Set the ammeter and the voltmeter to appropriate measurement ranges. Close the switch and turn the power supply on. Step 5: Vary the voltage of the PS between -5 V and +5 V in steps of 1 V and record the measurements of the current through the resistor and the voltage across it. Note that to obtain a negative voltage; you need to reverse the + and − terminals of the PS. Plot the current i versus the voltage v and find the slope of the graph. Verify that the plot satisfies Ohm’s law: v Ri= Disconnect the circuit and configure the multimeter as an ohmmeter. Connect the terminals of the ohmmeter to the terminals of the resistor that you used above (the resistor should not be connected to anything else). Measure and record the value of the resistance and compare its value with the one you obtained from the v-i plot.


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RESISTIVE CIRCUITS

In the remainder of this lab, students will build simple series and parallel circuits on the provided breadboards. These circuits will be used to verify fundamental circuit principles. You will also be given a potentiometer. The potentiometer is basically a variable resistor (i.e., an adjustable voltage divider circuit) where the total resistance of the potentiometer is fixed but one can obtain a variable resistance with values between 0 Ω and the maximum potentiometer resistance value.

A SERIES RESISTIVE CIRCUIT

Step 6: Use a power supply, two resistances (R1 = 1 kΩ, R2 = 10 kΩ) to construct the series circuit shown on Figure 2.4. Set the voltage of the power supply to 10 V. Use a voltmeter to measure the voltage across vs, v1 and v2. Record the measurements in your notebook. Verify that your measurements satisfy Krichhoff’s voltage law (KVL):

1 2sv v v= + (1.1)

Set the voltage of the PS to 15 V and repeat the voltage measurements and verify Eq. (1.1).

A PARALLEL RESISTIVE CIRCUIT

Step 7: Construct the circuit of Figure 2.5 by connecting the two resistances in parallel with the power supply. Set the power supply voltage to 2 V. Use an ammeter to measure the currents i1, i2, and i3 (see Figure 2.5). Record the measurements in your notebook. Take into account that direction matters when measuring DC currents. Verify that your current measurements satisfy Kirchhoff’s current law (KCL):

1 2 3i i i= + (1.2)

R2vs

v1

v2

+

−

+

−R1

vs R1 R2

i1i2

i3

Figure 2.4 A Series circuit. Figure 2.5 A Parallel circuit.

SERIES AND PARALLEL RESISTIVE CIRCUITS

You will use the resistors R1 = 1 KΩ and R2 = 10 KΩ to verify fundamental circuit properties.

Step 8: Measure the values of R1 and R2 using the ohmmeter. Calculate what the equivalent resistance would be if you connect R1 and R2 in series. Now connect them in series, and measure the total resistance. Compare the reading to your calculation.


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Step 9: Repeat Step 8 for the two resistors connected in parallel.

Include the following table in your report.

R1 R2 R1 in series with R2 R1 in parallel with R2 Value (theoretical) Measured value

VOLTAGE DIVIDER

Step 10: Set up the voltage divider circuit shown in Figure 2.6 using two resistors R1 = 1 KΩ and R2 = 10 KΩ. Set the PS to 5 V. Measure and record v2, and verify that it satisfies the voltage divider formula

22

1 2s

Rv vR R

=+

vs

R2

R1

v2

+

−

Figure 2.6 A Voltage divider circuit.

POTENTIOMETERS

A potentiometer is basically a variable voltage divider where the division ratio can be changed with the slider (see Figure 2.7 for a schematic). The total resistance of the potentiometer is the resistance between the terminals 1 and 3 which is equal to the resistance between terminal 3 and terminal 2 (denoted by R1 in Figure 2.7) plus the resistance between terminal 2 and terminal 1 (denoted by R2 in Figure 2.7). The arrow represents a slider, which can slide up and down over the length of the potentiometer. This results in changing the values of R1 and R2 while R1 + R2 = constant = the total resistance of the potentiometer.

3

1

2R2

R1

Figure 2.7 A potentiometer.

Step 11: Use the potentiometer provided to you and identify the terminals 1, 2, and 3. Use an ohmmeter to measure the values of R1, R2 and R1 + R2 as the slider is moved from its lowest value to its highest value. Determine the minimum and maximum values of R1, R2 and R1 + R2.

Step 12: Replace the two resistors of Figure 2.6 with the potentiometer provided to you. Set the PS voltage to 2 V and measure v2 (the voltage across R2). Change the slider position and determine the minimum and maximum attainable values of v2? Compare the minimum and maximum values of v2 to 2V (the power supply voltage).


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Laboratory 3: THEVENIN’S EQUIVALENT CIRCUIT, MESH ANALYSIS, AND MAXIMUM

POWER TRANSFER

OBJECTIVES

• To illustrate that a linear circuit containing one or more voltage sources can be replaced by an ideal voltage source and a resistance in series with it.

• To illustrate that current and voltage within a circuit can be determined by means of mesh current analysis.

• To illustrate that power transferred from an ideal voltage source with an internal resistance depends on the load and can be maximized by the choice of load (this is known as impedance or resistance matching).

BACKGROUND

Thevenin’s Theorem

Thevenin's Theorem states that a linear circuit containing ideal sources and resistors may be represented by an equivalent circuit consisting of an ideal voltage source in series with an equivalent resistance. Thevenin’s theorem simplifies circuit analysis by reducing a linear circuit which may contain several voltage sources, current sources and resistances by a single voltage source in series with a resistance (see Figure 3.1). The Thevenin equivalent voltage is equal to the open circuit voltage after the load is removed (see Figure 3.2 (a)) and the Thevenin equivalent resistance is give by the ratio of the open circuit voltage to the short circuit current (see Figure 3.2 (b)). Thevenin’s theorem is particularly useful when doing power calculations and selecting a load resistance that consumes the maximum amount of power from a circuit. It applies to both DC and AC linear circuits.

Circuit with resistances and voltage/current

sources

a

b

A linear circuit.

+−

Rth

Vth

a

b

Thevenin’s equivalent circuit.

Figure 3.1 Demonstration of Thenvenin’s theorem.


sources

a

b

VOC

+

−

(a) th OCV V= .


sources

a

b

ISC

(b) th OC

thSC SC

V VRI I

= = .

Figure 3.2 Calculation of the equivalent circuit parameters.


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Mesh-Current Analysis

The Mesh current analysis method is a general circuit analysis technique that is used to determine mesh currents in a planar circuit. Unlike branch currents, mesh currents are assumed to flow in a closed path (see Figure 3.3). Mesh current equations are found by applying Kirchhoff’s voltage law (KVL) around all the meshes (simple loops) in the circuit. This results in a system of linear equations where the unknowns are the mesh currents. Once the mesh currents of a circuit are determined, all other voltages and branch currents can be determined using Ohm’s law and Kirchhoff’s current law.

(a) Circuit with branch currents. (b) Circuit with mesh currents.

Figure 3.3 Mesh current analysis method. Impedance Matching or Maximum Power Transfer Maximum power transfer by a circuit to a load resistance is achieved when the load resistance is equal to the Thevenin’s equivalent resistance of the circuit as seen from the load terminals. This is also called impedance matching, that is, the load resistance matches the equivalent resistance of the circuit:

L thR R=

It is straightforward to show that the maximum power delivered to the load by the circuit is given by

max

2

4th

Lth

VPR

=


sources

a

b

RL

(a) A linear circuit with a load resistance.

+−

Rth

Vth

a

b

RL

(b) Thevenin’s equivalent circuit with load

resistance.

Figure 3.4 Application of Thenvenin’s theorem for a circuit with a load.


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EXPERIMENT: "EQUIVALENT" CIRCUITS

This experiment illustrates that a single ideal voltage source with a resistor in series can be used to replace a more complicated circuit of resistances and voltage sources.

1. Use Mesh current analysis to calculate the open circuit voltage in the circuit shown in Figure 3.5 (a). Use resistors with the following values: R1 = R2 = R3 = R4 = R5 = 100 Ω.

2. Use Mesh current analysis to calculate the short circuit current in the circuit shown in Figure 3.5 (a). 3. Use Thevenin’s Theorem to replace the circuit with an equivalent voltage source and a resistor in

series with the voltage source. Draw a schematic diagram of your equivalent circuit. 4. Use the variable DC power supply and resistors to create the circuit shown in Figure 3.5 (a) on the

breadboard. Make sure that the negative terminals of the two voltage sources are not connected (i.e., V1 and V2 have separate grounds).

5. Measure the open circuit voltage and the short circuit current at the output terminals (i.e., between the terminals a-b). Record your observations.

6. Add each load resistor (all are 240 Ω) one by one across the output of the original circuit (Figure 3.5 (a)) and measure the output voltage and current every time you add a resistor. Record your observations.

7. On the breadboard, build your equivalent circuit (which has a single equivalent voltage source and a single resistor in series with it) and repeat the measurements of the open circuit voltage and the short circuit current. Record your observations.

8. Calculate the power absorbed by the load (and generated by the circuit) and plot versus the load resistance.

9. For what resistance value is the power maximized? Compare the load resistance that absorbs the most power with the Thevenin equivalent resistance. Record your observation.

+−

R2

V1

a

b+−

V2

R1

R4

R3

R5

RL1 RL2 RL3 RL4 RL5

(a) R1 = R2 = R3 = R4 = R5 = 100 Ω and V1 = 5 V, V2 = 10 V.

(b) RL1= RL2= RL3= RL4= RL5= 240 Ω.

Figure 3.5 The circuit used in the experiment.

Include in your report: 1. The Mesh current analysis for calculating the short circuit current and the open circuit voltage,

2. The calculation of the Thevenin’s equivalent circuit and the schematic of the equivalent circuit,

3. All data measurements in a table format.

4. The plot of the load power as a function of the load resistance and indicate for what value of resistance the power is maximized.


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5. What is the relationship between the load resistance that maximizes the load power and the Thevenin’s equivalent resistance for the circuit?

6. Calculate the power absorbed by an arbitrary load on the Thevenin equivalent circuit as a function of the load resistance. Differentiate the expression to determine the value of load resistance that results in the maximum power absorbed.

REFERENCE

Electrical Engineering, Principles and Applications, by Allan R. Hambley (any edition).


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Laboratory 4: INTRODUCTION TO PSPICE

OBJECTIVES:

• To become familiar with the circuit simulation software PSpice. • To simulate/analyze simple circuits using PSpice.

BACKGROUND: Spice (Simulation Program with Integrated Circuit Emphasis) is a program widely used to simulate analog electronic circuits and mixed mode analog and digital circuits. PSpice is a personal computer version of Spice. PSpice can be used to perform transient and steady state analysis. Spice was developed at the University of California at Berkeley in the mid-1970s. Since its development, it has been widely used in educational and research institutions. I. Starting PSpice To run PSpice, go to Start menu Programs Cadence SPB16.01 Design Entry CIS. The following window (Figure 4.1 (a)) may appear. If it appears, choose the first option Allegro PCB Librarian XL and click OK. The window shown in Figure 4.1 (b) will appear.

Figure 4.1 (a)

Figure 4.1 (b) Starting PSpice.


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To start a new session, go to File New Project Choose Analog or Mixed A/D (see Figure 4.2). Choose a name for the new project and type a path in the location field then click OK. May sure you copy your files on a flash drive or email them to yourself before you leave the computer lab.

Figure 4.2 Starting a new project in PSpice. In the "Create PSpice Project" window, make sure that the "Create based upon an existing project" is checked then click OK. Double click on your project name, click on Schematics then choose Page 1. A schematic page window will appear. If the schematic page is not empty, highlight everything on the page by pressing CTRL + A and then delete. II. Drawing the circuit A. Getting the Parts Before building a circuit, you need to place all the components in the schematic window. This can be done by selecting Place from the menu then choosing Part or by pressing the keyboard letter p. Make sure all the libraries are loaded by pressing p Add Library then highlight all the files (refer to Figure 4.3) then click Open. Click "Cancel" after completing loading the libraries.


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Figure 4.3 Loading the libraries in PSpice

Circuit components can be placed by going to the place part window (keyboard shortcut “p”) and either scrolling down the list of components and selecting the desired component or by typing a shortcut for the component (for example, type "r" for resistor).


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Figure 4.4 Placing circuit components (in this example placing a resistor).

Figure 4.5 Placing a DC source by using the keyboard shortcuts VDC.

Upon selecting your part, click OK and place it in the Schematic page. Table 4.1 below lists keyboard shortcuts for some commonly used circuit components.


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Table 4.1 Keyboard shortcuts for commonly used circuit components.

Keyboard shortcut Component R Resistor C Capacitor L Inductor

VAC AC voltage source VDC DC voltage source

0 Ground or Zero reference voltage D Diode

Once you have the parts in the Schematic page, you can build the circuit by connecting the components using wires. You can rotate a part by highlighting the part and pressing "r" (or by choosing “Edit” then “Rotate”). Flipping a part can be achieved by pressing "f" (or by choosing “Edit” then “Flip”).

Figure 4.6 Sample circuit components placed in the schematic page.


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C. Connecting the Circuit: Once all the parts are placed in the schematic page, connect the components using wires. This is done by going to the tool bar on the right of the screen and selecting “Wire” (or by using the keyboard shortcut “w”). With the plus “+” looking pointer, click on one end of a component, when you move the mouse around, a solid line appears. Attach the other end of the wire to the next component in the circuit then right click and press END WIRE to get rid of the “+” looking pointer.

Figure 4.7 Connecting components using wires.

Repeat this process until your circuit is completely wired. An example is shown in Figure 4.8 below.

Figure 4.8 A circuit example.


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Creating Netlist: After the circuit is completely wired, a netlist must be created before starting the simulation. To create a netlist, go to PSPICE then click CREATE NETLIST. D. Changing the Name/Value of a Circuit Part or Element: You can change the label/value of a part by double clicking on the present label/value. For example, double clicking on a resistor value results in the Display Properties window shown in Figure 4.9.

Figure 4.9 Display properties window.

E. Circuit Ground "GND" : In PSpice, every circuit must have a ground before simulation can be performed. If you aren't sure where to put the ground, place it near the negative side of your voltage source (if any) or connect it to the bottom line of the circuit (with no voltage source). You can place a gound by typing “0” in the place part window or by going to the menu and selecting Place GND. F. Voltage and Current Measurements: Voltage and current markers are used to measure voltages and currents in a circuit. The voltage marker measures the voltage with respect to ground. The current marker measures the current in the branch where the current marker is placed. To add a voltage or a current marker, from the tool bar go to PSPICE Markers Select Voltage Level for Voltages and Current into Pin for currents. Voltage Makers have to be placed on the nodes. Current Markers have to be placed at the terminal of the component (beginning or end) as seen in Figure 4.10 below.


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Figure 4.10 Placement of voltage and current markers.

Figure 4.11 Enabling voltage and current display on a circuit.

Voltages and currents in a circuit can be displayed on the circuit itself by enabling voltage and current bias display (see Figure 4.11). G. Editing the Simulation Profile and Simulating the Circuit:

Before starting circuit simulation, go to PSPICE click Edit Simulation Profile. This launches the Simulation Settings window (see Figure 4.12).

Figure 4.12 Simulation setting window.

Enable voltage Bias display

Enable current Bias display


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On the Simulation Settings window, choose Time Domain (Transient) for Analysis type. (Note that a different analysis type will be used when simulating an AC circuit), then set the Run to time to 5 seconds (for example). Before you run the simulation, make sure that:

• The circuit is properly drawn and has a ground. • No unattached components are in the schematic page. • All parts have desired values. • There are no extra wires. • The "Simulation Edit Profile" has the right settings provided by the instructor.

Starting Circuit Simulation:

To start simulation, go to PSPICE RUN (or press F11 or click on the blue play button). A sample output from the circuit of Figure 4.8 is shown in Figure 4.13.

Figure 4.13 Sample circuit simulation output.


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EXAMPLE 4.1 Draw the circuit shown in Figure 4.14.

R1

5

R2

12

R38

R45

V130Vdc

0

Figure 4.14 Circuit for example 4.1.

• Create a Netlist. • Choose Time domain (Transient) in the Edit Simulation Profile window. • Place current and voltage markers as shown in Figure 4.15.

Figure 4.15 The circuit of Example 4.1 with voltage and current markers placed. Start the simulation by pressing F11. The output of the simulation should be similar to that shown in Figure 4.16.


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Figure 4.16 Sample output for Example 4.1.

Figure 4.17 Shortcuts for doing various operations in PSpice.

Run

Voltage Marker

Current Marker

Display Voltages Display Currents


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EXERCISE 4.1 CIRCUIT SIMULATION USING PSPICE

1. Draw the circuit shown in Figure 4.18 below in PSpice. 2. Display voltages and currents on the circuit (see Figure 4.11 (b)). Include a copy of the

circuit with voltages and currents displayed in your lab report. 3. Use voltage markers to find the node voltages Va, Vb and Vc. Save the output graphs and

include them in your report. 4. Use current markers to find the branch currents in R1, R2, R3, R4, R5 and R7.

R2

7k

Vb

R6

12.5k

V2100Vdc

V325Vdc

R513k

R7

9kVa

0

R1

5k

R4

9k

R3

11k

Vc

Figure 4.18 Circuit for Exercise 4.1.

In your report, calculate the node voltages and branch currents using node voltage analysis and compare the theoretical results with those obtained using PSpice.


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Laboratory 5: DC CIRCUIT ANALYSIS USING PSPICE

OBJECTIVES:

• To simulate/analyze DC circuits using PSpice. • To use PSpice to find Thevenin/Norton equivalent circuits.

INTRODUCTION

In the previous lab, circuit simulation and analysis using PSpice was introduced. The procedure for building and simulating circuits was covered and simulation/analysis of simple circuits was performed. In this lab, PSpice will be used to simulate/analyze DC resistive circuits to find currents and voltages in these circuits. Moreover, PSpice will be used to find Thevenin and Norton equivalent circuits. Recall that the Thevenin/Norton equivalent circuits from two terminals in a circuit can be found by calculating the short circuit current and the open circuit voltage. The short circuit current is calculated by removing the load (if any) and connecting a short circuit (or a wire) between the two terminals. A short circuit is equivalent to a zero resistance. In PSpice, a short circuit can be achieved by placing a very small resistance between the two terminals (e.g., place a resistance R = 0.001µ Ω, in PSpice a mico is denoted by u). An open circuit is equivalent to an infinite resistance. In PSpice, an open circuit can be achieved by placing a very large resistance between the two terminals (e.g., R = 1000MEG Ω).


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Exercise 5.1

1. Draw the circuit shown in Figure 5.1 using PSpice. The DC current sources in this circuit are independent current sources. Independent current sources can be placed by typing IDC in the place part field.

2. Find the values of the node voltages Va, Vb, Vc and Vd. Include a copy of the circuit with voltage values displayed on the circuit in your report.

3. Find the current through the resistors R2, R3, R4, R6 and R13. Include a copy of the circuit with the requested currents displayed on the circuit.

4. Simulate the circuit and generate a graph that shows the values of the node voltages Va, Vb, Vc and Vd. Generate another graph that shows the currents through the resistors R2, R3, R4, R6 and R13. Include both graphs in your report.

Recall from the previous lab that before you can simulate a circuit using PSpice you need to:

• Create a Netlist. • Edit the simulation profile and choose appropriate simulation settings. • Make sure that the circuit has a ground.

R9

2.5

R4

10

V2

13Vdc

R5

11.25

R12

2.5

R6

6

V1

25Vdc

R13

10

V4

30Vdc

Va

R8

5

0

I2-10Adc

R10

5.5

R1

7.5

R7

20

R2

2.5

R11

3

I1

15Adc

Vb

VdR3

5

Vc

Figure 5.2 The circuit for Exercise 5.1. The values of the resistors are in Ω.


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Exercise 5.2

Use PSpice to find the equivalent resistance for the circuit shown in Figure 5.3 from the terminals a-b, i.e., find Rab.

Rab

6k

a

6k

3k 9k

9k

10k

9k

9k

3kb

12k

Figure 5.3 The circuit for Exercise 5.2. Describe the method used to calculate Rab. Include all simulation results. Does your method apply to any circuit? Hint: Apply a voltage source with a specified value VS between the terminals a-b and calculate the current through the voltage source (call it IVS) using PSpice. The equivalent resistance is VS/IVS .

Bonus (3 points) You get a bonus grade if you calculate the equivalent resistance from the terminals a-b analytically. Show the details of your calculations in your report. Exercise 5.3

Use PSpice to find the Thevenin and Norton equivalent circuits seen from the terminals of the load resistance RL.

RL0.5k

4.7k1.6k

3.2k

0

1k

V110V

1k

V2

12V

Figure 5.4 The circuit for Exercise 5.3. Briefly describe your method for finding the Thevenin/Norton equivalent circuits. Include the simulation results in your report and draw the Thevenin and Norton equivalent circuits.


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Exercise 5.4 Use PSpice to find the value of Ix in the circuit shown in Figure 5.4. Note that the circuit has a current controlled current source (CCCS) where the controlling variable is Ix. Simulate the circuit and find the value of Ix. Figure 5.5 shows the circuit of Figure5.4 drawn in PSpice.

5

Ix

2.Ix

0

5V310Vdc

Figure 5.4 The circuit for Exercise 5.4.

2Ix

Ix

5

0

F1

F

V310Vdc5

Figure 5.5 The circuit of Figure 5.4 drawn in PSpice.

Note: A dependent current source (CCCS) can be placed by typing F/Analog in the place part field. The gain can be changed by double clicking on the part F1 in Figure 5.5 and setting the gain to the desired value (in Exercise 5.4, the gain is 2).

F2

F

Figure 5.6 Symbol for current controlled current source in PSpice.

In your report, compare the value of Ix obtained using PSpice with the theoretical value for Ix. Include a copy of the circuit with the current displayed on it.


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Laboratory 6: FIRST ORDER CIRCUITS: RC AND RL TRANSIENTS USING

PSPICE

OBJECTIVE

• To simulate/analyze first order circuits (RC and RL circuits) using PSpice and understand the transient response of such circuits;

• To calculate the time constant of first order RC and RL circuits from the time response.

INTRODUCTION

In this lab, PSpice will be used to simulate/analyze DC resistive circuits that contain one capacitor (RC circuits) or one inductor (RL circuits). Such circuits are called first order circuits. The term “first order” is used to describe a circuit with one capacitor or one inductor because such circuits can be described using a first order differential equation. Capacitors and inductors are the energy storage elements in a circuit. The circuits studied in this lab also contain a switch. Examples of first order circuits are shown below in Figure 6.1. Changing the topology of the circuit by opening or closing a switch causes a transient to occur. The transient response typically dies away after a short period of time. PSpice will be used to study the transient response of both RC and RL circuits.

Vs

t = 0

C

R

Vs

t = 0

L

R

(a) (b)

Figure 6.1 First order circuits; (a) an RC circuit and (b) an RL circuit.

An important parameter of first order circuits is the time constant denoted by τ. The time constant of a first order circuit is the time interval it takes the response to reach 63% of the steady state value. The response of a first order circuit reaches steady state in approximately five time constants (5τ). The time constant of an RC circuit is give by

RCτ = . (6.1) The time constant of an RL circuit is give by

LR

τ = . (6.2)

If a first order circuit contains more than one resistor, then R in Eq. (6.1) and Eq.(6.2) is the Thevenin equivalent resistance seen from the terminals of the capacitor or the terminals of the inductor in the circuit. Denote by x(t) the voltage across the capacitor or the current through the inductor. It can be shown that x(t) for a general RC or RL circuit takes the form


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/( ) ( ) [ (0) ( )] , 0tx t x x x e tτ−= ∞ + − ∞ ≥ where (0)x is the initial voltage across the capacitor or the initial current through the inductor and ( )x ∞ is the steady state voltage across the capacitor or the steady state current through the inductor.

EXERCISES Exercise 6.1 RC Transients

Find the voltage across the capacitor Vc and the current IC as a function of time and plot them using voltage/current probe for the circuit shown in Figure 6.2 below. Assume that the capacitor has an initial voltage of 5 volts.

R1

1k

R21k

C11uF

-5V

1 2U1

1ms

V15Vdc

0 Figure 6.2 An RC circuit for Exercise 6.1.

1. First get the parts and draw the circuit in PSpice Schematics. (In the place part field type

"Sw_tclose" for the switch and "C" for the capacitor). 2. Edit the initial value of the capacitor by double clicking on the capacitor. 3. Change the initial condition IC to -5 V. It shows no value by default. (Note that the value of the

initial condition −5 V actually means 5 V, but in Pspice the polarity of the initial condition is reversed).

4. Double click on the switch, edit the TCLOSE and change it to 1ms (it is all the way to right of the screen).

5. Create Netlist. 6. Edit Simulation Profile, and choose Time Domain in the analysis type. Set Run to time to

6ms and check the box for SKIPBP. 7. Add a voltage probe (voltage marker) to the node Vc. 8. Simulate the circuit and save a copy of the graph of Vc to be included in your report. 9. Replace the voltage probe by a current probe to view the current through the capacitor, and save

a copy of the graph of Ic to be included in your report. 10. Now reduce the value of R2 by an order of magnitude (divide the value of R2 by 10) and re-

simulate the circuit again. Keep reducing the magnitude of R2 and simulate each time. What do you observe? Explain?

11. Fix the value of R2 at 1 kΩ and reduce R1 by an order of magnitude (divide the value of R1 by 10) and re-simulate the circuit again. Keep reducing the magnitude of R1 and simulate each time. What do you observe? Include copies of the Vc and Ic for R1 = 1 kΩ, 100 Ω and 10 Ω.

Include in your report a copy of the circuit and the graphs of the voltage Vc and Ic versus time for the following values of R1 and R2: (R1,R2) = (1000 Ω, 1000 Ω), (1000 Ω, 100 Ω) and (100 Ω, 1000 Ω), and comment on the graphs. Calculate the steady state capacitor voltage and current for these values of R1, R2 and compare your calculations with the results of PSpice.


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Exercise 6.2 RL Transients Find the current in the inductor and the voltage across the inductor as a function of time and plot them using probe for the circuit shown in Figure 6.3 below. Assume that the initial current in the inductor is zero.

R1

1k

R350V1

10Vdc

0

1

2

L11H

R2

100

1 2U1

40ms

Figure 6.3 An RL circuit for Exercise 6.2.

1. Draw the circuit shown in Figure 6.3 in PSpice Schematics (to place an inductor, type L in the place part field).

2. Create Netlist. 3. Edit Simulation Profile, and choose Time Domain in the analysis type. Set Run to

time to 200ms and check the box for SKIPBP. 4. Double click on the switch and change the value of TCLOSE to 40 ms. 5. Add a current probe on the inductor branch to measure the current through the

inductor in the simulation graph. Save a copy of the output for your report. 6. Replace the current probe by a voltage probe and repeat the simulation to view the

voltage across the inductor. Save a copy of the output for your report. 7. Repeat Steps (5) and (6) for R3 = 100 Ω.

Include in your report a copy of the circuit and the graphs of the voltage IL and VL as a function of time and comment on the graphs. Calculate the steady state inductor current and voltage and compare your calculations with the results of PSpice.


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Exercise 6.3 Time Constant for RC and RL Circuits Determine the time constant for the circuits shown in Figure 6.4.

V15Vdc

0

TCLOSE = 01 2

C10.5u

R1

10k

R215k

R215k

R1

10k

V15Vdc

0

TCLOSE = 01 2

L1

12H

1

2

(a) (b)

Figure 6.4 Circuits for Exercise 6.3.

The initial voltage across the capacitor in the circuit shown in Figure 6.4 (a) is zero. Simulate each circuit in PSpice and find the time constant from the response (capacitor voltage and inductor current). In your report, include graphs of the capacitor voltage and the inductor current and indicate the time constant on the graph. Compare the values for the time constant obtained from PSpice with the theoretical values.


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Laboratory 7: RC CIRCUITS TRANSIENT RESPONSE

OBJECTIVES

To illustrate circuits with resistors and one capacitor (such circuits are called RC circuits). To illustrate charging and discharging of the capacitor in RC circuits. To measure the time constant τ of an RC circuit using the oscilloscope.

INSTRUMENTS NEEDED

Power Supply (PS) Function Generator (FG) Digital Multimeter (DMM) Oscilloscope

PARTS NEEDED

Solderless Breadboard Switch 16 KΩ, 270 KΩ, and 1 MΩ Resistors 1 μF, and 10 μF Capacitors

RC CIRCUITS A circuit with resistors and (voltage and/or current) sources connected to a single capacitor can be represented as a single voltage source connected in series with a resistor and the capacitor using Thevenin’s Theorem.

EXERCISE 7.1: CHARGING OF A CAPACITOR USING A DC SOURCE Step 1. Construct the circuit shown in Figure 7.1. Use the single-pole, double-throw switch provided and set the switch to position 2 as in Figure 7.1. Use a resistor R = 1 MΩ and a capacitor C = 10 μF. Note the polarity on the capacitor and make sure you connect the capacitor in the circuit with the correct polarity. Make sure that the capacitor has no initial charge (before connecting the capacitor to the circuit, discharge it by connecting a small resistor between its terminals for a few seconds).

Step 2. Set the output voltage of the power supply (PS) to 5 V.

PS

R

C Voltmeter+ vC

−

5 V

1

2

Figure 7.1 An RC circuit for exercise 7.1.

Step 3. Set the switch to position 1 (use this time instant as t=0), and use a voltmeter and a stop watch to record the capacitor voltage, vC, versus time, t (in s) for several values of t. (If you make a mistake, you need to start over after you discharge the capacitor completely). Is the steady state value of the voltage across the capacitor as you expect it to be?


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Plot the capacitor voltage as a function of time. Does the graph agree with the theory? In terms of the time constant of the circuit, how long does it take the capacitor to reach steady state? In your report, calculate vC(t) analytically and compare your measurements to the theoretical results. Also, include answers to all the questions posed above.

EXERCISE 7.2: DISCHARGING OF A CAPACITOR THROUGH A RESISTOR In this part, discharging the capacitor through a resistor is studied. You will use the same circuit as in exercise 7.1. Keep the circuit connected as in Exercise 7.1 with the switch at position 1.

Step 4. Set the switch to position 2 and observe the discharging of the capacitor. Consider the time instant of setting the switch to position 2 as t = 0. Record the capacitor voltage, vC, versus time, t for several values of t. Plot the voltage across the capacitor as a function of time and calculate the time constant of the circuit using the discharge plot (the time constant is the time it takes the voltage to decrease to 0.37 of its initial value). Does this value agree with the theoretical value τ = RC? Justify your answer. EXERCISE 7.3: OBSERVING THE RC TRANSIENT USING A SCOPE Step 5: Use R = 270 KΩ and C = 1 μF. The time constant for this circuit is much smaller than the one in Exercise 7.1 and Exercise 7.2. The DMM is not going to be useful to measure the voltage across the capacitor as a function of time since the capacitor voltage is changing quickly. Instead, the oscilloscope will be used to view the response of the capacitor and to perform measurements. Monitor the PS output on the scope on channel 1 and the voltage across the capacitor on channel 2. Use the same scale (Volts/Div) for both channels. Set the input coupling of the scope to DC and triggering to AUTO. Use an appropriate setting for the sweep rate so that you can see a few cycles on the screen.

Step 6. Observe the capacitor voltage on the scope. Set the switch to position 2 and observe the capacitor voltage. Sketch the waveforms in your lab notebook and include copies in your report.

Step 7. Replace the resistor in the circuit with a smaller value (16 KΩ) and set the switch at position 1. Use an appropriate setting for the sweep rate on the scope for convenient observation.

Step 8. Think of the voltage waveform produced between points A and B when you throw the switch back and forth. What is its shape? Include sketches of the capacitor voltage in your lab notebook to be included in your report. Comment on the graphs and briefly explain the graphs based on the circuit. EXERCISE 7.4: THE RC CIRCUIT WITH PERIODIC EXCITATION In this part an AC source (a square wave signal) instead of a DC source will be used to power the circuit.


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For each period, the square wave takes two values, -Vmax and +Vmax. Therefore, using a square wave generator is similar to having a DC supply voltage with value Vmax and manually switching between position 1 and 2 (as was done in Part III) in the circuit of Figure 7.1 every T/2 seconds where T is the period of the square wave.

Step 9: Replace the DC power supply in the circuit of Figure 7.1 with a function generator and set the output of the function generator to square wave. Use R = 270 KΩ and C = 1 μF. Set the switch to position 1 and keep it there for the remainder of this part (your circuit should be similar to the circuit shown in Figure 7.2). Set the amplitude of the square wave to 5 V and the frequency to 1 Hz. Monitor the function generator output on the scope on channel 1 and the voltage across the capacitor on channel 2 of the scope. Be careful with the ground connections. Set the scope’s trigger to channel 1 and the triggering slope to positive.

Vgen

R

C + vC

−

Connect to channel 2 on scope

Connect to channel 1 on scope

+ vR −+−

Figure 7.2 The circuit of Figure 7.1 with a function generator as voltage source and

the switch is at position 1.

Step 10. Replace the resistor in the circuit with a smaller value (16 KΩ) and observe the capacitor voltage on the scope. Use an appropriate setting for the sweep rate on the scope for convenient observation.

Step 11. Use the scope display to determine the time constant, and compare it to the value you expect. Can you predict what the waveform of the voltage VR across the resistor should look like? MEASURING A FLOATING VOLTAGE WITH THE SCOPE

To measure the voltage across the resistor using the scope, you cannot connect a probe’s input across the resistor because none of the two ends of the resistor is connected to the ground. If you did so, where would the ground clip of the probe be attached? Voltages like VR, defined across two terminals, neither of which is grounded, are sometimes referred to as floating voltages.

Step 12. To display VR, notice that VR = Vgen – VC (using Kirchhoff’s voltage law) where Vgen is the function generator voltage. Use the math menu on the scope to set the scope to display difference between channel 1 and channel 2 (i.e., channel 1 − channel 2). Observe the waveform for VR and compare it to your prediction in step 11. Include sketches of the voltage across the resistor in your lab notebook to be included in your report. Comment on the graphs and briefly explain the graphs based on the circuit.


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Laboratory 8: RLC CIRCUITS: SINUSOIDAL STEADY-STATE ANALYSIS,

PHASOR ANALYSIS, AND RESONACE

OBJECTIVE

• To simulate/analyze second order circuits (RLC circuits) with sinusoidal excitation and study the circuit response as a function of frequency using PSpice.

• To become familiar with the concept of resonance in second order circuits.

INTRODUCTION

In this lab, PSpice will be used to simulate/analyze second order circuits with sinusoidal sources. The circuit response will be studied as a function of the source frequency. Steady state analysis of circuits with sinusoidal excitation is greatly simplified using phasors and complex impedances. You will use PSpice to analyze two second order circuits. Complex Impedance, Generalized Ohm’s Law and Phasors:

Phasor analysis is used for steady state AC analysis. A phasor is a complex number representation of sinusoidal currents and voltages in a circuit. In AC steady state analysis, capacitors and inductors are replaced with their complex impedances (see Table 8.1 below).

Table 8.1 R, L, C and their equivalent impedances for AC steady state analysis.

Circuit Element R C L

Impedance

RZ R= 12 2C

jZj fC fCπ π

−= =

2LZ j fLπ=

Note that the impedance of a capacitor and an inductor is a function of frequency whereas the resistance is not a function of frequency. The generalized Ohm’s law can be applied to circuit elements represented with their equivalent impedances in AC steady state analysis. The generalized Ohm’s law is stated as

V ZI= , where

Z = the impedance of the element (refer to Table 8.1), V = the voltage across the element represented as a phasor, and I = the current through the element represented as a phaosr.

Once the circuit elements are represented by their equivalent impedances and the sources are represented using phasors; KVL, KCL, mesh current analysis, node voltage analysis, Thevenin and Norton Theorems can be used to solve for phasor currents and phasor voltages in the circuit.


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Resonance

Resonance is a phenomenon that occurs in a variety of engineering systems (e.g., mechanical and electrical systems). A system is said to be at resonance if the system tends to oscillate at a high oscillations when excited close to or exactly at the system’s natural frequency. A second order circuit is said to be at resonance if the equivalent impedance for the circuit is resistive, i.e., the impedance is real. For example, a series RLC circuit has equivalent impedance given by

1 2 - 2 -2 2eq R L C

jZ Z Z Z R j fL R j fLfC fC

π ππ π

= + + = + = +

.

At resonance, the equivalent impedance for the circuit is resistive, i.e., Zeq = R. This

implies that the imaginary part of Zeq is zero, i.e., 122

fLfC

ππ

= . This occurs when the

source frequency is equal to the resonant frequency for the circuit, i.e. 01

2f

LCπ= [Hz].

It can be easily shown that the resonant frequency for a parallel RLC circuit is also given by 0

12

fLCπ

= [Hz].

EXERCISE 8.1 A SERIES RLC CIRCUIT

Consider the circuit shown in Figure 8.1 below. Use PSpice to study the circuit response (voltage and current) as a function of frequency.

1. Draw the circuit of Figure 8.1 in PSpice and set the amplitude of the input source

to 50V (an AC voltage source can be placed by typing VAC in the place part field).

2. Create a Simulation Profile. In the Simulation Settings window (From PSpice menu/Edit Simulation Profile), select AC Sweep/Noise.

3. Enter the start and end frequencies and the number of points per decade. Use 100 Hz, 10 GHz and 10, respectively.

4. Plot the magnitude of the phasor current as a function of frequency (go to PSpice, choose Markers/Advanced then “dB Magnitude of current”). Run the simulation and save the figure.

5. Plot the phase of the phasor current as a function of frequency (go to PSpice, choose Markers/Advanced then “Phase of Current”). Run the simulation and save the figure.

6. Plot the magnitude of the phasor voltage across the inductor as a function of frequency (go to PSpice, choose Markers/Advanced then “dB Magnitude of voltage”). Run the simulation and save the figure.

7. Plot the phase of the phasor voltage across the inductor as a function of frequency (go to PSpice, choose Markers/Advanced then “Phase of voltage”). Run the simulation and save the figure.

In your report, include the magnitude and phase plots for the circuit current and the inductor voltage. Calculate analytically the circuit current, I, and the inductor voltage, VL, using phasors and plot the magnitude and phase plots of I and VL. Compare your analytical results with the simulation results obtained using PSpice for the frequency range 100 Hz − 10 GHz.


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Determine the resonant frequency (f0) for this circuit both analytically and from the simulations. Are the two values in agreement? Explain.

Figure 8.1 Circuit for Exercise 8.1 (R = 1 kΩ, C=1 nF, and L = 10 µH). EXERCISE 8.2 Use PSpice to draw and simulate the circuit shown in Figure 8.2. The voltage source and the current source can be placed using VAC and IAC, respectively, from the place menu.

1. Plot the magnitude and phase of the phasor current through R2 as a function of frequency over the range 1 Hz to 10 MHz and number of points 100.

2. Plot the magnitude and phase of the phasor voltage across L and as a function of frequency over the range 1 Hz to 10 MHz and number of points 100.

Include a discussion on the results in your report.

R1

1k

C1

1u

L11HV1

50Vac0Vdc

0

R21k

I1

0Adc100Aac

Figure 8.2 Circuit for Exercise 8.2 (R1 = R2 = 1 kΩ, C =1 µF, and L = 1 H.).

Note: The dB magnitude plot of a certain variable, say I(f), as a function of frequency is the plot of 1020log ( )I f versus frequency. Reference

Chapter 5 and Chapter 6 of text book, Electrical Engineering, Principles and Applications, by Allan R. Hambley (any edition).


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Laboratory 9: DIODES AND THEIR APPLICATIONS

OBJECTIVES

To illustrate the current-voltage (I-V) characteristics of diodes. To illustrate applications of diodes in rectifier circuits and in wave-shaping circuits.

INSTRUMENTS NEEDED


PARTS NEEDED

Solderless Breadboard 1 KΩ, 10 KΩ Resistors 1 μF, 10 μF Capacitors Diode IN4007

BACKGROUND

A diode is a two terminal device that passes current in one direction only (analogous to valves in mechanical systems). The symbol for a diode is shown in Figure 9.1 (a). The current-voltage characteristics for a typical diode is shown in Figure 9.1 (b). If the voltage across the diode (VD) is greater than a threshold voltage (VT), the diode conducts and the current increases exponentially as a function of voltage. If on the other hand, VD < 0, then no current passes through the diode. In such a biasing scenario, the diode is reverse biased. The threshold voltage VT is approximately 0.7 V for Silicon diodes.

Figure 9.1 Diode symbol and v-i characteristics. A simple diode circuit is shown in Figure 9.2 (a). If vs> VT then the diode conducts and current flows in the circuit. Kirchhoff’s voltage law applied to this circuit gives vS = vD + v, or v = vS - vD= vS – vT. If vS is sinusoidal, then the diode conducts only in the positive half-cycle when vS > vT. In the negative half cycle, the diode blocks the current and the voltage across R is zero (see Figure 9.2 (b)).


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(a) A simple diode circuit.

(b) Resistor voltage when the source voltage is sinusoidal (vs=Vp sin(ωt))

Figure 9.2 EXERCISE 9.1 DETERMINING THE CURRENT-VOLTAGE CHARACTERISTICS OF DIODES

1. Set up the circuit shown in Figure 9.3. Use R = 1 kΩ. 2. Vary the voltage of the power supply between -3 V and 5 V in steps of 0.5 V.

For each value of vs, measure iD and vD. Plot iD versus vD, (this is called the current-voltage characteristics of the diode). Does the slope ∆iD /∆vD increase or decrease as the current through the diode increases? Does this agree with the theory?

3. For values of vs > vT , how is vD related to the power supply voltage? Explain?

+

-

vD

iD

R

vS


In your report, in addition to answering the questions posed above, plot the diode current versus diode voltage and compare the resulting plot with the theoretical current voltage characteristic of a typical diode.


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APPLICATIONS OF DIODES EXERCISE 9.2 RECTIFIER CIRCUITS

4. Set up the circuit shown in Figure 9.4. Use a function generator (FG) and set the output of the FG to sinusoidal with peak value 5 V and frequency 1000 Hz. Use R = 1 KΩ.

+-

+

-

R vR

iD + vD -

vs


5. Use the oscilloscope to view both the output of the function generator (on

Channel 1) and the voltage across the resistor vR (on Channel 2). Use DC coupling for both channels and set the time/div control to an appropriate value so that you can view a few cycles on the screen. (Pay attention to the ground connections)

6. Draw the waveform vR. What is the peak value of vR? In your report, include a sketch of the voltage across the resistor and the voltage across the diode and compare these voltages with the supply voltage. AC TO DC CONVERTERS

7. Setup the circuit shown on Figure 9.5. Use a function generator and set the

output of the FG to sinusoidal with peak value 5 V and frequency 1000 Hz. Use R=10 kΩ , C=1 μF, and a diode.

8. Use the oscilloscope to view both the output of the function generator (on Channel 1) and the voltage across the resistor v (on Channel 2). Use DC coupling for both channels and set the time/div control to an appropriate value so that you can view a few cycles on the screen.

9. What is the average value of the waveform v? 10. What is the ripple (variation) of the waveform v in volts? What is the ripple as

a percentage of the average value found in step 8? 11. Replace the 1 μF capacitor with a 10 μF capacitor and repeat steps 9 and 10.

What is the effect of the capacitor value on the ripple. Explain qualitatively. Include answers to the questions posed in steps 9 through 11 in your report.


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+-

+

-R v

+ vD -

vs C

Figure 9.5 AC to DC conversion circuit.

VOLTAGE LIMITERS

12. Setup the circuit shown in Figure 9.6. Use R=10 kΩ and both the function

generator (for vin) and the power supply (for vDC). Keep both the power supply and the function generator off.

13. Use the oscilloscope to view both the output of the function generator vin (on Channel 1) and the output voltage vout (on Channel 2).

14. Set the power supply output to 2 V and the output of the function generator to sinusoidal with peak value 5 V and frequency 1000 Hz. Use DC coupling for both channels of the scope and set the time/div control to an appropriate value so that you can view a few cycles on the screen.

15. Change the output of the power supply to 3 V and observe both vin and vout. 16. How is vout related to vin. Explain. 17. (17 & 18 are optional, bonus 3 pts) Design a circuit that limits the voltage in

both the negative and positive half cycles. (Hint: the circuit should be a variation of the one shown in Figure 6).

18. Build the circuit and test it. Include a sketch of the circuit and a sketch of the circuit output in your report.

+

-vD

R

+-

vin

+

-

vout+-vDC

Figure 9.6 A Voltage limiter circuit.

Include your observations/sketches and answers to the questions in your report.


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Laboratory 10: OPERATIONAL AMPLIFIERS

OBJECTIVES

• To build and analyze an inverting amplifier circuit using an operational amplifier (op-amp).

• To learn the basics of operational amplifier circuits and how the gain of an amplifier changes with frequency.

INSTRUMENTS NEEDED


PARTS NEEDED

Solderless breadboard 1 kΩ, 10 kΩ Resistors 741- operational amplifier

DESCRIPTION

Amplifiers are used to increase the magnitude (amplify) a voltage signal. Typically, the output signal of an ideal amplifier is a scaled up version of the input signal. In this lab, students will build an inverting amplifier circuit based on the schematic shown in Figure 10.1. It is straightforward to show that the input-output relationship

for the inverting amplifier is given by 2

1out in

RV VR

= −

. This amplifier is called an

inverting amplifier because the amplifier gain is negative. A 741 op-amp and resistors will be provided in addition to a breadboard and wire for circuit construction. A picture of a 741 op-amp is given in Figure 10.2. Pin layouts for the 741 op-amp are provided in Figure 10.3.

+

−

VinVout

+

−

+

−

R1

R2

Figure 10.1 An inverting amplifier circuit.


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Figure 10.2 A picture of a 741 op-amp.

Figure 10.3 The 741 op-amp pin layout.

EXERCISE 10.1: INVERTING AMPLIFIER EXPERIMENTAL SETUP:

1. Make sure that the function generator, DC power supply and the oscilloscope are turned off. Turn the amplitude knobs on the function generator and DC power supply counterclockwise to zero.

2. Build the inverting amplifier circuit shown in Figure 10.1 on the provided breadboard using the two resistors (R1 = 1 kΩ and R2 = 10 kΩ) and wire provided by the lab instructor.

3. Set the output voltages on the DC power supply to +5 V and −5 V. Check the output voltages with a multimeter and/or oscilloscope before applying any power to the amplifier circuit. Ask the lab instructor for assistance to check the power supply readings and inverting amplifier circuit before continuing.

4. With the power off, connect the DC power supply to the op-amp power terminals (connect the +5 V to the +V pin and the −5 V to −V pin, refer to Figure 10.3). Set the function generator to output a 100 Hz sine wave. Connect the function generator, while it is off, to the inverting input of the op-


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amp and connect the non-inverting input to the ground. Finally, connect the oscilloscope to monitor the function generator and inverting amplifier output signals.

5. Turn on the power for the oscilloscope and then the DC power supply. Next, turn on the function generator.

6. Slowly increase the function generator sine wave voltage from a minimal value until the output of the inverting amplifier begins to clip or saturate. Record the Vout peak-to-peak and Vin peak-to-peak values over this range of voltage with increments of 0.1 V for Vin peak-to-peak and record the phase difference between Vout and Vin. Include this data in your report.

7. Sketch Vin and Vout versus time for 3 different Vin peak-to-peak settings. Include these plots in your report.

8. Estimate the amplification factor (Vout/Vin) for the 0.4 Vin peak-to-peak and frequency 100 Hz. Compare the experimental based amplification factors to the theoretical amplification factor ( 12 RR ). Include these comparisons in your report.

9. Set the function generator to output a 1000 Hz sine wave and 0.4 V peak-to-peak. Calculate the gain. Vary the frequency of the output of the function generator to 10 kHz, 20 kHz, 50 kHz and calculate the gain each time. Plot the gain as a function of frequency. How does the gain vary as a function of frequency?

Include your observations, sketches and answers to the questions posed above in your report.


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APPENDIX A. REPORT WRITING Report writing is an important skill that engineers need to master. As an engineer, you need to communicate your results using technical reports. In ENME 350/351 labs, upon the completion of an experiment, each member of the lab group should submit an individual report. The purpose of the report is to document the results of the experiment. The lab report should be concise, neat, and complete. Although hand written reports are accepted, typed reports are preferred. You are strongly encouraged to use a word processor software for writing text and graphing software such as Excel or Matlab for producing graphs. When writing the report, be clear and concise and use complete sentences. Write as though the person reading your lab report is familiar with engineering principles but is not familiar with the particular experiment that you have performed. Check the course website on Blackboard for the times that the Teaching Assistants will be available for consultation (office hours). Consider taking your preliminary (not draft) report to your TA for comments. Also, make sure that you collect names and e-mail addresses of all your partners before you leave the lab. Each partner should have a copy of the saved data (i.e., don’t depend on getting the data from your partners later).

WHAT SHOULD BE INCLUDED IN THE REPORT

A full technical report includes all of the following sections shown below. For Spring 2011 semester we are trying to cut down on the amount of work required to prepare a report. For Spring 2011 the report should only include sections; (1) title page, (5) Data and Observations, (6) Analysis, (7) Summary & Conclusion, and (9) Appendix – if any

. The goal is to make the report 3-5 pages in length (including tables and figures – assuming the tables and figures are not full page in size). Some experiments may require a longer report to answer all questions posed in the experiment. Note, all figures and tables should be described. It is NOT proper to just say the results are shown in figure x. State specifically what is shown in a figure or table.

(1) Title page (a) Title of experiment (b) Your name and names of partners (c) Course number and section number (d) Date of experiment (This is the date when the experiment was performed)

(2) Objective(s)

Briefly summarize the objective(s) of the experiment. Use your own description; do not copy from the lab manual.

Items (1) should be on the first page (title page). See page 3 for a sample title page. The second page should start with item (2). (3) Instruments used


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(4) Description of experiment and experimental setup

In this section, briefly describe the experiment and the experimental setup. Do not include step-by-step description as in the lab manual. Use sketches/diagrams to demonstrate the experimental setup.

(5) Data and observations

Tables and graphs should be used for data presentation and should be included inline with the text of the report. All tables and graphs must be numbered and cited in the text. A short discussion on each graph should be included. Clearly label the tables and the graphs using a title for each. For graphs, the x and y axes on each graph should be clearly labeled with the variables including the units used (e.g., time [s]). Similarly, for tables, each column should have a header with the variable and units (e.g., acceleration [m/s2]) (see Table 1 for an example).

Table A.1 Load versus voltage for the half bridge circuit (given here as an example)

Load [kg] Voltage [mV] 0.2 1.5 0.5 3.2 1.0 6.5 1.5 9.1

(6) Analysis and discussion

Compare your results with theoretical results (if any) and discuss possible sources of errors and discrepancies. Make sure to address any questions that are presented in the lab manual. Also, briefly comment on every figure you include in the report.

(7) Summary/conclusion

Summarize the main results of the experiment and write your conclusions. (8) Literature cited.

Include a list of all resources used (books, papers, and websites). (9) Appendices (if any)

Details that would make the report very long should be included as an appendix and should be cited in the text.


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Laboratory #

Write the Title of the Experiment Here

Your name

Names of partners

ENME 35x Section 010x

Date: Day MM/DD/YYYY (This is the date when the experiment was performed)

Sample report.


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SAMPLE REPORT: VERIFICATION OF OHM’S LAW Objectives

The objectives of this experiment are to learn how voltages and currents are measured in direct current (DC) circuits using a multimeter, to determine the voltage-current (v-i) characteristics of a resistor from voltage and current measurements, and to verify Ohm’s law.

Instruments Used

• Power supply (PS) • Digital Multimeter (DMM)

Parts Used

• A resistor (20 k Ω) • Wires

Experimental Setup and Procedure

The schematic of the circuit used in this experiment is shown in Figure A.1. A resistor R with value 20 kΩ is used in this experiment. However, the actual measured value of the resistor is 19.89 kΩ. Electric current in a branch in the circuit is measured by connecting the DMM in series with the branch whereas the voltage across an element is measured by connecting the DMM in parallel with the element. The source voltage VS is varied between −5 V and 5 V in steps of 1 V and the current through the resistor, denoted by IR, and the voltage across the resistor, denoted by VR, are measured for each value of VS. The data collected is shown in Table 2 below.

Vs

IR

R +−

+

−

VR

Figure A.1 The circuit used to verify Ohm’s law

Table A.2 Resistor voltage and current for different values of source voltage.

Source Voltage [V] Resistor Voltage [V] Current [mA] -5.07 -5.05 -0.25 -3.99 -3.98 -0.20 -3.08 -3.08 -0.15 -1.95 -1.95 -0.10 -0.92 -0.92 -0.05 0.00 0.00 0.00 1.02 1.02 0.05 2.07 2.05 0.10 3.01 3.01 0.15 3.94 3.94 0.20 5.02 5.01 0.25


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Analysis and Discussion

The voltage across the resistor is plotted against the current. The resulting plot is shown in Figure A.2. A trend line is fit to the data points and has the equation 19.89R RV I= , where VR is the voltage across the resistor and IR is the current through it.

Votage vs Current

V = 19.89i

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30

Current (mA)

Vol

tage

(V)

Figure A.2 The v-i characteristic for a resistor.

This simple exercise verifies Ohm’s law by demonstrating the linear relationship between the resistor voltage and current. The measured resistance is equal to the slope of the data points as expected from Ohm’s law:

19.89R RV I= . Conclusion

In this experiment, the way voltage and current are measured in DC circuits using a DMM were demonstrated. Ohm’s law was verified through the plot of the voltage-current (v-i) characteristic of a resistor. The v-i characteristic for a resistor was obtained by measuring the voltage across the resistor and current through it for several source voltages. The v-i characteristic plot of a resistor obtained in this experiment was linear with the slope of the graph equal to the resistor value R which is in agreement with Ohm’s law.


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APPENDIX B. SOLDERLESS BREADBOARDS

A solderless breadboard (also called plugboard) is used to facilitate building simple circuits without the need to solder components. It is typically used to build temporary circuits. The breadboard is ideal for use in educational settings where students can experiment with building various circuits and have the flexibility of modifying the circuit. Another advantage of using breadboards is that circuits built on the breadboard can be easily stripped and the circuit components can be reused to build other circuits. Figure A2.1 shows a schematic of the breadboard used in the lab. The way the holes are connected internally is demonstrated on the schematic. For example, to make a node with 5 branches or less, you can use the vertical holes A-E or F-J. To make a node with more than 5 branches, one needs to use the horizontal holes along one of the horizontal line W, X, Y or Z.

Figure B.1 A schematic of the breadboard used in the laboratory showing how the holes are

connected internally.

Documents

enme350-LabManual Spring 11-2