First Order Low Pass Filter

Here an explanation of the operation of low pass filter was made, the operation principle of active low pass filter was made, of active low pass filter was made, I designed an active low pass filter & finally I have drawn the frequency response of designed active filter by using filter gain equation & plotting the frequency vs. gain curve. 

An electric filter is frequency-selective circuit that passes a specified band of frequencies & blocks or attenuates signals of frequencies outside this band. Active filters can be designed using op-amps, resistors, capacitors or inductors. RC filters are used for audio or low frequency operation, where LC filters are used for high frequencies. For designing audio filters I used capacitors, because inductors are very large, costly & may dissipate more power. I chose active filters instead of passive filters because,

a.        It has gain & frequency adjustment flexibility.

b.       It has no loading problem.

c.        It has very high input impedance & very low output impedance.

d.       It is more economical than passive filters.

I designed first order low pass butter-worth filter with RC network in my present assignment. The key characteristic of butter-worth filter is it has a flat pass-band & a flat stop-band. The ideal and practical frequency response of a first order low pass filter is given below,

           

The above figure shows the frequency response of a 1^st order low pass butter-worth filter. The ideal frequency response is shown by the dashes line while the practical response is shown by the solid line. We can see from the frequency response that, the filter allow signal with frequencies less than f_H to pass through it & the signal appears at the output with predefined gain.

Ideally it attenuates the signal appearing at the input which has frequencies greater than f_H & gives zero output. Ideally at f_H, the frequency response curve changes sharply from A_F (closed loop gain) to zero.  Hence the frequencies from f to f_H are called pass-band frequencies & frequencies greater than f_H are called stop-band frequencies.

f_H is called high cutoff frequency. Unfortunately the change is not so sharp at f_H in practical low pass filters. In practical 1^st order low pass butter-worth filter gain changes with 20dB/decade with frequencies greater than f_H.