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Transcript
Decoupling Capacitance Allocation for
Power Supply Noise Suppression
Shiyou Zhao, Kaushik Roy, Cheng-Kok Koh
School of Electrical & Computer Engineering
Purdue University
Supported in part by SRC, Intel, NSF
Outline
•
•
•
•
•
•
Motivation
Power Supply Noise Estimation
Decoupling Capacitance (decap) Budget
Allocation of Decoupling Capacitance
Experiment Results
Conclusion
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
• Decoupling capacitance is an effective way to
alleviate power supply noise
– Decap buffers switching activities by supplying part of the
current demand
– Peak noise can be reduced
Problem Formulation
• Given a floorplan with switching activities
information available for each module:
– Determine how much decap is required by each module
to keep the supply noise below a specified upper limit
– Allocate white-space to each module to meet its decap
budget
• Related issue
– Determine worst case power supply noise for each
module in the floorplan
– Allocate the existing white space in the floorplan
Power Supply Network—RLC Mesh
VDD
Rp
:Current
Source
Lp
: VDD pin
VDD
VDD
VDD
Current Distribution in Power Supply Mesh
Illustration
:Connection
point,
Current
contribution
Current flowing
path
VDD (1)
(3)
:VDD pin
(5)
VDD
(2)
(6)
Module A
B
C
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
minimal impedance --shortest, second shortest, …
I1  I 2    I n  I
Z1 I1  Z 2 I 2    Z n I n
Ij 
Yj
n
 Yi
i 1
I,
j  1,2, n
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
i3(t)• Apply KVL:
VDD
R2 L2
R1 L1
C1
i1(t)
C2
k
i2(t)
V
(k )
noise


Pj T ( k )
(i j RP  LP
jk
jk
di j
dt
)
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
Noise ratio :
Decap :
  max(1, V
V
(k )
noise
(lim)
)
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
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
Allocation of Existing White Space
B
w2
A
D
WS
C
w1
E
w3
Allocation of Existing WS--Linear
Programming (LP) Approach
• LP Approach:
• Objective: Maximize the
utilization of available WS
• Existing WS can be
allocated to neighboring
modules using LP
• Notation:
S:
Sk :
( j)
S :
sum of
allocated
area of WS k
decap
budget
H
k 1 jN k
s.t.
xk( j ) : ws allocated
to
mod j
N k : neighbors set
of
WS k
( j)
x
 k  Sk ,
jN k
WS
of
S    xk( j ) ,
max imize
k 1, 2 ,, H
k H
( j)
( j)
x

S
,
k
mod j
from WS k
k 1
xk( j )  0,
j, k
j 1, 2 ,, M
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
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)
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
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
Budget
(nF)
Floorplan of playout Before/After WS
Insertion
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