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Solution of Networks with dependant sources.

Linear graphs : Introductory definitions, The incidence matrix A, the loop matrix B, relationship between sub matrix of A and B. Cutsets and cutset matrix, Fundamental cutsets and fundamental tiesets, Planar graphs, A and B matrices, Loop, node, node pair equations, duality.

Network Equations: Time domain analysis, first and second order differential equations,initial conditions, evaluation and analysis of transient and steady state responses to step, ramp, impulse and sinusoidal input functions.

Laplace Transform : Its applications to analysis of network for different input functions described above.

Network Functions: Driving point and Transfer functions. Two port networks, open circuit and short circuit parameters, transmission parameters, hybrid parameters, chain parameters, interconnection of two port networks, cascade connection, series and parallel, permissibility of connection.

Representation of Network Functions : Pole, Zeros and natural frequencies, location of poles, even and odd parts of a function, magnitude and angle of a function, the delay function, all pass and minimum phase functions. Net change in angle, Azimuth polynomials, ladder networks, constant resistance network, maximally flat response, Chebyshev response, calculation of a network function from a given angle and a real part, Bode method.

Fundamentals of Network synthesis : Energy functions, passive reciprocal networks, the impedance function,condition on angle, positive real functions, necessary and sufficient conditions , the angle property of a positive real function, Bounded real function. Reactance functions, Realisation of reactance functions, ladder form of a network, Azimuth polynomials and reactance functions. Impedance and admittance of RC networks. Ladder network realisation, resistance inductance network.

 

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