COMP541
Flip-Flop Timing
Montek Singh
Oct 6, 2014
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Topics
 Timing analysis
 flip-flops
 sequential systems
 clock skew
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Lab 7: VGA Display
 Anyone having trouble with Lab 7?
 Be careful about the “Sync Polarity”
 A “1” means a downward going pulse
 sync signal is normally high, but goes low during the pulse
 A “0” means an upward going pulse
 Use my self-checking text bench!
 simulates my VGA driver …
 … and compares your outputs with mine
 flags any mismatches
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Timing of sequential circuits
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Input Timing Constraints
 Setup time: tsetup = time
before the clock edge that
data must be stable (i.e.
not changing)
 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)
CLK
D
tsetup thold
ta
Output Timing Constraints
 Propagation delay:
tpcq = max time after clock edge
by which output Q is guaranteed to have stabilized
(i.e., not changing anymore)
 Contamination delay: tccq = min time after clock edge
during which Q will not have started changing yet
CLK
Q
tccq
tpcq
Dynamic Discipline
 The input to a synchronous sequential circuit must be
stable during the aperture (setup and hold) time
around the clock edge
 Specifically, the input must be stable
 at least tsetup before the clock edge
 at least until thold after the clock edge
Implications on Design
 Constrains operation
 Given a clock period,
constrains circuit delays
 Given a circuit, constraints
clock period
 The delay between registers
(which impacts clock period)
has a minimum and maximum
delay, dependent on the
delays of the circuit elements
 Delays of both comb. logic
and flip-flops must be taken
into account
CLK
CLK
Q1
(a)
CL
R1
R2
Tc
CLK
Q1
D2
(b)
D2
Setup Time Constraint
 Setup time
 input to R2 must be stable at least tsetup before the clock edge
 constrains max delay from R1 through combinational logic
 What’s min clock period?
CLK
CLK
Q1
CL
D2
R1
R2
What’s Tc?
Tc ≥ tpcq + tpd + tsetup
tpd ≤ Tc – (tpcq + tsetup)
Tc
CLK
So, clock period constrained by:
• Delay in CL
• Delay in previous reg (R1)
• Setup requirement in next reg (R2)
Q1
D2
tpcq
tpd
tsetup
Hold Time Constraint
 Hold time
 input to R2 must be stable for at least thold after clock edge
 constrains the minimum delay from register R1 through the
combinational logic
 often try to design circuits with 0 hold time requirement
CLK
CLK
Q1
R1
CL
D2
R2
CLK
Q1
D2
tccq tcd
thold
thold < tccq + tcd
tcd > thold - tccq
Timing Analysis
CLK
CLK
Timing Characteristics
tccq = 30 ps (FF contamination)
A
tpcq = 50 ps (FF propagation)
B
tsetup = 60 ps
D
X'
X
Y'
Y
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
thold = 70 ps
per gate
C
tpd = 35 ps
tcd = 25 ps
Hold time constraint:
tccq + tcd > thold ?
(30 + 25) ps > 70 ps ? No!
Fixing Hold Time Violation
Add buffers to the short paths:
CLK
Timing Characteristics
CLK
tccq = 30 ps
A
tpcq = 50 ps
tsetup = 60 ps
B
D
tpd = 3 x 35 ps = 105 ps
X'
X
Y'
Y
thold = 70 ps
per gate
C
tpd = 35 ps
tcd = 25 ps
tcd = 2 x 25 ps = 50 ps
Hold time constraint:
Setup time constraint:
tccq + tpd > thold ?
Tc ≥ (50 + 105 + 60) ps = 215 ps
(30 + 50) ps > 70 ps ? Yes!
fc = 1/Tc = 4.65 GHz
Hold Time
 Often flip-flops are designed for a hold time of zero
 To avoid these tricky problems
Clock Skew
 Clock doesn’t arrive at all registers at the same time
 Skew is the difference between the arrival times of the clock
edge at two different (typically neighboring) flip-flops
 Examine the worst case:
 guarantee that discipline is not violated for any register pair
 many registers in a system!
delay
CLK
CLK1
CLK2
Q1
R1
t skew
CLK1
CLK2
CLK
C
L
D2
R2
Setup Time Constraint with Clock Skew
 Worst case: CLK2 is earlier than CLK1
CLK1
CLK2
Q1
C
L
R1
Tc
D2
R2
Tc ≥ tpcq + tpd + tsetup + tskew
tpd ≤ Tc – (tpcq + tsetup + tskew)
CLK1
CLK2
Q1
D2
tpcq
tpd
tsetup tskew
Similar Issue w/ Hold Time
 We won’t go over example
 Have a look in book
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Next Time
 Read Section 3.5.1-3.5.3
 Then we’ll move on to memories
 Section 5.5
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