James Morizio 1

Sequential Circuit Design: Part 1

• Design of memory elements– Static latches– Pseudo-static latches– Dynamic latches

• Timing parameters• Two-phase clocking• Clocked inverters

James Morizio 2

Sequential Logic

2 s torage mechanis ms• pos itive feedback• charge-bas ed

Φ

LOGIC

tp,combInOut

FFs

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Sequencing• Combinational 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

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Sequencing Cont.

• If tokens moved through pipeline at constant speed, no sequencing elements would be necessary

• Ex: 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 circuits• In most circuits, dispersion is high

– Delay fast tokens so they don’t catch slow ones.

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Sequencing Overhead

• Use flip-flops to delay fast tokens so they move through exactly one stage each cycle.

• Inevitably adds some delay to the slow tokens• Makes 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

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Sequencing Elements• Latch: 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)

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Flip-Flop: Timing Definitions

DATASTABLE

In

t

tsetup thold

DATASTABLE

Out

t

tpFF

t

Φ

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Maximum Clock Frequency

LOGIC

tp,comb

FFs

Φ

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Latch Design• Pass Transistor Latch• Pros

+ Tiny+ Low clock load

• Cons– Vt drop– nonrestoring– backdriving– output noise sensitivity– dynamic– diffusion input

D Q

φ

Used in 1970’s

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Latch Design

• Transmission gate+ No Vt drop- Requires inverted clock

D Q

φ

φ

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Latch Design

• Inverting buffer+ Restoring+ No backdriving+ Fixes either

• Output noise sensitivity• Or diffusion input

– Inverted output

D

φ

φ

X Q

D Q

φ

φ

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Latch Design

• Buffered input+ Fixes diffusion input+ Noninverting

φ

φ

QD X

φ

φ

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Latch Design

• Buffered 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

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Latch Design

• Tristate feedback+ Static– Backdriving risk

• Static latches are now essential

φ

φ φ

φ

QD X

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Latch Design

• Datapath latch+ Smaller, faster- unbuffered input

φ

φ φ

φ

Q

D X

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Design of Memory Elements

Q

C

C

C

CD

ΦΦ Φ Φ Q

Positive edge-triggered D flip-flopWhy use inverters on outputs?

Skew Problem : Φ may be delayed with respect to Φ (both may be 1 at the same time)

This is what happens-

Q

QD

C Φ

ΦΦin1 Transmission gate acts a

buffer, should have samedelay as inverter

Eliminating/Reducing skew:

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Latch design

Static D latch “Jamb” latch Weak inverter

C

ΦΦ

C

C

D

ΦΦ

DQ Q

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Latch Design

CD

Φ

C

ΦQ

Variant of D latch

Φ

ΦD

Φ

ΦQ

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Flip-Flop Design• Flip-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

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Enable• Enable: 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

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Reset• Force output low when reset asserted• Synchronous 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 R

esetA

synchronous Reset

Sym

bol Flo

p

D Q

Latc

h

D Q

reset reset

φ φ

φ

φ

Q

reset

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Set / Reset

• Set 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

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Dynamic Latches

• So far, all latches have been static-store state when clock is stopped but power is maintained

• Dynamic latches reduce transistor count• Eliminate feedback inverter and transmission gate• Latch value stored on the capacitance of the input

(gate capacitance)

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Dynamic Latch and Flip-Flop

• Difficult to ensure reliable operation• Similar to DRAM• Refresh cycles are required

CD

Φ

QC

Data stored asCharge on gate capacitance

Dynamic D latch

Φ

CD

Φ

QDynamic negativeedge-triggered D flip-flop

C

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Charge-Based Storage

Schematic diagram

Non-overlapping clocks

P s e udo -s ta tic Latc h

QD

QΦ

Φ

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Master-Slave Flip-Flop

AB

Overlapping Clocks Can Caus e• Race Conditions• Undefined Signals

Φ Φ

Φ ΦD

Q

To reduce skew: generatecomplement of clock within the cellExtra inverter per cell

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Two-Phase Clocking

• Inverting a single clock can lead to skew problems• Employ two non-overlapping clocks for master and slave

sections of a flip-flop• Also, use two phases for alternating pipeline stages

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Two-Phase Clocking

Φ1(t) . Φ2(t) = 02

Φ1=1, Φ2 = 0

Φ

Φ

1

2 Φ

CD

Φ

QC

1

D Q

Φ1=0, Φ2 = 1D Q

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2-phase non-overlapping clocks

1

2

t

Φ

ΦImportant:Non-overlap time t must bekept small

2

1

1

2Φ

Φ

Φ

Φ

Q

D

Pseudo-staticD flip-flop

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2-phase dynamic flip-flop

φ2φ1

Input Sampled

Output Enable

φ1

φ2

D Q

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Use of “p” LeakersΦ Φ

Q

Degraded voltage VDD-Vt

Flip-flopbased on nMOSpass gates

1 2

D

Φ Φ

Q

1 2

D

No need to routeΦ signals

pMOS leaker transistorsprovide full-restored logiclevelsProblem: Increased delay

(extra inverter)

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Clocked Inverters

Q

Φ

Similar to tristate buffer Φ = 1, acts as inverterΦ = 0, output = Z

Φ

Φ

D

Φ Φ

i1 i2 i3Q

D

D Latch

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Flip-flop insensitive to clock overlap

DIn

φ

φ φ

φ

VDDVDD

M1

M3

M4

M2 M6

M8

M7

M5

φ−section φ−section

CL1 CL2

X

C2MOS flip-flop

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C2MOS avoids Race Conditions

DIn

1

M1

M3

M2 M6

M7

M5

1

DIn

VDDVDD

M1

M4

M2 M6

M8

M5

0 0

VDDVDD

(a) (1-1) overlap (b) (0-0) overlap

X X