Delay Model and Simulation

1
Delay Model and Simulation
2
Simulation with Delay
A
X
B
X
A
C
D
C
3
2
X
13
B
D
X
0 10 20 30
40 50
15
tsim
A x B x C x D x
A 1 B 0
B 1
A 0
B 0
C 1
C 0
C 0
D 0
D 1
D 1
3
Delay Models

• Gate delay
• Intrinsic delay
• Layout-induced delay due to capacitive load
• Waveform slope-induced delay
• Net delay/transport delay
• Signal propagation delay along interconnect wires
• Module path delay
• Delay between input port and output port

4
Inertial Delay

• Delay is caused by charging and discharging node
  capacitors in circuit
• Gate delay and wire delay
• Pulse rejection
• If pulse with is less than delay, the pulse is
  ignored

A
C
D
B
5
Gate Delay

• and (yout, x1, x2) // default, zero gate delay
• and 3 (yout, x1, x2) // 3 units delay for all
  transitions
• and (2,3) G1(yout, x1, x2) // rising, falling
  delay
• and (2,3) G1(yout, x1, x2), G2(yout2, x3, x4)
• // Multiple instances
• a_buffer (3,5,2) (yout, x) // UDP, rise, fall,
  turnoff
• bufif1 (345, 679, 578) (yout, xin,
  enable)
• // mintypmax / rise, fall, turnoff

• Simulators simulate with only one of min, typ and
  max delay values
• Selection is made through compiler directives or
  user interfaces
• Default delay is typ delay

6
Gate and Wire Model
C
R
r resistance per unit length c capacitance
per unit length
L
rL
cL/2
cL/2
7
Example of Model
8
Delay Estimation
2
R2
R
R1
C2
0
1
C0
C1
3
R3
C3

• D0 R ( C0 C1 C2 C3 )
• D1 D0 R1 ( C1 C2 C3 )
• D2 D1 R2 C2
• D3 D1 R3 C3

9
Clock Scheduling
LD logic delay
i
j
ti
tj
Clock
10
Timing Constraints
hold
setup
tj
LDmin
ti
LDmax

• skewij ti tj gt holdmax LDmin
• skewij ti tj lt CP LDmax setupmax
• CP clock period

11
Assignment
12
Blocking and Non-blocking Assignment

• initial
• begin
• a 1
• b 0
• a b // a 0
• b a // b 0
• end
• initial
• begin
• a 1
• b 0
• a lt b // a 0
• b lt a // b 1
• end

• Blocking assignment
• Statement order matters
• A statement has to be executed before next
  statement
• Non-blocking assignment lt
• Concurrent assignment
• Normally the last assignment at certain
  simulation time step
• If it triggers other blocking assignments, it is
  executed before the blocking assignment it
  triggers
• If there are multiple non-blocking assignments to
  same variable in same behavior, latter overwrites
  previous

13
Procedural Continuous Assignment

• Continuous assignment establishes static binding
  for net variables
• Procedural continuous assignment (PCA)
  establishes dynamic binding for variables
• assign deassign for register variables only
• force release for both register and net
  variables

14
Intra-assignment Delay Blocking Assignment

• // B 0 at time 0
• // B 1 at time 4
• 5 A B // A 1
• C D
• A 5 B // A 0
• C D
• A _at_(enable) B
• C D
• A _at_(named_event) B
• C D

• If timing control operator(,_at_) on LHS
• Blocking delay
• RHS evaluated at (,_at_)
• Assignment at (,_at_)
• If timing control operator(,_at_) on RHS
• Intra-assignment delay
• RHS evaluated immediately
• Assignment at (,_at_)

15
Example
initial begin a 10 1 b 2 0 c 3 1
end initial begin d lt 10 1 e lt 2 0 f lt
3 1 end
t a b c d e f 0 x x x x x x 2 x x x x 0 x
3 x x x x 0 1 10 1 x x 1 0 1 12 1 0 x 1 0 1 15
1 0 1 1 0 1
16
Tell the Differences
always _at_ (a or b) y ab always _at_ (a or
b) 5 y ab always _at_ (a or b) y 5
ab always _at_ (a or b) y lt 5 ab
Which one describes or gate?
Event control is blocked
17
Race Condition

• always _at_ ( posedge clk ) // c will get previous
  b or new b ?
• c b
• always _at_ ( posedge clk )
• b a

18
Avoid Race Condition

• always _at_ ( posedge clk ) // Solution 1 merge
  always
• begin
• c b b a
• end
• always _at_ ( posedge clk ) // Solution 2
  intra-assignment delay
• c 1 b
• always _at_ ( posedge clk )
• b 1 a
• always _at_ ( posedge clk ) // Solution 3
  non-blocking assignment
• c lt b
• always _at_ ( posedge clk )
• b lt a

19
Finite State Machine
20
FSM Example Speed Machine
21
Verilog Code for Speed Machine

• // Explicit FSM style
• module speed_machine ( clock, accelerator, brake,
  speed )
• input clock, accelerator, brake
• output 10 speed
• reg 10 state, next_state
• parameter stopped 2b00
• parameter s_slow 2b01
• parameter s_medium 2b10
• parameter s_high 2b11
• assign speed state
• always _at_ ( posedge clock )
• state lt next_state

• always _at_ ( state or accelerator or brake )
• if ( brake 1b1 )
• case ( state )
• stopped next_state lt stopped
• s_low next_state lt stopped
• s_medium next_state lt s_low
• s_high next_state lt s_medium
• default next_state lt stopped
• endcase
• else if ( accelerator 1b1 )
• case ( state )
• stopped next_state lt s_low
• s_low next_state lt s_medium
• s_medium next_state lt s_high
• s_high next_state lt s_high
• default next_state lt stopped
• endcase
• else next_state lt state
• endmodule

22
State Encoding Example
23
State Encoding

• A state machine having N states will require at
  least log2N bits register to store the encoded
  representation of states
• Binary and Gray encoding use the minimum number
  of bits for state register
• Gray and Johnson code
• Two adjacent codes differ by only one bit
• Reduce simultaneous switching
• Reduce crosstalk
• Reduce glitch

24
One-hot Encoding

• Employ one bit register for each state
• Less combinational logic to decode
• Consume greater area, does not matter for certain
  hardware such as FPGA
• Easier for design, friendly to incremental change
  
• case and if statement may give different result
  for one-hot encoding
• Runs faster

• define state_0 3b001
• define state_1 3b010
• define state_2 3b100

25
Transistor Level Model
26
Static CMOS Circuits

• module cmos_inverter ( out, in )
• output out
• input in
• supply0 GND
• supply1 PWR
• pmos ( out, PWR, in )
• nmos ( out, GND, in )
• endmodule

Vdd
in
out
d
drain
source
gate
27
Pull Gates

• module nmos_nand_2 ( Y, A, B )
• output Y
• input A, B
• supply0 GND
• tri w
• pullup ( Y )
• nmos ( Y, w, A )
• nmos ( w, GND, B )
• endmodule

Vdd
Vdd
Y
Y
A
A
B
B
28
Assign Drive Strengths

• nand ( pull1, strong0 ) G1( Y, A, B )
• wire ( pull0, weak1 ) A_wire net1 net2
• assign ( pull1, weak0 ) A_net reg_b

• Drive strength is specified through an unordered
  pair
• one value from supply0, strong0, pull0, weak0 ,
  highz0
• the other from supply1, strong1, pull1, weak1,
  highz1
• Only scalar nets may receive strength assignment
• When a tri0 or tri1 net is not driven , it is
  pulled to indicated logic value with strength of
  pull0 or pull1
• The trireg net models capacitance holds a charge
  after the drivers are removed, the net has a
  charge strength of small, medium(default) or
  large capacitor

29
Signal Strength Levels

• Su0
• St0
• Pu0
• La0
• We0
• Me0
• Sm0
• HiZ0

Su1
St1
Pu1 La1 We1
Me1 Sm1 HiZ1
Supply Drive Strong Drive Pull Drive Large
Capacitor Weak Drive Medium Capacitor Weak
Capacitor High Impedance

• Signal strength signals ability to act as a
  logic driver determining the resultant logic
  value on a net
• Signal contention between multiple drivers of
  nets
• Charge distribution between nodes in a circuit
• Default strong drive
• Capacitive strengths may be assigned only to
  trireg nets

30
Strength Reduction

• Dependence of output strength on input strength
• Combinational and pull gate NO, except 3-state
  gates
• Transistor switch and bi-directional gates YES
• In general, output strength lt input strength

31
Transistor Switch and Bi-directional Gate

• Transistor switch
• nmos, pmos, cmos
• Bi-directional gate
• tran, tranif0, tranif1
• If input ( supply0 or supply1 )
• Output ( strong0, strong1 )
• Otherwise
• Output strength input strength

32
Signal Contention Known Strength and Known Value

• Signal with greater strength dominates
• Same strength, different logic values
• wand -gt and, wor -gt or
• Otherwise -gt x

We0
driver1
Pu1
Pu1
driver2
33
Synthesis
34
Unexpected and Unwanted Latch

• Combinational logic must specify output value for
  all input values
• Incomplete case statements and conditionals (if)
  imply
• Output should retain value for unspecified input
  values
• Unwanted latches

35
Example of Unwanted Latch

• module myMux( y, selA, selB, a, b )
• input selA, selB, a, b
• output y
• reg y
• always _at_ ( selA or selB or a or b )
• case ( selA, selB )
• 2b10 y a
• 2b01 y b
• endcase
• endmodule

b
selA
en
selB
y
selA
latch
selB
a
36
Synthesis of case and if

• case and if statement imply priority
• Synthesis tool will determine if case items of a
  case statement are mutually exclusive
• If so, synthesis will treat them with same
  priority and synthesize a mux
• A synthesis tool will treat casex and casez same
  as case
• x and z will be treated as dont cares
• Post-synthesis simulation result may be different
  from pre-synthesis simulation

37
Example of if and case

• input 30 data
• output 10 code
• reg 10 code
• always _at_(data)
• begin // implicit priority
• if ( data3 ) code 3
• else if (data2) code 2
• else if (data1) code 1
• else if (data0) code 0
• else code 2bx
• end

• input 30 data
• output 10 code
• reg 10 code
• always _at_(data)
• case (data)
• 4b1000 code 3
• 4b0100 code 2
• 4b0010 code 1
• 4b0001 code 0
• default code 2bx
• endcase

38
Synthesis of Register Variables

• A hardware register will be generated for a
  register variable when
• It is referenced before value is assigned in a
  behavior
• Assigned value in an edge-sensitive behavior and
  is referenced by an assignment outside the
  behavior
• Assigned value in one clock cycle and referenced
  in another clock cycle
• Multi-phased latches may not be supported in
  synthesis

39
Synthesis of Arithmetic Operators

• If corresponding library cell exists, an operator
  will be directly mapped to it
• Synthesis tool may select among different options
  in library cell, for example, when synthesize an
  adder
• Small wordlength -gt ripple-carry adder
• Long wordlength -gt carry-look-ahead adder
• Need small area -gt bit-serial adder
• Implementation of and /
• May be inefficient when both operands are
  variables
• If a multiplier or the divisor is a power of two,
  can be implemented through shift register

40
Static Loops without Internal Timing Controls gt
Combinational Logic

• module count1sA ( bit_cnt, data, clk, rst )
• parameter data_width 4 parameter cnt_width
  3
• output cnt_width-10 bit_cnt
• input data_width-10 data input clk, rst
• reg cnt_width-10 cnt, bit_cnt, i reg
  data_width-10 tmp
• always _at_ ( posedge clk )
• if ( rst ) begin cnt 0 bit_cnt 0 end
• else begin cnt 0 tmp data
• for ( i 0 i lt data_width i i 1 )
• begin
• if ( tmp0 ) cnt cnt 1
• tmp tmp gtgt 1 end
• bit_cnt cnt
• end
• endmodule

41
Static Loops with Internal Timing Controls gt
Sequential Logic

• module count1sB ( bit_cnt, data, clk, rst )
• parameter data_width 4 parameter cnt_width
  3
• output cnt_width-10 bit_cnt
• input data_width-10 data input clk, rst
• reg cnt_width-10 cnt, bit_cnt, i reg
  data_width-10 tmp
• always _at_ ( posedge clk )
• if ( rst ) begin cnt 0 bit_cnt 0 end
• else begin
• cnt 0 tmp data
• for ( i 0 i lt data_width i i 1 )
• _at_ ( posedge clk )
• begin if ( tmp0 ) cnt cnt 1
• tmp tmp gtgt 1 end
• bit_cnt cnt
• end
• endmodule

42
Non-Static Loops without Internal Timing Controls
gt Not Synthesizable

• module count1sC ( bit_cnt, data, clk, rst )
• parameter data_width 4 parameter cnt_width
  3
• output cnt_width-10 bit_cnt
• input data_width-10 data input clk, rst
• reg cnt_width-10 cnt, bit_cnt, i reg
  data_width-10 tmp
• always _at_ ( posedge clk )
• if ( rst ) begin cnt 0 bit_cnt 0 end
• else begin
• cnt 0 tmp data
• for ( i 0 tmp i i 1 )
• begin if ( tmp0 ) cnt cnt 1
• tmp tmp gtgt 1 end
• bit_cnt cnt
• end
• endmodule

43
Non-Static Loops with Internal Timing Controls gt
Sequential Logic

• module count1sD ( bit_cnt, data, clk, rst )
• parameter data_width 4 parameter cnt_width
  3
• output cnt_width-10 bit_cnt
• input data_width-10 data input clk, rst
• reg cnt_width-10 cnt, bit_cnt, i reg
  data_width-10 tmp
• always _at_ ( posedge clk )
• if ( rst ) begin cnt 0 bit_cnt 0 end
• else begin bit_counter
• cnt 0 tmp data
• while ( tmp )
• _at_ ( posedge clk ) begin
• if ( rst ) begin cnt 0 disable
  bit_counter end
• else begin cnt cnt tmp0 tmp
  tmp gtgt 1 end
• bit_cnt cnt
• end
• end
• endmodule

44
VHDL
45
Example

• -- eqcomp4 is a four bit equality comparator
• -- Entity declaration
• entity eqcomp4 is
• port ( a, b in bit_vector( 3 downto 0 )
• equals out bit ) -- equal is
  active high
• end eqcomp4
• -- Architecture body
• architecture dataflow of eqcomp4 is
• begin
• equals lt 1 when ( a b ) else 0
• end dataflow

46
Behavioral Descriptions

• library ieee
• use ieee.std_logic_1164.all
• entity eqcomp4 is port (
• a, b in std_logic_vector( 3 downto 0 )
• equals out std_logic )
• end eqcomp4
• architecture behavioral of eqcomp4 is
• begin
• comp process ( a, b ) -- sensitivity list
• begin
• if a b then equals lt 1
• else equals lt 0 -- sequential
  assignment
• endif
• end process comp
• end behavioral

47
Dataflow Descriptions

• library ieee
• use ieee.std_logic_1164.all
• entity eqcomp4 is port (
• a, b in std_logic_vector( 3 downto 0 )
• equals out std_logic )
• end eqcomp4
• architecture dataflow of eqcomp4 is
• begin
• equals lt 1 when ( a b ) else 0
• end dataflow
• -- No process
• -- Concurrent assignment

48
Structural Descriptions

• library ieee
• use ieee.std_logic_1164.all
• entity eqcomp4 is port (
• a, b in std_logic_vector( 3 downto 0 )
  equals out std_logic )
• end eqcomp4
• use work.gatespkg.all
• architecture struct of eqcomp4 is
• signal x std_logic_vector( 0 to 3)
• begin
• u0 xnor2 port map ( a(0), b(0), x(0) ) --
  component instantiation
• u1 xnor2 port map ( a(1), b(1), x(1) )
• u2 xnor2 port map ( a(2), b(2), x(2) )
• u3 xnor2 port map ( a(3), b(3), x(3) )
• u4 and4 port map ( x(0), x(1), x(2), x(3),
  equals )
• end struct

49
Test and Design For Testability
50
Single Stuck-at Fault

• Three properties define a single stuck-at fault
• Only one line is faulty
• The faulty line is permanently set to 0 or 1
• The fault can be at an input or output of a gate
• Example XOR circuit has 12 fault sites ( ) and
  24 single stuck-at faults

Faulty circuit value
Good circuit value
c
j
0(1)
s-a-0
d
a
1(0)
g
h
1
z
i
0
1
e
b
1
k
f
Test vector for h s-a-0 fault
51
Stuck-Open Example
Vector 1 test for A s-a-0 (Initialization vector)
Vector 2 (test for A s-a-1)
VDD
pMOS FETs
Two-vector s-op test can be constructed
by ordering two s-at tests
A
1 0
0 0
Stuck- open
B
C

0
1(Z)
Good circuit states
nMOS FETs
Faulty circuit states
52
Stuck-Short Example
Test vector for A s-a-0
VDD
PFETs
IDDQ path in faulty circuit
A
Stuck- short
1 0
B
Good circuit state
C

0 (X)
NFETs
Faulty circuit state
53
Test Pattern for Stuck-At Faults
Ygood (a?b?c)
SA1
Ya-SA1 (b?c)
No need to enumerate all input combinations to
detect a fault
Test pattern a,b,c 011
54
Fault Simulation

• Fault simulation Problem Given
• A circuit
• A sequence of test vectors
• A fault model
• Determine
• Fault coverage - fraction (or percentage) of
  modeled faults detected by test vectors
• Set of undetected faults
• Motivation
• Determine test quality and in turn product
  quality
• Find undetected fault targets to improve tests

55
Goal of Design for Testability (DFT)

• Improve
• Controllability
• Observability
• Predictability

56
Scan Storage Cell
Q, So
D
Si
SSC
N/T
SSC
Clk
Q
D
57
Integrated Serial Scan
PI
PO
SFF
SCANOUT
Combinational logic
SFF
SFF
Control
SCANIN
58
Interconnect Timing Optimization
59
Buffers Reduce Wire Delay
t_unbuf R( cx C ) rx( cx/2 C ) t_buf
2R( cx/2 C ) rx( cx/4 C ) tb t_buf
t_unbuf RC tb rcx2/4
60
Buffers Improve Slack
RAT 300 Delay 350 Slack -50
slackmin -50
RAT 700 Delay 600 Slack 100
RAT Required Arrival Time Slack RAT - Delay
RAT 300 Delay 250 Slack 50
Decouple capacitive load from critical path
slackmin 50
RAT 700 Delay 400 Slack 300
61
Slew Constraints

• When a buffer is inserted, assume ideal slew rate
  at its input
• Check slew rate at downstream buffers/sinks
• If slew is too large, candidate is discarded

62
Cost-Slack Trade-off
63
Wire Sizing Monotone Property

• Ancestor edges cannot be narrower than downstream
  edges

64
Area or Radius?
Radius the longest source-sink path length

• Dijkstras shortest path tree
• Short path to sinks
• Large total wire length

• Prims minimum spanning tree
• Small total wire length
• Long path to sinks

65
Area Radius Trade-off

• Find a solution in middle
• Not too much area
• Not too long radius
• How to find an ideal point?

66
Gate Characteristics
67
I-V Characteristics

• Cutoff region
• Vgs lt Vt
• Ids 0
• Linear region
• Vgs gt Vt, 0 lt Vds lt Vgs-Vt
• Ids B(Vgs-Vt)Vds V2ds/2
• Saturation region
• Vgs gt Vt, 0 lt Vgs-Vt lt Vds
• Ids B(Vgs-Vt)2/2
• B a W/L

d
g
s
Ids
Vds
68
Falling Time

• Falling time t1 t2
• t1 Vout drops from 0.9Vdd to Vdd-Vt
• t2 Vout drops from Vdd-Vt to 0.1Vdd
• Falling time rising time k
  C / (B Vdd)
• Delay Falling time / 2

69
Gate Power Dissipation

• Leakage power
• Dynamic power
• Short circuit power

70
Leakage Power

• Static
• Leakage current a ? Vdd
• Leakage current b/Vt
• Killer to CMOS technology

Vdd
Vdd
Leakage
out
out
Leakage
Linear
Saturation
71
Dynamic Power

• Occurs at each switching
• Pd CL?Vdd2?fp
• fp switching frequency

Vdd
Vdd
out
out
Linear
Saturation
72
Short Circuit Power

• During switching, there is a short moment when
  both PMOS and CMOS are partially on
• Ps Q?(Vdd-Vt)3?tr?fp
• tr rising time

Input falling
Vdd
Vdd
out
out
Input rising
73
Low Power Design
74
Clock Gating

• Gate off clock to idle functional units
• e.g., floating point units
• need logic to generate
  disable
  signal
• increases complexity of control logic
• consumes power
• timing critical to avoid clock glitches
  at
  OR gate output
• additional gate delay on clock signal
• gating OR gate can replace a buffer in the clock
  distribution tree

75
Active Power Reduction - Supply Voltage Reduction
Static
Dynamic

• Adjusting operation voltage and frequency to
  performance requirements
• High performance high Vdd frequency
• Power saving low Vdd frequency

• Pros
• Doesnt limit performance
• Cons
• Penalty of transition between different power
  states can be high (in performance and power)
• Additional control logic

• Pros
• Always active in saving
• Cons
• Additional power delivery network
• Needs special care of interface between power
  domains
• signals close to Vt excessive leakage and
  reduced noise margins

76
Dynamic Frequency and Voltage Scaling

• Always run at the lowest supply voltage that
  meets the timing constraints
• DFS (dynamic frequency scaling) saves only power
• DVS (dynamic voltage scaling) DFS saves both
  energy and power
• A DVSDFS system requires the following
• A programmable clock generator (PLL)
• PLL from 200MHz ? 700MHz in increments of 33MHz
• A supply regulation loop that sets the minimum
  VDD necessary for operation at the desired
  frequency
• 32 levels of VDD from 1.1V to 1.6V
• An operating system that sets the required
  frequency supply voltage to meet the task
  completion deadlines
• heavier load ? ramp up VDD, when stable speed up
  clock
• lighter load ? slow down clock, when PLL locks
  onto new rate, ramp down VDD

77
Design with Dual Vth
Dual Vth evaluation

• Dual Vth design
• Two flavors of transistors slow high Vth, fast
  low Vth
• Low Vth are faster, but have 10X leakage

78
Power Gating Using Sleep Transistors

• Or can reduce leakage by gating the supply rails
  when the circuit is in sleep mode
• in normal mode, sleep 0 and the sleep
  transistors must present as small a resistance as
  possible (via sizing)
• in sleep mode, sleep 1, the transistor stack
  effect reduces leakage by orders of magnitude

• Or can eliminate leakage by switching off the
  power supply (but lose the memory state)