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Concept# RL circuit

Summary

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. 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. It is one of the simplest analogue infinite impulse response electronic filters.
The fundamental passive linear circuit elements are the resistor (R), capacitor (C) and inductor (L). These circuit elements can be combined to form an electrical circuit in four distinct ways: the RC circuit, the RL circuit, the LC circuit and the RLC circuit, with the abbreviations indicating which components are used. These circuits exhibit important types of behaviour that are fundamental to analogue electronics. In particular, they are able to act as passive filters.
In practice, however, capacitors (and RC circuits) are usually preferred to inductors since they can be more easily manufactured and are generally physically smaller, particularly for higher values of components.
Both RC and RL circuits form a single-pole filter. Depending on whether the reactive element (C or L) is in series with the load, or parallel with the load will dictate whether the filter is low-pass or high-pass.
Frequently RL circuits are used as DC power supplies for RF amplifiers, where the inductor is used to pass DC bias current and block the RF getting back into the power supply.
The complex impedance ZL (in ohms) of an inductor with inductance L (in henrys) is
The complex frequency s is a complex number,
where
j represents the imaginary unit: j2 = −1,
σ is the exponential decay constant (in radians per second), and
ω is the angular frequency (in radians per second).
The complex-valued eigenfunctions of any linear time-invariant (LTI) system are of the following forms:
From Euler's formula, the real-part of these eigenfunctions are exponentially-decaying sinusoids:
Sinusoidal steady state is a special case in which the input voltage consists of a pure sinusoid (with no exponential decay).

Official source

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