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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
The nonlinear wave equation is an inhomogeneous differential equation. The general solution comes from the study of ordinary differential equations and can be obtained by the use of a Green's function. Physically one gets the normal electromagnetic wave solutions to the homogeneous part of the wave equation:
Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider an input signal that contains three frequency components at f a {\displaystyle ~f_{a}} , f b {\displaystyle ~f_{b}} , and f c {\displaystyle ~f_{c}} ; which may be expressed as
Unlike the inverting amplifier, a non-inverting amplifier cannot have a gain of less than 1. A mechanical analogy is a class-2 lever , with one terminal of R 1 as the fulcrum, at ground potential. V in is at a length R 1 from the fulcrum; V out is at a length R 2 further along.
Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using full systems of governing equations of fluid dynamics (for sound waves in liquids and gases) and elasticity (for sound waves in solids).
When overdriving an amplifier beyond its the linear range, gain compression will occur [1] due to nonlinear circuit characteristics. The output of large amplitude inputs will be less than expected than using the small signals gain of the amplifier, such that an increase in input will not be matched by a proportional increase in output. Gain ...
Other physical systems that involve energy storage for waves, and nonlinear generation of new waves, can make use of the same relations. John Manley and Harrison Rowe were protégés of Ralph Hartley at Bell Laboratories. The work with nonlinear reactances (inductors and capacitors) was started back in 1917 by John Burton and Eugene Peterson. [7]
The circuit diagram shows one common implementation. The nonlinear resistor is implemented by two linear resistors and two diodes. At the far right is a negative impedance converter made from three linear resistors and an operational amplifier, which implements the locally active resistance (negative resistance).