circuit analysis laboratory Lecture notes 1-4 PDF

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Faculty of Engineering Department of Biomedical Engineering

Department of Electrical and Electronics Engineering

EEE255 / BME211 Circuit Analysis Laboratory Manual PART I: DC Circuits Prepared by

BME Dr. Özlem BİRGÜL Dr. Görkem SAYGILI Gökhan GÜNEY Büşra ÖZGÖDE Abdullah Eyidoğan

EEE Dr. Gökhan SOYSAL Dr. Deniz KARAÇOR Fatma Gül ALTUN Cansel FIÇICI

Contents Introduction .................................................................................................................................................. 3 Laboratory Guidelines .................................................................................................................................. 3 Laboratory Safety ......................................................................................................................................... 4 Basic Laboratory Equipments ....................................................................................................................... 5 Experiment #1: Resistors in DC Circuits, Measurement of Voltage and Current, Ohm’s Law ................... 10 Experiment #2: Kirchhoff’s Voltage and Current Laws, Equivalent Resistance, Resistive Voltage and Current Dividers.......................................................................................................................................... 17 Experiment #3: Superposition Principle, Power Calculations, Power Balancing........................................ 23 Experiment #4: Thevenin and Norton Equivalent Circuits, Maximum Power Transfer ............................. 26 APPENDIX A International System of Units ................................................................................................ 29 APPENDIX B Quick References for Devices................................................................................................. 31

Introduction This manual is prepared for an Electrical Circuits Laboratory Course which is taken simultanously with a Circuit Analysis Course of a related Engineering Undergraduate Program. The manual starts with the guidelines to be followed in the laboratory, introductory safety instructions and explanations for the basic devices. Ten experiments for DC and AC electrical circuits cover the topics ranging from basic resistive circuits, Ohm’s and Kirchhoff’s Laws, superposition theorem, power calculations and maximum power transform, Thevenin’s Theorem, operational amplifiers, inductors and capacitors, first and second order circuits and frequency selective circuits. The equipments and components used in each experiment are listed at the end of each procedure and are supplied by the department. Each station includes a digital oscilloscope, a signal generator, a DC power supply and a desk-type multimeter. An electronic breadboard, which is a unit for building temporary circuits, is required for all experiments. The students are encouraged to obtain and bring their own boards for the experiments, yet, one will be provided to each station if needed. Similary, students can use their own handheld digital multimeters if they prefer. Students are not allowed to swap equipments between stations without approval of their assistants. A set of appendices including useful informations that students may need during the experiments are provided at the end of the manual. Appendix A gives a summary of the international system of units which may be helpful in prepation of reports. In Appendix B, Quick Reference for Devices available in our own laboratory are provided. Basic components (resistors, capacitor, etc.) available in the laboratory are listed in Appendix C to guide the students in their design assigments.

Laboratory Guidelines In this section specific guidelines for BME211 Electrical Circuits Laboratory class taken in the second year of Ankara University Biomedical Engineering Undergraduate Program are given. The laboratory is designed to be carried out consequently with BME201 Circuit Analysis Course. The content can be summarized as: -

Introduction to the class, safety guidelines, 11 experiments, written midterm, experimental final Preliminary work Quiz Short summary by the assistant Procedure, Groups of two Report Performance

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Laboratory Safety Safety is crucial in both our daily life and in laboratory work. We are responsible for creating safe working environment for you in the laboratory and you yourself are responsible for your own safety by following and maintaining safety precautions. Help ensure your safety when working around electricity and electronic devices by learning to :   

Recognize and avoid potantial dangers. Pay attention to all warnings and cautions. Follow good personal and laboratory safety habits.

In this course, your chances of working with any equipment that could cause an electrically related accident are as small as possible. Any work around electricity and electronic devices, however, can be dangerous under certain conditions. Thus, you must be aware of what causes accidents and pay attention to all warnings and cautions. You must also develop and follow good safety habits. Save all practical jokes for outside the work area. Such behaviour has no place in laboratory or at work.

PRE VEN CCID EN TS OW THES E ADV ICE PREVEN VENTT A ACCID CCIDEN ENTS TS:: FOLL FOLLOW THESE ADVICE ICESS

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Never hurry. Work deliberately and carefully.

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Use appropriate safety equipment when required to do so.

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Check over all tools and equipment before using them. Report any defects or problems to your instructor.

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Connect to the power source LAST.

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If you are working with a lab kit that has internal power supplies, turn the main power switch OFF before you begin work on the circuits. Wait a few seconds for power supply capacitors to discharge. These steps will also help prevent damage to circuits.

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If you are working with a circuit that will be connected to an external power supply, turn the power switch of the external supply OFF before you begin to work on the circuit.

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Check the power supply voltages for proper value and for type (DC, AC, frequency) before connecting it to your circuit.

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Do not run wires over moving/rotating equipment, or on the floor, and do not string them across walkways from bench-to-bench.

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Remove conductive watch bands or chains, finger rings, wrist watches, etc., and do not use metallic pencils, metal or metal edge rulers, etc. when working with exposed circuits.

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When using large electrolytic capacitors be sure to wait long enough (approximately five time constants) for the capacitors to discharge before working on the circuit.

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All conducting surfaces intended to be at ground potential should be connected together.

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In case there is a smoke or over-heating on your circuit, or you think there is something wrong in your experimental setup (laboratory equipments, circuit elements on your board, etc.), ask help from your instructors. Do not touch any device on your circuit or on your desk.

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Basic Laboratory Equipments Multime ltimete terr Mu ltime te A digital multimeter (DMM) is a test tool used to measure electrical values. It is a standard diagnostic tool in the electrical/electronic industries. Measurements that can commonly be done using a multimeter are;      

Resistance Voltage Current Capacitance Frequency Temperature, etc.

Caution! Multimeters are connected serially to measure the current and in parallel to measure the voltage. Before starting the measurement, checking the connections on the multimeter is highly important to avoid burning the fuses and making the correct measuments.

Wavefo eform rmss and Fu Func nctio tion Gene nerato rators Wav efo rm nc tio n Ge ne rato rs Waveforms A waveform graphically represents a variable as a function of time. A DC (direct current) voltage or current is a fixed value and does not vary with time. An AC (alternating current) voltage or current varies with time.

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The basic waveshapes used in electronics are shown in Figure 1. The sine wave is one of the fundamental waveshapes used in electrical systems and many electronic analog circuits such as audio amplifiers. The square wave and rectangle wave are used extensively in digital circuits as well as analog electronics. The triangle wave and sawtooth wave are used in wave shaping and timing circuits. A sawtooth voltage is used in televisions and oscilloscopes to control the trace of the electron beam on the surface of the screen (called cathode ray tube, CTR). The exponential waveform is also used in timing and wave-shaping circuits [3].

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Figure 1.a Sinusoidal wave

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Figure 1.b Square wave 5

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Figure 1.c Triangle wave

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Figure 1.d Sawtooth wave

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Figure 1.e Exponential wave

Important Parameters for Alternating Waveforms Period (T ): The time interval between successive repetitions of a periodic waveform. Frequency ( f ): The number of cycles that occur in 1 second. Instantaneous value: The magnitude of a waveform at any instant of time. Peak amplitude: The maximum value of a waveform as measured from its average, or mean, value, denoted by the letters Em or Vm. Peak-to-peak value: The sum of the magnitude of the positive and negative peaks; denoted by Ep-p or Vp-p.

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Figure 2. Important parameters for a sinusoidal voltage

Phase Relationships Alternating current (AC) voltages and currents can be in phase or out of phase with each other by a difference in angle. This is called phase angle and is represented by the Greek letter theta (θ). When two sine waves are at the same frequency and their waveforms pass through zero at different times, and when they do not reach maximum positive amplitude at the same time, they are out of phase with each other. On the other hand, when two sine waves have the same frequency, and when their waveforms pass through zero and reach maximum positive amplitude at the same time, they are in phase with each other [4]. An example of out-of-phase sine waves are shown in Figure 3. The equation for determining the phase angle can be introduced using the definition in Figure 3. Both sinusoidal functions have the same frequency, hence permitting the use of either waveform to determine the period. For the waveform in Figure 3, the period encompasses four divisions. The phase shift between the waveforms is one division. Since the full period represents a cycle of 360o, the phase angle between waveforms can be found using the following formula. 𝜃=

𝑝ℎ𝑎𝑠𝑒 𝑠ℎ𝑖𝑓𝑡(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛) 𝑃𝑒𝑟𝑖𝑜𝑑 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛)

𝑥 360𝑜

Substituting measurements in the equation, θ = (1/4)x360o = 90o

Therefore; signal 𝑒 leads signal 𝑖 by 90o

Figure 3. Finding the phase difference

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Effective (RMS) Value The effective value of an AC signal is the value of a direct current which when applied to a given circuit for a given time, produces the same expenditure of energy as produced by the alternating current when flowing through the same circuit for the same period [5]. Effective value is also called the root-meansquare (rms) value. This term comes from the mathematical method used to find its value [4]. The effective value of any quantity plotted as a function of time can be found as 𝐼𝑒𝑓𝑓

𝑇

∫ 𝑖 2 (𝑡)𝑑𝑡 =√ 0 𝑇

For the case of a pure sinusoidal waveform, the rms value equals to 1 ⁄√2 or 0.707 times it peak value.

Function Generators The function generator is an instrument which generates different types of waveforms. The most common waveforms are sine wave, sawtooth wave, triangular wave and square wave. Function generators typically provide a DC offset adjustment that allows the user to add a positive or negative DC level to the generator output. Figure 4(a), 4(b) and 4(c) show how adding variying amount of DC to a sine wave can produce different waveforms.

Figure 4(a). Sine wave with no DC

Figure 4(b). Sine wave with positive DC

Figure 4(c). Sine wave with negative DC 8

Osc illos cop e Oscillos illoscop cope

The primary function of an oscilloscope is to display an exact replica of a voltage waveform as a function of time. This picture of the waveform can be used to determine quantitive information such as the amplitude and frequency of the waveforms as well as qualitive information such as the shape of the waveform. The oscilloscope can also display more than one waveform at the same time for comparison. and measure their time and phase relationships. Figure 5 shows a typical display of a sine wave using an oscilloscope. The sine wave parameters can be determined from the display using the known settings of the oscilloscope and measurements from the screen. The peak-to-peak value can first be found in terms of display divisions and then converted to volts. The peak-to-peak value of the sine wave in Figure 5 is ten divisions. If the vertical sensitivity is set to 0.5 volts per division, then the peak-to-peak voltage is 10 x 0.5 = 5 Volts.

Figure 5 RMS voltage is not as easy to determine, at least not directly from an analog oscilloscope. But the relationship between the zero-to-peak and RMS values for a sine wave is known. Since, VRMS = 0.707 for our example V0-p = 0.707 (2.5 Volt) = 1.76 Volts RMS. So, an analog oscilloscope cannot measure RMS voltage directly, but it does give the user enough information to compute the value for simple waveforms. With the advancement of technology, most digital osciloscopes can calculate the RMS value internally and display the result on the screen. Calculations above used the vertical scale to determine voltage information. The horizontal (or time) scale can be used to determine the period of the waveform. The period of the waveform in Figure 5 is 2.5 divisions. For example, If the horizontal axis is set at 10 msec/div, the period of the signal is (2.5x10 msec/div) = 25 msec. Although the frequency cannot be read from an analog oscilloscope directly, it can be computed by using the relation 𝑓 = 1 ⁄𝑇 and is equal to 40kHz for our example. Similarly, most digital oscilloscopes can compute and display this and other measurements directly.

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Experiment #1: Resistors in DC Circuits, Measurement of Voltage and Current, Ohm’s Law Objectiv ctive Obje ctiv e The objective of this experiment is to become familiar with the concept of resistance, to learn resistor types and color coding, to measure DC voltage and current using digitial multimeters and to examine Ohm’s Law using different circuits.

Bac kgro und Backgro kground Resistors 1. Resis tors The flow of charge through any material encounters an opposing force similar in many respects to mechanical friction. This opposition, due to the collisions between electrons and between electrons and other atoms in the material, which converts electrical energy into another form of energy such as heat, is called the resistance of the material. The circuit element used to model this behaviour is the resistor [1]. The unit of measurement of resistance is the ohm (Ω, the capital Greek letter omega). The circuit symbol and notation for resistance is given in Figure 1.1.

Figure 1.1 Resistance symbol and notation

Typ es ooff res ist ors Types resist istors Resistors are made in many forms, but all belong in either of two groups: fixed or variable.

Fixed resistors are classified into

,

, and

Wire-Wound Resistors

The spiral winding has inductive and capacitive characteristics that make it suitable for operating above 50kHz. The frequency limit can be raised by noninductive winding so that the magnetic field produced by the two parts of the winding is cancelled [2].

This mixture is molded into a cylindirical shape and hardened by baking. Leads are attached axially to each end, and the assembly is encapsuled in a protective encapsulation coating. Color 10

Figure 1.2 Wire-Wound Resistor [2]

Figure 1.3 Composition Resistor [2]

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bands on the outer surface indicate the resistance value and tolerance. Composition resistors are economical and exhibit low noise levels for resistance above 1MΩ. Composition resistors are usually rated for temperatures in the neighborhood of 70⁰C for power ranging from 1/8 to 2W. Composition resistors have end-to-end shunted capacitance that may be noticed at frequencies in the neighborhood of 100 kHz, especially for resistance values above 0.3 MΩ [2].

Metal-Film Resistors Metal film resistors are commonly made of nichrome, tin-oxide or tantalum nitride, either hermetically sealed or using molded-phenolic cases. Metal-film resistors are not as stable as the wire-wound resistors [2]. Figure 1.4 Metal Film Resistor [2]

b) Variable Resistors Variable resistors, as the name implies, have a terminal resistance that can be varied by turning a dial, knob, screw, or whatever seems appropriate for the application. They can have two or three terminals, but most have three terminals. Device which is used for controlling potential levels is called as potentiometer. The symbol and the basic construction of potantiometer is shown in Figure 1.5 [1].

Figure 1.5 a) Symbol of potantiometer

b) Construction of potantiometer [1]

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The resistance between the outside terminals a and c is always fixed at the full rated value of the potentiometer, regardless of the position of the wiper arm b.

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The resistance between the wiper arm and either outside terminal can be varied from a minimum of 0 Ω to a maximum value equal to the full rated value of the potentiometer.

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The sum of the resistances between the wiper arm and each outside terminal will equal the full rated resistance of the potentiometer. Terminal resistance of a potentiometer is demonstrated by Figure 4 [1]. 𝑅𝑎𝑐 = 𝑅𝑎𝑏 + 𝑅𝑏𝑐

(Eq. 1.1) (a)

(b)

Figure 1.6 Terminal resistance of a potentiometer (a) between outside terminals; (b) among all three terminals [1].

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Color C odi ng aand nd St anda rt Resis tor Val ues Codi oding Standa andart...