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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.
In electronics, cutoff frequency or corner frequency is the frequency either above or below which the power output of a circuit, such as a line, amplifier, or electronic filter has fallen to a given proportion of the power in the passband.
For some filter classes, such as the Butterworth filter, the insertion loss is still monotonically increasing with frequency and quickly asymptotically converges to a roll-off of 20n dB/decade, but in others, such as the Chebyshev or elliptic filter the roll-off near the cut-off frequency is much faster and elsewhere the response is anything ...
A resistor–inductor circuit or RL filter 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 and is the simplest type of RL circuit. A first-order RL circuit is one of the simplest analogue infinite impulse response electronic ...
In an RL circuit composed of a single resistor and inductor, the time constant (in seconds) is = where R is the resistance (in ohms ) and L is the inductance (in henrys ). Similarly, in an RC circuit composed of a single resistor and capacitor, the time constant τ {\displaystyle \tau } (in seconds) is: τ = R C {\displaystyle \tau =RC}
where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in hertz (Hz). The cutoff frequency when expressed as an angular frequency ( ω c = 2 π f c ) {\displaystyle (\omega _{c}{=}2\pi f_{c})} is simply the reciprocal of the time constant.
A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with = 4/3 F, = 1 Ω, = 3/2 H, and = 1/2 H. [3] Taking the impedance of the capacitors to be / and the impedance of the inductors to be , where = + is the complex frequency, the circuit equations yield the transfer function for this device:
The bandwidth is defined as = and since the lower cutoff frequency f L is usually several decades lower than the higher cutoff frequency f H, All systems analyzed here have a frequency response which extends to 0 (low-pass systems), thus f L = 0 f H = B W {\displaystyle f_{L}=0\,\Longleftrightarrow \,f_{H}=BW} exactly.