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This is the case for all linear elements, but also, for example, an ideal diode, which in circuit theory terms is a non-linear resistor, has a constitutive relation of the form = (). Both independent voltage and independent current sources can be considered non-linear resistors under this definition. [3]
A linear circuit is one that has no nonlinear electronic components in it. [1] [2] [3] Examples of linear circuits are amplifiers, differentiators, and integrators, linear electronic filters, or any circuit composed exclusively of ideal resistors, capacitors, inductors, op-amps (in the "non-saturated" region), and other "linear" circuit elements.
Linear vs nonlinear: A straight line through the origin represents a linear circuit element, while a curved line represents a nonlinear element. For example, resistors, capacitors, and inductors are linear, while diodes and transistors are nonlinear.
The diode equation above is an example of an element constitutive equation of the general form, (,) = This can be thought of as a non-linear resistor. The corresponding constitutive equations for non-linear inductors and capacitors are respectively; (,) = (,) =
The term is often used exclusively to refer to linear time-invariant (LTI) systems. Most real systems have non-linear input-output characteristics, but many systems operated within nominal parameters (not over-driven) have behavior close enough to linear that LTI system theory is an acceptable representation of their input-output behavior.
Another contrast is between linear and non-linear models. Most early models of communication are linear models. They present communication as a unidirectional process in which messages flow from the communicator to the audience. Non-linear models, on the other hand, are multi-directional: messages are sent back and forth between participants.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing , and telecommunications .
Due to the delocalization of electrons in π bonds electrons are more easily responsive to applied optical fields and tend to produce larger linear and nonlinear optical responses than those in single (𝜎) bonds. In these systems linear response scales with the length of the conjugated pi system, while nonlinear response scales even more rapidly.