Lecture 10: Sequential Networks: Timing and Retiming CSE 140: - - PowerPoint PPT Presentation

Lecture 10: Sequential Networks: Timing and Retiming

CSE 140: Components and Design Techniques for Digital Systems Spring 2014

CK Cheng, Diba Mirza

• Dept. of Computer Science and Engineering

University of California, San Diego

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Timing

• Clock specifies a precise time for the next state
• Too late: fail to reach for the setup of the next

state.

• Too early: Race to disturb the holding of the

next state.

• Analysis: Verify the timing of the system.
• Goal: A robust design.

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A typical sequential network has combinational circuit between registers (R1 to R2). The registers are synchronized by clocks (CLK1 to CLK2). Timing is set between clocks (CLK1 and CLK2).

Sequential Networks

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Combinational CLK1 CLK2 A B C D R1 R2

Combinational CLK1 CLK2 A B C

tcq + tcomb + tsetup ≤ T thold < tcq + tcomb

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So far ….

Combinational CLK

This lecture …

• When does our (seemingly logically correct) design go wrong?
• How can we design a circuit that works under real constraints?

Combinational CLK

Timing Constraints of flip flops

D Q Q’

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D

t1 time Q: What is the output of the flip flop at time t1?

• A. One
• B. Zero
• C. Can’t say for sure

CLK

Timing Constraints of flip flops

D Q Q’

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t1 time What if the input transition happens late, close to the rising edge?

• A. Output will still be one at t1
• B. Output will be zero at t1
• C. Can’t say for sure

D

Input Timing Constraint: Set up time

D Q Q’

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D

t1 time I. Setup time: tsetup This is the time before the clock edge that data must be stable (i.e. not change) CLK

Input Timing Constraint: Hold time

D Q Q’

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D

t1 time I. Is it okay for the input to the flip flop to change right after the rising edge? CLK

Input Constraints: Set up and hold time

D Q Q’

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CLK tsetup D thold ta

I. Setup time: tsetup Time before the clock edge that data must be stable (i.e. not change)

• II. Hold time: thold

Time after the clock edge that data must be stable Aperture time: ta Time around clock edge that data must be stable (ta = tsetup + thold)

Set up and hold time violations

D Q Q’

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CLK tsetup D thold ta

I. Setup time violation This occurs if the input data signal does not remain unchanged for at least tsetup before the clock edge.

• II. Hold time violation

This occurs if the input data signal does not remain unchanged for at least tsetup after the clock edge

Output Timing Constraints

CLK tccq tpcq Q

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D Q Q’

Output Timing Constraints

I. Contamination delay: tccq Time after clock edge that Q might be unstable (i.e., start changing) II. Propagation delay: tpcq Time after clock edge that the output Q is guaranteed to be stable (i.e., to stop changing)

CLK tccq tpcq Q

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D Q Q’

PIQ: A hold time violation is likely to occur when

• A. The input signal (into the flip flop) fails to change to a

desired value fast enough

• B. The output signal (out of the flip flop) takes too long to

stabilize

• C. The input signal (into the flip flop) does not remain stable

long enough after the clock edge

• D. The output signal (out of the flip flop) changes too quickly

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PIQ: The timing of which of the following signals can cause a

setup-time violation?

• A. The input signal T(t)
• B. The output signal Q(t)
• C. The clock signal, CLK
• D. Some of the above
• E. None of the above

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T Q Q’ T(t) CLK Q(t)

PIQ: For a given flip-flop implementation which of its timing

parameters can we modify when designing a sequential network (depicted below)

• A. Set up and hold time
• B. Propagation and

Contamination delays

• C. All of the above
• D. None of the above

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Combinational

CLK

Fact 1: Once a flip flop has been ‘built’ we are stuck with its timing characteristics: tsetup , thold, tccq, tpcq Now let’s look at the timing characteristics of the combinational part

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Combinational

CLK

Combinational Logic: Output timing constraints

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X1 X2 X4

I. Why don’t we have input constraints? Combinational circuit

X3 Y1 Y2 Y4 Y3

Combinational Logic: Output timing constraints

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X1 X2 X4

Combinational circuit

X3 Y1 Y2 Y4 Y3

I. Contamination delay: tcd

Minimum time from when an input changes until any output starts to change

Combinational Logic: Output timing constraints

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X1 X2 X4

I. Contamination delay: tcd

Minimum time from when an input changes until any output starts to change

II. Propagation delay: tpd

Maximum time from when an input changes until the output or outputs of a combinational circuit are guaranteed to reach their final value (i.e., stop changing)

Combinational circuit

X3 Y1 Y2 Y4 Y3

Combinational Logic: Output timing constraints

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A B C D Y PI Q: Which path in the above circuit determines the contamination delay of the circuit (assuming the delay of all the gates is the same)?

• A. AND- OR – NOR
• B. AND-OR
• C. NOR
• D. OR-NOR

Combinational Logic: Output timing constraints

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A B C D Y PI Q: Which path in the above circuit determines the propagation delay of the circuit (assuming the delay of all the gates is the same)?

• A. AND- OR – NOR
• B. AND-OR
• C. NOR
• D. OR-NOR

R1 Combinational CLK R2 CLK D1 Q1 D2

An alternate view of the sequential circuit

Combinational CLK

The delay between registers has a minimum and maximum delay, dependent on the delays of the circuit elements (Dynamic Discipline)

C L CLK CLK R1 R2 Q1 D2 (a) CLK Q1 D2 (b) Tc

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C L CLK CLK R1 R2 Q1 D2 (a) CLK Q1 D2 (b) Tc

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PI Q: Suppose input to R1 changed before t1, what is the maximum delay (from t1) after which D2 reaches a stable value?

• A. Setup time of R1+

Propagation delay of CL + Propagation delay of R2

• B. Hold time of R1+

Propagation delay of CL + setup time of R1

• C. Propagation delay of R1+

Propagation delay of CL + Propagation delay of R2

• D. Propagation delay of R1+

Propagation delay of CL E. Propagation delay of CL + Propagation delay of R2

t1

C L CLK CLK R1 R2 Q1 D2 (a) CLK Q1 D2 (b) Tc

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PI Q: Suppose input to R1 changed before t1, what is the minimum delay (from t1) after which D2 starts to change?

• A. Setup time of R1+

propagation delay of CL + propagation of R2

• B. Hold time of R1+

propagation time of CL +setup time of R1

• C. Hold time of R1+

Contamination delay of CL + Propagation time of R2

• D. Contamination delay of R1+

Contamination delay of CL E. Contamination delay of CL + Contamination delay of R2

Setup Time Constraint

• The setup time constraint depends on the maximum delay from register R1

through the combinational logic.

• The input to register R2 must be stable at least tsetup before the clock edge.

CLK Q1 D2 Tc tpcq tpd tsetup C L CLK CLK Q1 D2 R1 R2

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Maximum delay, tmax = Setup Time Constraint:

Setup Time Constraint

CLK Q1 D2 Tc tpcq tpd tsetup C L CLK CLK Q1 D2 R1 R2

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Tc ≥ tpcq + tpd + tsetup tpd ≤ Tc – (tpcq + tsetup)

Hold Time Constraint

• The hold time constraint depends on the minimum delay from register R1

through the combinational logic.

• The input to register R2 must be stable for at least thold after the clock edge.

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Minimum delay, tmin = Hold Time Constraint:

CLK Q1 D2 tccq tcd thold C L CLK CLK Q1 D2 R1 R2

Hold Time Constraint

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CLK Q1 D2 tccq tcd thold C L CLK CLK Q1 D2 R1 R2

thold < tccq + tcd tcd > thold - tccq

Timing Analysis

CLK CLK A B C D X' Y' X Y

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps

tpd = tcd = Setup time constraint: Tc ≥ fc = 1/Tc = Hold time constraint: tccq + tcd > thold ?

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Timing Analysis

CLK CLK A B C D X' Y' X Y

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps

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tpd = 3 x 35 ps = 105 ps tcd = 25 ps Setup time constraint: Tc ≥ (50 + 105 + 60) ps = 215 ps fc = 1/Tc = 4.65 GHz Hold time constraint: tccq + tcd > thold ? (30 + 25) ps > 70 ps ? No!

Fixing Hold Time Violation

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps

tpd = tcd = Setup time constraint: Tc ≥ fc = Hold time constraint: tccq + tcd > thold ?

CLK CLK A B C D X' Y' X Y

Add buffers to the short paths:

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Fixing Hold Time Violation

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps

tpd = 3 x 35 ps = 105 ps tcd = 2 x 25 ps = 50 ps Setup time constraint: Tc ≥ (50 + 105 + 60) ps = 215 ps fc = 1/Tc = 4.65 GHz Hold time constraint: tccq + tcd > thold ? (30 + 50) ps > 70 ps ? Yes!

CLK CLK A B C D X' Y' X Y

Add buffers to the short paths:

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Clock Skew

• The clock doesn’t arrive at all registers at the same time
• Skew is the difference between two clock edges
• Examine the worst case to guarantee that the dynamic discipline is not

violated for any register – many registers in a system!

t skew

CLK1 CLK2 C L CLK2 CLK1 R1 R2 Q1 D2 CLK delay CLK

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Setup Time Constraint with Clock Skew

• In the worst case, the CLK2 is earlier than CLK1

Tc ≥ tpcq + tpd + tsetup + tskew tpd ≤ Tc – (tpcq + tsetup + tskew)

CLK1 Q1 D2 Tc tpcq tpd tsetuptskew C L CLK2 CLK1 R1 R2 Q1 D2 CLK2

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Timing Analysis with clock skew

CLK CLK A B C D X' Y' X Y

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps tskew = 50 ps

tpd = 3 x 35 ps = 105 ps tcd = 25 ps Setup time constraint: Tc ≥ 265 ps fc = 1/Tc =3.77 GHz Without skew we got fc =4.65 GHz

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Hold Time Constraint with Clock Skew

• In the worst case, CLK2 is later than CLK1

tccq + tcd > thold + tskew tcd > thold + tskew – tccq

tccq tcd thold Q1 D2 tskew C L CLK2 CLK1 R1 R2 Q1 D2 CLK2 CLK1

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Hold Time Violation

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps tskew = 50 ps

tpd = 3 x 35 ps = 105 ps tcd = 2 x 25 ps = 50 ps Hold time constraint: tccq + tcd > thold + tskew? (30 + 50) ps > (70 ps +50) ps ?

CLK CLK A B C D X' Y' X Y

Add buffers to the short paths:

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Using Clock Skew advantageously (Retiming)

• Suppose CLK2 is later than CLK1 by tskew(1,2)

tccq + tcd > thold + tskew(1,2) tskew(1,2)< tccq + tcd - thold

tccq tcd thold Q1 D2 tskew C L CLK2 CLK1 R1 R2 Q1 D2 CLK2 CLK1

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Tc+ tskew(1,2) ≥ tpcq + tpd + tsetup

Retiming

Timing Characteristics

tccq = 30 ps tpcq = 50 ps tsetup = 60 ps thold = 70 ps tpd = 35 ps tcd = 25 ps tskew = ?

tpd = 3 x 35 ps = 105 ps tcd = 2 x 25 ps = 50 ps

CLK CLK A B C D X' Y' X Y

Add buffers to the short paths:

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tskew(1,2)< tccq + tcd - thold Tc+ tskew(1,2) ≥ tpcq + tpd + tsetup

(215ps) (10 ps)

Timing and Retiming

• Retiming: Adjust the clock skew so that

the clock period can be reduced.

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