This paper proposes a closed-form eye-diagram model for on-chip distortionless transmission lines with intentionally inserted shunt conductance. We derive expressions of eye-opening both in voltage and time, by assuming a piece-wise linear waveform model. The model is experimentally verified with various length, shunt conductance and resistive termination. We also apply the proposed model to design space exploration, and demonstrate that the proposed model helps estimate the optimal shunt conductance and resistive termination according to required signaling length and throughput.

In this paper, an efficient method is proposed to accurately analyze large-scale power/ground (P/G) networks, where inductive parasitics are modeled with the partial reluctance. The method is based on frequency-domain circuit analysis and the technique of vector fitting, and obtains the time-domain voltage response at given P/G nodes. The frequency-domain circuit equation including partial reluctances is derived, and then solved with the GMRES algorithm with rescaling, preconditioning and recycling techniques. With the merit of sparsified reluctance matrix and iterative solving techniques for the frequency-domain circuit equations, the proposed method is able to handle large-scale P/G networks with complete inductive modeling. Numerical results show that the proposed method is orders of magnitude faster than HSPICE, several times faster than INDUCTWISE, and capable of handling the inductive P/G structures with more than 100,000 wire segments.

Boundary Constraints of VLSI floorplanning require a set of blocks to be placed along the boundaries of the chip. Thus, this set of blocks can be adjacent to I/O pads for external communication. Furthermore, these blocks are kept away from the central area so that they do not form blockage for internal routing. In the paper, we devise an algorithm of VLSI floorplanning with boundary constraints using a Corner Block List (CBL) representation. We identify the necessary and sufficient conditions of the CBL representation for the boundary constraints. We design a linear time approach to scan the conditions and formulate a penalty function to punish the constraint violation. A simulated annealing process is adopted to optimize the floorplan. Experiments on MCNC benchmarks show promising results.

Inductive effect becomes important for on-chip global interconnects, like the power/ground (P/G) grid. Because of the locality property of partial reluctance, the inverse of partial inductance, the window-based partial reluctance extraction has been applied for large-scale interconnect structures. In this paper, an efficient method of partial reluctance extraction is proposed for large-scale regular P/G grid structures. With a block reuse technique, the proposed method makes full use of the structural regularity of the P/G grid. Numerical results demonstrate the proposed method is able to efficiently handle a P/G grid with up to one hundred thousands wire segments. It is several tens times faster than the window-based method, while generating accurate frequency-dependent partial reluctance and resistance.

This paper introduces a step response based method to predict the eye diagram for high-speed signaling systems. The method is able to predict accurately the worst-case eye diagram, and is orders of magnitude faster than the method using SPICE simulation with input of random bits. The proposed method is applied to search optimal equalizer parameters for lower-power transmission-line signaling schemes. Simulation results show that the scheme with driver-side series capacitor achieves much better eye area, and signaling throughput than the conventional scheme with only resistive terminations.