Overview and Recent Report of Integrated Filter Design Employing Frequency Dependent Negative Resistor (FDNR) - Matsumoto, Fujihiko; Ito, Tsuyoshi (Digital Technologies Research and Applications, 2025)
Filters are essential circuits for various signal processing circuits. One of the main methods of filter integration is to design an LC filter first as a prototype filter, and then simulate the function of the inductor with active components. Considering that the accuracy of elements implemented on a semiconductor chip is significantly lower than that of individual elements, this method, which uses a resistive doubly terminated LC ladder filter with low element sensitivity as the prototype, has been widely adopted. The Bruton Transformation is known as one of the methods to integrate the LC filter. The method avoids the use of inductor elements, which make integration difficult, and requires a component called a Frequency Dependent Negative Resistor (FDNR) . An FDNR is a negative resistance whose impedance is inversely proportional to the square of the frequency. Because the FDNR does not exist as a passive element, it is realized using an active block such as an operational amplifier. This paper provides an overview of the Bruton Transformation and the FDNR. The first half of this paper briefly describes the Bruton transformation and reviews the FDNRs proposed to date since the Bruton transformation was first presented. The second half of the paper presents the latest examples of filter integration methods using FDNR proposed by the authors.