Classification of Electrical Networks - Active network contains at least one voltage source or current source - Passive network does not contain an active source - Active elements can inject power, provide power gain, and control current flow - Passive networks consist of resistors and capacitors - Active networks are generally nonlinear and require complex design and analysis tools - By passivity, active network contains electromotive force sources like batteries or generators - Passive network does not contain any electromotive force sources - Passive networks consist of resistors and capacitors - Active elements can inject power, provide power gain, and control current flow - Passive networks are generally linear, but there are exceptions - By linearity, linear network obeys the principle of superposition - Nonlinear network does not obey the principle of superposition - Passive networks are generally linear, but there are exceptions - Inductor with an iron core can exhibit nonlinear behavior - Linear networks are easily analyzed using frequency domain methods - By lumpiness, discrete passive components are called lumped elements - Lumped elements assume resistance, capacitance, and inductance are located at one place - Lumped-element circuits are designed based on the lumped-element model - At high frequencies or for long circuits, the lumped assumption no longer holds - Distributed-element circuits are designed for such cases

Classification of Sources - Sources can be independent or dependent - Independent sources maintain constant voltage or current regardless of the circuit - Dependent sources deliver power or voltage or current depending on the circuit element - Ideal independent sources have constant or sinusoidal values - Dependent sources rely on specific elements in the circuit for their operation

Applying Electrical Laws - Kirchhoff's current law states that the sum of currents entering a node equals the sum of currents leaving the node - Kirchhoff's voltage law states that the sum of potential differences around a loop is zero - Ohm's law relates voltage, resistance, and current in a resistor - Norton's theorem states that any network can be replaced by an ideal current source in parallel with a resistor - Thevenin's theorem states that any network can be replaced by a voltage source in series with a resistor

Design Methods - Electrical circuits can be designed using linear network analysis - Components and elements play a crucial role in circuit design - Series and parallel circuits are fundamental building blocks - Impedance transforms help analyze circuits with complex impedances - Network theorems like Norton's and Thevenin's aid in circuit simplification

Network Simulation Software - Complex circuits can be analyzed numerically with software like SPICE or GNUCAP - Symbolic software like SapWin can be used for circuit analysis - Steady state solution is found to determine operating points of each circuit element - Small signal analysis linearizes non-linear elements around their operating points - Linear circuit matrix can be solved using Gaussian elimination