Closed Form Expressions for Delay to Ramp Inputs for On-Chip VLSI RC Interconnect

In high speed digital integrated circuits, interconnects delay can be significant and should be included for accurate analysis. Delay analysis for interconnect has been done widely by using moments of the impulse response, from the explicit Elmore delay (the first moment of the impulse response) expression, to moment matching methods which creates reduced order trans impedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delay can be estimated accurately at an early physical design stage. For RC trees it is demonstrated that the inverse gamma function provides a provably stable approximation. We used the PERI [13] (Probability distribution function Extension for Ramp Inputs) technique that extends delay metrics for ramp inputs to the more general and realistic non-step inputs. The accuracy of our model is justified with the results compared with that of SPICE simulations. Keywords¾ Moment Matching, On-Chip Interconnect, Probability Distribution function, Cumulative Distribution function, Delay calculation, Slew Calculation, Beta Distribution, VLSI

Fast high-order variation-aware IC interconnect analysis

Interconnects constitute a dominant source of circuit delay for modern chip designs. The variations of critical dimensions in modern VLSI technologies lead to variability in interconnect performance that must be fully accounted for in timing verification. However, handling a multitude of inter-die/intra-die variations and assessing their impacts on circuit performance can dramatically complicate the timing analysis. In this thesis, three practical interconnect delay and slew analysis methods are presented to facilitate efficient evaluation of wire performance variability. The first method is described in detail in Chapter III. It harnesses a collection of computationally efficient procedures and closed-form formulas. By doing so, process variations are directly mapped into the variability of the output delay and slew. This method can provide the closed-form formulas of the output delay and slew at any sink node of the interconnect nets fully parameterized, in-process variations. The second method is based on adjoint sensitivity analysis and driving point model. It constructs the driving point model of the driver which drives the interconnect net by using the adjoint sensitivity analysis method. Then the driving point model can be propagated through the interconnect network by using the first method to obtain the closedform formulas of the output delay and slew. The third method is the generalized second-order adjoint sensitivity analysis. We give the mathematical derivation of this method in Chapter V. The theoretical value of this method is it can not only handle this particular variational interconnect delay and slew analysis, but it also provides an avenue for automatical linear network analysis and optimization. The proposed methods not only provide statistical performance evaluations of the interconnect network under analysis but also produce delay and slew expressions parameterized in the underlying process variations in a quadratic parametric form. Experimental results show that superior accuracy can be achieved by our proposed methods

Assessment of 50%-Propagation-Delay for Cascaded PCB Non-Linear Interconnect Lines for the High-Rate Signal Integrity Analysis

This paper presents an enlarged study about the 50-% propagation-time assessment of cascaded transmission lines (TLs). First and foremost, the accurate modeling and measurement technique of signal integrity (SI) for high-rate microelectronic interconnection is recalled. This model is based on the reduced transfer function extracted from the electromagnetic (EM) behavior of the interconnect line RLCG-parameters. So, the transfer function established takes into account both the frequency dispersion effects and the different propagation modes. In addition, the transfer function includes also the load and source impedance effects. Then, the SI analysis is proposed for high-speed digital signals through the developed model. To validate the model understudy, a prototype of microstrip interconnection with w = 500 µm and length d = 33 mm was designed, simulated, fabricated and tested. Then, comparisons between the frequency and time domain results from the model and from measurements are performed. As expected, good agreement between the S-parameters form measurements and the model proposed is obtained from DC to 8 GHz. Furthermore, a de-embedding method enabling to cancel out the connectors and the probe effects are also presented. In addition, an innovative time-domain characterization is proposed in order to validate the concept with a 2.38 Gbit/s-input data signal. Afterwards, the 50-% propagation-time assessment problem is clearly exposed. Consequently an extracting theory of this propagation-time with first order RC-circuits is presented. Finally, to show the relevance of this calculation, propagation-time simulations and an application to signal integrity issues are offered

A Fast Symbolic Computation Approach to Statistical Analysis of Mesh Networks with Multiple Sources *

Abstract-Mesh circuits typically consist of many resistive links and many sources. Accurate analysis of massive mesh networks is demanding in the current integrated circuit design practice, yet their computation confronts numerous challenges. When variation is considered, mesh analysis becomes a much harder task. This paper proposes a symbolic computation technique that can be applied to the moment-based analysis of mesh networks with multiple sources. The variation issues are easily taken care of by a structured computation mechanism, which can naturally facilitate sensitivity based analysis. Applications are addressed by applying the computation technique to a set of mesh circuits with varying sizes

Time interleaved counter analog to digital converters

The work explores extending time interleaving in A/D converters, by applying a high-level of parallelism to one of the slowest and simplest types of data-converters, the counter ADC. The motivation for the work is to realise high-performance re-configurable A/D converters for use in multi-standard and multi-PHY communication receivers with signal bandwidths in the 10s to 100s of MHz. The counter ADC requires only a comparator, a ramp signal, and a digital counter, where the comparator compares the sampled input against all possible quantisation levels sequentially. This work explores arranging counter ADCs in large time-interleaved arrays, building a Time Interleaved Counter (TIC) ADC. The key to realising a TIC ADC is distributed sampling and a global multi-phase ramp generator realised with a novel figure-of-8 rotating resistor ring. Furthermore Counter ADCs allow for re-configurability between effective sampling rate and resolution due to their sequential comparison of reference levels in conversion. A prototype TIC ADC of 128-channels was fabricated and measured in 0.13μm CMOS technology, where the same block can be configured to operate as a 7-bit 1GS/s, 8-bit 500MS/s, or 9-bit 250MS/s dataconverter. The ADC achieves a sub 400fJ/step FOM in all modes of configuration

Modeling and Simulation of Advanced Nano-Scale Very Large Scale Integration Circuits

With VLSI(very large scale integration) technology shrinking and frequency increasing, the minimum feature size is smaller than sub-wavelength lithography wavelength, and the manufacturing cost is significantly increasing in order to achieve a good yield. Consequently design companies need to further lower power consumption. All these factors bring new challenges; simulation and modeling need to handle more design constraints, and need to work with modern manufacturing processes. In this dissertation, algorithms and new methodology are presented for these problems: (1) fast and accurate capacitance extraction, (2) capacitance extraction considering lithography effect, (3) BEOL(back end of line) impact on SRAM(static random access memory) performance and yield, and (4) new physical synthesis optimization flow is used to shed area and reduce the power consumption. Interconnect parasitic extraction plays an important role in simulation, verification, optimization. A fast and accurate parasitic extraction algorithm is always important for a current design automation tool. In this dissertation, we propose a new algorithm named HybCap to efficiently handle multiple planar, conformal or embedded dielectric media. From experimental results, the new method is significantly faster than the previous one, 77X speedup, and has a 99% memory savings compared with FastCap and 2X speedup, and has an 80% memory savings compared with PHiCap for complex dielectric media. In order to consider lithography effect in the existing LPE(Layout Parasitic Extraction) flow, a modified LPE flow and fast algorithms for interconnect parasitic extraction are proposed in this dissertation. Our methodology is efficient, compatible with the existing design flow and has high accuracy. With the new enhanced parasitic extraction flow, simulation of BEOL effect on SRAM performance becomes possible. A SRAM simulation model with internal cell interconnect RC parasitics is proposed in order to study the BEOL lithography impact. The impact of BEOL variations on memory designs are systematically evaluated in this dissertation. The results show the power estimation with our SRAM model is more accurate. Finally, a new optimization flow to shed area blow in the design synthesis flow is proposed, which is one level beyond simulation and modeling to directly optimize design, but is also built upon accurate simulations and modeling. Two simple, yet efficient, buffering and gate sizing techniques are presented. On 20 industrial designs in 45nm and 65nm, our new work achieves 12.5% logic area growth reduction, 5.8% total area reduction, 10% wirelength reduction and 770 ps worst slack improvement on average