Digital Delay Model
Effective Switching resistance
https://www.eecis.udel.edu/~vsaxena/courses/ece445/s19/Lecture%20Notes/lec15_ece445.pdf
wire delay
The Elmore Delay
Basic idea: use of mean of \(v'(t)\) to approximate median of \(v'(t)\)
Elmore delay approximates the median of \(h(t)\) by the mean of \(h(t)\)
Distributed RC-Line
Lumped approximations
\(rc\)-models
If your simulator does not support a distributed \(rc\)-model, or if the computational complexity of these models slows down your simulation too much, you can construct a simple yet accurate model yourself by approximating the distributed \(rc\) by a lumped RC network with a limited number of elements
The accuracy of the model is determined by the number of stages. For instance, the error of the \(\Pi -3\) model is less than 3%, which is generally sufficient.
Why use "\(\Pi\) Model"
examples
Wire Inductive Effect
- RC delay increases quadratically with length
- LC delay (speed of light flight time) increases linearly with length
Inductance will only be important to the delay of low-resistance signals such as wide clock lines
wave
Signal propagates over the wire as a wave (rather than diffusing as in \(rc\) only models)
Signal propagates by alternately transferring energy from capacitive to inductive modes
reference
Akio Kitagawa, Analog layout design https://mixsignal.files.wordpress.com/2013/03/analog-layout.pdf
THE WIRE http://bwrcs.eecs.berkeley.edu/Classes/icdesign/ee141_f01/Notes/chapter4.pdf
Anoop Veliyath, Design Engineer, Cadence Design Systems. Accurately Modeling Transmission Line Behavior with an LC Network-based Approach [pdf]
Mark Horowitz. Lecture 2: Wires and Wire Models [pdf]
Neil Weste and David Harris. 2010. CMOS VLSI Design: A Circuits and Systems Perspective (4th. ed.). Addison-Wesley Publishing Company, USA.
Cheng-Kok Koh. EE695K Modeling and Optimization of High Performance Interconnect [lec3a_pdf]
Vishal Saxena. ECE 445 Intro to VLSI Design: Lectures for Spring 2019 https://www.eecis.udel.edu/~vsaxena/courses/ece445/s19/ECE445.htm