# Elliptic / Cauer Filter

### - basics of the Elliptic or Cauer Filter - its performance, key facts and how it can be used in RF filter applications.

The elliptic filter of Cauer filter is a form of RF filter that provides a very fast transition from pass-band to the ultimate roll off rate.

The Cauer or elliptic filter is characterised by the fact that it has both pass-band and stop-band ripple.

Despite the ripple, the elliptic filter offers very high levels of rejection and as a result it is used in many RF filter applications where rejection levels are key.

## Cauer filter naming

The elliptic filter is also often referred to as the Cauer filter. It takes its name from Wilhelm Cauer.

Cauer was born in Berlin, Germany in 1900. He trained as a mathematician and then went on to provide a solid mathematical foundation for the analysis and synthesis of filters. This was a major step forwards because prior to this the performance and operation of filters was not well understood.

Cauer provided the solid mathematical approach required to enable filters to be designed to meet a requirement rather than the approximate methods that had previously been used.

Graduating from the Technical University of Berlin in 1924, Cauer worked as a lecturer at Institute of Mathematics at the University of Gottingen. However as a result of the depression he moved to the USA, studying at MIT and Harvard, but later returned to Germany.

Sadly Cauer was in Berlin at the end of the Second World War and his body was found in a mass grave in Berlin.

## Elliptic Cauer filter basics

The elliptic filter is characterised by the ripple in both pass-band and stop-band as well as the fastest transition between pass-band and ultimate roll-off of any RF filter type.

The levels of ripple in the pas-band and stop-band are independently adjustable during the design. As the ripple in the stop-band approaches zero, the filter becomes a Chebyshev type I filter, and as the ripple in the stop-band approaches zero, it becomes a Chebyshev type II filter.

If the ripple in both stop-band and pass-band become zero, then the filter transforms into a Butterworth filter.

There are two circuit configurations used for the low pass filter versions of the Cauer elliptic filter. One has the parallel capacitor and inductor in the signal line as shown below:

The other version of the Elliptic filter of Cauer filter has a series inductor and capacitor between the two signal lines as below:

By Ian Poole

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