Why Digital Timing Simulation Matters

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