Aresistive 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.[1]
An active network contains at least onevoltage source orcurrent source that can supply energy to the network indefinitely. Apassive network does not contain an active source.
An active network contains one or more sources ofelectromotive force. Practical examples of such sources include abattery or agenerator. Active elements can inject power to the circuit, provide power gain, and control the current flow within the circuit.
Passive networks do not contain any sources of electromotive force. They consist of passive elements like resistors and capacitors.
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 arelinearly superimposable. They are thus more easily analyzed, using powerfulfrequency domain methods such asLaplace transforms, to determineDC response,AC response, andtransient response.
Passive networks are generally taken to be linear, but there are exceptions. For instance, aninductor with an iron core can be driven intosaturation if driven with a large enough current. In this region, the behaviour of the inductor is very non-linear.
Discretepassive components (resistors, capacitors and inductors) are calledlumped elements because all of their, respectively, resistance, capacitance and inductance is assumed to be located ("lumped") at one place. This design philosophy is called thelumped-element model and networks so designed are calledlumped-element circuits. This is the conventional approach to circuit design. At high enough frequencies, or for long enough circuits (such aspower transmission lines), the lumped assumption no longer holds because there is a significant fraction of awavelength across the component dimensions. A new design model is needed for such cases called thedistributed-element model. Networks designed to this model are calleddistributed-element circuits.
A distributed-element circuit that includes some lumped components is called asemi-lumped design. An example of a semi-lumped circuit is thecombline filter.
An ideal independent source maintains the same voltage or current regardless of the other elements present in the circuit. Its value is either constant (DC) or sinusoidal (AC). The strength of voltage or current is not changed by any variation in the connected network.
Dependent sources depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is.
A number of electrical laws apply to all linear resistive 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 loop must be zero.
Ohm's law: The voltage across a resistor is equal to the product of the resistance and the current flowing through it.
Norton's theorem: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
Thévenin's theorem: Any network of voltage or current sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
Superposition theorem: In a linear network with several independent sources, the response in a particular branch when all the sources are acting simultaneously is equal to the linear sum of individual responses calculated by taking one independent source at a time.
Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically. The laws can generally be extended to networks containingreactances. They cannot be used in networks that contain nonlinear or time-varying components.
To design any electrical circuit, eitheranalog ordigital,electrical engineers need to be able to predict the voltages and currents at all places within the circuit. Simplelinear circuits can be analyzed by hand usingcomplex number theory. In more complex cases the circuit may be analyzed with specializedcomputer programs or estimation techniques such as the piecewise-linear model.
Circuit simulation software, such asHSPICE (an analog circuit simulator),[2] and languages such asVHDL-AMS andverilog-AMS allow engineers to design circuits without the time, cost and risk of error involved in building circuit prototypes.
When faced with a new circuit, the software first tries to find asteady state solution, that is, one where all nodes conform to Kirchhoff's current lawand the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.
Once the steady state solution is found, theoperating 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 withGaussian elimination.
Software such as thePLECS interface toSimulink usespiecewise-linear approximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network ofideal diodes. Every time a diode switches from on to off or vice versa, the configuration of the linear network changes. Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time.
^Kumar, Ankush; Vidhyadhiraja, N. S.; Kulkarni, G. U . (2017). "Current distribution in conducting nanowire networks".Journal of Applied Physics.122 (4): 045101.Bibcode:2017JAP...122d5101K.doi:10.1063/1.4985792.
