# What is an Elliptic / Cauer Filter: the basics

## The Elliptic or Cauer filter provides the fastest transition from pass to stop band but with ripple in passband and stopband.

The Elliptic or Elliptical filter is also known as a Cauer filter and sometimes even a Zolotarev filter.

The filter is used in many RF applications where a very fast transition between the passband and stopband frequencies is required. The elliptic filter produces the fastest transition of any type of filter, but it also exhibits gain ripple in both passband and stopband.

The key application for the elliptic filter is for situations where very fast transitions are required between passband and stopband. It could be that spurious signals fall just outside the required bandwidth and these need to be removed. Sometimes where non-amplitude sensitive forms of signal are used, a form of gain equalisation may be possible to counteract the ripple of the RF filter.

## Naming of elliptic filter

The elliptic filter is also often referred to as the Cauer filter after 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.

The filter is also sometimes called a Zolotarevwas filter after Yegor (Egor) Ivanovich Zolotarevwas who was a Russian mathematician. He was born and lived in St Petersburg. After gain his degree he became a lecturer at St Petersburg University, lecturing main on elliptic functions.

Sadly Zolotarevwas met an untimely death when was on his way to his dacha and was run over by a train in the Tsarskoe Selo station, later dying from the resultant blood poisoning on 19 July 1878.

## 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 .