2-D Inductor-Capacitor Lattice Synthesis

We consider a general class of 2-D passive propagation media, represented as a planar graph where nodes are capacitors connected to a common ground and edges are inductors. Capacitances and inductances are fixed in time but vary in space. Kirchhoff's laws give the time dynamics of voltage and current in the system. By harmonically forcing input nodes and collecting the resulting steady-state signal at output nodes, we obtain a linear, analog device that transforms the inputs to outputs. We pose the lattice synthesis problem: given a linear transformation, find the inductances and capacitances for an inductor-capacitor circuit that can perform this transformation. Formulating this as an optimization problem, we numerically demonstrate its solvability using gradient-based methods. By solving the lattice synthesis problem for various desired transformations, we design several devices that can be used for signal processing and filtering.

[1]  Stephen P. Boyd,et al.  Optimal design of a CMOS op-amp via geometric programming , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  A discrete-time formulation for the variable wave speed scattering problem in two dimensions , 1996 .

[3]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[4]  Gilbert Strang,et al.  Computational Science and Engineering , 2007 .

[5]  John W. Bandler,et al.  Circuit optimization: the state of the art , 1988 .

[6]  Harish S. Bhat,et al.  Diffraction on the Two-Dimensional Square Lattice , 2009, SIAM J. Appl. Math..

[7]  Anyong Qing.  Automated Analog Electronic Circuits Sizing , 2009 .

[8]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[9]  Liliana Borcea,et al.  Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements , 2010 .

[10]  Ieee Circuits,et al.  IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems information for authors , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[11]  L. Brillouin.  Wave propagation in periodic structures : electric filters and crystal lattices , 1953 .

[12]  Braxton Osting,et al.  Emergence of Periodic Structure from Maximizing the Lifetime of a Bound State Coupled to Radiation , 2010, Multiscale Model. Simul..

[13]  Robert K. Brayton,et al.  A new algorithm for statistical circuit design based on quasi-newton methods and function splitting , 1979 .

[14]  Ehsan Afshari,et al.  Ultrafast analog Fourier transform using 2-D LC lattice , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Alberto L. Sangiovanni-Vincentelli,et al.  DELIGHT.SPICE: an optimization-based system for the design of integrated circuits , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Xin Li,et al.  Robust Analog/RF Circuit Design With Projection-Based Performance Modeling , 2007, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[17]  Andrew E. Yagle,et al.  Forward and inverse scattering for discrete layered lossy and absorbing media , 1997 .

[18]  B. Osting,et al.  Kirchhoff's Laws as a Finite Volume Method for the Planar Maxwell Equations , 2011, IEEE Transactions on Antennas and Propagation.

[19]  Y M Tousi,et al.  2-D Electrical Interferometer: A Novel High-Speed Quantizer , 2010, IEEE Transactions on Microwave Theory and Techniques.

[20]  Rob A. Rutenbar,et al.  Hierarchical Modeling, Optimization, and Synthesis for System-Level Analog and RF Designs , 2007, Proceedings of the IEEE.

[21]  An inverse problem for Toeplitz matrices , 1984 .

[22]  Robert K. Brayton,et al.  The Sparse Tableau Approach to Network Analysis and Design , 1971 .

[23]  Jerome Levine.  Classical Circuit Theory , 1980 .

[24]  A.L. Sangiovanni-Vincentelli,et al.  A survey of optimization techniques for integrated-circuit design , 1981, Proceedings of the IEEE.

[25]  Rob A. Rutenbar,et al.  Computer-aided design of analog and mixed-signal integrated circuits , 2000, Proceedings of the IEEE.

[26]  Ehsan Afshari,et al.  Extremely wideband signal shaping using one- and two-dimensional nonuniform nonlinear transmission lines , 2006 .

[27]  Elwood S. Buffa,et al.  Graph Theory with Applications , 1977 .

[28]  Eli Yablonovitch,et al.  Inverse Problem Techniques for the Design of Photonic Crystals (INVITED) , 2004 .

[29]  Thomas S. Angell,et al.  Optimization methods in electromagnetic radiation , 2004 .

[30]  Russel E. Caflisch,et al.  An inverse problem for Toeplitz matrices and the synthesis of discrete transmission lines , 1981 .

[31]  Sawal Hamid Md Ali.  System level performance and yield optimisation for analogue integrated circuits , 2009 .

[32]  Nikolay Korovkin,et al.  Inverse Problems in Electric Circuits and Electromagnetics , 2006 .

[33]  Jun Zou.  Hierarchical Optimization of Large-Scale Analog/Mixed-Signal Circuits Based-on Pareto-Optimal Fronts , 2009 .

[34]  R. Bansal,et al.  Antenna theory; analysis and design , 1984, Proceedings of the IEEE.

[35]  O. Momeni,et al.  Electrical Prism: A High Quality Factor Filter for Millimeter-Wave and Terahertz Frequencies , 2009, IEEE Transactions on Microwave Theory and Techniques.

[36]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[37]  Robert Hägglund.  An optimization-based approach to efficient design of analog circuits , 2006 .

[38]  Andrew E. Yagle,et al.  On the feasibility of impulse reflection response data for the two-dimensional inverse scattering problem , 1996 .

[39]  John R. Koza,et al.  Automated synthesis of analog electrical circuits by means of genetic programming , 1997, IEEE Trans. Evol. Comput..

[40]  Alfred M. Bruckstein,et al.  Inverse scattering for discrete transmission—line models , 1987 .