Transcript Combinational Networks 2

Topics
Interconnect design.
 Crosstalk.
 Power optimization.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Interconnect

Even assuming logic structure is fixed, we
can:
–
–
–
–
change wire topology;
resize wires;
add buffers;
size transistors.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Multipoint nets
Two-point nets are easy to design.
 Multipoint nets are harder:

– How do we connect all the pins using two-point
connections?
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Styles of wiring trees
source
Spanning tree
Steiner tree
Steiner point
sink 1
sink 2
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Copyright  2008 Wayne Wolf
Sized Steiner tree
source
Feeds both branches
sink 1
Smaller currents in each branch
sink 2
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Buffer insertion in wiring trees

More complex than placing buffers along a
transmission line:
– complex topology;
– unbalanced trees;
– differing timing requirements at the leaves.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Van Ginneken algorithm

Given:
– placements of sources and sinks;
– routing of wiring tree.

Place buffers within tree to minimize the
departure time at the source to meet all the
sink arrival times:
– Tsource = min i (T i -D i)
– T i = arrival time at node i, D i = delay to node
I.
Copyright  2008 Wayne Wolf
Modern VLSI Design 4e: Chapter 4
Delay calculation

Use Elmore model to compute delay along
path from source to sink.
Modern VLSI Design 4e: Chapter 4
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Recursive delay calculation

Recursively compute Elmore delay through
the tree.
– Start at sinks, work back to source.
– r, c are unit resistance/capacitance of wire.
– Lk is total capacitive load of subtree rooted at
node k.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Modifying the tree

Add a wire of length l at node k:
– Tk’ = Tk - r/Lk - 0.5rcl.
– Lk’ = Lk + cl.

Buffer node k:
– Tk’ = Tk - Dbuf - Rbuf Lk.
– Lk’ = Cbuf.

Join two subtrees m and n at node k:
– Tk’ = (Tm , Tn).
– Lk’ = Lm + Ln.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk
Capacitive coupling introduces crosstalk.
 Crosstalk slows down signals to static gates,
can cause hard errors in storage nodes.
 Crosstalk can be controlled by
methodological and optimization
techniques.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Interleaved power/ground
VDD
VSS
VDD
VSS
VDD
VSS
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Twizzled wires
a
b
a
b
d
b
c
a
c
d
c
d
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Coupling and crosstalk

Crosstalk current depends on capacitance,
voltage ramp.
ic
w1
w2
t
Cc
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk analysis
Assume worst-case voltage swings, signal
slopes.
 Measure coupling capacitance based on
geometrical alignment/overlap.
 Some nodes are particularly sensitive to
crosstalk:

– dynamic;
– asynchronous.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Coupling situations
bus[0]
a
x sig1
r
bus[1]
bus[2]
better
Modern VLSI Design 4e: Chapter 4
worse
Copyright  2008 Wayne Wolf
Layer-to-layer coupling

Long parallel runs on adjacent layers are
also bad.
siga
bus[0]
SiO2
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Methodological solutions

Add ground wires between signal wires:
– coupling to VSS, a stable signal, dominates;
– can use VSS to distribute power, so long as
power line is relatively stable.

Extreme case—add ground plane. Costs an
entire layer, may be overkill.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Ground wires
VSS
sig1
VSS
sig2
VSS
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk and signal routing
Can route wires to minimize required
adjacency regions.
 Take advantage of natural holes in routing
areas to decouple signals.
 Minimizes need for ground signals.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Assumptions
Take into account coupling only to wires in
adjacent tracks.
 Ignore coupling of vertical wires.
 Assume that coupling/crosstalk is
proportional to adjacency length.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk example
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk analysis
Want to estimate delays induced by
crosstalk.
 Effect of coupling capacitance Cc depends
on relative transitions.

– Aggressor changes, victim does not: Cc.
– Aggressor, victim move in opposite directions:
2Cc.
– Aggressor, victim move in same direction: 0.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Crosstalk analysis, cont’d.
Coupling effects depend on relative
switching time of nets.
 Must use iterative algorithm to solve for
coupling capacitances and delays.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Power optimization
Glitches cause unnecessary power
consumption.
 Logic network design helps control power
consumption:

– minimizing capacitance;
– eliminating unnecessary glitches.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Glitching example

Gate network:
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Glitching example behavior

NOR gate produces 0 output at beginning
and end:
– beginning: bottom input is 1;
– end: NAND output is 1;

Difference in delay between application of
primary inputs and generation of new
NAND output causes glitch.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Adder chain glitching
bad
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good
Copyright  2008 Wayne Wolf
Explanation
Unbalanced chain has signals arriving at
different times at each adder.
 A glitch downstream propagates all the way
upstream.
 Balanced tree introduces multiple glitches
simultaneously, reducing total glitch
activity.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Signal probabilities
Glitching behavior can be characterized by
signal probabilities.
 Transition probabilities can be computed
from signal probabilities if clock cycles are
assumed to be independent.
 Some primary inputs may have nonstandard signal probabilities— control
signal may be activated only occasionally.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Delay-independent probabilities

Compute output probabilities of primitive
functions:
– PNOT = 1 - Pin
– POR = 1 -  Pi)
– PAND = Pi

Can compute output probabilities of
reconvergent fanout-free networks by
traversing tree.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Delay-dependent probabilities
More accurate estimation of glitching.
Glitch accuracy depends on accuracy of
delay model.
 Can use simulation-style algorithms to
propagate glitches.
 Can use statistical models coupled with
delay models.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Power estimation tools

Power estimator approximates power
consumption from:
– gate network;
– primary input transition probabilities;
– capacitive loading.

May be switch/logic simulation based or
use statistical models.
Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Factorization for low power

Proper factorization reduces glitching.
bad
Modern VLSI Design 4e: Chapter 4
good
Copyright  2008 Wayne Wolf
Factorization techniques
In example, a has high transition
probability, b and c low probabilities.
 Reduce number of logic levels through
which high-probability signals must travel
in order to reduce propagation of glitches.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf
Layout for low power
Place and route to minimize capacitance of
nodes with high glitching activity.
 Feed back wiring capacitance values to
power analysis for better estimates.

Modern VLSI Design 4e: Chapter 4
Copyright  2008 Wayne Wolf