First Order Low Pass Filter:

Fig. 2, shows a first order low pass Butter-worth filter that uses an RC network for filtering, opamp is used in non-inverting configuration, R₁ and R_f decides the gain of the filter.

According to voltage divider rule, the voltage at the non-inverting terminal is:

Fig. 2

Thus the low pass filter has a nearly constant gain A_f from 0 Hz to high cut off frequency f_H. At f_H the gain is 0.707 A_f and after f_H it decreases at a constant rate with an increases in frequency. f_H is called cutoff frequency because the gain of filter at this frequency is reduced by 3dB from 0Hz.

Filter Design:

A low pass filter can be designed using the following steps:

1. Choose a value of high cutoff frequency f_H.
2. Select a value of C less than or equal to 1 µF.
3. Calculate the value of R using .
4. Finally, select values of R1 and RF to set the desired gain using .

Example - 1

Design a low pass filter at a cutoff frequency of 1 kH z with a pass band gain of 2.

Solution:

Given f_H = 1 kHz. Let C = 0.01 µF.

Therefore, R can be obtained as

A 20 kΩ potentiometer can be used to set the resistance R.

Since the pass band gain is 2, R₁ and R_F must be equal. Let R₁ = R₂ = 10 kΩ.

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