# High Pass Filter Design

### - high pass filter design techniques, equations and concepts and how to transform the design from a low pass starting point.

The design of low pass and high pass filters is relatively straightforward.

Normally, a low pass filter is used as the starting point and then this is transformed to provide the high pass filter design.

The concepts for the basic low pass filter design are provided on the previous page. Once the basic design has been achieved, the high pass filter design can then be effected by easily transforming the values to give the required high pass filter functionality.

## High pass filter design basics

Although there are programmes that will enable the design of a high pass filter circuit, often a more manual method may be required. The typical approach that is used is to design a low pass filter, and then transform this to a high pass filter design.

When choosing the basic requirements for the high pass filter design, elements such as in-band ripple will remain the same.

It is possible to utilise the same response curves by inverting the f/fc axis. This is because the response of the high pass filter is the inverse of the low pass filter in frequency terms. In other words in a high pass filter design, it is necessary to measure the attenuation at frequencies at a proportion below the cut-off frequency rather than above the cut-off frequency. For example an attenuation level at 1/2 the cut-off frequency may be required for a high pass filter design rather than 2 times the frequency.

Using this information and any other it is possible to find a response that satisfies the requirements. The next stage is to determine the values of the circuit elements for the normalised low pass filter version.

## Circuit element transformation

After the circuit elements have been determined, the next stage in the high pass filter design is to transform the circuit elements from the low pass version into one for the high pass filter design.

To complete the high pass filter design, the element values are easily determined by replacing each filter element with an element of the opposite type, i.e. replace a capacitor by an inductor and an inductor by a capacitor. The value of the capacitor is equal to the reciprocal of the inductor and vice versa, i.e. Ln = 1/Cn and Cm = 1/Lm.

The values in the above example and purely fictional and only to be sued for the purposes of the explanation. These would then transform to:

By Ian Poole

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