Harish Bhat, assistant professor of mathematics, has received a grant from the National Science Foundation's Division of Mathematical Sciences to fund interdisciplinary research over the next three summers on the analysis and simulation of large inductor-capacitor networks.
The grant enables Bhat and Ehsan Afshari, an assistant professor of electrical and computer engineering at Cornell University, to continue their collaborative efforts to apply mathematics to circuit design. The NSF has awarded just over $95,000 to fund Bhat's research at CMC, and just over $100,000 to fund Afshari's research at Cornell.
New technologies in areas such as wireless communication, portable computing, and handheld electronics have increased the demand for signal processing at high frequencies and consequently, the need for this kind of research, Bhat says.
Bhat and Afshari propose using two-dimensional networks of inductors and capacitors as a building block in signal processing chips. Previous work by Afshari and Bhat has shown that these networks can be modeled effectively using differential equations.
"The next step is to develop mathematical methods to simplify and solve the models," Bhat says. "One problem is that the models involve thousands of variables. Mathematical analysis is necessary to simplify the models before they can be used by engineers to simulate and design circuits."
"This is a case where mathematics can be used to develop an idea that has a lot of merit from an engineer's point of view," Bhat says. "The proposed research has the potential to revolutionize high-frequency analog signal processing, leading to low-cost chips that operate 100-1000 times faster than current ones."
The grant also benefits CMC students in the way of research opportunities, enabling an undergraduate to assist with Bhat's research over the next three summers.
"It's certainly exciting to be part of that link," Bhat says of the student-professor research component.
Bhat is a graduate of Harvard, where he earned an A.B. in mathematics, and from the California Institute of Technology, where he earned a Ph.D. in control and dynamical systems. In 2005, he and two other collaborators won the Stanford-Berkeley-Caltech Innovators Challenge for Solitonic Pulse Shaping on Silicon.
Bhat joined the mathematics department at CMC this fall.
Emily Meinhardt '10