11: Sequential Circuits 2CMOS VLSI DesignCMOS VLSI Design 4th Ed.
OutlineSequencingSequencing Element DesignMax and Min-DelayClock SkewTime BorrowingTwo-Phase Clocking
11: Sequential Circuits 3CMOS VLSI DesignCMOS VLSI Design 4th Ed.
SequencingCombinational logic– output depends on current inputs
Sequential logic– output depends on current and previous inputs– Requires separating previous, current, future– Called state or tokens– Ex: FSM, pipeline
CL
clk
in out
clk clk clk
CL CL
PipelineFinite State Machine
11: Sequential Circuits 4CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Sequencing Cont.If tokens moved through pipeline at constant speed, no sequencing elements would be necessaryEx: fiber-optic cable– Light pulses (tokens) are sent down cable– Next pulse sent before first reaches end of cable– No need for hardware to separate pulses– But dispersion sets min time between pulses
This is called wave pipelining in circuitsIn most circuits, dispersion is high– Delay fast tokens so they don’t catch slow ones.
11: Sequential Circuits 5CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Sequencing OverheadUse flip-flops to delay fast tokens so they move through exactly one stage each cycle.Inevitably adds some delay to the slow tokensMakes circuit slower than just the logic delay– Called sequencing overhead
Some people call this clocking overhead– But it applies to asynchronous circuits too– Inevitable side effect of maintaining sequence
11: Sequential Circuits 6CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Sequencing ElementsLatch: Level sensitive– a.k.a. transparent latch, D latch
Flip-flop: edge triggered– A.k.a. master-slave flip-flop, D flip-flop, D register
Timing Diagrams– Transparent– Opaque– Edge-trigger
D
Flop
Latc
h
Q
clk clk
D Q
clk
D
Q (latch)
Q (flop)
D
Flop
Latc
h
Q
clk clk
D Q
clk
D
Q (latch)
Q (flop)
11: Sequential Circuits 7CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignPass Transistor LatchPros+ Tiny+ Low clock load
Cons– Vt drop– nonrestoring– backdriving– output noise sensitivity– dynamic– diffusion input
D Q
φ
Used in 1970’s
11: Sequential Circuits 8CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignTransmission gate+ No Vt drop- Requires inverted clock D Q
φ
φ
11: Sequential Circuits 9CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignInverting buffer+ Restoring+ No backdriving+ Fixes either
• Output noise sensitivity• Or diffusion input
– Inverted output
D
φ
φ
X Q
D Q
φ
φ
11: Sequential Circuits 10CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignTristate feedback+ Static– Backdriving risk
Static latches are now essentialbecause of leakage
φ
φ φ
φ
QD X
11: Sequential Circuits 11CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignBuffered input+ Fixes diffusion input+ Noninverting
φ
φ
QD X
φ
φ
11: Sequential Circuits 12CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignBuffered output+ No backdriving
Widely used in standard cells+ Very robust (most important)- Rather large- Rather slow (1.5 – 2 FO4 delays)- High clock loading
φ
φ
Q
D X
φ
φ
11: Sequential Circuits 13CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Latch DesignDatapath latch+ smaller+ faster- unbuffered input
φ
φ φ
φ
Q
D X
11: Sequential Circuits 14CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Flip-Flop DesignFlip-flop is built as pair of back-to-back latches
D Q
φ
φ
φ
φ
X
D
φ
φ
φ
φ
X
Q
Qφ
φ
φ
φ
11: Sequential Circuits 15CMOS VLSI DesignCMOS VLSI Design 4th Ed.
EnableEnable: ignore clock when en = 0– Mux: increase latch D-Q delay– Clock Gating: increase en setup time, skew
D Q
Latc
h
D Q
en
en
φ
φ
Latc
hDQ
φ
0
1
en
Latc
h
D Q
φ en
DQ
φ
0
1
enD Q
φ en
Flop
Flop
Flop
Symbol Multiplexer Design Clock Gating Design
11: Sequential Circuits 16CMOS VLSI DesignCMOS VLSI Design 4th Ed.
ResetForce output low when reset assertedSynchronous vs. asynchronous
D
φ
φ
φ
φ
Q
Qφ
φ
φ
φ
reset
D
φ
φφ
φ
φ
φ
Qφ
φ
Dreset
φ
φ
Qφ
φ
Dreset
reset
φ
φ
reset
Synchronous Reset
Asynchronous R
esetS
ymbol Fl
opD Q
Latc
h
D Q
reset reset
φ φ
φ
φ
Q
reset
11: Sequential Circuits 17CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Set / ResetSet forces output high when enabled
Flip-flop with asynchronous set and reset
D
φ
φ
φ
φφ
φ
Q
φ
φ
reset
set reset
set
11: Sequential Circuits 18CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Sequencing MethodsFlip-flops2-Phase LatchesPulsed Latches
Flip-FlopsFl
opLa
tch
Flop
clk
φ1
φ2
φp
clk clk
Latc
h
Latc
h
φp φp
φ1 φ1φ2
2-Phase Transparent Latches
Pulsed Latches
Combinational Logic
CombinationalLogic
CombinationalLogic
Combinational Logic
Latc
h
Latc
h
Tc
Tc/2
tnonoverlap tnonoverlap
tpw
Half-Cycle 1 Half-Cycle 1
11: Sequential Circuits 19CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Timing Diagrams
Flop
A
Y
tpdCombinational
LogicA Y
D Q
clk clk
D
Q
Latc
h
D Q
clk clk
D
Q
tcd
tsetup thold
tccq
tpcq
tccq
tsetup tholdtpcq
tpdqtcdqLatch/Flop Hold Timethold
Latch/Flop Setup Timetsetup
Latch D->Q Cont. Delaytcdq
Latch D->Q Prop. Delaytpdq
Latch/Flop Clk->Q Cont. Delaytccq
Latch/Flop Clk->Q Prop. Delaytpcq
Logic Cont. Delaytcd
Logic Prop. Delaytpd
Contamination and Propagation Delays
11: Sequential Circuits 20CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Max-Delay: Flip-Flops
F1 F2
clk
clk clk
Combinational Logic
Tc
Q1 D2
Q1
D2
tpd
tsetuptpcq
( )setup
sequencing overhead
pd c pcqt T t t≤ − +
11: Sequential Circuits 21CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Max Delay: 2-Phase Latches
Tc
Q1
L1
φ1
φ2
L2 L3
φ1 φ1φ2
CombinationalLogic 1
CombinationalLogic 2
Q2 Q3D1 D2 D3
Q1
D2
Q2
D3
D1
tpd1
tpdq1
tpd2
tpdq2
( )1 2
sequencing overhead
2pd pd pd c pdqt t t T t= + ≤ −
11: Sequential Circuits 22CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Max Delay: Pulsed Latches
Tc
Q1 Q2D1 D2
Q1
D2
D1
φp
φp φp
Combinational LogicL1 L2
tpw
(a) tpw > tsetup
Q1
D2
(b) tpw < tsetup
Tc
tpd
tpdq
tpcq
tpd tsetup
( )setup
sequencing overhead
max ,pd c pdq pcq pwt T t t t t≤ − + −
11: Sequential Circuits 23CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Min-Delay: Flip-Flops
holdcd ccqt t t≥ − CL
clk
Q1
D2
F1
clk
Q1
F2
clk
D2
tcd
thold
tccq
11: Sequential Circuits 24CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Min-Delay: 2-Phase Latches
1, 2 hold nonoverlapcd cd ccqt t t t t≥ − −CL
Q1
D2
D2
Q1
φ1
L1
φ2
L2
φ1
φ2
tnonoverlap
tcd
thold
tccq
Hold time reduced by nonoverlap
Paradox: hold applies twice each cycle, vs. only once for flops.
But a flop is made of two latches!
11: Sequential Circuits 25CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Min-Delay: Pulsed Latches
holdcd ccq pwt t t t≥ − +CL
Q1
D2
Q1
D2
φp tpw
φp
L1
φp
L2tcd
thold
tccq
Hold time increased by pulse width
11: Sequential Circuits 26CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Time BorrowingIn a flop-based system:– Data launches on one rising edge– Must setup before next rising edge– If it arrives late, system fails– If it arrives early, time is wasted– Flops have hard edges
In a latch-based system– Data can pass through latch while transparent– Long cycle of logic can borrow time into next– As long as each loop completes in one cycle
11: Sequential Circuits 27CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Time Borrowing Example
Latc
h
Latc
h
Latc
h
Combinational Logic CombinationalLogic
Borrowing time acrosshalf-cycle boundary
Borrowing time acrosspipeline stage boundary
(a)
(b) Latc
h
Latc
hCombinational Logic Combinational
Logic
Loops may borrow time internally but must complete within the cycle
φ1
φ2
φ1 φ1
φ1
φ2
φ2
11: Sequential Circuits 28CMOS VLSI DesignCMOS VLSI Design 4th Ed.
How Much Borrowing?
Q1
L1
φ1
φ2
L2
φ1 φ2
Combinational Logic 1Q2D1 D2
D2
Tc
Tc/2 Nominal Half-Cycle 1 Delay
tborrow
tnonoverlap
tsetup
( )borrow setup nonoverlap2cTt t t≤ − +
2-Phase Latches
borrow setuppwt t t≤ −
Pulsed Latches
11: Sequential Circuits 29CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Clock SkewWe have assumed zero clock skewClocks really have uncertainty in arrival time– Decreases maximum propagation delay– Increases minimum contamination delay– Decreases time borrowing
11: Sequential Circuits 30CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Skew: Flip-Flops
F1 F2
clk
clk clk
Combinational Logic
Tc
Q1 D2
Q1
D2
tskew
CL
Q1
D2
F1
clk
Q1
F2
clk
D2
clk
tskew
tsetup
tpcq
tpdq
tcd
thold
tccq
( )setup skew
sequencing overhead
hold skew
pd c pcq
cd ccq
t T t t t
t t t t
≤ − + +
≥ − +
11: Sequential Circuits 31CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Skew: Latches
Q1
L1
φ1
φ2
L2 L3
φ1 φ1φ2
CombinationalLogic 1
CombinationalLogic 2
Q2 Q3D1 D2 D3
( )
( )
sequencing overhead
1 2 hold nonoverlap skew
borrow setup nonoverlap skew
2
,
2
pd c pdq
cd cd ccq
c
t T t
t t t t t t
Tt t t t
≤ −
≥ − − +
≤ − + +
2-Phase Latches
( )
( )
setup skew
sequencing overhead
hold skew
borrow setup skew
max ,pd c pdq pcq pw
cd pw ccq
pw
t T t t t t t
t t t t t
t t t t
≤ − + − +
≥ + − +
≤ − +
Pulsed Latches
11: Sequential Circuits 32CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Two-Phase ClockingIf setup times are violated, reduce clock speedIf hold times are violated, chip fails at any speedIn this class, working chips are most important– No tools to analyze clock skew
An easy way to guarantee hold times is to use 2-phase latches with big nonoverlap timesCall these clocks φ1, φ2 (ph1, ph2)
11: Sequential Circuits 33CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Safe Flip-FlopPast years used flip-flop with nonoverlapping clocks– Slow – nonoverlap adds to setup time– But no hold times
In industry, use a better timing analyzer– Add buffers to slow signals if hold time is at risk
D
φ2
X
Q
Q
φ1
φ2
φ1
φ1φ1
φ2
φ2
11: Sequential Circuits 34CMOS VLSI DesignCMOS VLSI Design 4th Ed.
Adaptive SequencingDesigners include timing margin– Voltage– Temperature– Process variation– Data dependency– Tool inaccuracies
Alternative: run faster and check for near failures– Idea introduced as “Razor”
• Increase frequency until at the verge of error• Can reduce cycle time by ~30%