write and explain operation of active low pass filter circuit

An active low-pass filter is an electronic circuit that allows low-frequency signals to pass through while attenuating or blocking high-frequency signals. It is called "active" because it employs active components, usually operational amplifiers (op-amps), to achieve its filtering function. In an active low-pass filter, the output voltage is low (closer to zero) for high-frequency input signals and rises towards the maximum value for low-frequency input signals. Here's a basic circuit diagram of an active low-pass filter using an operational amplifier: ```

``` Explanation of the circuit: 1. **Vin**: This is the input voltage signal that you want to filter. It is connected to the non-inverting terminal of the operational amplifier. 2. **Vout**: This is the output voltage of the low-pass filter. It is taken from the output terminal of the operational amplifier. 3. **R1**: This is a resistor connected in series with the input signal. It sets the input impedance of the filter. The larger the resistance, the higher the impedance. 4. **R2**: This is a feedback resistor connected between the output of the op-amp and the inverting terminal. The resistance value determines the gain and cutoff frequency of the filter. 5. **C**: This is a capacitor connected in parallel with R2. The value of this capacitor, along with the value of R2, determines the cutoff frequency of the filter. The operation of the active low-pass filter can be explained as follows: 1. At low frequencies (below the cutoff frequency), the impedance of the capacitor (1/jωC) is high, effectively making R2 dominant in the feedback loop. This results in a high gain for low-frequency signals. 2. As the frequency of the input signal increases and approaches the cutoff frequency, the impedance of the capacitor decreases. This, in turn, reduces the effective feedback resistance (R2) and attenuates the high-frequency components of the signal. 3. Above the cutoff frequency, the impedance of the capacitor becomes very low, effectively short-circuiting R2. This leads to minimal feedback and a significant attenuation of high-frequency signals, making the output voltage low. In summary, an active low-pass filter allows low-frequency signals to pass through with minimal attenuation, while attenuating high-frequency signals. The cutoff frequency (determined by the values of R2 and C) is the frequency at which the filter starts attenuating the signal. The gain of the filter for low-frequency signals can be adjusted by choosing appropriate values for R1 and R2.