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
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An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often imprecisely referred to as "circuits"). Linear electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.
A resistive network is a network containing only resistors and ideal current and voltage sources. Analysis of resistive networks is less complicated than analysis of networks containing capacitors and inductors. If the sources are constant (DC) sources, the result is a DC network. The effective resistance and current distribution properties of arbitrary resistor networks can be modeled in terms of their graph measures and geometrical properties.
A network that contains active electronic components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools.
