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MT-144 NETWORK ANALYSIS Mechatronics Engineering (01) 1 Instructor: Gp Capt (R) Muzaffar Ali • • • • • MS Aerospace Systems – Cranfield, UK 1979 BE Avionics – CAE, Karachi University 1974 Pakistan Air Force – 1970 to 2002 MCS, NUST – 2002 to 2009 Mechatronics Engineering Dept. at AU – September 2009 onward 2 Course Details: Textbook: Sergio Franco, Electric Circuits Fundamentals, Oxford University Press Reference Books: 1. Irwin, Basic Engineering Circuit Analysis, 9th Edition, Wiley 2. W. H. Hayt et al., Engineering Circuit Analysis, 6th edition, McGraw-Hill Higher Education, 2002 Course Assessment: Homework: 5 – 10 % Quizes: 10 % Mid Term: 20 % Labs: 20% Final: 40 - 45% 3 LIKELY TOPICS Review: • Basic concepts • Notations and Symbols • Voltage and Current Sources Network Analysis: • Natural response of 1st order circuits • 1st order circuits with dependent sources • Response of 1st order circuits to constant forcing function • Response of 1st order circuits to non-constant forcing function • Complete response of 2nd order circuits, • AC response 4 LIKELY TOPICS… • • • • • • • • Laplace transform and inverse Laplace transform Solving Circuit differential equations using Laplace transform Laplace transform of special signals Direct transformation of circuits in to s-domain AC steady state power Concepts of average power, complex power and power factor Frequency response of 1st order circuits Asymptotic magnitude and phase Bode plots 5 A Crude History of Electricity • 600 BC: Ancient Greeks rub amber on cat fur to produce static charge • Circa 0 AD: Persians in present-day Iraq invent the battery for unknown (probably medical) purposes • 1720’s: Stephen Gray shows that static charges can be ‘conducted’ from point to point 6 History (Cont.) • 1750’s: Benjamin Franklin’s One Fluid Theory of Electricity unifies scientific approaches to electricity and forms the foundation of modern electrical theory • 1800’s: Alessandro Volta makes his Voltaic Pile using zinc and copper disks submersed in an electrolytic solution (acid), thus re-inventing the battery, 1800 years after the Persians 7 History (Cont.) • 1820’s: Hans Oerstad discovers electromagnetism with his famous “compass and current-carrying wire” experiments – Andre-Marie Ampere defines electric current and electromagnetism, invents the ammeter – Georg Ohm delivers his theory of electricity, including what later became Ohm’s Law • 1830’s: intense Michael Faraday enters the game and things get 8 Basic Concepts We will review the basic concepts and some laws relevant to the field of electrical engineering: charge, electric field, voltage current, energy and power. We will also learn about an electric signal, circuit, circuit elements and a few of the relevant laws. These concepts were (assumed to be) covered earlier in the various courses of physics undertaken by you, here as well as at the Intermediate college level. These concepts are critical for developing physical insight into the operation of the electric circuits, we are about to study. 9 Basic Concepts § 1.1 UNITS AND NOTATIONS SI Units. We use the ‘International system of Units’. ,which is based on the meter as the unit of length, the kilogram as the unit of mass, the second as the unit of time, the kelvin as the unit of temperature, the ampere as the unit of current, the candela as the unit of light intensity. Please carefully study at home, the table 1.1 at page 2 of your text book. This table gives summary of various SI Units. Also study table 1.2 (at page 3) giving magnitude prefixes, which are going to be confronted frequently, in engineering. Unit Prefixes. It is usual to use the standard prefixes of table 1.2. You are required to revise and learn the use of these prefixes. 10 Basic Concepts § 1.1 UNITS AND NOTATIONS … Consistent Sets of Units. We say that a system of unit is consistent if an equation as expressed in the SI system remains unchanged when expressed in the new system e.g. Ohm’s law, which relates voltage v, resistance R, and current I as v = Ri. In SI units this law may be expressed as [V] = [Ω] [A]., we can write it in consistent sets of units as [V] = [103Ω] [10-3A], and so on. It is exactly same way as you have been treating mm, cm, meters, KM etc , as a measure of length (or distance). 11 Basic Concepts § 1.2 ELECTRICAL QUANTITIES. Let us review the basic concepts of charge, electric field, voltage, current and power. A clear understanding of these concepts is necessary for developing physical insight into the operation of electric circuits. Charge (q). Fundamental quantity of electricity is the electric charge; measured in Coulombs (C). Charge may be positive or negative. The most elementary positive charge is that of the proton, and the most elementary negative charge is that of the electron One electron has a charge of - 1.602 x 10-19 C One hole/ proton has a charge of + 1.602 x 10-19 C 12 Basic Concepts § 1.2 ELECTRICAL QUANTITIES. … Potential Energy (w). As a consequence the force exerted by the electric field (E), a charge (q) posses potential energy. This energy is denoted by w. It depends upon the magnitude of the charge as well as the its location in space. It is similar to a mass exposed to the gravitational earth. (w = mgh, in that case). Just as in the gravitational case it is often convenient to choose sea level as the zero level of potential energy. In the electrical case it has been agreed to regard earth as the zero level of potential energy for charges. 13 Basic Concepts § 1.2 ELECTRICAL QUANTITIES. … Voltage (v). The rate at which the potential energy varies with charge is denoted as v and is called electrical potential, V ≡ dw / dq ….. (1.5) This electrical potential could also be viewed as potential energy per unit charge, or potential energy density. But we are most interested in the potential difference or voltage and not the earlier discussed potential. The physical interpretation of equation (1.5) is as follows: if a charge dq gives up an amount of energy dw in going from one point to another in space, then we define the voltage between those points as v = dw / dq. 14 Basic Concepts § 1.2 ELECTRICAL QUANTITIES. … Relation Between Electric Field and Potential. By establishing a potential difference, a battery generates an electric field. Field and potential are related by the important law of physics, E = – grad v ….(1.7a) E = - [ dv/dx i + dv/dy j + dv/ dz K ] Pl check the correctness through your mathematics book. If we orientate the battery terminals such that the field is same as that of the x-axis, then we get a simplified expression for the above relation: E =- dv/ dx ….. (1.7b) 15 Basic Concepts § 1.2 ELECTRICAL QUANTITIES. … Electric Current (i). If charges are free to move, exposing them to an electric field will force them to drift either along or opposite to E, depending on charge polarity. The resulting stream of charges is called Current. The electric current measures the rate of change in Charge per unit time; unit of measurements is Amperes (C/s) By definition: i ≡ dq/dt …. (1.13) 16 Basic Concepts • Charge (q) – fundamental property of atomic structures; measured in Coulombs (C) – One electron has a charge of - 1.602 x 10-19 C – One holes has a charge of + 1.602 x 10-19 C • Electric Current (i) – measures the rate of change in Charge; unit is Amperes (C/s) – Relationship: i = dq/dt 17 Physics - Continued • Voltage (v) – The Electromotive Force (emf) required to move Charge around a circuit. Indicative of the Electric Field. Also called Potential Difference; measured in Volts (J/C or N-m/C) – Relationship to charge: v = dw/dq 18 Physics – Continued Some More • Power (p) – Rate of change in work (the expending of energy in time); measured in Watts (J/s) p = dw/dt = dw/dq * dq/dt = vi 19 Electric Conventions: • Current Convention: 20 Electric Conventions (Cont.) • Voltage Rise/Drop Convention 21 Electric Conventions (Cont.) • Source/Load Convention 22 Fundamental Laws • Ohm’s Law: V = I*R • Kirchoff’s Laws: – Voltage: Sum the voltages around a loop to Zero – Current: Sum the currents around a node to Zero • Power Equation: P = V*I 23 Maximum Power Transfer • Power Transfer is maximized when load impedance equals source impedance 24 Laboratory Equipment • Oscilloscope – 1 M-Ohm Impedance – “Shunt” Device – Measures Voltages – Always measure voltages with respect to scope ground 25 Laboratory Equipment (Cont.) • Multimeter – Measures Voltage, Current, Resistance, etc. – “Shunt” Device for Voltage (High Impedance) – “Series” Device for Current (Low Impedance) – Acts as a DC source when measuring Resistance – NEVER measure resistance on an Energized Circuit 26 SAFETY • CONTACT WITH ELECTRIC CURRENT CAN CAUSE DEATH • As little as 100 milliamperes (0.1 Amp) of electric current can kill, if it travels across the heart 27 SAFETY (Cont.) • Follow Instructions, Ask for Clarification • Know where Safety Equipment is Located - Fire Extinguishers, Telephones, Fire Blankets, Eye Wash Stations, etc. • Always Assume an Electric Circuit is Hot (Energized) and Dangerous and Act Accordingly 28 SAFETY (Cont.) • Keep Work Areas Clean and Uncluttered • Double Check Circuit Wiring before Energizing • Never Work Alone • Wire with One Hand - Minimizes exposure to the Heart 29 SAFETY CONCLUSIONS Always understand the Laboratory Procedures before touching anything. Always assume that electric circuits are potentially live and dangerous. Make sure there are adequate life saving resources available and know how to use them. 30 Resistor Color Code Blk BR Red Or Yel Gr Blu Vi Gry Wht 0 1 2 3 4 5 6 7 8 9 First Band – “Tens” Column Second Band – “Ones” Column Third Band – Power of 10 Fourth Band – Tolerance: Gold = 5% , Silver = 10% Fifth Band – Ignore for now In this example: 10 x 102 =1000 Ohms +/- 5% 31