RL (Resistor-Inductor) circuits are electronic filters used to block or pass specific ranges of frequencies. They are characterized by the interplay between resistance and inductive reactance.
A **Low-Pass Filter** allows frequencies *below* a certain cutoff frequency to pass through, while attenuating frequencies above it. In a simple series RL low-pass filter, the inductor (L) is connected in series with the input, and the output is taken across the resistor (R). At low frequencies, the inductor’s impedance ($X_L$) is low, acting almost like a short circuit, allowing the signal to pass primarily through the resistor to the output. At high frequencies, the inductor’s impedance increases significantly, effectively blocking the high-frequency signals and diverting them away from the output.
A **High-Pass Filter** allows frequencies *above* a certain cutoff frequency to pass through, while attenuating frequencies below it. In a simple series RL high-pass filter, the resistor (R) is in series with the input, and the output is taken across the inductor (L). At low frequencies, the inductor’s impedance ($X_L$) is low, effectively shorting the signal. At high frequencies, the inductor’s impedance increases, allowing more of the signal to drop across the inductor, thus passing the high-frequency components to the output.
The **cutoff frequency ($f_c$)** (also known as the -3dB frequency or half-power frequency) is the point where the output power of the filter is half of the input power, or the output voltage is approximately 70.7% of the input voltage. For a simple RL filter, the cutoff frequency is determined by the values of R and L:
$$f_c = \frac{R}{2\pi L}$$
Where: