ee 447/547 vlsi design lecture 9: sequential circuits
DESCRIPTION
EE 447/547 VLSI Design Lecture 9: Sequential Circuits. Outline. Floorplanning Sequencing Sequencing Element Design Max and Min-Delay Clock Skew Time Borrowing Two-Phase Clocking. Project Strategy. Proposal Specifies inputs, outputs, relation between them Floorplan - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/1.jpg)
Sequential circuits 1VLSI Design EE 447/547
EE 447/547 VLSI Design
Lecture 9: Sequential Circuits
![Page 2: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/2.jpg)
Sequential circuits 2VLSI Design EE 447/547
Outline
Floorplanning Sequencing Sequencing Element Design Max and Min-Delay Clock Skew Time Borrowing Two-Phase Clocking
![Page 3: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/3.jpg)
Sequential circuits 3VLSI Design EE 447/547
Project Strategy
Proposal Specifies inputs, outputs, relation between them
Floorplan Begins with block diagram Annotate dimensions and location of each block Requires detailed paper design
Schematic Make paper design simulate correctly
Layout Physical design, DRC, NCC, ERC
![Page 4: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/4.jpg)
Sequential circuits 4VLSI Design EE 447/547
Floorplan
How do you estimate block areas? Begin with block diagram Each block has
Inputs Outputs Function (draw schematic) Type: array, datapath, random logic
Estimation depends on type of logic
![Page 5: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/5.jpg)
Sequential circuits 5VLSI Design EE 447/547
MIPS Floorplan
datapath2700 x 1050
(2.8 M2)
alucontrol200 x 100
(20 k2)
zipper 2700 x 250
2700
1690
wiring channel: 30 tracks = 240
mips(4.6 M2)
bitslice 2700 x 100
control1500 x 400
(0.6 M2)
3500
3500
5000
5000
10 I/O pads
10 I/O pads
10 I/O pads
10 I/O pads
![Page 6: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/6.jpg)
Sequential circuits 6VLSI Design EE 447/547
Area Estimation
Arrays: Layout basic cell Calculate core area from # of cells Allow area for decoders, column circuitry
Datapaths Sketch slice plan Count area of cells from cell library Ensure wiring is possible
Random logic Compare complexity do a design you have done
![Page 7: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/7.jpg)
Sequential circuits 7VLSI Design EE 447/547
MIPS Slice Plan
mux2
inv
flop
flop
flop
flop
mux2
inv
writedriver
dualsram
dualsram
dualsram
dualsrambit0
srampullup
readmux
flop
mux4
flop
mux2
inv
flop
mux4
and2
flop
and2
inv
mux2
and2
or2
fulladder
mux4
register fileramslice
ALU
adrmux
flop
MD
R
IR3...0
writem
ux
srcB srcA aluout
zerodetect
PC
memdatawritedata
adr
pcimmediate
aluout
aluresult
srcBsrcAbitlines
44 24 93 93 93 93 93 44 24 52 48 48 48 48 16 86 93 93 93 9344 24 4424131 131 13139 39 39 39 160
![Page 8: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/8.jpg)
Sequential circuits 8VLSI Design EE 447/547
Typical Layout Densities
Typical numbers of high-quality layout Derate by 2 for class projects to allow routing and some
sloppy layout. Allocate space for big wiring channels
Element AreaRandom logic (2 metal layers) 1000-1500 2 / transistor
Datapath 250 – 750 2 / transistor
Or 6 WL + 360 2 / transistor
SRAM 1000 2 / bit
DRAM 100 2 / bit
ROM 100 2 / bit
![Page 9: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/9.jpg)
Sequential circuits 9VLSI Design EE 447/547
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
![Page 10: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/10.jpg)
Sequential circuits 10VLSI Design EE 447/547
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.
![Page 11: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/11.jpg)
Sequential circuits 11VLSI Design EE 447/547
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
![Page 12: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/12.jpg)
Sequential circuits 12VLSI Design EE 447/547
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
Flo
p
Latc
h
Q
clk clk
D Q
clk
D
Q (latch)
Q (flop)
![Page 13: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/13.jpg)
Sequential circuits 13VLSI Design EE 447/547
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
Flo
p
Latc
h
Q
clk clk
D Q
clk
D
Q (latch)
Q (flop)
![Page 14: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/14.jpg)
Sequential circuits 14VLSI Design EE 447/547
Latch Design
Pass Transistor Latch Pros
+ +
Cons
D Q
![Page 15: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/15.jpg)
Sequential circuits 15VLSI Design EE 447/547
Latch Design
Pass Transistor Latch Pros
+ Tiny+ Low clock load
Cons Vt drop nonrestoring backdriving output noise sensitivity dynamic diffusion input
D Q
Used in 1970’s
![Page 16: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/16.jpg)
Sequential circuits 16VLSI Design EE 447/547
Latch Design
Transmission gate+
- D Q
![Page 17: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/17.jpg)
Sequential circuits 17VLSI Design EE 447/547
Latch Design
Transmission gate+ No Vt drop
- Requires inverted clock D Q
![Page 18: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/18.jpg)
Sequential circuits 18VLSI Design EE 447/547
Latch Design
Inverting buffer+
+
+ Fixes either
D
XQ
D Q
![Page 19: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/19.jpg)
Sequential circuits 19VLSI Design EE 447/547
Latch Design
Inverting buffer+ Restoring
+ No backdriving
+ Fixes either Output noise sensitivity Or diffusion input
Inverted output
D
XQ
D Q
![Page 20: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/20.jpg)
Sequential circuits 20VLSI Design EE 447/547
Latch Design
Tristate feedback+
QDX
![Page 21: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/21.jpg)
Sequential circuits 21VLSI Design EE 447/547
Latch Design
Tristate feedback+ Static Backdriving risk
Static latches are now essential
QDX
![Page 22: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/22.jpg)
Sequential circuits 22VLSI Design EE 447/547
Latch Design
Buffered input+
+
QDX
![Page 23: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/23.jpg)
Sequential circuits 23VLSI Design EE 447/547
Latch Design
Buffered input+ Fixes diffusion input
+ Noninverting
QDX
![Page 24: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/24.jpg)
Sequential circuits 24VLSI Design EE 447/547
Latch Design
Buffered output+
Q
D X
![Page 25: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/25.jpg)
Sequential circuits 25VLSI Design EE 447/547
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
Q
D X
![Page 26: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/26.jpg)
Sequential circuits 26VLSI Design EE 447/547
Latch Design
Datapath latch+
-
Q
D X
![Page 27: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/27.jpg)
Sequential circuits 27VLSI Design EE 447/547
Latch Design
Datapath latch+ Smaller, faster
- unbuffered input
Q
D X
![Page 28: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/28.jpg)
Sequential circuits 28VLSI Design EE 447/547
Flip-Flop Design
Flip-flop is built as pair of back-to-back latches
D Q
X
D
X
Q
Q
![Page 29: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/29.jpg)
Sequential circuits 29VLSI Design EE 447/547
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
Latc
hDQ
0
1
en
Latc
h
D Q
en
DQ
0
1
enD Q
en
Flo
p
Flo
p
Flo
p
Symbol Multiplexer Design Clock Gating Design
![Page 30: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/30.jpg)
Sequential circuits 30VLSI Design EE 447/547
Reset
Force output low when reset asserted Synchronous vs. asynchronous
D
Q
Q
reset
D
Q
D
reset
Q
Dreset
reset
reset
Synchronous R
esetA
synchronous Reset
Sym
bol Flo
p
D QLa
tch
D Q
reset reset
Q
reset
![Page 31: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/31.jpg)
Sequential circuits 31VLSI Design EE 447/547
Set / Reset
Set forces output high when enabled Flip-flop with asynchronous set and reset
D
Q
reset
setreset
set
![Page 32: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/32.jpg)
Sequential circuits 32VLSI Design EE 447/547
Sequencing Methods
Flip-flops 2-Phase Latches Pulsed Latches
Flip-F
lopsF
lop
Latc
h
Flo
p
clk
1
2
p
clk clk
Latc
h
Latc
h
p p
1 12
2-Phase T
ransparent LatchesP
ulsed Latches
Combinational Logic
CombinationalLogic
CombinationalLogic
Combinational Logic
Latc
h
Latc
h
Tc
Tc/2
tnonoverlap tnonoverlap
tpw
Half-Cycle 1 Half-Cycle 1
![Page 33: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/33.jpg)
Sequential circuits 33VLSI Design EE 447/547
Timing Diagrams
Flo
p
A
Y
tpdCombinational
LogicA Y
D Q
clk clk
D
Q
Latc
h
D Q
clkclk
D
Q
tcd
tsetup thold
tccq
tpcq
tccq
tsetup tholdtpcq
tpdqtcdq
tpd Logic Prop. Delay
tcd Logic Cont. Delay
tpcq Latch/Flop Clk-Q Prop Delay
tccq Latch/Flop Clk-Q Cont. Delay
tpdq Latch D-Q Prop Delay
tpcq Latch D-Q Cont. Delay
tsetup Latch/Flop Setup Time
thold Latch/Flop Hold Time
Contamination and Propagation Delays
![Page 34: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/34.jpg)
Sequential circuits 34VLSI Design EE 447/547
Max-Delay: Flip-Flops
F1
F2
clk
clk clk
Combinational Logic
Tc
Q1 D2
Q1
D2
tpd
tsetuptpcq
sequencing overhead
pd ct T
![Page 35: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/35.jpg)
Sequential circuits 35VLSI Design EE 447/547
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
![Page 36: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/36.jpg)
Sequential circuits 36VLSI Design EE 447/547
Max Delay: 2-Phase Latches
Tc
Q1
L1
1
2
L2 L3
1 12
CombinationalLogic 1
CombinationalLogic 2
Q2 Q3D1 D2 D3
Q1
D2
Q2
D3
D1
tpd1
tpdq1
tpd2
tpdq2
1 2
sequencing overhead
pd pd pd ct t t T
![Page 37: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/37.jpg)
Sequential circuits 37VLSI Design EE 447/547
Max Delay: 2-Phase Latches
Tc
Q1
L1
1
2
L2 L3
1 12
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
![Page 38: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/38.jpg)
Sequential circuits 38VLSI Design EE 447/547
Max Delay: Pulsed Latches
Tc
Q1 Q2D1 D2
Q1
D2
D1
p
p p
Combinational LogicL1 L2
tpw
(a) tpw > tsetup
Q1
D2
(b) tpw < tsetup
Tc
tpd
tpdq
tpcq
tpd tsetup
sequencing overhead
max pd ct T
![Page 39: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/39.jpg)
Sequential circuits 39VLSI Design EE 447/547
Max Delay: Pulsed Latches
Tc
Q1 Q2D1 D2
Q1
D2
D1
p
p p
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
![Page 40: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/40.jpg)
Sequential circuits 40VLSI Design EE 447/547
Min-Delay: Flip-Flops
cdt CL
clk
Q1
D2
F1
clk
Q1
F2
clk
D2
tcd
thold
tccq
![Page 41: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/41.jpg)
Sequential circuits 41VLSI Design EE 447/547
Min-Delay: Flip-Flops
holdcd ccqt t t CL
clk
Q1
D2
F1
clk
Q1
F2
clk
D2
tcd
thold
tccq
![Page 42: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/42.jpg)
Sequential circuits 42VLSI Design EE 447/547
Min-Delay: 2-Phase Latches
1, 2 cd cdt t CL
Q1
D2
D2
Q1
1
L1
2
L2
1
2
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!
![Page 43: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/43.jpg)
Sequential circuits 43VLSI Design EE 447/547
Min-Delay: 2-Phase Latches
1, 2 hold nonoverlapcd cd ccqt t t t t CL
Q1
D2
D2
Q1
1
L1
2
L2
1
2
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!
![Page 44: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/44.jpg)
Sequential circuits 44VLSI Design EE 447/547
Min-Delay: Pulsed Latches
cdt CL
Q1
D2
Q1
D2
p tpw
p
L1
p
L2tcd
thold
tccq
Hold time increased by pulse width
![Page 45: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/45.jpg)
Sequential circuits 45VLSI Design EE 447/547
Min-Delay: Pulsed Latches
holdcd ccq pwt t t t CL
Q1
D2
Q1
D2
p tpw
p
L1
p
L2tcd
thold
tccq
Hold time increased by pulse width
![Page 46: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/46.jpg)
Sequential circuits 46VLSI Design EE 447/547
Time Borrowing
In 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
![Page 47: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/47.jpg)
Sequential circuits 47VLSI Design EE 447/547
Time Borrowing Example
Latc
h
Latc
h
Latc
h
Combinational LogicCombinational
Logic
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
1
2
1 1
1
2
2
![Page 48: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/48.jpg)
Sequential circuits 48VLSI Design EE 447/547
How Much Borrowing?
Q1
L1
1
2
L2
1 2
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
![Page 49: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/49.jpg)
Sequential circuits 49VLSI Design EE 447/547
Clock Skew
We have assumed zero clock skew Clocks really have uncertainty in arrival time
Decreases maximum propagation delay Increases minimum contamination delay Decreases time borrowing
![Page 50: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/50.jpg)
Sequential circuits 50VLSI Design EE 447/547
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
![Page 51: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/51.jpg)
Sequential circuits 51VLSI Design EE 447/547
Skew: Latches
Q1
L1
1
2
L2 L3
1 12
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
![Page 52: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/52.jpg)
Sequential circuits 52VLSI Design EE 447/547
Two-Phase Clocking
If setup times are violated, reduce clock speed If hold times are violated, chip fails at any speed In 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 times
Call these clocks 1, 2 (ph1, ph2)
![Page 53: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/53.jpg)
Sequential circuits 53VLSI Design EE 447/547
Safe Flip-Flop
In class, use flip-flop with nonoverlapping clocks Very 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
X
Q
Q
![Page 54: EE 447/547 VLSI Design Lecture 9: Sequential Circuits](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56812d1f550346895d921b85/html5/thumbnails/54.jpg)
Sequential circuits 54VLSI Design EE 447/547
Summary
Flip-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