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NETWORK THEORY UNIT-1 Node and Mesh Analysis

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NETWORK THEORY UNIT-1 Node and Mesh Analysis NETWORK THEORY Subject Code:3EC4-06 UNIT-1 Node and Mesh Analysis Prepared By Abhinandan Jain Assistant Professor, ECE SKIT, Jaipur Abhinandan Jain, Asst. Professor, ECE, SKIT 1 Contents • Introduction • Classification of Network • Network Terminology • Kirchhoff’s Current Law(KCL) • Kirchhoff’s Voltage Law(KVL) • Nodal Analysis • Super Node Analysis • Mesh Analysis Abhinandan Jain, Asst. Professor, ECE, SKIT 2 Contents…….. • Super Mesh analysis • Matrix approach of network containing voltage and current sources and reactance based circuits • Source Transformation • Duality Abhinandan Jain, Asst. Professor, ECE, SKIT 3 Introduction of Subject • Network Theory is a very basic subject which includes theorems and techniques to solve a complex network in a very simple form. • An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces. Abhinandan Jain, Asst. Professor, ECE, SKIT 4 Continued……… • Network/ Circuit analysis is the process of finding the voltages across, and the currents through, every component in the network. • A useful procedure in network analysis is to simplify the network by reducing the number of components. Abhinandan Jain, Asst. Professor, ECE, SKIT 5 Importance of Subject • Network Theory is a core subject for undergraduate students in Electronics and Communication Engineering. • By learning Network Theory we will be able to analyze the different circuit and calculate the voltage, current and power delivered/ absorbed in the circuit elements. • Knowledge gain by the Network Theory will help students in subjects like Electronics Devices, Analog Circuits, Signal and System and Control system etc. • Very important subject for competitive exams like IES, GATE and PSU’s entrance exams Abhinandan Jain, Asst. Professor, ECE, SKIT 6 Applications • Communications systems, Electronics circuits and power systems all consist of more or less complicated electric circuits which themselves are made up of a number of circuit elements. • The devices and equipment may be represented by ‘equivalent circuits’ consisting of basic circuit elements, and an equivalent circuit must behave to all intents and purposes in the same way as the device or equipment which it represents. Abhinandan Jain, Asst. Professor, ECE, SKIT 7 Syllabus Unit Contents 1 Node and Mesh Analysis, matrix approach of network containing voltage and current sources, and reactance's, source transformation and duality. 2 Network theorems: Superposition, reciprocity, Thevenin’s, Norton’s, Maximum power Transfer, compensation and Tallegen's theorem as applied to AC. circuits. 3 Trigonometric and exponential Fourier series: Discrete spectra and symmetry of waveform, steady state response of a network to non sinusoidal periodic inputs, power factor, effective values, Fourier transform and continuous spectra, three phase unbalanced circuit and power calculation. 4 Laplace transforms and properties: Partial fractions, singularity functions, waveform synthesis, analysis of RC, RL, and RLC networks with and without initial conditions with Laplace transforms evaluation of initial conditions. 5 Transient behavior, concept of complex frequency, Driving points and transfer functions poles and zeros of immittance function, their properties, sinusoidal response from pole-zero locations, convolution theorem and Two four port network and interconnections, Behaviors of series and parallel resonant circuits, Introduction to band pass, low pass, high pass and band reject filters. Abhinandan Jain, Asst. Professor, ECE, SKIT 8 3EC4-06 Network Theory COURSE PLAN UNIT UNIT NAME NO OF LECTURE REQUIRED 1 Node and Mesh Analysis 8 2 Network theorems 10 3 Trigonometric and exponential Fourier 10 series: 4 Laplace transforms 9 5 Transient behavior, Two port Network, 13 Network Function Abhinandan Jain, Asst. Professor, ECE, SKIT 9 Marking Scheme 1. Internal There will be two internal exams (1st and 2nd Mid Terms) 1st Mid Term (covering nearly 50% syllabus) 2nd Mid Term (covering the remaining 50% syllabus) Two Mid Terms (32 Marks Each) Average of both Two Assignment (08 marks each) Average of both Final Marks- 40 marks internal 2. External University Exam: 160 marks (covering entire syllabus) 3. Total 40 + 160 =200 marks, Credits: 4 Abhinandan Jain, Asst. Professor, ECE, SKIT 10 Course Outcomes of Network Theory Students will be able to: • Apply the knowledge of basic circuital law and simplify the network using network • Apply the Fourier series techniques to solve different types of circuit problem. • Examine the transient and steady state behavior of the different circuits with the help of Laplace transform and differential method. • Evaluate different two port network and network functions • Analyze the resonant behavior of different circuits comprising of Resister, Inductor and Capacitor Abhinandan Jain, Asst. Professor, ECE, SKIT 11 TEXT BOOKS /REFERENCE BOOKS: 1. Network Analysis & Synthesis, Kuo, Wiley 2. Circuits and Network, Sudhakar & Shyam mohan, Tata McGraw-Hill 3. Sivanagaraju – Electrical circuit analysis, Cengage learning 4. Networks and Systems, Asfaq Hussain, Khanna Publishing House, Delhi 5. Networks and systems, D. Roy Choudhary, New Age International Publishers 6. Circuit Theory, A. Chakrabarti, Dhanpat rai and Co. Abhinandan Jain, Asst. Professor, ECE, SKIT 12 Classification of Network • Linear circuits: It is a circuit whose parameters remain constant with change in voltage or current. Examples are a resistance, inductance or capacitance. • Non-linear Circuits: A linear circuit obeys ohm’s Law i.e current remains directly proportional with applied voltage, while in non linear circuit, ohm’s Law is not satisfied. Abhinandan Jain, Asst. Professor, ECE, SKIT 13 Continued……… • Unilateral Circuit: when the direction of current is changed, the characteristics or properties of the circuit may change. Example: diode, transistors etc. • Bilateral circuit: when with change in direction of current, the characteristics or properties of the circuit may not change, it is then called bilateral circuit. Abhinandan Jain, Asst. Professor, ECE, SKIT 14 Continued……… • Active Network: It is a network which contains one or more than one source of e.m.f. An active network consists of an active element like a battery or transistor. • Passive Network: When a network does not contain any source of e.m.f., it is called passive network. A passive network consists of resistance, inductance or capacitance as passive element. Abhinandan Jain, Asst. Professor, ECE, SKIT 15 Continued…………… • Lumped and Distributed Network: Physically separate network elements like R, L, or C are known as lumped elements. • A transmission line or a cable is an example of distributed parameter network as throughout the line they are not physically separate. – If the network is fabricated with its element in lumped form, it is called lumped network and if in distributed form it is called as distributed network Abhinandan Jain, Asst. Professor, ECE, SKIT 16 Network Terminology • Loop and mesh – A loop is any closed path of a circuit, while mesh is a loop which does not contain any other loop within it. Loop: (ABCDEFA & ABEF & BCDE) – The all the meshes are loops and a loop is not necessary a Mesh. Mesh: (ABEF and BCDE) Abhinandan Jain, Asst. Professor, ECE, SKIT 17 Network Terminology • Node and Junction • A point where two or more branches meet is called a node, while a junction is a point at which three or more branches are joined together. • All the junction are nodes and a node is not necessarily a junction. Abhinandan Jain, Asst. Professor, ECE, SKIT 18 Sign Assumption: • When we are traverse from negative to positive(- to +) in supply the consider the Polarity of Voltage is Positive. • When we are traverse from Positive to Negative (+ to -) in supply the consider the Polarity of Voltage is Negative. • When we are traverse in the direction of current, consider negative sign of current(Due to current flow from high voltage to low voltage) • When we are traverse in the opposite direction of current the consider Positive sign of current(Due to current flow from Low voltage to High voltage) Abhinandan Jain, Asst. Professor, ECE, SKIT 19 Kirchhoff’s Current Law(KCL) “The algebraic sum of all branch current leaving or entering a node is zero at all instant of time.” “The algebraic sum of current entering a node must be equal to the algebraic sum of the current leaving a node.” It is based on conversation of charge. Abhinandan Jain, Asst. Professor, ECE, SKIT 20 Ex.1: Find the currents i1,i2 and i3 in the given circuit. Abhinandan Jain, Asst. Professor, ECE, SKIT 21 Solution: Apply the KCL at node ‘A’: 퐸푛푡푒푟푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐴 = 퐿푒푎푣푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐴 푖1 = 1 + 6 = 7 퐴 풊ퟏ = ퟕ 푨 Apply the KCL at node ‘B’ 퐸푛푡푒푟푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐵 = 퐿푒푎푣푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐵 6 = 푖2 + 7 푖2 = 6 − 7 = −1 퐴 풊ퟐ = −ퟏ 푨 Abhinandan Jain, Asst. Professor, ECE, SKIT 22 Continued……… Apply the KCL at node ‘C’ 퐸푛푡푒푟푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐶 = 퐿푒푎푣푖푛푔 푐푢푟푟푒푛푡 푎푡 푛표푑푒 퐶 7 = 2 + 푖3 푖3 = 7 − 2 = 5 퐴 풊ퟑ = ퟓ 푨 푆표 푡푕푎푡 푡푕푒 푐푢푟푟푒푛푡 푖1, 푖2 푎푛푑 푖3: 풊ퟏ = ퟕ푨, 풊ퟐ = −ퟏ 푨, 풊ퟑ = ퟓ푨 Abhinandan Jain, Asst. Professor, ECE, SKIT 23 Kirchhoff’s Voltage Law(KVL) • “The algebraic sum of voltage or voltage drop in any closed path of network that is traversed in a single direction is zero” 푉푠 − 퐼푅1 − 퐼푅2 = 0 푉푠 = 퐼(푅1+푅2) • It is based on conversation of energy. Abhinandan Jain, Asst. Professor, ECE, SKIT 24 Ex.2: Find the voltage Vs in the circuit if the current i=1.4 A. Abhinandan Jain, Asst. Professor, ECE, SKIT 25 Solution: • Apply the KVL in the loop “CDABC”: −10푖1 − 30푖1 + 10푖2 = 0 −40푖1 + 10푖2 = 0 … … … … … … . (1) • Apply the KCL at node C: 푖 = 푖1 + 푖2 푖1 = 푖 − 푖2 … … … … … . (2) Abhinandan Jain, Asst. Professor, ECE, SKIT 26 Continued……… • Put the value of i1 from equation (2) to the equation (1) −40(푖 − 푖2) + 10푖2 = 0 50푖2 = 40푖 40 푖 = × 푖 2 50 • If i=1.4 A 40 푖 = × 1.4 = 1.12 퐴 2 50 Abhinandan Jain, Asst.
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