With the rise of many-core chips that require substantial bandwidth from the network on chip (NoC), integrated photonic links have been investigated as a promising alternative to traditional electrical interconnects While numerous opto-electronic NoCs have been proposed, evaluations of photonic architectures have thus-far had to use a number of simplifications, reflecting the need for a modeling tool that accurately captures the tradeoffs for the emerging technology and its impacts on the overall network In this paper, we present DSENT, a NoC modeling tool for rapid design space exploration of electrical and opto-electrical networks We explain our modeling framework and perform an energy-driven case study, focusing on electrical technology scaling, photonic parameters, and thermal tuning Our results show the implications of different technology scenarios and, in particular, the need to reduce laser and thermal tuning power in a photonic network due to their non-data-dependent nature

/pdf/dsent-a-tool-connecting-emerging-photonics-with-electronics-36kgq89po0.pdf

DSENT - A Tool Connecting Emerging Photonics with Electronics for Opto-Electronic Networks-on-Chip Modeling

http://users.ece.gatech.edu/limsk/www/pdfs/integration97.pdf

Performance optimization of VLSI interconnect layout

Elmore delay has been widely used to estimate interconnect delays in the performance-driven synthesis and layout of very-large-scale-integration (VLSI) routing topologies. For typical RLC interconnections, however, Elmore delay can deviate significantly from SPICE-computed delay, since it is independent of inductance of the interconnect and rise time of the input signal. Here, we develop an analytical delay model based on first and second moments to incorporate inductance effects into the delay estimate for interconnection lines under step input. Delay estimates using our analytical model are within 15% of SPICE-computed delay across a wide range of interconnect parameter values. We also extend our delay model for estimation of source-sink delays in arbitrary interconnect trees. We observe significant improvement in the accuracy of delay estimates for interconnect trees when compared to the Elmore model, yet our estimates are as easy to compute as Elmore delay. Evaluation of our analytical models is several orders of magnitude faster than simulation using SPICE. We also illustrate the application of our model in controlling response undershoot/overshoot and reducing interconnect delay through constraints on the moments.

/pdf/an-analytical-delay-model-for-rlc-interconnects-18wzpot6o0.pdf

An analytical delay model for RLC interconnects

This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistor-capacitor (RC) time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing signal fall and rise times, and the effects of signal transition times. We then consider more complex formulations such as robust design over corners, multimode design, statistical design, and problems in which threshold and power supply voltage are also variables to be chosen. Finally, we look at the detailed design of gates and interconnect wires, again using a formulation that is compatible with GP or GGP.

/pdf/digital-circuit-optimization-via-geometric-programming-5083zz09tz.pdf

Digital Circuit Optimization via Geometric Programming

In this paper, we study the interconnect layout optimization problem under a higher-order RLC model to optimize not just delay, but also waveform for RLC circuits with non-monotone signal response. We propose a unified approach that considers topology optimization, wiresizing optimization, and waveform optimization simultaneously. Our algorithm considers a large class of routing topologies, ranging from shortest-path Steiner trees to bounded-radius Steiner trees and Steiner routings. We construct a set of required-arrival-time Steiner trees or RATS-trees, providing a smooth trade-off among signal delay, waveform, and routing area. Using a new incremental moment computation algorithm, we interleave topology construction with moment computation to facilitate accurate delay calculation and evaluation of waveform quality. Experimental results show that our algorithm is able to construct a set of topologies providing a smooth trade-off among signal delay, signal settling time, voltage overshoot, and routing cost.

/pdf/interconnect-design-for-deep-submicron-ics-1wpzzxlew8.pdf

Interconnect design for deep submicron ICs

The Elmore delay is an extremely popular delay metric, particularly for RC tree analysis. The widespread usage of this metric is mainly attributable to it being the most accurate delay measure that is a simple analytical function of the circuit parameters. The only drawbacks to this delay metric are the uncertainty as to whether it is an optimistic or a pessimistic estimate, and the restriction to step response delay estimation. In this paper, we prove that the Elmore delay is an absolute upper bound on the 50% delay of an RC tree response. Moreover, we prove that this bound holds for input signals other than steps, and that the actual delay asymptotically approaches the Elmore delay as the input signal rise time increases. A lower bound on the delay is also developed using the Elmore delay and the second moment of the impulse response. The utility of this bound is for understanding the accuracy and the limitations of the Elmore delay metric as we use it for design automation.

/pdf/the-elmore-delay-as-a-bound-for-rc-trees-with-generalized-4kp132crz2.pdf

The Elmore Delay as a Bound for RC Trees with Generalized Input Signals

RLC transmission line synthesis is a difficult problem because minimal net delay cannot be achieved or accurately predicted unless: 1) a termination scheme is chosen and properly implemented, and 2) output driver transition rates are constrained at or below the net's capability. This paper describes a method to concurrently find, for any RLC net, an optimal termination value, a maximum source transition rate, and an approximate net delay using the first few response moments. When optimal termination is accomplished and transition rates do not exceed the capabilities of the net, the resulting delay metrics are an interesting extension of the popular Elmore delay metric for RC interconnects. The task of physical RLC interconnect design is facilitated by the ease with which these first few moments are calculated for generalized RLC lines.

/pdf/transmission-line-synthesis-30z9qlppxk.pdf

Transmission Line Synthesis

As electronic systems grow in functional complexity, hence size, the design is often forced into a multi-chip solution. For such systems, the power dissipation due to the off-chip drivers (OCDs) and the off-chip interconnect capacitance can contribute to a significant portion of the overall system power. Often, however, this excessive power dissipation is unwarranted, since a smaller OCD can be used to drive the transmission line load, hence reducing the net capacitance being switched. The objective of this paper is to enable power dissipation trade-off decisions during the high-level phases of design and to minimize the power dissipation of OCDs and their associated interconnect. First, a termination metric is described that uses width optimization of RLC interconnects. Then, in terms of a proposed linear driver model, the low power design objective is posed as an integer programming problem and a branch and bound enumeration algorithm is presented. The driver and interconnect sizes are determined which will preserve signal quality, dispense with additional termination components, meet delay requirements, and minimize the overall power dissipation.

John Willis

Papers

The Elmore Delay as a Bound for RC Trees with Generalized Input Signals

Transmission Line Synthesis

Low power design of off-chip drivers and transmission lines : A branch and bound approach