Transcript ppt - UCSD VLSI CAD Laboratory

ECE260B – CSE241A
Winter 2005
Power Distribution
Website: http://vlsicad.ucsd.edu/courses/ece260b-w05
ECE 260B – CSE 241A Power Distribution 1
http://vlsicad.ucsd.edu
Motivation
 Power supply noise is a serious issue in DSM design

Noise is getting worse as technology scales

Noise margin decreases as supply voltage scales

Power supply noise may slow down circuit performance

Power supply noise may cause logic failures
ECE 260B – CSE 241A Power Distribution 2
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Power = …
 Routing resources


Vcc
20-40% of all metal tracks used by Vcc, Vss
Increased power  denser power grid
Vss
Vcc
 Pins



Vss
Vcc or Vss pin carries 0.5-1W of power
Pentium 4 uses 423 pins; 223 Vcc or Vss
More pins  package more expensive
(+ package development, motherboard redesign, …)
Vcc
 Battery cost

1kg NiCad battery powers a Pentium 4 alone for less than 1 hour
 Performance




High chip temperatures degrade circuit performance
Large across-chip temperature variations induce clock skew
High chip power limits use of high-performance circuits
Power transients determine minimum power supply voltage
ECE 260B – CSE 241A Power Distribution 3
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Power = Package
Pentium 4 die is about 1.5g and less than 1cm^3
Pentium-4 in package with interposer, heat sink, and fan can be 500g and 150cm^3
Fan
Heat Sink
Processor
Processor
Pins
Integrated
Heat Spreader
Decoupling
Capacitors
OLGA Pins
Package Pins
Interposer
Modern processor packaging is complex and adds significantly to product cost.
http://www.intel.com/support/processors/procid/ptype.htm
ECE 260B – CSE 241A Power Distribution 4
Courtesy M. McDermott UT-Austin
http://vlsicad.ucsd.edu
Planning for Power
 Early simulation of major power dissipation components
 Early quantification of chip power
- Total chip power
- Maximum power density
- Total chip power fluctuations
– inherent & added fluctuations due to clock gating
 Early power distribution analysis (dc, ac, & multi-cycle)

I.e., average, maximum, multi-cycle fluctuations
 Early allocation & coordination of chip resources
-
Wiring tracks for power grid
Low Vt devices
Dynamic circuits
Clock gating
Placement and quantity of added decoupling capacitors
ECE 260B – CSE 241A Power Distribution 5
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Power and Ground Routing

Floorplanning includes planning how the power, ground
and clock should route

Power supply distribution


Tree: trunk must supply current to all branches
Resistance must be very small since when a gate switches, its
current flows through the supply lines
- If the resistance of supply lines is too large, voltage supplied to
gates will drop, which can cause the gate to malfunction
- Usually, want at most 5-10% IR drop due to supply resistance

 Usually on the top layers of metal, then distributed to lower
wiring layers
ECE 260B – CSE 241A Power Distribution 6
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Planar Power Distribution

Topology of VDD/VSS networks.



Inter-digitated
Design each macrocell such that all
VDD and VSS terminals are on
opposite sides.
If floorplan places all macrocells
with VDD on same side, then no
crossing between VDD and VSS.
VSS
VDD
cell
VSS
VDD
cut line
VDD
VSS
B
VDD
VDD
VSS
no cut line
C
cut line
VDD
VSS
A
VDD
VSS
VDD
VSS
no connection
ECE 260B – CSE 241A Power Distribution 7
Courtesy K. Yang, UCLA
VSS
http://vlsicad.ucsd.edu
Gridded Power Distribution

With more metal layers, power is striped

Connection between the stripes allows a power grid
- Minimizes series resistance

Connection of lower layer layout/cells to the grid is through vias
- Note that planar supply routing is often still needed for a strong
lower layer connection.
- There may not be sufficient area to make a strong connection in
the middle of a design (connect better at periphery of die)
ECE 260B – CSE 241A Power Distribution 8
Courtesy K. Yang, UCLA
http://vlsicad.ucsd.edu
Power Supply Drop/Noise

Supply noise = variations in power supply voltage that act as noise source
for logic gates



Solution approach




Power supply wiring resistance  voltage variations with current surges
Current surges depend on dynamic behavior of circuit
Measure maximum current required by each block
Redesign power/ground network to reduce resistance
Worst case: move activity to another clock cycle to reduce peak current 
scheduling problem
Example: Drive 32-bit bus, total bus wire load = 2pF, with delay 0.5ns



R for each transistor needs to be < 0.25kW to meet RC = 0.5ns
Effective R of bits together is 250/32 = 7.5W
For < 10% drop, power distribution R must be < 1W
ECE 260B – CSE 241A Power Distribution 9
Courtesy K. Yang, UCLA
http://vlsicad.ucsd.edu
Electromigration

Physical migration of metal atoms due to “electron wind” can
eventually create a break in a wire




MTTF (mean time to failure)  1/J2 where J= current density
Current density must not exceed specification  wire Ii/wi < Jspec
Specified as mA per m wire width (e.g., 1mA/ m) or mA per via cut
EM occurs both in signal (AC=bidirectional) and power wires (DC =
unidirectional)

Much worse for DC than AC; DC occurs inside cells and in power buses

May need more contacts on transistor sources and drains to meet
EM limits


Width of power buses must support both iR and EM requirements
Issues in IR and EM constraint generation



Topology is most likely not a tree
How do we determine current patterns?
Effects of R, L
ECE 260B – CSE 241A Power Distribution 10
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What Happens?

Example of an AlCu line seen under
microscope.



Accelerated by higher temperature
and high currents
Voids form on grain boundaries
Metal atoms move with current away
from voids and collect at boundaries
Catastrophic
failure
ECE 260B – CSE 241A Power Distribution 11
Courtesy K. Yang, UCLA
http://vlsicad.ucsd.edu
Taken from http://www.nd.edu/~micro/fig20.html
Taken from Sverre Sjøthun, “Electromigration
In-Depth,” from www.dpwg.com
ECE 260B – CSE 241A Power Distribution 12
Courtesy S. Sapatnekar, UMinn
http://vlsicad.ucsd.edu
Power Supply Rules of Thumb
 Rules depend on technology

Tech file has rules for resistance and electromigration
 Examples:



Must have a contact for each 16l of transistor width (more is
better)
Wire must have less than 1mA/m of width
Power/Gnd width = Length of wire * Sum (all transistors
connected to wire) / 3*106l (very approximate)
 For small designs, power supply design is non-issue
ECE 260B – CSE 241A Power Distribution 13
Courtesy K. Yang, UCLA
http://vlsicad.ucsd.edu
Basic Methodology Concepts
 Reliability (slotting, splitting)
 Alignment of hierarchical rings, stripes
 Isolation of analog power
 Styles of power distribution




Rings and trunks
Uniform grid
Bottom-up grid generation
Depends on:
-
Package: flip-chip vs. wire-bond; I/O count (fewer pads  denser grid)
Power budget
IR drop limits
Floorplan constraints (hard macros, etc.)
ECE 260B – CSE 241A Power Distribution 14
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Metal Slotting vs. Splitting
 Required by metal layout
Easy connections
through standard via
arrays
rules for uniform CMP
(planarization)
GND
 Split power wires



GND
Less data than traditional
slotting
More accurate R/C
analysis of power mesh
Not supported by all tools
GND
GND
M1
M1
Difficult to connect where should vias go?
ECE 260B – CSE 241A Power Distribution 15
Courtesy Cadence Design Systems, Inc.
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Trunks and Rings Methodology
Each Block has its own ring

Rings may be inside the blocks or part of the top level
Each Block has trunks connecting top level to block
V
block 3
V
Rings may be shared with
abutted blocks
G
V
V
G
G
G
block 5
Individual trunks
connecting
blocks to top level
block 2
V
block 4
V
G
G
ECE 260B – CSE 241A Power Distribution 16
V
G
V
G
V
block 1
G
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V
http://vlsicad.ucsd.edu
Trunks and Rings
Advantages
Disadvantages

Power tailored to the demands
of each block (flexible)


More area efficient since the
demands of each block are
uniquely met


Limited redundancy, power grid
built to match needs


Simple implementation
supported by many tools
Non regular structure requires
more detailed IR drop/EM
analysis

Rings can be shared between
blocks by abutted blocks

missing vias/connections fatal
Rings will require
slotting/splitting due to wide
widths

ECE 260B – CSE 241A Power Distribution 17
Assumptions in design may
change or be invalid
Increase in data volume
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Uniform Chip Grid Methodology
Robust and redundant power
network
global grid
higher layers
Implementation

G
Typically pushed into blocks
V

Blocks typically abut
G
block 4
ECE 260B – CSE 241A Power Distribution 18
block 1
G
V
- Global buffer insertion
G
Courtesy Cadence Design Systems, Inc.
block 4
block 5
- Requires block grids to align
Rows/Followpins should align with block
pins
V
block 3


G
V
G
- Lower layers in blocks to connect to top
through via stacks
V
Primary distribution through upper metal
layers
Fine or custom grid
or no grid
on lower layers
G

mainly in microprocessors and high end
large ASICs
V

V

V
G
V
G
V
http://vlsicad.ucsd.edu
Uniform Chip Grid
Advantages
Disadvantages


Easily implemented

Path redundancy allows less
sensitively to changes in current
pattern


Takes up significant routing
Lends itself to straightforward hand
calculations
Mesh of power/ground provides
shielding (for capacitance) and
current returns (for inductance)
Top-down propagation easy to use
on this style
ECE 260B – CSE 241A Power Distribution 19
resources (20%-40% of all
routing tracks if not already
reserved for power/ground)
Fine grids may slow down P&R
tools
Imposes grid structure into each
block which may be unnecessary
Top and blocks coupled closely if
top level routing pushed into
blocks

Changes to block/top must be
reflected in other
Courtesy Cadence Design Systems, Inc.
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Bottom-Up Grid Generation Methodology
 Design and optimize power grid for block, merge at top
Advantages
• Able to tailor grid for routing resource
efficiency in each block
• Flexibility to choose the best grid for
the block (i.e. ring and stripe, power
plane, grid)
Disadvantages
• Designing grid in context of the “big picture” is more difficult
• Block grid may present challenging connections to top level
• Assumptions for block grid’s connection to top level must be analyzed
and validated
ECE 260B – CSE 241A Power Distribution 20
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Power Routing in Area-Based P&R
 Power routing approaches




(1) Pre-route parts of power grid during floorplanning
(2) Build grid (except connections to standard cells) before P&R
(3) Build entire grid before P&R
N.B.: Area-based P&R tools respect pre-routes absolutely
 Cadence tools:
power routing done inside SE, all other
tasks (clock, place, route, scan, …) done by point tools

Lab 5 tomorrow has a tiny bit of power routing (rings, stripes)
 Miscellany




ECOs: What happens to rings and trunks if blocks change size?
Layer choices: What is cost of skipping layers (to get from thick
top-layer metal down to finer layers)?
How wide should power wires be?
Post-processing strategies
ECE 260B – CSE 241A Power Distribution 21
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Power Routing Wire Width Considerations


Slotting rules: Choose maximum width below slotting width

Choose power routing widths carefully to avoid blocking extra
tracks (and, use the space if blocking the track!)
Halation (width-dependent spacing) rules: Do as much as
possible of power routing below wide wire width to save
routing space
What is better power width here?
ECE 260B – CSE 241A Power Distribution 22
Courtesy Cadence Design Systems, Inc.
Blocked tracks
http://vlsicad.ucsd.edu
Power Routing Tool Usage
 4 layer power grid example (HVHV)






Turn on via stacking
Route metal2 vertically
Route metal4 vertically (use same coordinates)
Route metal3 horizontally (make coincident with every N metal1
routes)
Turn off via stacking
Route metal1 horizontally
metal2/metal4
coincident
metal1 inside cells
metal3 every n micron
ECE 260B – CSE 241A Power Distribution 23
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Post-Processing Flows (DEF or Layout Editing)
During PnR
ECE 260B – CSE 241A Power Distribution 24
After post processing
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(Tree) Supply Network Design
 Tree topology assumption not very useful in practice, but
illustrates some basic ideas
 Assume R dominates, L and C negligible

marginally permissible assumption
 Current drawn at various points in
the tree (time-varying waveform)
 Current causes a V=IR drop


Supply
“Ground” is not at 0V
“Vdd” is not at intended level
ECE 260B – CSE 241A Power Distribution 25
Courtesy S. Sapatnekar, UMinn
= sinks
http://vlsicad.ucsd.edu
IR Drop Constraints
 Chowdhury and Breuer, TCAD 7/88
 Can write V drop to each sink as



Supply
 Ri Ii < Vspec
for all sink current patterns made available
Tree structure: can compute Ii easily
Ri   li / wi
 Change wi to reduce IR drop
 Objective: minimize  ai wi
 Current density must never exceed a specification

For each wire, Ii/wi < Jspec
ECE 260B – CSE 241A Power Distribution 26
Courtesy S. Sapatnekar, UMinn
http://vlsicad.ucsd.edu
P/G Mesh Optimization (R only)


Dutta and Marek-Sadowska, DAC 89

Constraints
Cost function:  ai li wi =  ai cili2
// = total wire area
(since ci = conductance = wi/( li)
- EM: Ii  e wi // current density I/w less than upper bound
– Substitute Ii = vi (wi/  li) // I = V/R
 vp - vq  e  li // divide by wi, *  li
- Wire width constraints: Wmin  wi  Wmax (translate to ci)
- Voltage drop constraints: va - vb  Vspec1 and/or vi  Vspec2
- Circuit equations that determine the v’s

Variables: ci’s
ECE 260B – CSE 241A Power Distribution 27
(vi’s depend on ci’s)
Courtesy S. Sapatnekar, UMinn
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Solution Technique

Method of feasible directions




Find an initial feasible solution (satisfies all constraints)
Choose a direction that maintains feasibility
Make a move in that direction to reduce cost function
Given a set of ci’s, must find corresponding vi’s



Feasible direction method: move from point c* to c+
c* and c+ must be close to each other (i.e., if you have the
solution at c*, the solution at c+ corresponds to a minor change
in conductances)
Solving for vi’s : solving a system of linear equations
- Solution at c* is a good guess for the solution at c+
- Converges in a few iterations
ECE 260B – CSE 241A Power Distribution 28
Courtesy S. Sapatnekar, UMinn
http://vlsicad.ucsd.edu
Modeling Gate Currents
 Currents in supply grid caused by charging/discharging of
capacitances by logic gates
 All analyses require generation of a “worst-case switching”
scenario
 Enumeration is infeasible  Two basic approaches


Simulation based methods: designer supplies “hot” vectors, or we
try to generate these hot vectors automatically
“Pattern-independent” methods: try to estimate the worst-case (can
be expensive, very inaccurate)
 Once current patterns are available, apply them to supply
network to find out if constraints are satisfied
ECE 260B – CSE 241A Power Distribution 29
Courtesy S. Sapatnekar, UMinn
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Complexity of Hot Vector Generation
 Devadas et al., TCAD 3/92:



Assume zero gate delays for simplicity
Find the maximum current drawn by a block of gates
Using a current model for each gate
- Find a set of input patterns so that the total current is maximized
- Boolean assignment problem: equivalent to Weighted MaxSatisfiability
– Given a Boolean formula in conjunctive normal form
(product of sums), is there an assignment of truth values to
the variables such that the formula evaluates to True?
- Checking for Satisfiability (for k-sat, k > 2) is NP-complete

 Difficult even under zero gate delay assumption
ECE 260B – CSE 241A Power Distribution 30
Courtesy S. Sapatnekar, UMinn
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Pattern-Independent Methods
 iMAX approach: Kriplani et al., TCAD 8/95

Current model for a single gate
Ipeak
 Delay


Gates switch at different times
Total current drawn from Vdd (ignoring supply network C) is the
sum of these time-shifted waveforms
 Objective: find the worst-case waveform
ECE 260B – CSE 241A Power Distribution 31
Courtesy S. Sapatnekar, UMinn
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Example
(Not to scale!)
 Maximum current not just a sum of individual maximum
currents
 Temporal dependencies
 [Using deliberate clock skews can reduce the peak
current, as we saw in the Useful-Skew discussion]
ECE 260B – CSE 241A Power Distribution 32
Courtesy S. Sapatnekar, UMinn
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Maximum Envelope Current (MEC)
 Find the time interval during which a gate may switch


Manufacturing process variations can cause changes
Actual switching event can cause changes
(unit gate delays)



Switching at second gate can occur at t=1 or at t=2
In general, a large number of paths can go through a gate;
assume (conservatively) that switching occurs in t  [1,2]
Assume that all gate inputs can switch independently – provides
an upper bound on the switching current
ECE 260B – CSE 241A Power Distribution 33
Courtesy S. Sapatnekar, UMinn
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(Large) Errors in MEC Approach

Correlation Problem





G1
Switching at G0, G1, G2 and G3 not
independent
G0 = 0 implies that G1, G2, G3 switch; G0 =
1 means that other inputs will determine
gate activity
If the other inputs cannot make the gate
switch in the same time window, then iMAX
estimates are pessimistic
G0
G3
Reconvergent Fanout Problem

Signals that diverge at G0 reconverge at Gk
 inputs to Gk are not independent

Assumption of independent switching is not
valid
Many heuristic refinements proposed, but
guardbanding (error) of power estimation
still a huge issue
ECE 260B – CSE 241A Power Distribution 34
Courtesy S. Sapatnekar, UMinn
G2
G1
G0
G2
Gk
G3
http://vlsicad.ucsd.edu
Outline
 Motivation
 Power Supply Noise Estimation
 Decoupling Capacitance (decap) Budget
 Allocation of Decoupling Capacitance
 Experiment Results
 Conclusion
ECE 260B – CSE 241A Power Distribution 35
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Why Decoupling Capacitance
 Frequency point of view

Decaps form low-pass filters

They cancel anti- effects
 Physical point of view

Decaps serve as charge reservoirs

They shortcut supply current paths and reduces voltage drop
 No effect to DC supply currents
ECE 260B – CSE 241A Power Distribution 36
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Power Supply Network—RLC Mesh
VDD
Rp
:Current
Source
Lp
: VDD pin
VDD
VDD
VDD
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 37
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Current Distribution in Power Supply Mesh Illustration
:Connection
Current
contribution
point,
Current flowing
path
VDD (1)
(3)
:VDD pin
(5)
VDD
(2)
(6)
Module A
B
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 38
C
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Current Distribution in Power Supply Network
 Distribute switching current for each module
in the
power supply mesh
 Observation: Currents tend to flow along the leastimpedance paths
 Approximation: Consider only those paths with
impedance --shortest, second shortest, …
minimal
I1  I 2    I n  I
Z1 I 1  Z 2 I 2    Z n I n
Ij 
Yj
n
 Yi
i 1
I,
j  1,2, n
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 39
http://vlsicad.ucsd.edu
Current Flowing Paths and Power Supply
Noise Calculation

Power supply noise at a target
module is the voltage difference
between the VDD pin and the
module

Apply KVL:
i3(t)
VDD
R2 L2
R1 L1
C1
i1(t)
C2
k
i2(t)
V
(k )
noise


(i j RP  LP
Pj T ( k )
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 40
jk
jk
di j
dt
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)
Why Decoupling Capacitance?
i3(t)
VDD
R2 L2
R1 L1
C1
i1(t)


C2
P/G network wiresizing won’t
change voltage drop frequency
spectrum
To reduce Vdrop by k times needs
to size up wires by k times along
the supply current path
ECE 260B – CSE 241A Power Distribution 41
k
i2(t)

Decoupling caps act as a low-pass
filter

Efficient to remove high frequency
elements of Vdrop
http://vlsicad.ucsd.edu
Decoupling Capacitance Budget

Decap budget for each module can be determined based on its
noise level

Initial budget can be estimated as follows:

Ch arg e :
Q
(k )
  I ( k ) (t )dt
0
(k )
Noise ratio :
Decap :

noise
  max(1, V (lim)
)
V
noise
1
(lim)
C ( k )  (1  )Q ( k ) /V noise,

k  1,2, M
Iterations are performed if necessary until noise at each module in
the floorplan is kept under certain limit
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 42
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Allocation of Decoupling Capacitance
 Decap needs to be placed in the vicinity of
each target
module
 Decap requires WS to manufacture on

Use MOS capacitors
 Decap allocation is reduced to WS allocation
 Two-phase approach:


Allocate the existing WS in the floorplan
Insert additional WS into the floorplan if required
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 43
http://vlsicad.ucsd.edu
Allocation of Existing White Space
B
w2
A
D
WS
C
w1
E
w3
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 44
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Allocation of Existing WS--Linear Programming
(LP) Approach


Objective: Maximize the
utilization of available WS

Existing WS can be allocated to
neighboring modules using LP

LP Approach:
H
k 1 jN k
Notation:
S:
Sk :
( j)
S :
sum of
allocated
area of WS k
decap
S    xk( j ) ,
max imize
budget
s.t.
WS
of
xk( j ) : ws allocated
to
mod j
N k : neighbors set
of
WS k
( j)
x
 k  Sk ,
jN k
k H
mod j
from WS k
( j)
( j)
x

S
,
k
k 1
xk( j )  0,
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 45
k 1, 2 ,, H
j 1, 2 ,, M
j, k
http://vlsicad.ucsd.edu
Insert Additional WS into Floorplan If
Necessary
 Update decap budget for each module after existing WS
has been allocated
 If additional WS if required, insert
WS into floorplan by
extending it horizontally and vertically
 Two-phase procedure:

insert WS band between rows based the decap budgets of the
modules in the row

insert WS band between columns based on the decap budgets
of the modules in the column
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 46
http://vlsicad.ucsd.edu
Moving Modules to Insert WS
Original floorplan
0
Moving modules in y+ direction
ExtY
B
A
1
A
2
B
1
D
3
E
D
C
2
C
WS
band
F
3
F
E
4
G
(a)
G
(b)
Slide courtesy of S Zhao, K Roy & C.-K. Kok
ECE 260B – CSE 241A Power Distribution 47
http://vlsicad.ucsd.edu
Experimental Results
Comparison of Decap Budgets
(Ours vs “Greedy Solution”)
Circuit
decap budget
(nF)
(our method)
decap budget
(nF)
(“greedy solution”)
Percentage
(%)
apte
27.73
32.64
85.04
xerox
8.00
13.50
59.30
hp
3.45
6.18
55.80
ami33
0
0.80
0.00
ami49
10.28
24.80
41.50
playout 42.91
61.67
69.6
ECE 260B – CSE 241A Power Distribution 48
http://vlsicad.ucsd.edu
Experimental Results for MCNC Benchmark
Circuits
Modules Existing
WS
(m2)
(%)
9
751652
(1.6)
decap Inacc.
27.73
WS
(m2)
(%)
0 (0)
xerox
10
1071740
(5.5)
8.00
hp
11
695016
(7.8)
ami33
33
ami49
playout
Circuit
apte
Added
WS
(m2)
(%)
4794329
(10.3)
Est. Peak
Noise
(V)
before
1.95
Est. Peak
Noise
(V)
after
0.24
0 (0)
528892
(2.7)
0.94
0.20
3.45
306076
(3.5)
300824
(3.4)
1.09
0.23
244728
(21.3)
0
N/A
0
0.16
0.16
49
2484496
(7.0)
10.28
891672
(2.5)
463615
(1.3)
1.45
0.25
62
5837072
(6.6)
42.91
792110
(0.9)
3537392
(4.0)
1.23
0.24
ECE 260B – CSE 241A Power Distribution 49
Budget
(nF)
http://vlsicad.ucsd.edu
Floorplan of playout Before/After WS Insertion
ECE 260B – CSE 241A Power Distribution 50
http://vlsicad.ucsd.edu
Conclusion
 A methodology for decoupling capacitance allocation at
floorplan level is proposed
 Linear programming technique is used to allocate
existing WS to maximize its utilization
 A heuristic is proposed for additional WS insertion
 Compared with “Greedy” solution, our method produces
significantly smaller decap budgets
ECE 260B – CSE 241A Power Distribution 51
http://vlsicad.ucsd.edu
ECE 260B – CSE 241A Power Distribution 52
http://vlsicad.ucsd.edu