An active low-pass filter is an electronic circuit designed to pass low-frequency signals while attenuating higher-frequency signals. It consists of an operational amplifier (op-amp) as its active component, along with resistors and capacitors.
The basic configuration of an active low-pass filter involves placing a capacitor in parallel with a resistor in the feedback loop of an op-amp. This feedback network determines the filter's cutoff frequency and its response to different frequencies. The op-amp provides amplification to the filtered output.
Here's a step-by-step explanation of how an active low-pass filter works:
Op-Amp Setup: The operational amplifier is connected in the non-inverting configuration. The non-inverting input terminal (+) is connected to the input signal, and the inverting input terminal (-) is grounded.
Feedback Network: A resistor (Rf) and a capacitor (Cf) are connected in series between the output of the op-amp and the inverting input (-) of the op-amp. The junction between the resistor and the capacitor is connected to the output of the filter.
Capacitor Charging and Discharging: When the input signal changes, the capacitor charges and discharges accordingly. At low frequencies, the capacitor charges and discharges relatively slowly, allowing the signal to pass through. However, at higher frequencies, the capacitor reacts more quickly, attenuating those signals.
Cutoff Frequency: The cutoff frequency (fc) of the low-pass filter is determined by the combination of the resistor (Rf) and capacitor (Cf) values and is given by the formula: fc = 1 / (2π * Rf * Cf). At this frequency, the output signal is attenuated by -3 dB (half power) relative to the passband.
Amplification: The operational amplifier provides gain to the filtered output signal. The gain of the filter can be adjusted by appropriately selecting the resistor values in the non-inverting input path of the op-amp.
Signal Output: The filtered and amplified output signal is obtained from the output terminal of the op-amp.
In summary, an active low-pass filter allows low-frequency signals to pass through with little attenuation, while attenuating higher frequencies. The cutoff frequency of the filter is determined by the values of the resistor and capacitor in the feedback network, and the op-amp amplifies the filtered output signal to the desired level.