Why Digital Timing Simulation Matters

From logic gates to fast, history-aware timing models

Sina Mohammadi Ali Akbar — Matrikelnummer: 12249534

The Problem

Every nanosecond counts.

A signal arriving too late is indistinguishable from a wrong answer.

CLK Edge

Deadline

Signal

Arrives Late

Result

Wrong Answer

Roadmap

The Journey Ahead

From physical gates to fast, history-aware simulation

The Physics

Voltage transitions in silicon

The Models

Pure delay, inertial delay, their limits

The History Effect

Past switching shapes future delay

The Goal

Fast, trace-aware simulation

Timing Failure

Late = Wrong

A correct value after the clock edge is a failure.

Value

Correct

Arrival

Too Late

🔔 CLK Edge

Deadline Missed

Result

Failure

Physical Reality

Code Becomes Voltage

Every instruction ultimately executes as a voltage transition in silicon.

Software

Instructions & algorithms

Silicon Chip

Physical integrated circuit

Logic Gates

NAND, NOR, inverters

Voltage Edges

Rising & falling transitions

Verification

WHAT + WHEN = Correct

Functional correctness alone is not enough.

WHAT

Correct Boolean value

WHEN

Arrives before deadline

Industry Method

STA: Fast but Conservative

Scales to billions of gates — but uses worst-case margins, not real signal history.

Fast & Scalable

No input vectors needed

📏 Conservative Margins

Worst-case assumptions, not actual traces

🔍 No Trace History

Dynamic switching effects not captured

Reference Method

SPICE: Accurate but Slow

Solves transistor-level equations — the reference for accuracy, but doesn't scale.

🎯 Gold Standard

Captures transistor-level analog effects

🐢 Doesn't Scale

Cost grows rapidly with circuit size

🔬 Validation Only

Used to validate other timing models

Middle Ground

Digital Dynamic Timing

Trace-aware. Event-driven. No analog equations.

Input Trace

Real signal history

Delay Model

History-aware delay function

Event Engine

Discrete switching events

Output Timing

Predicted waveform

Faster than SPICE. More faithful than STA.

Model Limitations

Simple Models Break Down

Real gates degrade pulses — fixed-delay models cannot capture this.

Pure Delay

Shifted pulse. Glitches unchanged.

Inertial Delay

Short pulses filtered. Shape ignored.

Physical Reality

Amplitude reduced. Threshold shifted.

History Effects

The Gate Remembers

Delay depends on history — the time since the last transition.

Digital Input

Switching event arrives

Internal State

Analog charge not fully settled

History T

Time since last transition

Output Delay

Varies with T

Same input. Different delay. The gate remembers.

Multi-Input Effects

The Charlie Effect

When two inputs switch close together, delay can change by ~30%.

Input A + B

Switching with separation Δ

NOR Gate

Internal currents interact

Output Delay

Can change by ~30%

Same NOR gate. Smaller Δ. Different output delay.

Research Direction

The Road Forward

From one NOR gate to full circuit-level symbolic timing.

NOR Gate

History-aware single-gate model

NAND Gate

Different topology, same framework

Muller C-Gate

Gate with persistent internal memory

Composed Circuits

Multi-gate timing composition

Symbolic Timing Analysis

Full circuit-level verification

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