Signals and Systems 1

Basic concepts. The concept of signals, systems, networks, and their classification. The system represented by a network. Fundamentals of electrical networks. Properties of two-poles. Kirchhoff's laws. The fundamental system of loops and cuts. Tellegen's theorem. The complete system of network equations.

Analysis of resistive networks. Concept of resistive networks and their analysis; regularity of the network. Analysis methods: superposition principle, method of nodal voltages, method of mesh currents. Coupled two-poles, characteristics, and their treatment in network calculation. Equivalent circuits of two-pole networks: resultant resistance, Thévenin and Norton generators. Maximum power transfer. Linear two-port networks. Reciprocity, symmetry, passivity. Equivalent circuits of two-port networks. Input and transfer characteristics of terminated two-ports.

Analysis of dynamic networks. Concept of dynamic networks and state variables. State-space representation of electrical networks. Initial conditions. Regularity. Sequential switching in first and second order dynamic networks. The natural response and the forced response. Time constant. Step function and Dirac delta function. Step response and impulse response. Generalized derivative. Convolution. Stability concepts (BIBO and asymptotic stability). 

Time-harmonic steady state. Concept of time-harmonic steady state and its physical meaning. Phasor representation of sinusoidal signals; operations on phasors. Network equations with phasors. Impedance. Network analysis methods. Phasor diagrams. Transfer ratio and frequency response. Bode plot. Logarithmic scale and unit. Powers in time-harmonic steady state: instantaneous, active, reactive, complex power, power factor. Maximum power transfer.

Nonlinear networks. Resistive nonlinerities. Determination of the operating point. Solvability of nonlinear network equations. Introduction to numerical solution techniques. Linearization around the operating point (small-signal analysis). Dynamic resistance. Small-signal analysis of nonlinear two-ports.

Periodic steady-state. Definition and mean values of periodic signals. Fourier polynomial and Fourier series. Mathematical and engineering real form, complex form of the Fourier series. Convergence properties. System analysis utilizing Fourier series. Calculation of active power, Parseval's theorem.