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# Note for Network Theory - NT by MD WESH KARNI

• Network Theory - NT
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DEPARTMENT OF ELECTRICAL ENGINEERING THIRD SEMESTER ,(EE/EEE) SUBJECT:NETWORK THEORY SUBJECT CODE-1303 SYLLABUS :NETWORK THEORY (3-1-0) MODULE-I (10 HOURS) Coupled Circuits: Self-inductance and Mutual inductance, Coefficient of coupling, dot convention, Ideal Transformer, Analysis of multi-winding coupled circuits, Analysis of single tuned and double tuned coupled circuits. Transient study in RL, RC, and RLC networks by Laplace transform method with DC and AC excitation. Response to step, impulse and ramp inputs. Two Port networks: Two port parameters, short circuit admittance parameter, open circuit impedance parameters, Transmission parameters, Image parameters and Hybrid parameters. Ideal two port devices, ideal transformer. Tee and Pie circuit representation, Cascade and Parallel Connections. MODULE-II (10 HOURS) Network Functions & Responses: Concept of complex frequency, driving point and transfer functions for one port and two port network, poles & zeros of network functions, Restriction on Pole and Zero locations of network function. Impulse response and complete response. Time domain behavior form pole-zero plot. Three Phase Circuits: Analysis of unbalanced loads, Neutral shift, Symmetrical components, Analysis of unbalanced system, power in terms of symmetrical components MODULE-III (10 HOURS) Network Synthesis: Realizability concept, Hurwitz property, positive realness, properties of positive real functions, Synthesis of R-L, R-C and L-C driving point functions, Foster and Cauer forms MODULE-IV (10 HOURS) Graph theory: Introduction, Linear graph of a network, Tie-set and cut-set schedule, incidence matrix, Analysis of resistive network using cut-set and tie-set, Dual of a network. Filters: Classification of filters, Characteristics of ideal filters BOOKS . Mac.E Van Valkenburg, “Network Analysis”, . Franklin Fa-Kun. Kuo, “Network Analysis & Synthesis”, John Wiley & Sons.

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. M. L. Soni, J. C. Gupta, “A Course in Electrical Circuits and Analysis”, . Mac.E Van Valkenburg, “Network Synthesiss”, . Joseph A. Edminister, Mahmood Maqvi, “Theory and Problems of Electric Circuits”, Schaum's Outline Series, TMH

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MODULE- I (10 hrs) 1.Magnetic coupled circuits. (Lecture -1) 1.1.Self inductance When current changes in a circuit, the magnetic flux linking the same circuit changes and e.m.f is induced in the circuit. This is due to the self inductance, denoted by L. di V L dt FIG.1 1.2.Mutual Inductance The total magnetic flux linkage in a linear inductor made of a coil is proportional to the current passing through it; that is,

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Fig. 2   Li . By Faraday‟s law, the voltage across the inductor is equal to the time derivative of the total influx linkage; given by, di d L N dt dt 1.3. Coupling Coefficient A coil containing N turns with magnetic flux Ø_ linking each turn has total magnetic flux linkage λ=NØ . By Faraday‟s law, the induced emf (voltage) in the coil is  d   d  e     N    dt   dt  . A negative sign is frequently included in this equation to signal that the voltage polarity is established according to Lenz‟s law. By definition of self-inductance this voltage is also given by Ldi=dtÞ; hence, The unit of flux(Ø) being the weber, where 1 Wb = 1 V s, it follows from the above relation that 1 H = 1 Wb/A. Throughout this book it has been assumed that Ø and i are proportional to each other, making L = (NØ) /I = constant Fig.3 In Fig.3 , the total flux resulting from current i1 through the turns N1 consists of leakage flux,