04/21/23

Based on text by S. Mourad "Priciples of Electronic Systems" and M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory and Mixed-Signal

VLSI Circuits

Digital Testing: Role of Simulation in Testing

Outline

Verification and Simulation Verification Types of Simulation Fault Simulation Parallel Simulation Concurrent Simulation Deductive Simulation Fault Coverage Fault Dictionary

Types of simulation

Event is a change in signal valueUseful for accurate timing modelsUseful for asynchronous circuits

Compiled simulator (table-driven)

• Functional verification

Activity directed (event-driven)simulator

Types of Simulators

Logic versus Fault Compiled versus event driven Functional versus timing Logic versus other levels (RTL or switch) Mixed level Emulators

Simulation of Large Systems

Explosion in number of gates usedNot possible with software to complete

Move to simulation of the whole circuit on

RTL level e.g. use of testbench in HDL

Cycle based Simulationsimulation of components at different levels using different simulatorrelate the results using the same clock

Simulation System

StimuliDesignModel

Simulator

Response

Library

Testbench: Example in Verilog

' timescale 1ns/1ns // Time unit is 1nsmodule adder; // Design Testbenchreg PA, PB, PCI;wire PCO,PSUM;

FA_Behav F1(PA, PB, PCI, PSUM,PCO); // Instantiate module under test

initialbegin: ONLY_ONCEreg[3:0] Count; // Count hold the count of stimuli

//4 bits are needed to accommodate up to 8.

for (Count=0; Count < 8; PAL =Count +1)begin{PA, PB, PCI} =Count; //The stimuli are the values of Count

#5 $display ("PA, PB, PCI=%b%b%b", PA, PB, PCI,":::PCO,PSUM=%b%b", PCO, PSUM);

//Creation of the response display

endendendmodule

Logic Simulation

Verifies both function & timing Check that operation is :

independent on initial statenot sensitive to variations in delaysfree of races, oscillations, illegal & hung-up states

Logic Simulation Software Based

Slow

Hardware AcceleratorsSimulation algorithm is

hardwiredImproves performance with

large set of inputs

EmulatorPrototyping and real time simulatione.g. using FPGAs to implement the designPentium was emulated on 3500 Xilinx3000 FGPAs

EPROM Emulator

Logic Simulation Levels

Circuitdescription

Programminglanguage-like HDL

Connectivity ofBoolean gates,flip-flops andtransistors

Transistor sizeand connectivity,node capacitances

Transistor technologydata, connectivity,node capacitances

Tech. Data, active/passive componentconnectivity

Signalvalues

0, 1

0, 1, Xand Z

0, 1and X

Analogvoltage

Analogvoltage,current

Timing

Clockboundary

Zero-delayunit-delay,multiple-delay

Zero-delay

Fine-graintiming

Continuoustime

Modelinglevel

Function,behavior, RTL

Logic

Switch

Timing

Circuit

Application

Architecturaland functionalverification

Logicverification

and test

Logicverification

Timingverification

Digital timingand analogcircuitverification

0 1 X0 0 01 1 1X 0 1 X

A cube of the Boolean function is a vector

A simplified truth table based on singular cubes is called a singular cover

Rules for intersection of cubes in Boolean logic

Z x x xn( , ,..., )1 2

{( , ,..., | ): ( , ,..., )}v v v v v Z v v vn z z n1 2 1 2

Singular cover

ExerciseCheck if the following cubes describe a logic functionC1 1 1 x 0C2 0 1 0 1C3 0 x 1 1C4 0 0 x 0

ExerciseCheck if the following cubes describe a logic functionC1 1 1 x 0C2 0 1 0 1C3 0 x 1 1C4 0 0 x 0

No, since 001 would cause 2 different output values as it belongs to both c3 and c4

( , , ) ( , , ) ( , , )

( , , ) ( , , ) ( , , )

0 0 1 0 1 0 0 1 1

0 0 1 0 0 0 0 1 0

x output

x output

Unknown logic value

Initial state of powered-up FF & RAMs is unpredictableu -- denotes unknown logic value (0 or 1)Boolean operation with u is a union of all operations on different values like

OR(0,u)=OR{{0},{0,1}}={OR(0,0),OR(0,1)}={1,0}=u 0 1 X U0 0 0 1 1 1 X 0 1 X UU U U

Intersection of cubes in 3 valued logic

u

1

u0

u

u

u

Pessimistic result in 3-valued simulation

Since not(u) = u

Determine value of the logic function defined by the following cubesa) X10 0b) 11X 0c) X0X 1d) 0 1 1 1

For the input vector I=(10u) using simulation

Exercise

True-Value Simulation Algorithms

Compiled-code simulation• Applicable to zero-delay combinational logic

• Also used for cycle-accurate synchronous sequential circuits for logic verification

• Efficient for highly active circuits, but inefficient for low-activity circuits

• High-level (e.g., C language) models can be used

Event-driven simulation• Only gates or modules with input events are evaluated (event

means a signal change)

• Delays can be accurately simulated for timing verification

• Efficient for low-activity circuits

• Can be extended for fault simulation

Compiled-Code Algorithm

Step 1: Levelize combinational logic and encode in a programming language

Step 2: Initialize internal state variables (flip-flops)

Step 3: For each input vectorSet primary input variables

Repeat (until steady-state or max. iterations)

• Execute compiled code

Report or save computed variables

Levelization for Compiled Simulation

G4

G5 G8

G6

G7 G9

G3

G10

G2

G1CD

E

G

IJ

H

AB

Level 0 Level 1 Level 2 Level 3 Level 4

F

Event-driven simulation flow

Advance simulation time

Propagate events

Schedule resulting events

Evaluate activated elements

Update values

Determine current events done

No more events

Delay models

(a) Nominal transition-independent

transport delay

(b) Rise and fall delays

(c) Ambiguous delay

(d) Inertial delay (pulse suppression)

(e) Output inertial delay

A

C

C

C

C

C

3

2 3

1 5

3

R1 R21

(a) d=2

(b) dr=1, df=3

(c) dm=1, dM=3

(d) dI = 4,

(e) dI=2, d=3

A

B=1

C

Delay models(a) Nominal transition-independent transport delay

(b) Rise and fall delays

(c) Ambiguous delay

(d) Inertial delay (minimum duration of input pulse)

(e) Output inertial delay

3

Output inertial delay

A

B

C

dI = 3

A

B

C

2

3 2

The gate cannot produce impulse shorter than dI

A

B

C

2

2 1

3 3

Output inertial delay

dI = 3

A

B

C

d1

d2

Wire delays modeled by delay elements

c x x c ix c x c ix x c c ic’ c’ c’ c’ i

c iAND 0 0OR 1 0NAND 0 1NOR 1 1

Truth tables• quires 2n entriesInput Scanning• gates described by

- c -- controlling value- i -- inversion

Element evaluation

Evaluate (G, c, i)begin

u_values = FALSEfor every input value v of G

beginif v = c then return c iif v = u then u_values = TRUE

endif u_values return ureturn c’ i

end

Gate evaluation in 3-valued logic by scanning input values

evaluate (G, c, i)begin

if c_count > 0 then return c iif u_count > 0 then return ureturn c’ i

endAdvantage:No need to store the multiple input values (only two counters for c_count and u_count are updated during simulation)For instance in AND gate 1->0 change on its input increases c_count while 0->u transition increases u_count and decreases c_count.

Gate evaluation in 3-valued logic based on input counting

Hazard Detection

R Q

S

AB

Z

(Static hazard)

A

B

Z

Latch may be reset

Unknown signal value

B

t t’ t+1

==> B(t)B(t’)B(t+1) = 0u1

Also : A(t)A(t’)A(t+1) = 1u0

Z = (AB)’ = 1u1 {101, 111}- possible static hazard

Static Hazard DetectionDenote by E the set of inputs changing between t and t+1

Procedure 3.11. Set every input E to u and simulate to get output Z(t’)2. Set every input E to its value at t+1 and simulate to get Z(t+1)

Theorem 3.1In a combinational circuit, a static hazard exists iff Z(t)Z(t’)Z(t+1) is 1u1 or 0u0

Hazard Detection

(a) 0 delay : B = 101, C = 000 (b) unit delay : B = 1101, C = 0100(c) arbitrary delay : A = 0u1u0, B = 1u0u1

=> C = 0u0u0 (hazard)

CA

B

If A = 010 then:

Check the following circuit for static hazards

6-valued logic for static hazard analysis

Value Sequence(s) Meaning0 000 Static 01 111 Static 10/1, R {001, 011} = 0u1 Rise (0 to 1) transition1/0, F {110, 100} = 1u0 Fall (1 to 0) transition0* {000, 010} = 0u0 Static 0-hazard1* {111, 101} = 1u1 Static 1-hazard

AND 0 1 R F 0* 1*0 0 0 0 0 0 01 0 1 R F 0* 1*R 0 R R 0* 0* RF 0 F 0* F 0* F0* 0 0* 0* 0* 0* 0*1* 0 1* R F 0* 1*

AND truth table for 6-valued logic

Dynamic Hazards

Dynamic hazards occur during transition 1->0 or 0->1So they require 4 bit sequences to detect1010 or 0101

To detect them in simulation 8 valued logic is used.8 valued logic can detect both static and dynamic hazards

8-valued logic Logic value

Output Sequence Meaning

0 0000 Static 0 1 1111 Static 1 0/1, R {0x11, 00x1} Rise 1/0, F {11x0, 1x00} Fall 0* {0ux0, 0xu0} Static 0 hazard 1* {1ux1, 1xu1} Static 1 hazard R* {0u01, 01u1} Dynamic 1 hazard F* {1u10, 10u0} Dynamic 0 hazard

ExerciseTo determine result of Boolean operation in 8 valued logic all possible sequences must be used

For instance to calculate AND(R,1*) we have

AND(R,1*)=AND({0x11,00x1},{1ux1,1xu1})={0uu1,00u1}=R*

Rules for inversion

NOT(F)=R, NOT(0*)=1*, NOT(F*)=R*

NAND 0 1 R F 0* 1*0 1 1 1 1 1 11 1 0 F R 1* 0*R 1 F F 1* 1* FF 1 R 1* R 1* R0* 1 1* 1* 1* 1* 1*1* 1 0* F R 1* 0*R* 1 F* 1* 1* F*

F* 1 R* 1* R*

R* F*1 1F* R*

F* 1*1* R*

1* 1* 1*F* R*

NAND truth table for 8-valued logic

Exercise: Calculate NAND(R,R*)

NAND 0 1 R F 0* 1*0 1 1 1 1 1 11 1 0 F R 1* 0*R 1 F F 1* 1* FF 1 R 1* R 1* R0* 1 1* 1* 1* 1* 1*1* 1 0* F R 1* 0*R* 1 F* 1* 1* F*

F* 1 R* 1* R*

R* F*1 1F* R*

F* 1*1* R*

1* 1* 1*F* R*

NAND truth table for 8-valued logic

Exercise: Calculate NAND(R,R*)NAND(R,R*) = NAND({0x11,00x1},{0u01,01u1}) =NOT({0u01,01u1,0001,00u1}) ={1u10,10u0,1110,11u0}=F* Exercise:

Calculate NAND(F,R*)

Event-Driven Procedure Event-Driven-Simulator:

Read circuit descriptionRead input vectorsFOR each input vector to be simulated DO

Process new inputsUpdate input nodesSchedule connected elements on timing wheelWHILE elements left for evaluationEvaluate elementIF change on the output

THEN update all fanouts and schedule Connect element on timing wheel

END WHILE END FOR

End procedure

Gate level event-driven simulationOnly the activated gates are analyzed.Not all entries in the event list are events

AB

Z

A

B

Z 0 2 4 6 8 10 12

8 10 12(Z, 1) (Z, 0) (Z, 0) Not an event

Event Simulation

G4

G5

G6

G7 G9

G3

G10

G2E

G(1)

I(1)J(1)

H(1)

A(0)

B(0)

(1 => 0)

*

**

**

F(1)

(0 => 1)

11

1

0

0

0G1C(0)

D(0) G8 *0

While (event list not empty)begin t = next time in list process entries for time tend

There is no events on G3, G5, G7, G8, and G9 due to F=1

Time Wheel (Circular Stack)

t=0

1

2

3

4

5

6

7

maxCurrenttimepointer Event link-list

The Time Wheel

Time in ns is computed modulo M = tc mod Mfor events tc te tc + M-1

If tc+ M te then the event is put on the overflow queue

1

tc

M

i, vi’ j, vj’ *

Event-Driven Algorithm(Example)

2

2

4

2

a =1

b =1

c =1 0

d = 0

e =1

f =0

g =1

Time, t 0 4 8

g

t = 0

1

2

3

4

5

6

7

8

Scheduledevents

c = 0

d = 1, e = 0

g = 0

f = 1

g = 1

Activitylist

d, e

f, g

g

Tim

e s

tac

k

Timing Simulation

(a)

G

AND1

AND2

OR1

INV

A

B

C

D=1

C'

E

F

Delay

14 17

11 18 30 36 4526

37 404530

2620

22 24

38 41

E

F

G

XXXXXXXXXXXXXX

XXXXXXXXXXXX

XXXXXXXXXXXXXXXXXXXX

(b)

(d)

8 11

14 22 32 334

7 12 20 25

35

35

3631

30

21

20

13

122

3

10 255

A

B

C

C'

E

F

12 16

10 18 28 36 42

15 17 22 23 32 41 48

G

E

F

G

XXXXXXXXXXXX

XXXXXXXX

XXXXXXXXXXXXX(c)

Unit delayVariable delayRise and fall delay

Static Timing Simulation Critical path delay

Using the circuitand worst case analysis of delayslow complexity

ProblemsNo consideration for the functionFalse path

Oscillation Control

Local oscillation can be controlled by setting unstable feedback signals to uGlobal oscillations are hard to control -- they are avoided by limiting the simulation time.

When oscillation occur during simulation they waste simulator efforts – the same loops are traversed again and again

Other logic values

Tristate logic -- several devices share a bus. Each driving device is controlled by the enable signal E. Simulator should report potential conflicts when a bus is driven by 0 and 1

0 1 Z u

0 0 uc 0 u

1 uc 1 1 u

Z 0 1 Z u

u u u u u

Other logic valuesMOS logic -- Transmission gates act like bus driver, except when the gate is open the wire connected to its output retains its previous value.

u

0 1

Zu

Z0 Z1

Z

Relative strength of logic values used in MOS Simulation.

Weak values are caused by open circuits

Logic Strength

G1 G2A

S

B

S'

Signals A and Bmay be undetermined if S=1 depending on the drivers strength

Exercise for MOS simulation

AI

B

E

D H

G

C

F

Use inputs from the following table to find signals C,F,H,I

A B D E G

1 1 0 1 01 0 0 1 10 1 1 0 11 0 1 0 0

Exercise for MOS simulation

AI

B

E

D H

G

C

F

Use inputs from the following table to find signals C,F,H,I

A B D E G

1 1 0 1 01 0 0 1 10 1 1 0 11 0 1 0 0

C F H I

0 1 0 1Z0|1 1 0 01 Z1|1 0 0Z1 Z1 0 0