An electrical network'\ or electrical circuit' is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. It can be as small as an integrated circuit on a silicon chip, or as large as an electricity distribution network.
A circuit is a network that has a closed loop i.e. a return path. A network is a connection of 2 or more simple circuit elements, and may not be a circuit.
The goal when designing electrical networks for signal processing is to apply a predefined operation on potential differences (measured in volts) or currentss (measured in amperes). Typical functions for these electrical networks are amplification, oscillation and analog linear algorithmic operations such as addition, subtraction, multiplication, division, differentiation and integration.
In the case of power distribution networks, engineers design the circuit to transport the energy as efficiently as possible while at the same time taking into account economic factors, network safety and redundancy. These networks use components such as power lines, cables, circuit breakers, switches and transformers.
To design any electrical circuits, electrical engineers need to be able to predict the voltages and currents in the circuit. Linear circuits can be analysed to a certain extent by hand because complex number theory gives engineers the ability to treat all linear elements using a single mathematical representation.
A number of electrical laws apply to all electrical networks. These include
- Kirchhoff's Current Law: the sum of all currents entering a node is equal to the sum of all currents leaving the node.
- Kirchhoff's Voltage Law: the directed sum of the electrical potential differences around a circuit must be zero.
- Ohm's Law: the voltage across a resistor is the product of its resistance and the current flowing through it.
- Wye-delta transform
- Norton's theorem: any two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
- Thevenin's theorem: any two-terminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
Network simulation software
In more complex circuits, engineers need to turn to circuit simulation software. SPICE is the most famous of these.
Once the steady state solution is found, the operating points of each element in the circuit are known. For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents. This is an application of Ohm's Law. The resulting linear circuit matrix can be solved with Gauss-Jordan elimination.
Linearization around operating point
When faced with a new circuit, the software first tries to find a steady state solution. This is a solution where all nodes conform to Kirchhoff's Current Law and the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.Piece-wise linear approximation
This type of simulator uses piece-wise linear approximations of the equations governing the elements of a circuit. This approximation comes down to splitting the circuit into two parts: a completely linear network with a number of terminals that connect to ideal diodes. Every time a diode switches from on to off or vice versa, the linear network is configured differently. Increasing the accuracy of the simulation can be achieved by adding more detail to the approximation of the equations, this will increase the running time of the simulation. This flexibility allows an engineer to make a trade-off between simulation time and the precision of the results, something that is not easily done with the previous simulation technique.See also
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