@phdthesis{M22:PHD,

title = {Proper Abstractions for Digital Electronic Circuits: A Physically Guided Approach},

author = {Jürgen Maier},

url = {http://burin.at/wp-content/uploads/2024/03/Diss_Maier_Juergen.pdf},

doi = {10.34726/hss.2022.102506},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

school = {TU Wien, Vienna, Austria},

abstract = {Over the last decades, major improvements in handling semiconductor materials led

to a massive shrinkage of transistor sizes that, in turn, enabled engineers to realize

larger and faster digital circuits. The resulting increase in complexity had, however,

negative effects on verification: Although nowadays highly accurate models of the main

physical processes, which govern the behavior of a circuit, are available, the size and

complexity of these models makes it impossible to finish simulations/computations in

reasonable time. One possible solution is to introduce abstractions, which have the

goal to reduce the verification effort by hiding certain details while preserving accuracy.

Naturally, developing proper abstractions is a very challenging task: Too little or the

wrong information provide an incomplete picture while excessive models tend to be slow.



In this thesis, we, thus, study proper abstractions for digital electronic circuits. In

our opinion, the best results are achieved by (i) understanding the underlying physical

behaviors and (ii) picking appropriate abstract models and parameters based on the

gained insights. This effectively reduces the task to observation and conclusion, so no

assumptions or even guessing is required. Whereas the abstractions and models presented

in this thesis are not meant to replace existing approaches, they provide an alternative

in between highly sophisticated methods (e.g., ordinary differential equations in analog

simulations) and overly simplified ones (e.g., digital models utilizing pure and inertial

delays). Overall, we aim at achieving reliable models, which provide high coverage and

accuracy at low verification efforts compared to existing approaches.



To achieve this goal, we thoroughly studied the following model domains:



1) Analog abstractions: To describe the analog behavior of various logic gates in a

simplified fashion, we develop new models based on physically inspired basic transistor

equations. Although these provide reasonably accurate results, the required effort is

still too high for large-scale verification. Consequently, we employ further abstractions.

Using analytic calculations and fittings, we aim at mathematical functions that allow an

approximation of the analog waveforms. We show that unique rising and falling full-range

switching waveforms provide a very good basis, since their proper combination (more

specifically, the addition of time-shifted versions) is able to closely approximate every

observed shape. We are convinced that our approach will enable the development of an

analog simulation suite with high accuracy, which only needs a fraction of the verification

time required for established analog simulation methods.



2) Digital abstractions: We thoroughly analyze and extend the Involution Delay

Model, the only candidate for a faithful delay estimation method known so far. Based

on physically guided considerations, we (i) identify several shortcomings, (ii) provide a

proper explanation and (iii) develop improvements that remove the observed problems.

More specifically, we show how to calculate delay functions analytically, relax certain

restrictions that impaired easy applicability, and even introduce non-determinism to

improve the model coverage. Formal proofs and deductions are used to show the

correctness of our new abstractions. Simulations of simple circuits allow, for the first

time, a quantitative evaluation of the superior accuracy and the not insignificant, but

quite reasonable, overhead. This enables a fair comparison of the Involution Delay Model

and state-of-the-art digital delay models.



3) We complement our efforts on analog and digital abstractions by an in-depth

investigation of the Schmitt Trigger, in particular, its susceptibility to metastability

(intermediary output values, late transitions). By introducing and using various novel

methods, we are able to characterize the metastable behavior of this gate, i.e., when to

expect which effects. Exploiting this knowledge, we show, based on analog simulations,

how to generate an arbitrary output waveform in a common implementation by controlling

the input accordingly. We also argue that cascading Schmitt Triggers, as it is done with

Flip-Flops in a synchronizer, only improves the situation partially, as new undesired

effects are added. Overall, our results, however, show that a very fine-grained control of

the input is demanded to exploit metastable behavior in the Schmitt Trigger, making it

very unlikely in normal operation.



From the answers we obtained by investigating these interesting research questions,

we can conclude that there is no “silver bullet” w.r.t. modeling abstractions. Every

approach is unique in some respect and thus requires a careful analysis of the governing

physical behavior to achieve the optimal performance, accuracy and coverage.},

key = {2022},

keywords = {featured, OpenAccess},

pubstate = {published},

tppubtype = {phdthesis}

}