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COEN 451 Week_11

(A. review of pass logic) Pass Gate Logic The pass gate logic uses the pass gate or transmission gate to build a logic circuit.

Reviewing these two devices:

nMOS pass gate

NMOS passes good logic ‘0’

CMOS

TRANSMISSION GATE (TG)

PMOS passes good logic ‘1’

Together they cover the range of input from “0” to “1”.

The logic is built around series and parallel pass gates followed by an inverter.

Examples

AND, NAND

C=1 OUT=A

C=0 OUT=NO OUTPUT (OPEN CIRCUIT)

A B F

0 0 0

0 1 0

1 0 0

1 1 1


OR, NOR

A multiplexer

XOR

The ideal number of series pass gates is 4. More than this the delay will be impractical.

This is as a result of added series resistance and capacitance, rendering the circuit useless

for long chains. There is also charge distribution problems associated to such circuits.

Delay calculation

Consider the following circuit,

This is equivalent to:

A B F

0 0 0

0 1 1

1 0 1

1 1 1

C A B F C A B F

0 0 0 0 1 0 0 0

0 0 1 1 1 0 1 0

0 1 0 0 1 1 0 1

0 1 1 1 1 1 1 1

A B F

0 0 0

0 1 1

1 0 1

1 1 0


where each transmission gate is represented by its lumped

equivalent RC delay.

For such a circuit, the NMOS and PMOS transistors are

modeled as resistances in parallel.

The resistance is obtained from the linear Id formula for NMOS and PMOS,

If,

eq

eq

nptnDDeq

tptn

tpDDptnDDn

eq

eq

GR

BBVVG

VV

VVBVVR

G

1

))((

),()(1

The capacitance is obtained by assuming both transistors’ drain capacitances to be in

parallel,

)(2 dpdneq CCC

2

)1(**

nnCRDelay eqeq

Where n is the number of sections/pass gates/transmission gates.


Long chain of transmission gates is not desirable and is usually broken to small sections

with an inverter placed in between. If we have n transmission gates and m transmission

gates per sections, then the delay is:

buffereqeqeqm

nmnRC )1(]

2

)1([69.0

And the optimum value of m is: eqeq

bufferp

optRC

tm

7.1

Usually m cannot be too long, for CMOSIS4 (0.5um), it is about 3 to 4 transmission gate

per section.

The transmission gate can be of minimum sized transistors without affecting the

delay greatly. This also improves power, however it will affect the signal quality.

Four to one multiplexer using pass gates

The weak pull up at the end of the MUX is to supplement the current input to the inverter.

It is a weak pMOS with the smallest dimension or longer length. (Note that the

arrangement now is ratioed logic and the sizes of the transistors have to be calculated

for correct gate operation).


Increasing Drive capability in steps

The current drive capability of an inverter can be made to increase by adding parallel

transistors in the pull-up or down section of an inverter instead of making the width

bigger. This technique enhances the modularity of the design.


Tri-state buffer

The following circuit describes the principle of a tri-state buffer (inverter). When EN is

“LOW” the circuit works as an inverter and when EN is “HIGH” the output is floating.

XOR-NOR based on transmission gates


XNOR with driving output

XOR with driving output

Programmable Logic Array (PLA) design

Any combinational circuit can be described by a Sum of Products (SOP). Thus their

implementation is a two level structure of “AND” followed by an “OR”. Many

combinational circuits are designed in regular structures as PLAs


Example

Implement the following functions using the PLA method

cbabcy

acy

baabcy

3

2

1

Conventional CMOS will be difficult to implement this function in terms of regularity.

We will use pseudo-NMOS to implement the above functions due to its simplicity of

construction. The actual design is simpler if it is done in an inverted form. So change the

design from AND-OR to a NOT-NOR-NOR-NOT design.

Consider y1,

)()(

)()(

1

1

1

1

1

bacbay

bacbay

baabcy

baabcy

baabcy

Inverted output

Inverted input NOR

NOR

The implementation is as follows:


The transistor level implementation:

The CMOS layout implementation:


Latches, Flip Flops and Timing

Clocked sequential circuits using transmission gates

Single clock are not suitable for finite state machine applications.

Problem: Dependence of operation on the propagation delay of the combinational circuit

and the feedback path.

For correct operation, TW cl

That is, use a narrow clock pulse, to block the feedback path from changing the state

again (Impractical),. ie, select clW so that the signal does not go through the pass gate

(for the faster combinational block in the pipeline!).

Select Tcl so that the CL has enough time to settle time within one clock period

otherwise, the next clock comes and clocks un-settled values; putting these together,

TW cl

The first problem is remedied by using a two-clock system or use single clock and its

inverted version. The second problem is treated by making cl small either by parallelism

or pipelining or with somehow faster circuits (Carry look-ahead instead of ripple adder

for example).


Let us have another look at the clock.

One single clock to synchronize operations

Suitable for simple applications


Complementary single phase clocking

Race condition in single phase clocking can be avoided by using complementary single

phase clocking scheme.

Condition to achieve proper operation:

Tcl

Problem: Clock Skew


Two-phase Non-Overlapping clocking

To eliminate race problem

The difference between the D-Latch and flip flop can be shown in the set of diagrams

below:


Determining the set up hold time for the Master Slave Flip-Flop

Data arrives at D, and passes through G4,G5,G6. because CP= “0”

Data waits at input of Gate G3 until the CP = ”1” when data travels to the slave.

We have to hold the data stable for a period when the clock is changing (worst case).

The widths of the clock have to be sufficient to allow the latching of the data in each

section of the Master-Slave arrangement thus:

Setup time=G4+G5+G6

Hold time=G1+G2

W1=G5+G6+G3

W2=G9+G10+G7

Cycle time=W1+W2


Edge Triggered FlipFlop


CMOS latch circuits

a)Dynamic

b) Static latch with cross-coupled circuit

c) Static latch with clocked feedback


d) Buffered static latch with clocked feedback

CMOS two phase double latch circuits

a)Dynamic

.

b) Static unbeffered


c) Static buffered

.

D Flip-Flop with direct set and clear


Data is accepted when C is low and transferred to the output on the positive-going

edge of the clock. The asynchronous clear direct and set direct are independent and

override the clock.

Input Output

SD CD D C O O’

H L X X H L

L H X X L H

H H X X H H

On+1 O’n+1

L L L

L H

L L H

H L


JK Flip-Flop

Input Output

SD CD C J K O O’

H L X X X H L

L H X X X L H

H H X X X H H

On+1 O’n+1

L L

L L No Change

L L H L H L

L L L H L H

L L H H O’n On

.

coen 451 week 11 (a. review of pass logic)users.encs.concordia.ca/~asim/coen...

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