INTRODUCTION TO ENGINEERING AND LABORATORY EXPERIENCE Spring, 2015

Transcription

1 INTRODUCTION TO ENGINEERING AND LABORATORY EXPERIENCE Spring, 2015 Saeid Rahimi, Ph.D. Jack Ou, Ph.D. Engineering Science Sonoma State University A SONOMA STATE UNIVERSITY PUBLICATION

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3 CONTENTS 1 Electronic Components, Voltage, Current and Resistance Introduction Ohm s Law Experiment 3 2 DC Power Supply, Ohm s Law, Current Measurement, and Resistor Combinations DC Power Supplies Assignment Ohm s Law: A review Resistor Combinations Resistors in series Resistors in parallel Series and parallel combination Assignment Current measurement Assignment 13 iii

4 iv CONTENTS 3 Voltage and Current Dividers Voltage Law Assignment Current Law Voltage Divider Assignment A Variable Voltage Divider 19 4 Introduction to AC Measurements: AC Signals, Function Generators and Oscilloscopes Introduction Square Wave Ducy Cycle Monitoring AC Signals Procedure 24 5 RC Time-Constant Applications Introduction Low-pass and high-pass filter A low-pass filter 32 6 Diodes: Half-Wave and Full-Wave Rectifiers Introduction Half-Wave Rectifier Circuit Full-Wave Rectifier 37

5 CHAPTER 1 ELECTRONIC COMPONENTS, VOLTAGE, CURRENT AND RESISTANCE 1.1 Introduction The computers at your lab stations are connected to the SSU network. Open the Engineering Science department home page and open the link to the courses with web pages. Open ES 110 webpage and click on Lab 1 link within the course syllabus. Use your SSU user name and password to log on. Electronic instruments and circuits are made up of individual and integrated electronic components. In general both analog and digital components are involved. In this laboratory you will become familiar with some individual analog electronic components: switches, resistors, capacitors, inductors, diodes, and transistors. Figure 1.1 includes images of these components. In particular pay attention to the number of wires (legs, pins, leads) coming out of these devices. Generally the simple devices (resistors, capacitors, inductors, diodes) have two legs. Transistors and integrated circuits (ICs) have more than two pins. All electronic components are made up of one or more of the following materials: Conductors, semiconductors, semi-insulators, and insulators. Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

6 2 ELECTRONIC COMPONENTS, VOLTAGE, CURRENT AND RESISTANCE Figure 1.1: Analog electronic components. The electronic symbols for identifying some of these components are illustrated in Figure 1.2. Each of these components has a specific function in a circuit. Today we will examine the properties of resistors and will learn to identify the other components. In this introductory exercise you will learn about the properties of resistors. The functions and properties of the other components will be covered in the future laboratories and courses. But first let us learn about the materials from which these components are made of. 1.2 Ohm s Law The single most important formula in all of electronics is described by the Ohms Law: V = IR, where V is the voltage, I is the current, and R is the resistance. This formula may be written in different forms and it can be used to derive expressions for other parameters such as electric power, P = V I = RI 2 = V 2 /R (1.1) V is the voltage that is applied to the device and I is the electric current that flows through the device due to the voltage difference at the two ends of the device. Voltage difference is sometimes referred to as the voltage drop or potential difference. The magnitude of I is determined by the electrical resistance R. Units: V (Volt), I (Ampere), R (Ohm). In general, electric current and voltage are either direct or alternating. The definitions of these two current and voltage types will be covered at the lecture part of this course. In this lab we will use direct current (DC) which means that the direction of motion of charges within a piece of wire or resistor is constant and does not change.

7 EXPERIMENT 3 Figure 1.2: Circuit symbols. 1.3 Experiment In this section you will learn the color codes that determine the value of a resistor and then use the breadboard for connecting resistors and other electronic components without having to use clips or solder. You can determine t he value of a resistor by using a multimeter or by reading its color code. The manufacturers of resistors employ color bands for determining their value and tolerance. The tolerance of a component indicates the degree of accuracy of the value assigned to the resistor. For example, consider a 1,000 Ω resistor with a 5% tolerance. This means that the actual value of the resistance of this resistor could be anywhere between 1,000-5% (1,000), and 1, % (1,000). In another words, the actual value of the resistance of this resistor is 950Ω < R < 1, 050Ω. Examine the color chart in Figure 1.3: 1. From the resistor drawer (Figure 1.4a) pick three resistors, 300 Ω, 1 kω, and 68 kω. Check the value of these resistors from (a) the color code and (b) using a multimeter (Figure 1.4b). Create a table with three rows and indicate the value of the resistor using the color code and multimeter reading. Your instructor will demonstrate how to use a multimeter. Calculate and record the errors. Rotary

8 4 ELECTRONIC COMPONENTS, VOLTAGE, CURRENT AND RESISTANCE Figure 1.3: Color chart. dial of the multimeter should be on Ω. Note that the multimeter is also capable of measuring voltage, current, capacitance, and can be used for testing circuit continuity. (a) (b) Figure 1.4: Resistance measurement.

9 EXPERIMENT 5 2. From the capacitor drawers pick three ceramic capacitors: 22 nf, 0.1 µf, and 3.9 µf. Measure the capacitance of these capacitors with the Fluke multimeter and with the HP 4192A capacitance meter located behind the last row of the class (Figure 1.5). Calculate and record the three values in a table and indicate the errors for each label. Figure 1.5: HP 4192A capacitance meter. 3. Turn the protoboard power on. Use the multimeter to measure the voltage output of the 5 V terminal. For measuring voltage you need not disturb the circuit. Simply touch two points of the circuit with the red and black leads. Determine the % error of the power supply. Also use the multimeter to measure the output of the variable positive and negative voltage terminals as shown in Figure 1.6. Determine the maximum and minimum of each output and record the values in your lab book. Note that, in addition to the power supply, the protoboard has many other useful features including a function generator, LEDs, digital logic indicators, potentiometers, a speaker, digital and push-button switches. Your instructor will demonstrate the inner connections of the breadboard located on the protoboard. 4. Now insert the 1 kω resistor in the breadboard and apply 5 V to the resistor by connecting one end of it to the 5 V output of the power supply and the other end to the common terminal of the power supply (ground). Use the multimeter to measure the voltage across the resistor. Record this voltage in your lab book. Disconnect the power connections to the resistor.

10 6 ELECTRONIC COMPONENTS, VOLTAGE, CURRENT AND RESISTANCE Figure 1.6: Voltage measurement. 5. Next add the 300 Ω in series to the 1 kω resistor. Connect the free end of the 1 kω resistor to the 5 V source and the free end of the 300 Ω resistor to the ground. Measure the voltage across each resistor and record in your lab book. A meter that measures voltage is called a voltmeter. 6. Use the multimeter to measure the current through the circuit as shown in Figure 1.7. First unplug the read connector from the multimeter location marked by V and Ω, and plug it into the top left hole marked for current. CAUTION: DO NOT use the ammeter the same way that you use the voltmeter. In order to measure current you MUST open the circuit at the desired point and insert the meter in the circuit. The dial of the meter should be rotated to A. For a DC measurement you will need to press the yellow function button. A meter that measures current is called an ammeter. 7. Now the fun part: Light up a Light Emitting Diode (LED). You will be provided with LEDs. Insert a 220 Ω resistor in the breadboard. Connect your LED in series to the resistor. Connect one wire from the 5 V power supply to a pushbutton switch. Next connect the other end of the switch to the resistor, and the other end of the diode to the ground. Now push the switch and see if the diode lights up. Reverse the position of the diode and try the switch again. We will discuss the diode in detail in a later lab. Hold the switch down and measure the

11 EXPERIMENT 7 Figure 1.7: Current measurement. voltage drop across the resistor and the diode. Record the values in your lab book. 8. In the final part of this experiment search the internet and find an application that can be used to draw a circuit. Use your computer to draw the circuit diagram of the last step. Make sure that you download your desired circuit drawing application on your personal computer at home. 9. Show your work to your instructor for his signature!

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13 CHAPTER 2 DC POWER SUPPLY, OHM S LAW, CURRENT MEASUREMENT, AND RESISTOR COMBINATIONS 2.1 DC Power Supplies A power supply is a device that provides the energy required to power up a circuit. In this section we will experiment with DC (Direct Current) power supplies. We will experiment with the AC (Alternating Current) power supplies or function generators in the future labs. Batteries are the most common types of DC power supplies. In this lab we will experiment with the Agilent E3630A power supply as shown in Figure 2.1. The device output will be displayed on its front screen. However, multimeters are commonly used for measurement of basic electrical resistance, voltage, and current. Your station is equipped with a Fluke 179 multimeter. In this lab we will use both instruments. In order to become familiar with the use and accuracy of the DC power supply, try the following procedure Assignment 1. Set the function on Agilent E3630A to +6V. Adjust the voltage to 4.5 Volts. Measure the voltage using Fluke 179. Write down the results. Make sure you turn the output power on. Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

14 10 DC POWER SUPPLY, OHM S LAW, CURRENT MEASUREMENT, AND RESISTOR COMBINATIONS Figure 2.1: Agilent E3630A DC power supply. 2. Set the function to +20V. Adjust the voltage to +8 volts. Measure the voltage and record the result. 3. Set the function to -20V. Adjust the voltage to -10 volts. Measure the voltage and record the result. 4. Fluke 179 has a continuity function. Set it to that function and check the continuity of a piece of wire. If there is no cut in the wire, you should hear the buzzer sound. Test the continuity of a few cables by connecting the meter leads to the ends of the wires. 2.2 Ohm s Law: A review Ohm s law states that the voltage drop across a resistor has a linear relationship to the current flowing through the resistor. Graphically this linear relationship is represented by a line when the current through the resistor is plotted against the voltage across it. This graph is termed I-V characteristic of the device. A linear I-V graph indicates that the resistance of the device remains constant over a wide range of currents and voltages. For many electronic devices the resistance is not a constant and varies with the applied voltage and current. These devices possess non-linear I-V characteristics. However, the slope of the curve at any given point determines the resistance of the device for that particular current and voltage. 2.3 Resistor Combinations In order to achieve the desired purpose of a circuit it is necessary to have a specific value for the utilized resistors and capacitors. The resistor bins in the laboratory only stock certain common values of resistors. These resistors can be connected to each other (combined) to practically create any desired resistance. There are rules governing the combination of the electronic elements. Today we will work with the

15 RESISTOR COMBINATIONS 11 combination of resistors. Capacitors may also be combined, but their combination rules are different from resistors. Resistors may be connected in the following combinations Resistors in series For a serial combination of resistors as shown in Figure 2.2, the equivalent resistance for this combination is: R e = R 1 + R (2.1) R 1 R 2 R 3 Figure 2.2: Resistors in series. Clearly in a series combination of resistors the same current goes through all resistors. Eq. 2.1 can be easily obtained using Ohm s law. The derivation for the quivalent resistance of series and parallel combination of resistors can be found in the lecture part of this course, on the Internet, or in most elementary electronic text books Resistors in parallel For parallel combination of resistors in Figure 2.3, the equivalent resistance of the parallel combination is given by 1/R e = 1/R 1 + 1/R (2.2) R 1 R 2 R 3 Figure 2.3: Resistors in parallel Series and parallel combination Sometimes we may need to mix these two combinations to achieve a specific resistance. For cost reduction, the number of components in the circuit should be minimized. A mixed series and parallel combination of resistors is shown in Figure 2.4.

16 12 DC POWER SUPPLY, OHM S LAW, CURRENT MEASUREMENT, AND RESISTOR COMBINATIONS 12V + V 1 R 1 R 2 R 3 R 4 Figure 2.4: Series and parallel combination Assignment Combine two or more resistors (series and/or parallel) to create an electrical resistance of 1240 Ohms. Describe and justify your method and calculate the expected value of the resulting resistance. Use your multimeter to determine the value of each resistor and apply the series and/or parallel combination of resistors to determine the expected value of the resulting resistor. Compare the observed value and the expected value of the resistor combination, and make a note of the % error. Note that it is important to measure the value of resistors when they are disconnected from the circuit and from the breadboard. Please do all the calculations in your lab notebook. Show the calculation and measurement result to the instructor when you are done. 2.4 Current measurement Electric current may be measured by the Fluke multimeter and other electronic instruments. However, in this lab we use Ohm s law to measure current. To do so we measure the voltage drop across a resistor (V AB ) and divide by its resistance (i.e. R 1 ) as shown in Figure 2.5. I = V AB /R 1 (2.3) 12V + 4.7kΩ A R1 B V 1 Figure 2.5: Current calculation using Ohm s law.

17 CURRENT MEASUREMENT Assignment 1. Construct the circuit shown above using the breadboard. Use the Agilent DC power supply to provide the voltage to the circuit. Measure the voltage V AB across resistor R 1 and use Ohm s law to calculate the current through the resistor. 2. Next, add a second resistor in series with the first as shown in Figure 2.6. Measure the voltage across each resistor (V AB, V BC ) and calculate the current through R 1 and R 2. The two current values must be the same. Can you explain why! 12V + 4.7kΩ A R1 B V 1 R 2 C 1kΩ Figure 2.6: Determination of I meas. 3. Calculation: use the series resistor combination rule and calculate the equivalent resistance R e of the above series resistor combination. Redraw the circuit replacing the two resistors with the equivalent resistor. Use Ohm s law to calculate the current in the circuit and name it the expected current I exp. Calculate the % error between I exp and I meas : %error = I exp I meas I exp 100 (2.4) 4. Please show the % error calculation to the instructor. 5. Take the circuit apart and reconnect the resistors in parallel and apply the voltage as shown in Figure 2.7. Measure the current I 1 and I 2 through resistors R 1 and R 2, respectively. The total current supplied by the power supply is I total = I 1 + I Use the parallel resistor combination rule and calculate the equivalent resistance (R e ) of the two parallel resistors. Redraw the circuit replacing the two resistors with R e. Use Ohm s law to calculate the current through R e. Call this current I e. Ideally I e should be the same as I total. Calculate the % error between the measured and the expected values.

18 14 DC POWER SUPPLY, OHM S LAW, CURRENT MEASUREMENT, AND RESISTOR COMBINATIONS 6V + V 1 A R 1 B 1kΩ R 2 4.7kΩ Figure 2.7: Calculation of I total. 7. Next add resistor R 3 as shown below and use Ohm s law to measure (calculate) I 1, I 2, and I 3. Note that the current through R 3 branches out and a portion of it flows through R 1 and the rest of it goes through R 2. The current in these two branches I 1 and I 2 combine at point B and return to the negative terminal of the battery. 12V + 2.9kΩ C R3 A V 1 R 1 B 1kΩ R 2 4.7kΩ Figure 2.8: Current calculation 8. Calculate the equivalent resistance R e of the above circuit. Redraw the circuit substituting R e for the three resistors in the circuit. Use Ohm s law to calculate the current in this equivalent circuit. 9. Please show the calculation of R e to the instructor. 10. In order to demonstrate the difference between series and parallel resistor combinations, consider first the series combination of three resistors (Figure 2.9) and then the parallel combination of the same three resistors (Figure 2.10). Three identical LEDs are attached to each resistor so you can visually see the strength of the current in each resistor through the brightness of the LEDs. Construct each circuit and observe the LED brightness for each combination and translate that to the current values in each combination.

19 CURRENT MEASUREMENT Ω 200Ω 200Ω 200Ω 5V + R 0 R 1 LED 1 R 2 LED 2 R 3 LED 3 Figure 2.9: Series circuit. 1kΩ R 0 + 5V V 1 R 1 200Ω R 2 200Ω R 3 200Ω LED 1 LED 2 LED 3 Figure 2.10: Parallel circuit.

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21 CHAPTER 3 VOLTAGE AND CURRENT DIVIDERS This experiment is designed for practicing the voltage and current circuit laws discussed earlier. The application of the exercises in this laboratory will help you construct simple circuits that will deliver desired voltages using an available battery. For example, suppose you need a 5 V voltage source using an available 12 V battery. This is what a voltage divider circuit does. In a similar fashion one can create a desired small current using a larger current. Although we do not use a current divider as often as a voltage divider, nonetheless it is instructive to learn the process. In order to achieve this goal we need to cover some basic exercises first. 3.1 Voltage Law Let us start with the simple circuit in Figure 3.1, which includes a battery connected to resistors in series, R 1 = 1kΩ, and R 2 = 4.7kΩ. The circuit voltage law states that the battery s voltage equals the sum of voltage drops across the two resistors connected in series: V battery = V R1 + V R2 (3.1) Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

22 18 VOLTAGE AND CURRENT DIVIDERS 12V + 4.7kΩ A R1 B V 1 R 2 C 1kΩ Figure 3.1: Resistors in series Assignment 1. Measure the voltage drop across the two resistors (i.e. V AB, and V BC ). 2. Compare the measured voltages with with the voltages calculated using Eq. 3.1 and Eq V AB = R 1 R 1 + R 2 V battery (3.2) V BC = R 2 R 1 + R 2 V battery (3.3) 3. Please show the measured and calculated results to the instructor when you are done with this exercise. 3.2 Current Law Let us build the circuit in Figure V + V 1 A R 1 B 1kΩ R 2 4.7kΩ Figure 3.2: Resistors in parallel. 1. Connect the resistors in parallel.

23 VOLTAGE DIVIDER Measure the voltage across each resistor. Divide the voltage by the resistance of each resistor to calculate the current in each resistor. I 1 is the current in R 1 and I 2 is the current in R Calculate the equivalent resistance of the two parallel resistors. The results should be less than the smallest resistance. The result should be less than the smallest resistance. Measure the voltage across the battery and divide the battery voltage by the total resistance to get the total current (I). 4. Verify that I = I 1 + I Please show the measured and calculated results to the instructor when you are done with this exercise. 3.3 Voltage Divider We are going to create a 1.5 V voltage source and a 3.5 V voltage source from the 6 V output of the DC power supply at your lab station. In order to achieve this goal, you will need to connect more than two resistors in series to the battery. Assume the battery voltage is V battery. Here is a general formula for the voltage drop across any of the n resistors connected in series to a battery: V i = Where i designates any of the n resistors. R i R 1 + R 2 + R V battery (3.4) Assignment 1. Calculation: You will need to determine the minimum number of resistors you need to build such a voltage divider. Select R 1 to have a resistance of 1kΩ. Calculate the values of the rest of the required resistors. Show your calculation to your instructor before constructing the circuit. 2. Use the multimeter to demonstrate the desired voltages to your instructor. Once verified, draw the circuit diagram in your lab book, and clearly identify the points indicating the desired voltages. 3.4 A Variable Voltage Divider Let us replace resistor R 1 in Figure 3.3 with a variable resistor (potentiometer). If potentiometers are not available in the lab, use the potentiometers installed on the protoboards. Before you insert the potentiometer in the circuit, measure and record its minimum and maximum resistance by turning its control screw. Insert the potentiometer in the circuit as shown in the diagram below. Use your voltmeter to monitor

24 20 VOLTAGE AND CURRENT DIVIDERS the value of V AB across the constant resistor. Now change the value of the variable resistor by turning the screw of the potentiometer and observe the reading of the voltmeter. Make a note of the maximum and minimum voltage that you observe when you change the resistance of the potentiometer from minimum to maximum. You are observing a variable voltage divider at work. Please demonstrate the variable voltage divider circuit to the instructor to get a grade for this circuit. 10kΩ 12V + A R 1 V 1 B R 2 C 1kΩ Figure 3.3: Variable voltage divider.

25 CHAPTER 4 INTRODUCTION TO AC MEASUREMENTS: AC SIGNALS, FUNCTION GENERATORS AND OSCILLOSCOPES 4.1 Introduction Unlike a DC signal in which charges flow only in one direction, the direction of motion of electric charges in an alternating current (AC) signal varies with time. A DC current is characterized by its magnitude and direction. For an AC current the magnitude of current in each direction changes with time, but the current reaches a maximum or minimum (amplitude) in each direction (Figure 4.1). In addition to the magnitude of the maximum value of current, we also need to know how fast the current goes through a complete cycle and changes direction (frequency f, period T ). Figure 4.1: Alternating current (AC) signals. Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

26 22 INTRODUCTION TO AC MEASUREMENTS: AC SIGNALS, FUNCTION GENERATORS AND OSCILLOSCOPES The manner in which the current changes with time defines the type of the AC current. Sinusoidal, saw-tooth, triangular square and pulsed signals shown in Figure 4.2 are among the most common types of AC signals. The voltage across a resistor through which an AC current flows is an AC voltage. Figure 4.2: Most common AC signals. Figure 4.3 illustrates the variations of a sinusoidal waveform. This voltage is characterized by its amplitude (1/2 of peak-to-peak voltage) and its period (the distance in time between two consecutive peaks). This sinusoidal signal is mathematically defined by the following equation: V (t) = V o sin(ωt + φ) (4.1) where, V 0 is the amplitude, ω = 2πf, f is freqeuncy, and φ is the phase. φ is zero in Figure 4.3. Two identical sine waves with different phases are shown in Figure 4.4. Figure 4.3: A sinusoidal voltage signal.

27 MONITORING AC SIGNALS 23 Figure 4.4: Two sinusoids with difference φ Square Wave Ducy Cycle A pulse or square wave is a signal that is off (low) for a length of time and on (high) for another length of time. The graph below indicates a repetitive pulse with period T that is on for time τ. The signal s duty cycle is defined to be 100(τ/T ). For example, a signal with a 50% duty cycle is on for 50% of time, whereas a 20% duty cycle means that the signal is high only 20% of time (Figure 4.5). Figure 4.5: A repetative pulse with a duty cycle less than 50 %. 4.2 Monitoring AC Signals The goal of this section of the lab is to monitor a time-varying signal generated by a function generator using an oscilloscope. You will connect the output of the function generator directly to one of the inputs of the oscilloscope to monitor the following signals. You will need to use special cables with BNC connectors at one end. For the function generator, use a BNC cable that has a BNC connector at one end and a black alligator clip and a red grabber at the other end (Figure 4.6). For the oscilloscope, use the special BNC cable provided in the pouch on top of the scope. The amplitude

28 24 INTRODUCTION TO AC MEASUREMENTS: AC SIGNALS, FUNCTION GENERATORS AND OSCILLOSCOPES and frequency of each signal will be 1.2 V and 4.8 khz, respectively. The task is to display two full cycles of the signal and to use the scope s cursors to determine the period of each signal. Figure 4.6: Left, the probles for the oscilloscope. Right, the probes for the function generator. There is a setting we need to change on the 33220A function generator (Figure 4.7) before we start. Here is the procedure: 1. Press Utility. 2. Press Output Setup soft key. 3. Under Load, change to High Z. It is a good practice to change the settings on the function generator to its default values as follows: 1. Press Save/Recall. 2. From the soft menu on screen, press corresponding button to Default Setup (i.e. Select A for sine wave, B for sawtooth wave, C for a square wave with 50 % duty cycle, and D for a square wave with 20% duty cycle.) Procedure 1. Basic idea: Your instructor will demonstrate the use of the Agilent 54622A (100 MHz) (Figure 4.8) oscilloscope to show the waveform of the Agilent 33220A waveform/function generator. A function generator creates the desired wave and delivers it through its output. On the other hand, an oscilloscope is an instrument that captures and displays the shape and strength of the signal. The oscilloscope display is a two-dimensional screen that measures voltage, V on its vertical axis and time, t on its horizontal axis. To display a time-varying

29 MONITORING AC SIGNALS 25 Figure 4.7: 33220A function generator. signal, we should be able to monitor and record the height (voltage) of the signal as time progresses. The advantage of using a repetitive (periodic) signal is that shape of the signal during a certain period can be displayed. In order to obtain a digital waveform for the analog display of the scope, we can connect the scope to a computer and save, analyze, and record the data. You can find the manuals for function generator and oscilloscope user guide by going to the department s webpage, and look for the equipment user guide under the resources link. Again, the oscilloscope basically plots the input voltage as a function of time on a 2- dimensional graph. Voltage is displayed on the vertical axis and the horizontal axis indicates time. The units of the axes are displayed in volts/division and time/division, respectively. The oscilloscope also has a triggering mechanism that locks onto the waveform that it receives at its input. By adjusting the values of volts/div and time/div, you can zoom in or zoom out the waveform. You can measure the frequency of the AC signal by counting the length of time of one full cycle, called period. The signal s frequency is simply the inverse of its period (f = 1/T ). Also note that you will need special cables to connect the output of the function generator to the input of the oscilloscope. 2. Display the sine wave: Try zooming in and out so you can see a one full cycle on the screen. Yu can do this by changing the horizontal time scale (sec/div) and the vertical voltage scale (V/div). Now, activate the time cursors, X1 and X2. Move the cursors and locate them at the end points of the full cycle. Read X and record the value. This is the period T of the signal. Now switch the cursors to Y1 and Y2, and place the horizontal dotted lines at the top and

30 26 INTRODUCTION TO AC MEASUREMENTS: AC SIGNALS, FUNCTION GENERATORS AND OSCILLOSCOPES Figure 4.8: Agilent 54622A Oscilloscope bottom points of the sine signal. Read and record Y. This is the peak- topeak amplitude of the signal Vpp. Determine the frequency by inverting the period (f = 1/T ) and the amplitude of the signal (V A = V pp /2). Compare the measured f and V A with the expected values provided by the function generator. 3. Let us now use the function generator and oscilloscope in making AC voltage measurements across series and parallel resistors. So far we have seen that we can adjust the frequency of the function generator, select the shape or function (sine, triangle and rectangle functions), and change the amplitude level. We can also adjust the DC offset of the wave. The DC offset function superimposes a positive or negative DC voltage (called bias) to the AC signal. The entire AC waveform is lifted or lowered by the DC bias value (offset) with respect to the ground. Without an offset, the AC signal is vertically symmetric with respect to Zero (ground level). The dual trace oscilloscope helps us compare the two signals. The oscilloscope has two input ports labeled 1 and 2. We use input 1 to monitor the output signal of the function generator and input 2 to observe the time-varying voltage at a particular point on the circuit. Connect the BNC end of the oscilloscope cables

31 MONITORING AC SIGNALS 27 to input 1 and 2, respectively. At the other end of the cables you will find the main probe and a black alligator clip. Connect the main probe to that point of interest and the black alligator clip to the common point of the circuit. This common point is indicated by the ground in the following circuits. The dual trace oscilloscope helps us compare the two signals. The oscilloscope has two input ports labeled 1 and 2. We use input 1 to monitor the output signal of the function generator and input 2 to observe the time-varying voltage at a particular point on the circuit. Connect the BNC end of the oscilloscope cables to input 1 and 2, respectively. At the other end of the cables you will find the main probe and a black alligator clip. Connect the main probe to that point of interest and the black alligator clip to the common point of the circuit. This common point is indicated by the ground in the following circuits. 4. An input waveform without DC offset: Build the circuit shown in Figure 4.9. Select the following resistance values: R 1 = 300Ω, R 2 = 1kΩ, R 3 = 4.7kΩ. Set the frequency of function generator to 240 Hz sine wave with 1.0 V amplitude and zero offset. Carefully record the two waveforms with appropriate scales on a graph in your lab book. R 1 R 2 V s V 1 R 3 Figure 4.9: A series circuit. 5. Calculation and comparison: Record the amplitude of the voltage across the two resistors R 1 and R 2. Redraw the circuit replacing two resistors R 1 and R 2 with only one resistor with resistance R 1 + R 2. Name this resistor R 12.This is the circuit of a simple voltage divider. Calculate and record the amplitude of the expected voltage across R An input voltage with DC offset: Try the above with first +0.5 Volt and then Volt of offset and record the corresponding waveforms in your lab book. 7. Higher frequencies, without offset Repeat the procedure for 1200 Hz, 10 khz, and 200 khz (the maximum frequency delivered by the function generator). Do you observe any distortion or change of the waveform at any of these frequencies? Describe the change in your lab book.

32 28 INTRODUCTION TO AC MEASUREMENTS: AC SIGNALS, FUNCTION GENERATORS AND OSCILLOSCOPES 8. RMS Value of a sinusoidal signal: Consider a sine wave that is vertically symmetric about the x-axis (time axis). Since the voltage value of the signal varies with time, we will need to characterize the value of the signal using an average value. For a simple sine wave centered about zero, half of the cycles are positive and half are negative. The sum of all values cycles amount to zero. Therefore, regardless of its amplitude, the simple average of all sine wave signals is zero. Instead, one can first square the wave by raising all values of the wave (positive and negative) to power 2. The square root of the sum of the squared values is called the Root Mean Square or RMS value. The magnitude of a sine wave is therefore identified by its rms value. It turns out that the V rms = V 0 /2, where V 0 is the signal amplitude. When we say that the voltage of the signal from the wall power outlet is said to be 120 volts, we mean that its rms value is 120 volts. This is what the Fluke meter measures when its knob is set on Ṽ. 9. Calculate the rms value of the sine wave in Figure Figure 4.10: Illustration of the RMS value. 10. Calculate the amplitude of the 120 V AC voltage provided by PG&E.

33 CHAPTER 5 RC TIME-CONSTANT APPLICATIONS 5.1 Introduction Consider a resistor R in series with a capacitor C connected to a power supply as shown Figure 5.1. When the switch is closed (position 1), the capacitor begins to charge. The rate of charge of the capacitor depends on the circuit s RC time constant. Clearly a large resistance in the circuit limits the current, which slows down the charging of the capacitor. At the same time a capacitor with a large capacitance takes a longer time to fully charge. On the other hand when the switch is opened (position 2), the charged capacitor starts to discharge and the rate of discharge will depend on the value of the RC time constant. The significance of the value of RC can be seen by analyzing the charging or discharging equations for voltage or charge of the capacitor in Figure 5.2. When the capacitor is fully charged, its voltage is V C = V 0, the same as the voltage of the battery. As soon as the switch is thrown into position 2 (disconnected from the battery), the fully charged capacitor begins to discharge through the resistor. The capacitor voltage V C drops exponentially with time: V C = V 0 e t/(rc) (5.1) Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

34 30 RC TIME-CONSTANT APPLICATIONS C 1 R 1 V s 1 C 1 R 1 V s 2 (a) (b) Figure 5.1: A resistor in series with a capacitor. Figure 5.2: Discharging equation of a capacitor. This equation indicates that the larger the RC, the longer it takes for the capacitor to discharge. For t = RC, V C = V 0 /e 1, or the capacitor voltage drops to 1/e of its maximum value (V C = 0.368V 0 ). For t = 2RC, the voltage drops to V = 0.135V 0, etc... Therefore RC is a measure of the circuit s charging/discharging characteristics. One can measure the time that it takes for the capacitors voltage to drop to 0.37 of its fully charged value (Figure 5.3) and compare with the RC time constant of the circuit below. XFG1 represents the function generator and XSC1 represents the voltage displayed on the oscilloscope. In order to do so, one can monitor the voltage drop across the capacitor and carefully draw one waveform. Using the exact scale, mark the location of RC, 2RC and 3RC on the horizontal time axis as viewed on the oscilloscope (Figure 5.4).

35 LOW-PASS AND HIGH-PASS FILTER 31 XFG1 10kΩ + R1 10nF + XSC1 Figure 5.3: Circuit for measuring RC time constant. Figure 5.4: Charging and discharging of a capacitor. 5.2 Low-pass and high-pass filter In this part we will experiment two very simple filters consisting of a resistor and a capacitor. The idea is to demonstrate that one can filter out high frequency AC signals in Low-Pass filters and filter out the low frequency AC signals in High-Pass filters. The underlying principle of operation of RC filters is based on the fact that a capacitor exhibits a large electrical resistance at low frequencies, and a very low electrical resistance at high frequencies. Therefore we expect that a capacitor will act as an infinitely large resistor for DC signals and a conductor (negligible resistance) at very high frequencies. In a low-pass filter, the circuit blocks higher frequencies and in a high-pass filter, lower frequencies are blocked. Each filter has a threshold that is determined by the values of the resistance and capacitance of the two elements in the circuit. Therefore the threshold of the filters can be adjusted by changing the values of the resistance and capacitance of the elements in the circuit. For both filters we apply a sine wave input to a circuit consisting of a series combination of a resistor and a capacitor. In a low-pass filter the output voltage is taken across the capacitor (Figure 5.5) and in a high-pass filter the output voltage is taken across the resistor (Figure 5.7). In both cases the input and output voltages must share the ground connection.

36 32 RC TIME-CONSTANT APPLICATIONS A low-pass filter Figure 5.5 displays the schematic of a low pass filter. XFG1 the voltage generated by the function generator and XSC1 is the voltage displayed on the oscilloscope. In order to use these instruments, we have to make sure they are reset to the factory settings, after that, we would be able to set the input frequency and voltage. In order to use the oscilloscope and the function generator properly, the students should refer to the instructions given in the previous lab Measurement procedure Apply a sine wave with 5V pp and 0V offset. You will be using both channels of the oscilloscope. Make sure that Channel 2 is connected to the input and Channel 1 to the output. Also, make sure you press the Output button on function generator to turn the signal on. Here are the images of the breadboard layout and the connections of the parts and equipment: 10kΩ XFG1 + R1 10nF + XSC1 Figure 5.5: Schematic of a low-pass circuit. Figure 5.6: Breadboard layout of the low-pass filter and the low-pass filter measurement setup.

37 LOW-PASS AND HIGH-PASS FILTER 33 The idea is to first visually observe that at low frequencies the output has the same peak-to-peak voltage as the input signal at low frequencies (low pass!). You should gradually increase the frequency until you see a drop in the output peak-to-peak voltage. Now we need to define the usefulness range of the filter. The cut-off frequency (a.k.a. 3dB frequency) is defined to be a frequency at which the power of the output signal drops to 1/2 of the power of the input signal. It should noted that the output voltage is times the input voltage at the 3 db point. which is called the -3 db point, the amplitude of the output voltage is of the input voltage. Therefore the objective of this part of the experiment is to identify the cut-off (or -3 db) frequency. Set the cursors to measure and record the peak-to-peak output voltage when the output starts to drop. Choose an input peak-to-peak voltage of 5 V. Keep increasing the frequency until you observe that the peak-to-peak voltage V out = 0.707V in. Make a note of this frequency. Search the Internet or other sources to find a formula to calculate the expected value of this cut-off frequency and compare with your experimental value. In order to receive a grade for this lab, you must demonstrate the 3dB cut-off frequency of the low-pass filter to the instructor A high-pass filter This part of the experiment is identical to the previous part except, the output voltage is taken across the resistor and we start at high frequencies (high pass). This time you reduce the frequency until the -3dB point is reached, where V out = 0.707V in. Make a note of this cut-off frequency. The circuit and the set up are shown below. Search the Internet or other sources to find a formula to calculate the expected value of this cut-off frequency and compare with your experimental value. XFG1 + 10nF + XSC1 10kΩ Figure 5.7: Schematic of a high-pass filter.. The cut-off threshold for the high-pass and low-pass filters is defined to be the frequency at which the output voltage drops to of the input voltage. In general, the cut-off frequency is defined to be the frequency at which the output power drops to 12 of the input power. However, since the electrical power dissipated in a component is proportional to V 2, then we conclude that the cut-off frequency corresponds to the location where the voltage drops to 1/2 1/2 of its maximum, which is Note that this point is also called the 3dB point. In a logarithmic scale the ratio of the output power (P out ) to the input power (P in ) is measured in a decibel scale (or db scale) and is based on the following definition:

38 34 RC TIME-CONSTANT APPLICATIONS Figure 5.8: Breadboard layout of the high-pass filter and the high-pass filter measurement setup. db = 10 log 10(P out /P in ) (5.2) At the location where P out = (1/2)P in, then db = 10 log(1/2), which leads to - 3 db. The negative sign signifies attenuation of the signal. In order to receive a grade for this lab, you must demonstrate the 3dB cut-off frequency of the high-pass filter to the instructor.

39 CHAPTER 6 DIODES: HALF-WAVE AND FULL-WAVE RECTIFIERS 6.1 Introduction In this part of the experiment you will use a diode to remove the negative portion of a sinusoidal AC signal. The rectifying properties of a diode can be understood through its I-V diagram shown in Figure 6.1. When a positive voltage is applied to the diode, it allows current to flow through it. The current increases with the forward biased voltage. On the other hand when a negative voltage is applied, the diode allows very little current to pass through. The diode appears to block the current when a reverse bias voltage is applied. The diode will break down and conduct if the reverse voltage is increased beyond a maximum allowed value. The breakdown voltage and other characteristics of diodes are described in their manufacturer s specification sheets. You are provided with a general purpose diode 1N4001 (Figure 6.2) to examine its forward and reverse IV characteristics in a qualitative way. Look up the specifications of the diode 1N4001 on the Internet. The 1Nxxxx numbering system is an American standard (now adopted globally) used to mark semiconductor devices. The 1N means that it is a single junction semiconductor device (i.e. a diode) is a number given to the smallest diode in the 400x series (4001, 4002, and so on) - the number indicates the voltage, current Introduction to Engineering and Laboratory Experience, First Edition. Copyright c

40 36 DIODES: HALF-WAVE AND FULL-WAVE RECTIFIERS Figure 6.1: I-V characteristic curve of a diode. Figure 6.2: A 1N4001 diode. and power ratings of the diode. A transistor (which has 2 junctions) would be numbered 2Nxxxx. The 1N4001 diode has a voltage rating of 50 V and current rating of 1 A. Use the continuity function of your Fluke multimeter to examine the forward bias direction of the diode. Connect the red lead of the meter to one side of the diode and the black lead to the other. If you hear a beeping sound or observe a small resistance, then the forward bias direction of the diode is from the red side to the black side. The diode resistance in the reverse direction would be very large. Note the location of the line imprinted on the diode and see if you can relate the location of the line to the direction of conduction of the diode. 6.2 Half-Wave Rectifier Circuit 1. Connect a 1 kω resistor in series to the 1N4001 diode as shown in the circuit below. Apply the 1 khz sine wave with a peak-to-peak voltage of 2 V to the Vin points of the circuit and use the oscilloscope to measure the Vout by connecting the oscilloscope leads to the points A and B. Observe and explain the shape of the waveform. Explain the difference between V in and V out. Also Record the Peak voltage of the waveform. What do you expect the waveform to look like if you reverse the diode? Reverse the diode and record your observation. 2. Connect a 100 µf capacitor in parallel to the load resistor and observe the output signal on the scope. Record the peak voltage and observe the difference

41 HALF-WAVE RECTIFIER CIRCUIT 37 2V pp + 10 Hz A 1kΩ B Figure 6.3: Half-Wave Rectifier Circuit. between this waveform and that of Case A without a capacitor. Now, replace the capacitor in the circuit with a larger capacitor (around 0.1 F), and observe the resulting waveform. The output voltage should not drop to zero between the peaks. It gradually drops to a new level. The difference between the peak voltage and this new level is called the ripple voltage. Make a note of the peak voltage and the ripple voltage and carefully draw the waveform in your lab book. Make sure to indicate the scale of the voltage and time axes. 2V pp + A 10 Hz 1kΩ 100µF B Figure 6.4: Half-wave rectifier circuit with a capacitor.

42 38 DIODES: HALF-WAVE AND FULL-WAVE RECTIFIERS 6.3 Full-Wave Rectifier 1. Construct both half-wave and full-wave rectifier circuits on your breadboard without the capacitors. In both circuits replace the load resistors with a 33 Ω resistor in series with an LED as shown in the diagram. Use the function generator to apply a sine signal of amplitude 8.5 V pp (which is approximately 3 Vrms), and frequency of 2 Hz to the input of each circuit. Observe the blinking frequencies of LEDs in each circuit. Explain your observation. You could also build this circuit in Multisim and observe the frequency of the blinking LEDs, and increase the frequency (to 10 Hz) if the frequencies appear too slow. Green 33Ω 3V rms 2Hz 33Ω Red Figure 6.5: A full-wave rectifier circuit.