Synthesis method for LC filters

The study of resonant circuits soon highlighted the selective properties of inductance – capacitor networks. As early as 1915, Campbell and Wagner developed the first filters using coils and capacitors. In 1923, Zobel developed the first systematic LC filter design method based on the theory of image impedance filtering [13] .

This method, approximate but very simple [16], , has enabled us to produce highly selective and stable filters for several decades, thanks to the use of abacuses.

From around 1970 onwards, the emergence of integrated circuits on the one hand, and electronic computing on the other, profoundly changed both design methods and filter production technologies.

In terms of methods, image parameter synthesis was gradually replaced by the insertion method introduced around 1940 by Cauer and Darlington [14][15] . To make this method operational, difficult numerical calculation problems had to be solved at the time, so it was not until around 1975 that this method became widespread [7] .

As far as technology is concerned, inductances do not lend themselves well to integration, so inductance-free active filters were increasingly used from 1970 onwards. However, it soon became apparent that it was very difficult to produce highly selective active filters. Orchard demonstrated that there was a fundamental reason for this: LC filters inserted between two resistors, unlike the others, benefit from exceptionally low sensitivity to variations in the values of their components [20] .

This property is so important that, since 1975-1980, a highly selective active filter has often been made from an LC filter model [5] .

Today, in addition to their use as models, LC filters are used in the high-frequency range (> 1 MHz) and above all for microwave filtering (typically > 100 MHz-30 GHz), where it is possible to integrate inductors or use transmission line technologies with LC network-like behavior (distributed filters). In addition, the transposition of conventional LC filter synthesis methods to microwave filters will also be briefly outlined at the end of the article.