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In network analysis, rather than use the differential equations directly, it is usual practice to carry out a Laplace transform on them first and then express the result in terms of the Laplace parameter s, which in general is complex. This is described as working in the s-domain. Working with the equations directly would be described as ...
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ l ə ˈ p l ɑː s /), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex-valued frequency domain, also known as s-domain, or s-plane).
The tuning application, for instance, is an example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning that any voltage or current in the circuit can be described by a second-order differential equation in circuit analysis. The three circuit elements, R, L and C, can be combined in a number of different ...
The Laplace transform is a frequency-domain approach for continuous time signals irrespective of whether the system is stable or unstable. The Laplace transform of a function f ( t ) , defined for all real numbers t ≥ 0 , is the function F ( s ) , which is a unilateral transform defined by
The unilateral Laplace transform takes as input a function whose time domain is the non-negative reals, which is why all of the time domain functions in the table below are multiples of the Heaviside step function, u(t). The entries of the table that involve a time delay τ are required to be causal (meaning that τ > 0).
The term "transfer function" is also used in the frequency domain analysis of systems using transform methods, such as the Laplace transform; it is the amplitude of the output as a function of the frequency of the input signal.
Bode, Hendrik, Network Analysis and Feedback Amplifier Design, pp. 360–371, D. Van Nostrand Company, 1945 OCLC 1078811368. Brune, Otto , "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency" , MIT Journal of Mathematics and Physics , vol. 10, pp. 191–236, April 1931.
A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or current source. [1] A first-order RL circuit is composed of one resistor and one inductor, either in series driven by a voltage source or in parallel driven by a current source.