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# First-order butterworth active low-pass filter

2015-01-16 18:51
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Butterworth filter is a type of filter whose frequency response is flat over the passband region. Low-pass filter (LPF) provides a constant output from DC up to a cutoff frequency f(H) and rejects all signals above that frequency. Circuit diagram shown below is a first-order low-pass Butterworth filter that uses RC network for filtering. Loading of the RC network is avoided by using the Op-Amp which is configured for non-inverting mode. Resistors R1 and Rf determine the gain of the filter. The components needed for this circuit are:

Op-Amp ( 5 terminal )3 Resistors1 CapacitorVoltage sources

The voltage gain below the high cutoff frequency is called the passband gain. It is given by the formula :

##### Af = 1 Rf/R1

High cutoff frequency is given by the formula :

##### f (H) = 1/(2πRC)

In the above circuit the component XSC1 is the Oscilloscope which is used to verify the circuit so don’t get confused with it. In the above circuit the cutoff frequency is decided the resistor R and capacitor C. You can choose any desired value to fix the cutoff frequency. In the above circuit i choose the cutoff frequency to be approximately 5KHz so i used the resistor R of value 10KΩ and capacitor of value 3nF. You can change it if you want to by using the above cutoff frequency formula.

The first order low-pass filter has a practical slope of -20 dB/decade. The low-pass filter has a constant gain Af from 0 to high cutoff frequency f (H). At f(H) the gain is 0.707Af and after f (H) it decreases at a constant rate of 20 dB/decade. The frequency f = f (H) is called the high cutoff frequency because the gain of the filter at this frequency is down by 3 dB ( =20log(10) 0.707 ) from 0 Hz.

The AC analysis of the above circuit is given below. But it is not exactly for the above circuit. The cutoff frequency is now made 20kHz. For getting cutoff frequency 20kHz you need resistor of value 1KΩ and capacitor of value 7.96nF. If you have any doubt in the circuit please let us know by comments.