Active op amp high pass filter circuit

-a summary and overview for the design of an operational amplifier or op-amp active high pass filter with circuit details and design formulas or design equations.

Active filters using op amps are easy to design build and construct.

In particular active high pass filters can be used in many areas to eliminate unwanted signals or general noise.

These filters can be used to provide relatively high levels of performance for comparatively few components.

What is a high pass filter

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

This can be used in many instances, for example when needing to reject low frequency noise, hum, etc. from signals. This may be useful in some audio applications to remove low frequency hum, or within RF to remove low frequency signals that are not required.

Basic response curve of a high pass filter showing the way the response falls after a given point
High pass filter basic response curve

The shape of the curve is of importance. One of the most important features is the cut-off frequency. This is normally taken as the point where the response has fallen by 3dB.

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 op amp high pass filter

The simplest circuit high pass filter circuit using an operational amplifier can be achieved by placing a capacitor in series with one of the resistors in the amplifier circuit as shown. The capacitor reactance increases as the frequency falls, and as a result this forms a CR low pass filter providing a roll off of 6 dB per octave.

Active high pass filter circuit using an op amp and a single capacitor to give roll off
Single pole active high pass filter using an op amp

The cut off frequency or break point of the 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:

Capacitive reactance used in calculating the break point for a single pole active high pass filter

  Xc is the capacitive reactance in ohms
  Π is equal to 3.142
  f is the frequency in Hertz
  C is the capacitance in Farads

Two pole active high pass filter

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).

Active two pole  high pass filter circuit using an operational amplifier
Operational amplifier two pole high 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 vales determines this.

The equations or formulas for determining the component values for an active two pole  high pass filter circuit using an operational amplifier

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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