Shankar Balachandran*

Associate Professor, CSE Department

Indian Institute of Technology Madras

*Currently a Visiting Professor at IIT Bombay

Digital Circuits and Systems

Spring 2015 Week 6 Module 33

Timing Sequential Circuits

Analysis and Design of Sequential Logic Circuits 2

Sequential Circuit Timing

Once the functionality of a sequential network is designed,

its timing parameters must be determined. Timing problems

can be very subtle because timing parameters can vary with

device age and other operating conditions.

Analysis and Design of Sequential Logic Circuits 3

Global setup time (Tsu)

Global hold time (Th)

Maximum clock frequency

Clock skew.

These parameters are derived using the circuit (known) delays

described below.

tio – delay from input of IFL to output of OFL

tif – delay from circuit inputs of flip-flop inputs

tfo – delay from flip-flop outputs to circuit outputs

tff – delay from flip-flop outputs to flip-flop inputs

tc-q– clock to Q propagation delay of flip-flops

tsu – setup time of flip-flops

th – hold time of flip-flops

tc – clock delay; time required for clock to reach all flip-flops

Timing Parameters

Analysis and Design of Sequential Logic Circuits 4

X (at sequential circuit input)

Changes that occur at inputs can be delayed by as much as

maximum tif by the time they reach the flip-flop inputs. Hence,

we want to setup circuit inputs relative to clock edge appearing

at the flip-flops.

Similarly, hold time of the circuit inputs relative to the system

clock at the source is given by

max max minifu su cs t t tT

max min maxh if chT t t t

Global Setup and Hold Times

Tsu Th

th

tsu

CLK (at clock source) tc

CK (at FF clock input)

tif

tif

D (at FF input)

Analysis and Design of Sequential Logic Circuits 5

Maximum Clock Frequency

For an edge-triggered circuit: minimum clock period is,

Maximum Clock Frequency:

C Q ff sumax maxmax

clk t t tT

clk

clkT

f1

Comb.

logic

Λ

Qi Di

Qj Dj

CKi

CKj

tff

Λ

CLK

tsu

Tck (=Tclk)

CKi

Edge Triggering

tff

Dj

Qi

tC-Q

Analysis and Design of Sequential Logic Circuits 6

Timing Violations

The clock period (Tclk) has a lower bound of tff.max .

If the clock period is equal to (tff.max + tC-Q.max) then the

flip-flop state changes can violate setup times.

Remedy :

Use faster flip-flops (decrease tC-Q )

Use faster gates (decrease tff )

Use a slower clock (increase clock period, Tclk)

max maxmaxfC fl uc k Q st tT t

Analysis and Design of Sequential Logic Circuits 7

The previous discussion assumes that clock signals

arrive at all flip-flops simultaneously - this is not a good

assumption since it is not true in practice.

Because of different wire lengths over which the clock

signals travel and the load at the destination, there is a

slight difference in clock arrival times at different flip-flop

inputs.

Clock skew, tskew, is the difference in time between

triggering edges seen at different flip-flops. Clock skew

affects minimum Tclk.

Clock Skew

Analysis and Design of Sequential Logic Circuits 8

Therefore, for an edge-triggered circuit with clock skew,

Clock skew is a significant factor in determining the speed of high-

performance synchronous circuits. The larger the skew, the slower the circuit will operate.

max max max maxclk skew C Q ff suT t t t t

Max. Clock Frequency with Skew

tskew

Comb.

logic

Λ

Qi Di

Qj Dj

CKi

CKj

tff

Λ

CLK

tsu

Tck (=Tclk)

CKi tskew

CKj tC-Q

Qj tff

Di

Analysis and Design of Sequential Logic Circuits 10

For the circuit given below determine all the sequential

circuit timing parameters.

For a D flip-flop use: tsu = 2ns, th = 15ns and tC-Q = 20ns

For a NAND gate use: tp,max = 10ns and tp,min = 3ns

Timing Analysis Example

Analysis and Design of Sequential Logic Circuits 11

.

nstt

nstt

nstt

nstt

nstt

nstt

nandpc

nandpc

nandpff

nandpff

nandpif

nandpif

62

202

62

202

62

303

min,,min,

max,,max,

min,,min,

max,,max,

min,,min,

max,,max,

,max ,max ,min

,max ,min ,max

,max ,max ,max

,max

2 30 6 26

20 15 6 29

20 20 2 42

1/ 42 23.8

su su if c

h h if c

clk C Q ff su

clk

T t t t ns

T t t t ns

T t t t ns

f ns MHz

For a D flip-flop use: tsu = 2ns, th = 15ns, tC-Q = 20ns

For a NAND gate use: tp,max = 10ns, tp,min = 3ns

Analysis and Design of Sequential Logic Circuits 12

Sequential Systems Using Latches

Latches can be used to create sequential systems. However, since these

are level-triggered clocking must be done carefully – must ensure that state

changes only once per clock cycle.

Use narrow-width clock whose pulse width is less than the fastest possible path

through the combinational logic.

To guarantee correct next state, make sure that the clock period is longer than the

worst-case propagation delay through the combinational logic.

Comb.

logic Qi Di

Qj Dj

CKi

CKj

tff CLK

tw < tff.min+ tD-Q.min

> (tD-Q.max + tff.max+ tsu.max)

CLK

Analysis and Design of Sequential Logic Circuits 14

Clocking Frequency with Latches

Tclk

tskew

Comb.

logic Qi Di

Qj Dj

CKi

CKj

tff CLK

tsu

CKi

tD-Q

Q

j tff

Dj

tskew

CK

j

Di

max min max max maxclk skew w su D Q ff suT t t t t t t

tsu

tw

End of Week 6: Module 33

Thank You

Intro to State Machines 15