Elec 7770 advanced vlsi design spring 2008 clock skew problem
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ELEC 7770 Advanced VLSI Design Spring 2008 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_Spr08/course.html. Single Clock. FF A. FF B. Comb.

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ELEC 7770 Advanced VLSI Design Spring 2008 Clock Skew Problem

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Elec 7770 advanced vlsi design spring 2008 clock skew problem

ELEC 7770Advanced VLSI DesignSpring 2008Clock 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_Spr08/course.html

ELEC 7770: Advanced VLSI Design (Agrawal)


Single clock

Single Clock

FF A

FF B

Comb.

Data_out

Data_in

CKA

CKB

CK

CKA

CKB

Single-cycle path delay

ELEC 7770: Advanced VLSI Design (Agrawal)


Multiple clocks

Multiple Clocks

FF A

FF B

Comb.

Data_out

Data_in

CKA

CKB

CKA

CKB

Multi-cycle path delay

ELEC 7770: Advanced VLSI Design (Agrawal)


Clock skew

Clock Skew

  • Skew is the time delay of clock signal at a flip-flop with respect to some time reference.

  • For a given layout each flip-flop has a skew, measured with respect to the a common reference.

  • Skews of flip-flops separated by combinational paths affect the short-path and long-path constraints.

ELEC 7770: Advanced VLSI Design (Agrawal)


Skews for single cycle paths

Skews for Single-Cycle Paths

Combinational

Block

Delay:

FFi

CKi

FFj

CKj

δ(i,j) ≤ d(i,j) ≤ Δ(i,j)

xi

xj

xi and xj are arrival times of clock edges

ELEC 7770: Advanced VLSI Design (Agrawal)


Short path constraint double clocking

Short-Path Constraint (Double-Clocking)

Tck

CKi

xi

intended

Not intended

CKj

Thj

xj

δ(i,j)

xi + δ(i,j) ≥ xj + Thj

ELEC 7770: Advanced VLSI Design (Agrawal)


Long path constraint zero clocking

Long-Path Constraint (Zero-Clocking)

Tck

CKi

xi

Not intended

intended

CKj

xj

Tsj

Δ(i,j)

xi + Δ(i,j) ≤ xj + Tck – Tsj

ELEC 7770: Advanced VLSI Design (Agrawal)


Maximum clock frequency

Maximum Clock Frequency

Linear program:

Minimize Tck

Subject to:

For all flip-flop pairs (i,j),

xi + δ(i,j) ≥ xj + Thj

xi + Δ(i,j) ≤ xj + Tck – Tsj

ELEC 7770: Advanced VLSI Design (Agrawal)


Finding clock skews

Finding Clock Skews

xk

FFi

FFj

FFk

xi

Ri

Rj

Rk

CK

Ci

Cj

Ck

xj

Use Elmore delay formula to calculate xi, xj, xk.

ELEC 7770: Advanced VLSI Design (Agrawal)


Interconnect delay elmore delay model

Interconnect Delay: Elmore Delay Model

  • W. Elmore, “The Transient Response of Damped Linear Networks with Particular Regard to Wideband Amplifiers,” J. Appl. Phys., vol. 19, no.1, pp. 55-63, Jan. 1948.

i

Rj

Ri

Rk

j

k

CK

Ci

Cj

Ck

Shared resistance:

Rii = Ri

Rij = Rji = Ri

Rik = Rki = Ri

Rjj = Ri + Rj

Rjk = Rkj = Ri + Rj

Rkk = Ri + Rj + Rk

ELEC 7770: Advanced VLSI Design (Agrawal)


Elmore delay calculation

Elmore Delay Calculation

Delay at node k, xk= 0.69 (Ci × Rik + Cj × Rjk + Ck × Rkk )

= 0.69 [Ri Ci + (Ri + Rj) Cj + (Ri + Rj + Rk)Ck]

ELEC 7770: Advanced VLSI Design (Agrawal)


Finding i j and i j

Finding δ(I,j) and Δ(I,j)

Minimum delay

Maximum delay

, -

, -

A

1

, -

9, 10

H

3

j

, -

0, 0

3, 3

B

3

4, 4

i

E

1

G

2

6, 7

, -

, -

C

1

, -

6, 8

J

1

F

1

k

, -

, -

5, 5

D

2

, -

ELEC 7770: Advanced VLSI Design (Agrawal)


Maximum clock frequency for tolerance q 2 in skew

Maximum Clock Frequency for Tolerance ±q/2 in Skew

Linear program:Minimize Tck

Subject to:For all flip-flop pairs (i,j),

xi + δ(i,j) ≥ xj + Thj + q

xi + Δ(i,j) ≤ xj + Tck – Tsj – q

Where q is a constant

xi are variables, ximin ≤ xi

Tck is a variable

ELEC 7770: Advanced VLSI Design (Agrawal)


Maximum tolerance for given clock frequency

Maximum Tolerance for Given Clock Frequency

Linear program:Maximize q

Subject to:For all flip-flop pairs (i,j),

xi + δ(i,j) ≥ xj + Thj + q

xi + Δ(i,j) ≤ xj + Tck – Tsj – q

Where Tck is a constant

xi are variables, ximin ≤ xi

q is a variable

ELEC 7770: Advanced VLSI Design (Agrawal)


Tradeoffs

Tradeoffs

No solution because of

zero slack.

Increasing skew tolerance q

Increasing clock period Tck

ELEC 7770: Advanced VLSI Design (Agrawal)


Clock skew problem

Clock Skew Problem

  • N. Maheshwari and S. S. Sapatnekar, Timing Analysis and Optimization of Sequential Circuits, Springer, 1999.

  • J. P. Fishburn, “Clock Skew Optimization,” IEEE Trans. Computers, vol. 39, no. 7, pp. 945-951, July 1990.

ELEC 7770: Advanced VLSI Design (Agrawal)


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