# Active op amp low pass filter

### -an operational amplifier or op amp makes the ideal basis for an active low pass filter circuit design.

Active filters using op amps are an ideal circuit solution for many low pass filter requirements.

Active low pass filters can be used for many applications. One area in which these filters can be used is on the output of digital to analogue converters where they are able to remove the high frequency alias components. However they can be used in many other areas where it is necessary to pass the low frequency components of the signal, but remove the unwanted high frequency elements.

Active low pass filters are capable of providing a relatively high level of performance for a small number of components.

## What is a low pass filter?

As the name implies, a low pass filter is a filter that passes the lower frequencies and rejects those at higher frequencies.

Low pass filter basic response curve

The shape of the curve is of importance with features like the cut-off frequency and roll off being key to the operation.

The cut-off frequency is normally taken as the point where the response has fallen by 3dB as shown.

Another important feature is the final slope of the roll off. This is generally governed by the number of 'poles' in the filter. Normally there is one pole for each capacitor inductor in a filter.

When plotted on a logarithmic scale the ultimate roll-off becomes a straight line, with the response falling at the ultimate roll off rate. This is 6dB per pole within the filter.

## Single pole active low pass filter circuit

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.

Operational amplifier low pass filter - single pole

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:

Where:
Xc is the capacitive reactance in ohms
Π is the greek letter and equal to 3.142
f is the frequency in Hertz
C is the capacitance in Farads

The in band gain for these circuits is calculated in the normal way ignoring the effect of the capacitor.

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 greater 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 kΩ and 100 kΩ. This is advisable because the output impedance of the circuit rises with increasing frequency and values outside this region may affect the performance.

By Ian Poole

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