# Operational amplifier low pass filter circuit

### -a summary of operational amplifier or op-amp active low pass filter circuitry

Op-amp circuits include:

• Operational amplifier circuits

• Inverting op-amp

• Non-inverting op-amp

• Op-amp high pass filter

• Op-amp low pass filter

• Op-amp bandpass filter

• Op-amp variable gain amplifier

• Op-amp notch filter circuits

• Operational amplifier multivibrator

• Op-amp bistable

• Op-amp comparator

• Op-amp Schmitt trigger

• Op-amp integrator

• Op-amp differentiator

Operational amplifiers lend themselves to being used for active filter circuits, including a low pass filter circuit. Using a few components they are able to provide high levels of performance.

The simplest circuit low pass filter circuit using an operational amplifier simply places a capacitor across the feedback resistor. This has the effect as the frequency rises of increasing the level of feedback as the reactive impedance of the capacitor falls. The break point for this simple type of filter can be calculated very easily by working out the frequency at which the reactance of the capacitor equals the resistance of the resistor. This can be achieved using the formula:

**Xc = 1 / 2 pi f C**

where:

**Xc** is the capacitive reactance in ohms

**pi** is the greek letter and equal to 3.142

**f** is the frequency in Hertz

**C** is the capacitance in Farads

**Operational amplifier circuits with high frequency roll off**

While these operational amplifier circuits are useful to provide a reduction in gain at high frequencies, they only provide an ultimate rate of roll off of 6 dB per octave, i.e. the output voltage halves for every doubling in frequency. This type of filter is known as a one pole filter. Often a much grater rate of rejection is required, and to achieve this it is possible to incorporate a higher performance filter into the feedback circuitry.

## Two pole low pass filter op-amp circuit

Although it is possible to design a wide variety of filters with different levels of gain and different roll off patterns using operational amplifiers, the filter described on this page will give a good sure-fire solution. It offers unity gain and a Butterworth response (the flattest response in band, but not the fastest to achieve ultimate roll off out of band).

**Operational amplifier two pole low pass filter**

*Simple sure fire design with Butterworth response and unity gain*

The calculations for the circuit values are very straightforward for the Butterworth response and unity gain scenario. Critical damping is required for the circuit and the ratio of the resistor and capacitor values determines this.

When choosing the values, ensure that the resistor values fall in the region between 10 k ohms and 100 k ohms. This is advisable because the output impedance of the circuit rises with increasing frequency and values outside this region may affect he performance.

* By Ian Poole*

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