UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering Experiment No. 2 -Basic Circuit Elements Overview Resistors, capacitors, and inductors are the most fundamental components used in electrical circuits. It is important that electrical engineers have a good understanding of the types and values available and how they should be used in various design applications. The purpose of this experiment is to familiarize the student with these basic circuit elements and for selected elements evaluate their power ratings in a laboratory-controlled destruction. RESISTORS: resistors are related to electrical factors that is, voltage and current. Resistors are also affected by at least four physical factors, namely specific resistance of the material type, length, cross sectional-area and temperature. In this experiment the student will investigate specifically the power rating of resistors. There are a variety of resistors in use today, and they are best categorized by their required precision and power rating. Resistors can be divided into four different categories: * General purpose resistors * Semi-precision resistors * Precision resistors * Power resistors Some of the more important considerations when choosing a resistor for a given application are listed below: Power dissipation and maximum operating temperature: The maximum power rating of a resistor is generally specified at some rated temperature (power resistors are rated at room temperature). Power ratings of resistors can range from 1/20 of a Watt to 1000 Watts depending on the type of resistor. A reduction factor must be applied to the power rating of a resistor if it is operated above its rated temperature. The maximum operating temperature of a resistor is somewhat higher than its power-rated temperature and is a function of the resistor’s composition and construction. Tolerance: Tolerance is the amount by which a resistor can vary from the manufacturer’s specified value. Tolerance values range from 0.01% for precision resistors to 20% for the general purpose resistors. In General, the smaller the tolerance of a resistor the more expensive it will be. Resistors can be obtained with resistance values of from 0.1 ohm to 100 M depending on the type of resistor. 1 Stability: Stability is defined as the change in resistance value of a resistor from its originally manufactured value. This irreversible change is caused by high temperature, high humidity, poor retrace, and aging. It is less pronounced for resistors of lower resistance values. Maximum operating voltage: The maximum operating voltage of a resistor is determined mainly by its physical shape and its resistance value, which determines its maximum current. Frequency response: At higher frequencies, the self- capacitance of a resistor becomes predominant, lowering its effective impedance. This capacitance is primarily contributed by the lead terminals. The lead inductance and skin-effect will alter the value of impedance at frequencies above 100 MHz. Resistors used in high frequency applications must be evaluated for such effects. Temperature coefficient: The temperature coefficient defines the incremental resistance change per degree change in temperature. This change is a retraceable change in that there is no permanent change in resistance. Current noise: Resistors generate two types of noise: Johnson noise, due to thermal agitation, and current noise, which is caused by internal changes in the resistor when current is flowing. Fixed resistors: Fixed resistor types are normally classified as carbon composition, film, or wirewound, depending upon the material of the resistive element. A description of these various types of resistors and their general characteristics is given below: Carbon composition: This type of resistor is the most widely used with the widest range of available standard values and sizes at the lowest cost. It is composed of carbon mixed with a binder, molded under high temperature and pressure into a solid cylinder and covered with an insulated jacket. This type of resistor has the lowest operating temperature of all the types due to the effect of temperature upon the binding material used in making the resistor. Because of the lack of precise control over the manufacturing of the carbon composition resistor, it is difficult to achieve a tolerance of less than 5% without the uses of special methods. Carbon composition resistors can be expected to have a stability factor of +5% or less if operated at or below rated power and in a normal environment. Carbon composition resistors (up to10 K ) behave like resistors up to about 10 MHz. Above this frequency, they begin to look capacitive. In terms of temperature coefficient and current noise, the carbon composition resistor has the least desirable characteristics of all the types of resistors. 2 Carbon film: Film resistors are manufactured by depositing a thin layer of resistive material on a non-conductive substrate. The resistive element is usually laid in spiral form to increase the total resistance. The carbon film resistor costs a little more than the carbon composition resistor, but it also has somewhat better performance characteristics. The film resistors can be manufactured with accuracies (tolerances) more than an order of magnitude better than the carbon composition resistors. Film resistors perform better at higher frequencies than any of the other types. Metal film: This type of resistor is the most widely used resistor for applications requiring precise performance. The resistance element is made from nichrome alloys deposited on a rod substrate. The range of resistance values available for this type of resistor is 6 to 12 times larger than lower precision resistors due to its precision applications. Cermet film: The resistance element of this resistor is made by screening a layer of combined ceramic and metal or glass particles on a ceramic core and firing it at high temperatures. Although higher resistance values can be obtained for the cermet film resistor than any other type of film resistor, its electrical performance is not as good as a metal film resistor. Wire-wound: This resistor is used in high precision and high power applications. It is made of high resistivity wire, such as nichrome, wound on an insulated core. It has the best stability of all the resistor types but has the disadvantage of larger size and poor frequency response due to the distributed capacitance and inductance resulting from the wire-wound construction. CAPACITORS: Capacitors are used in a wide variety of applications such as: Filters, Suppression of Voltage Spikes, Coupling and By-passing, Wave-shaping, Resonant Circuits and Delay Lines and Timing Circuits The selection of the right capacitor for a particular application requires some knowledge of the different types of capacitors. The type of capacitor is generally identified by the type of dielectric used in its construction. Some of the more common types are: *Paper *Glass *Plastic Film *Mica *Ceramic *Electrolytic Some of the more important characteristics of a capacitor are described below. Dissipation factor: The dissipation factor is an indication of the power loss in a capacitor. The power loss is due to the internal (series) resistance of the capacitor. The dissipation factor is defined as the ratio of the pure capacitive reactance of the capacitor to its internal (series) resistance. It is the reciprocal of the Q-Factor of the capacitor. 3 Leakage current: Capacitors also have an equivalent parallel resistance that gives rise to leakage current. Typically this resistance is greater than 100 M ; however, in some capacitors, such as the electrolytic, this resistance is considerably less, and can discharge the capacitor in times of a few minutes and less. Capacitor Q-Factor: The quality of the component must be taken into account. The Q factor is a measure of the energy stored to that which is lost in the component due to its series resistive. Inductors store energy in the magnetic field surrounding the device. Capacitors store energy in the electric field between its plates. The energy is stored in one half of an AC cycle and returned in the second half. Any energy lost in the cycle is associated with a dissipative resistance and this gives rise to the Quality factor. The Quality factor is the ratio of maximum energy stored to the amount lost per AC cycle. In the design of electronic circuits such as RLC filters the Q of the capacitors and inductors used in the circuit will be a determining factor for such things as circuit efficiency and the 3db bandwidth. The Quality factor for a capacitor is Q =1/(2πfCRs) Thus, the lower the series resistance of a capacitor, the higher the Q, the less energy dissipated and the greater the selectivity. The current through a capacitor is equal to the time rate of change of voltage across the capacitor multiplied by the capacitance, or i(t) = C(dv/dt) Dielectric absorption: Dielectric absorption is the property of the capacitor dielectric to absorb charge when being used. This can cause some very subtle errors in capacitor applications which require the capacitor to hold a charge for some period of time. Often this charge reappears while the capacitor is “sitting on the shelf” and this can be a “shocking” experience for the unsuspecting. Sidebar on dielectric materials: A dielectric material is a substance that is a poor conductor of electricity, but an efficient supporter of electrostatic fields. If the flow of current between the oppositely charged electric poles is kept to a minimum while the electrostatic lines of flux are not impeded or interrupted, an electrostatic field can store energy. This property is useful in capacitors since it will increase capacitance without an increase in the capacitor size. 4 Insulation resistance: The insulation resistance of a capacitor is a measure of the capacitor’s ability to hold a charge; i.e., the magnitude of its leakage current. This resistance can often change due to moisture or other contaminants. Again, this can cause errors in capacitor applications, which require the capacitor to hold a charge for some period of time. Dielectric strength: The dielectric strength of a capacitor is defined as the voltage (DC) at which the dielectric breaks down (the capacitor becomes a conductor). This voltage is affected by temperature, humidity, and the magnitude and frequency of the applied voltage. Since temperature is affected by the power loss in the capacitor, it is important in some capacitor applications (such as power supply filtering) to size the capacitor, not only to maximum voltage capability but also the power rating. Stability: Stability is defined as the change in capacitance value of a capacitor from its original manufactured value. This change is the result of temperature, applied voltage, frequency, and time. Capacitance tends to change permanently with time, whereas changes due to the other factors are of a temporary nature. INDUCTORS: Inductors are important components in most electrical and electronic circuits. Even when lumped inductors are not present, the wires and cables of the circuit often introduce inductance which must be considered. The effects of parasitic inductance, like those of parasitic capacitance, are more of a concern at the higher frequencies. Inductors are used in tuned circuits, filters, coupling circuits, phase-shift circuits, for RF chokes, etc. An inductor can be constructed simply by rolling a coil of wire around a pencil or any cylindrically shaped form. When the length of the coil is greater than 0.5 d and the distance between turns is constant, the inductance is given by L= 2 oN A / (l +.45d) In this formula, L is the inductance in Henries, N is the number of turns, A is the crosssectional area in square meters, l is the length in meters, d is the diameter in meters and o is the permeability of free space in H/m. Of course, this formula is not applicable for many of the commercially available inductors not constructed in this form and often ferrite loaded to increase inductance. In integrated circuits inductors are avoided because of the difficulties encountered with their implementation on silicon wafers. Series resistance and shunt capacitance: The DC resistance of an inductor is simply the resistance of the wire used to wind the coil and appears in series with the inductance of the coil. Each turn of the coil is capacitively coupled with neighboring turns, resulting in an equivalent capacitance that shunts the series impedance of the 5 coil. In most cases this capacitance is small and insignificant but, at high frequencies, may become important. In addition to the inductance, series resistance, and shunt capacitance, inductors will also have a maximum power rating (related the wire size and winding geometry) that must not be exceeded. Inductor Q-Factor: As for the capacitor, the Q of an inductor is defined as the ratio of energy stored in the inductor per cycle to that of energy lost per cycle and is given by Q=2 fL/Rs If the series resistance is small the Q is large, the energy loss is small, and the selectivity of the circuit is good. The Q of a coil will influence the efficiency, and selectivity of the circuit in which it is used. The voltage developed across an inductor is equal to the time rate of change of current through the inductor multiplied by the inductance, or simply e(t) = L(di/dt) Resistor color code: Resistors are often marked with what is known as a resistor color code. Each band that surrounds the body of the resistor helps identify the value (in ohms), the tolerance (in percent), and in some cases the reliability rating and/or the recommended solder. Most resistors have a typical 5% - 10% tolerance value. As such normally only four (4) color bands are used. In Figure 2 you will find how and where each band is located. 6 Figure 2: Resistor Color Code Layout (4 Bands) Observe how the resistor bands are closer to one end than the other. The closest band to the end is generally the first or most significant digit, and the band on the opposite end (silver for 10% or gold for 5%) is the tolerance band. The absence of a silver or gold tolerance band indicates a tolerance of 20%. The first band will always be some color other than black with one rare exception, a “zero” Ohm resistor (i.e., a solid wire or jumper). In this case only one black band will exist. Figure 3 is the color chart for resistors. Color is used to represent a number, and in this way we are able to discern the value for each digit. If we have a resistor with the first band yellow, standing for the number 4, the second band violet, standing for the number 7, and the third band red, standing for the number 2, we place two zeros after the first two numbers (i.e., 47 + two zeros = 4700). The third band is often the most difficult band to decode; it represents the number of zeros or decimal places added to the previous two numbers. In this way we can describe a very large number of resistor values. For values less than 10 ohms the color gold or silver will be placed in the third color band. When these colors appear we will move the decimal place of the first two digits to the left. As an example if we are looking for a 4.7 resistor we should find a resistor with yellow (4), violet (7), and silver (10%) or gold (5%); the multiplier is 0.1. This becomes 47 X 0.1 or 4.7. It may take a little practice but with this method we are able to specify resistors that are less than ten ohms. For resistors of less than 5% tolerance there will generally be five bands. This is true because one additional significant figure is required to give the value. The first three 7 bands determine the numerical value, the fourth band the multiplier, and the fifth band the tolerance (red for 2% and brown for 1%). Figure 3: Resistor Color Chart Table 1 is a list of the standard values that you may find. Note that these are “standard values”. Parts kits, and suppliers often bundle values that are the “most” popular and as a result you may get more of one value than another. Typically decimal values (i.e. 10, 100, 1,000, 10,000) are the most popular with values like 22XX, 33XX, 47XX, and 56XX following second. Values of 75XX, 82XX, and 91XX series values are available but not often included in bundled kits. You may ask why this happens, but notice that many of these may be approximated by combining other values. Standard Resistor Values: Values available for 1 Million Ohms (1M ) and greater are generally limited because of their limited use. The values generally available follow the pattern; 1M, 2.2M, 3.3M, 4.7M, 5.6M, 6.8M, 7.5M, 8.2M, 9.1M. Normally, larger values of resistance are not quoted in standard numerical form (i.e., 8 1,000, 33,000, etc.). In electronics as in most scientific disciplines very large and small numbers are expressed in scientific notation. In electronics this notation is combine with standard metric prefixes (names that precede the units) to convey the desired value. Table 1: Typical examples of how different resistor values may be specified. Value Scientific Notation Decimal Multiplier Metric Prefix Metric Letter Example Value 1,000 1x10^3 X1000 Kilo K 1K 1,000,000 1x10^6 X1000000 Mega M 1M 0.001 1x10^-3 X0.001 milli m 1m 2,200 2.2x10^3 2.2x1000 Kilo K 2.2K 33,000 33x10^3 33x1000 Kilo K 33K 560,000 560x10^3 560x1000 Kilo K 560K 9,100,000 9.1x10^6 9.1x1000000 Mega M 9.1M 75 75x10^1 75x1 None None 75 0.47 47x10^-3 47x0.001 milli m 47m Capacitor Code: 9 Figure 4: Ceramic Disc Capacitor Value Table 10 Figure 5: Film Type Capacitor Value Table Inductor Code: Figure 6: Inductor and RF Chokes Value Table 11 Ohm’s Law Relationships: As part of this experiment Ohm’s law will be verified with experimental data. When considering the validity of your results, it will be necessary to allow of such things as resistor tolerance and meter accuracy. Ohms law states that the voltage in Volts is equal to the product of current in Amperes and the resistance in Ohms. That is E =IR Different forms of this law are easily obtained with simple algebraic manipulations. To determine the percentage error between measured and calculated values we use the following: % error = measured _ value − calculated _ value 100% calculated _ value 12 Pre Lab 2- Basic Elements 1. For resistors with the following color bands give the resistance and tolerances: a. Brown, Black, Red, Silver_______________________________ b. Blue, Grey, Black, None_________________________________ c. Green, Blue, Orange, Gold_______________________________ d. Red, Black, Blue, None__________________________________ 2. Determine the maximum current that a 470-Ohm, 1/4-watt resistor can have flowing through it without exceeding its power rating. 3. Determine the maximum voltage that a 470-Ohm, 1/4-watt resistor can have across it without exceeding its power rating. 4. Determine the maximum current that a 270-Ohm, 1/2-watt resistor can have flowing through it without exceeding its power rating. 5. Determine the maximum voltage that a 270-Ohm, 1/2-watt resistor can have across it without exceeding its power rating. 13 6. A constant current source of 2 mA is placed across a fully discharged capacitor of 100 F. In the time period before the capacitor reaches breakdown voltage, what is the time rate of change of voltage across the capacitor in V/s? 7. Assuming a 10 millihenry inductor operating at 2 kHz, find the value of the series resistance with a Q factor of 10. 8. A cylindrically shaped inductor with 20 equally spaced turns has a diameter of 2 cm and a length of 5 cm. What is the inductance in Henries? (INSTRUCTOR’S SIGNATURE_____________________________DATE______________) 14 ELVIS Introduction ELVIS, which stands for Educational Laboratory Virtual Instrumentation Suite, is new technology developed by National Instruments. It combines 12 of the most commonly used laboratory instruments into one streamlined circuit board. It offers precise measurements capabilities, eliminates the need for additional hardware and saves desk space for the user. To use ELVIS hardware, all that is needed is the ELVIS board, a laptop and the necessary cables to perform the given lab experiment. First, plug in the power cord of the ELVIS board into the wall outlet. Then connect the USB cable to both ELVIS and the laptop. The laptop should already have ELVIS software installed. Simply click on the NI ELVIS shortcut on the desktop to launch the ELVIS software. The following window will appear: Figure 7: ELVIS Instruments These are all of the instruments that ELVIS has to offer. Not all of them will be used with every laboratory experiment. We will introduce the four most basic instruments during this lab including the digital multimeter (DMM), variable power supply (VPS), function generator (FGEN) and oscilloscope (Scope). Digital Multimeter (DMM) The digital multimeter is one of the most basic tools which allows the user to measure resistance, voltage and current. The units for each of these is ohms, volts and amps, respectively. For ELVIS, the multimeter is integrated inside so there is no need for an additional device. Two probes (red and black) are used to measure the quantities. It is standard practice that the black lead is connected to the negative terminal (common or ground) and the red lead is connected to the positive terminal. A picture of the DMM (Digital Multimeter) in ELVIS is shown below: 15 The DMM in ELVIS can measure many different quantities compared to a traditional multimeter. The DMM can measure DC Voltage, AC Voltage, DC Current, AC Current, Resistance, Capacitance and Inductance, respectively. Using the Banana jack connections diagram, locate the V and COM connections on the right side of the ELVIS board. Connect the red and black leads to the V and COM, respectively. Note: All of the tools in ELVIS need to be running in order for them to function. The user much click ‘Run’ to activate the tool. If the user needs to stop using the tool, click ‘stop’. Variable Power Supply (VPS) The variable power supply is an adjustable voltage source. The user can specify a voltage or sweep a voltage (taught in future labs). The pins will be labeled and located on the bottom left side of the ELVIS breadboard. Note: As stated before, the user must click run In order to activate the tool. Also, for a majority of the instruments offered in ELVIS there is a manual mode in which the user can spin the digital dial and adjust the voltage rather than specify a specific value. To enable manual mode, simply click the manual checkbox. Function Generator (FGEN) The function generator is able to create a variety of waveforms including sine, triangle, square and ramp waveforms. All of these waveforms can be utilized at a variety of different frequencies. The user will use the function generator to provide a signal input to an electronic circuit. While using the function generator, the student must also use the oscilloscope which allows the user to visually see the signals. 16 Under the waveform settings, the user can select if they would like a sine, triangle or square wave. They can specify a frequency, amplitude and DC offset or use the manual mode. The sweep settings can be ignored for now and will be used in future labs. Be sure to click ‘Run’ or the function generator will not activate. Oscilloscope (Scope) The oscilloscope is a device used to measure different circuit quantities on an electronic circuit. The scope has many uses including: Saving waveform to an image file, AC and DC waveform outputs, frequency and voltage readings and Fourier transform analysis. The ELVIS scope includes two channels which represent two different inputs. For example, the user can compare the input of a circuit to the output of a circuit. In order to use each of the channels, be sure that the channel is enabled by checking the ‘Enabled’ checkbox. For the Probe setting, just be sure that the switch on the probe cable matches the Probe setting in ELVIS. There are two options, 1X and 10X. If the user is measuring an AC signal (i.e. signal from the function generator) be sure the coupling is set to AC coupling. This will center the waveform on the x-axis (time). Just like previous tools, the user can adjust the scale and vertical position manually or specify a value. Again, be sure to click ‘Run’ to enable the scope, there will be no reading if the tool is not running 17 Lab Procedure ELVIS Set-Up: • • • • • • Connect AC-DC power adapter to ELVIS at rear panel. Use the USB cable to connect the PC to ELVIS via the rear panel connector. Assure that ELVIS “Prototyping Board Power” switch (upper right corner) is off. Turn on ELVIS main power switch (rear panel). Power for the experimental circuit is obtained from the “Variable Power Supplies” connections at the lower left of the proto board. Note that each ELVIS virtual instrument must be in “RUN” mode to function. 1. Connect the circuit of Figure 12. 2. Use the multimeter to measure the voltage across the resistor, as indicated by the probe placement (parallel connection) in Fig. 12. Record the value in Table 3. 3. Reconfigure the circuit and multimeter to measure the current through the circuit (series connection). Record the value in Table 3. 4. Use the multimeter to measure the resistance of the resistor. Record the value in Table 3. 5. Obtain resistors having the values listed in the Pre-lab and measure them with the multimeter. Record values in Table in Table 4. Figure 12: Lab Circuit 6. Use the multimeter to measure the resistance of the inductor from the Pre-lab. Record the value in Table 5. 7. Place a 470-Ohm, 1/4-watt resistor in the SAFETY BOX in place of the 2kohm resistor in the above circuit, leaving the top off. Increase the voltage in steps while taking voltage and current readings. The benchtop multimeter may be used to measure voltage or current, to avoid having to reconfigure the circuit for every reading. For each voltage increase, calculate resistor power, stopping when the power rating of the resistor has been reached. Let the current stabilize at each voltage setting before taking a reading. At each voltage setting, CAREFULLY touch the resistor to feel it getting warm. BE CAREFUL NOT TO GET BURNED! Record the results in Table 1. 18 8. PLACE THE TOP ON THE SAFETY BOX! Continue to increase the voltage across the 470-Ohm, 1/4-watt resistor while taking voltage and current readings until the resistor fails. Note whether the resistor fails as an open-circuit or short-circuit. Record the results in Table 1. Complete the Power column with calculated power values. 9. Repeat steps 7 and 8 using a 270-Ohm, 1/2-watt resistor. Record the results in Table 2. Complete the Power column with calculated power values. 10. Place a polarized, 16-volt capacitor in the SAFETY BOX, WITH THE PROPER POLARITY! PLACE THE TOP ON THE SAFETY BOX! Increase the voltage in steps while taking voltage and current readings up to the 15 volt power supply maximum. Reduce the voltage to zero. Record the results in Table 6. 11. Reverse the 16-volt capacitor in the SAFETY BOX so that it is wired with IMPROPER POLARITY. PLACE THE TOP ON THE SAFETY BOX! The capacitor will explode. Increase the voltage in steps while taking voltage and current readings until the capacitor fails. Note whether the capacitor fails as an open-circuit or short circuit. Record the results in Table 6. 12. Connect the 14 V lamp as the load in Figure 12. Increase the voltage in steps while taking voltage and current readings up to the rated voltage of the lamp. Do not exceed the rated voltage. No safety box is needed for this step. Be careful the lamps will be very hot! Record the results in Table 7. 19 Lab Session – Basic Elements (Data Sheet) Table 1: Readings for 470 Power ¼ watt resistor Voltage 20 Current INSTRUCTOR' S INITIALS DAT Lab Session – Basic Elements (Data Sheet) 21 Table 2: Readings for 270 Power ½ watt resistor Voltage 22 Current INSTRUCTOR' S INITIALS DATE Lab Session – Basic Elements (Data Sheet) 23 Table 3: Meter readings for circuit in Figure 1 Voltage Current Resistance Table 4: Resistor measurement values Predicted Value Measured Value Table 5: DC resistance of inductor Inductor value (millihenries) DC resistance INSTRUCTOR' S INITIALS DATE Lab Session – Basic Elements (Data Sheet) 24 Table 6: Readings for 16 Volt polarized Capacitor Voltage Current 25 INSTRUCTOR' S INITIALS DATE Lab Session – Basic Elements (Data Sheet) 26 Table 7: Readings for 14V Lamp Voltage Current 27 INSTRUCTOR' S INITIALS DATE 28 Post Lab — Basic Elements 1. Discuss how you measured the voltage, amperes, and resistance. Where did you take the measurement and why? 2. Perform a percentage error calculation for the resistors measured in step 5 and the predicted color code values in the pre-lab. Why are these values, predicted and measured, different? 3. Plot current versus voltage for the 270-Ohm, 1/2-watt and the 470-Ohm, 1/4-watt resistors on the same graph. 4. Plot power versus voltage for the 270-Ohm, 1/2-watt and the 470-Ohm, 1/4-watt resistors on the same graph. 5. Tabulate the voltage and current data for the capacitor for both positive and negative connections. 6. Consider the following items when discussing the results of the experiment: a. The linear relationship between the voltage and current for the two resistors throughout the testing range? b. The current flow through the capacitor for the two different connections. c. The fail-open, fail-short characteristics of the resistors and capacitor. d. Effect of temperature on resistance. e. Component specifications and test results. All plots must be done on the computer! Hand drawn plots will not be accepted! 29