Design of Advanced Linear Circuits and Systems

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My research is aimed at designing and developing new circuits capable of performing some of the simplest mathematical functions using analog circuits. Several of these functions include amplification, filtering, multiplication, division, sensing, and the general processing of signals. There is a need to constantly reexamine such functions because technology is rapidly changing and what may work well in one integrated circuit technology may have to be revised in another. One example of such a function is a logarithmic or exponential digital to analog converter (DAC) function that I am seeking new ways to implement in new integrated circuit technologies. This is to meet the challenges associated with shrinking power supplies and transistor sizes. My research into new logarithmic and exponential multiplying D/A amplifiers is focused on using first and possibly second order approximations to logarithmic and exponential functions, and expanding the dynamic range of those functions to meet realistic requirements. The expectation is that hardware savings may be gained without excessive losses through the use of these approximation functions. Logarithmic DACs find application in automatic gain control circuits and gain or volume controls. Another example of general processing of signals is in filter design. All electronic circuits use filters that pass low or high frequencies, a band of frequencies, or eliminate a particular band of frequencies. Much of my proposed and yet untapped research is aimed at allowing more choice of several recently newly introduced parameters associated with the frequency response of these new filters, hence allowing more precise filter design, than conventional methods. To accomplish much of this, research into new filter circuit design is focused on an emerging and exciting use of fractional capacitors in filter structures. This unique and relatively unexplored element has the property that its impedance is no longer pure imaginary, but it has a real component to its impedance. This element whose properties are not found naturally in most materials has been used by our group to date to produce unusual characteristics in filters such as asymmetry and sharp filter responses that are not available through commercial capacitors or conventional means. As part of our ongoing research I have also discovered they can be used in modeling the electrical behavior of human tissue, agriculture and looking for cancers. While fractional capacitors are presently not available commercially, this entire research has the potential to revolutionize many other disciplines of electrical engineering, all the while being cross discipline. Why, because fractional calculus long time use in controls and system identification has not been really applied to addressing electrical engineering problems and seeking new ways of doing things. My research work therefore seeks to add to the general body of knowledge both in the area of analog fractional filtering and modeling element properties. The latter application, to possibly aid in bioimpedance measurements in general, or characterizing tissue or monitoring for physiological changes. Any discoveries made here can be further used as a potential diagnostic tool for cancer detection and monitoring physiological changes due to other health conditions. With this application, the need for low-cost, wearable/implantable monitoring devices using indirect measurement techniques becomes extremely useful in both monitoring and possibly keeping health costs down.