Spring 2010, Feb 19 . . . Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design ELEC 7770: Advanced VLSI Design (Agrawal) (Agrawal) 1 ELEC 7770 ELEC 7770 Advanced VLSI Design Advanced VLSI Design Spring 2010 Spring 2010 Clock Skew Problem Clock Skew Problem Vishwani D. Agrawal Vishwani D. Agrawal James J. Danaher Professor James J. Danaher Professor ECE Department, Auburn University ECE Department, Auburn University Auburn, AL 36849 Auburn, AL 36849 [email protected]http://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr10/ course.html
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ELEC 7770 Advanced VLSI Design Spring 2010 Clock Skew Problem
ELEC 7770 Advanced VLSI Design Spring 2010 Clock Skew Problem. Vishwani D. Agrawal James J. Danaher Professor ECE Department, Auburn University Auburn, AL 36849 [email protected] http://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr10/course.html. Single Clock. FF A. FF B. Comb. - PowerPoint PPT Presentation
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Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 11
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 22
Single ClockSingle Clock
FF A FF BComb.
CK
Data_in Data_out
CKA
CKA CKB
CKB
Single-cycle path delay
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 33
Multiple ClocksMultiple Clocks
FF A FF BComb.Data_in Data_out
CKA
CKA CKB
CKB
Multi-cycle path delay
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 44
Clock SkewClock Skew
Skew is the time delay of clock signal at a flip-Skew is the time delay of clock signal at a flip-flop with respect to some time reference.flop with respect to some time reference.
For a given layout each flip-flop has a skew, For a given layout each flip-flop has a skew, measured with respect to the a common measured with respect to the a common reference.reference.
Skews of flip-flops separated by combinational Skews of flip-flops separated by combinational paths affect the short-path and long-path paths affect the short-path and long-path constraints.constraints.
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 55
Skews for Single-Cycle PathsSkews for Single-Cycle Paths
CombinationalBlockDelay:
FFi
CKi
FFj
CKj
xi xj
xi and xj are arrival times of clock edges
δ(i,j) ≤ d(i,j) ≤ Δ(i,j)
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 66
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 88
Maximum Clock FrequencyMaximum Clock FrequencyLinear program:
Minimize Tck
Subject to:
For all flip-flop pairs (i,j),
si + δ(i,j) ≥ sj + Thj
si + Δ(i,j) ≤ sj + Tck – Tsj
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 99
Finding Clock SkewsFinding Clock Skews
FFi
Ci
Ri
FFj
Cj
Rj
FFk
Ck
RkCK
si
sj
sk
Use Elmore delay formula to calculate si, sj, sk.
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1010
Interconnect Delay: Elmore Delay ModelInterconnect Delay: Elmore Delay Model W. Elmore, “The Transient Response of Damped Linear Networks with W. Elmore, “The Transient Response of Damped Linear Networks with
Particular Regard to Wideband Amplifiers,” Particular Regard to Wideband Amplifiers,” J. Appl. PhysJ. Appl. Phys., vol. 19, ., vol. 19, no.1, pp. 55-63, Jan. 1948.no.1, pp. 55-63, Jan. 1948.
CKi j k
Ri Rj Rk
Ci Cj CkShared resistance:Rii = RiRij = Rji = RiRik = Rki = RiRjj = Ri + RjRjk = Rkj = Ri + RjRkk = Ri + Rj + Rk
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1111
Elmore Delay CalculationElmore Delay Calculation
Delay at node k, sk = 0.69 (Ci × Rik + Cj × Rjk + Ck × Rkk )
= 0.69 [Ri Ci + (Ri + Rj) Cj + (Ri + Rj + Rk)Ck]
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1212
Finding Finding δδ(I,j) and (I,j) and ΔΔ(I,j)(I,j)
A1
B3
C1
D2
E1
F1
J1
G2
H3
, -, -
, - 0, 0
, -, -
, -, -
i
j
k
3, 3
, -
, -
4, 4
5, 5
6, 7
6, 8
, -9, 10
Minimum delayMaximum delay
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1313
Maximum Clock Frequency for Maximum Clock Frequency for Tolerance Tolerance ±q/2 in Skew±q/2 in Skew
Linear program: Minimize Tck
Subject to: For all flip-flop pairs (i,j),
si + δ(i,j) ≥ sj + Thj + q
si + Δ(i,j) ≤ sj + Tck – Tsj – q
Where q is a constant
si are variables, simin ≤ si
Tck is a variable
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1414
Maximum Tolerance for Given Clock Maximum Tolerance for Given Clock FrequencyFrequency
Linear program: Maximize q
Subject to: For all flip-flop pairs (i,j),
si + δ(i,j) ≥ sj + Thj + q
si + Δ(i,j) ≤ sj + Tck – Tsj – q
Where Tck is a constant
si are variables, simin ≤ si
q is a variable
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1515
TradeoffsTradeoffs
Increasing clock period Tck
Incr
easi
ng s
kew
tole
ranc
e q
No
solu
tion
beca
use
ofze
ro s
lack
.
Spring 2010, Feb 19 . . .Spring 2010, Feb 19 . . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 1616
Clock Skew ProblemClock Skew Problem
N. Maheshwari and S. S. Sapatnekar, Timing Analysis and Optimization of Sequential Circuits, Springer, 1999.
J. P. Fishburn, “Clock Skew Optimization,” J. P. Fishburn, “Clock Skew Optimization,” IEEE IEEE Trans. ComputersTrans. Computers, vol. 39, no. 7, pp. 945-951, , vol. 39, no. 7, pp. 945-951, July 1990.July 1990.