Lecture 11: Sequential Circuit Design

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%

11: Sequential Circuits 35CMOS VLSI DesignCMOS VLSI Design 4th Ed.

SummaryFlip-Flops:– Very easy to use, supported by all tools

2-Phase Transparent Latches:– Lots of skew tolerance and time borrowing

Pulsed Latches:– Fast, some skew tol & borrow, hold time risk