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COEN6511 LECTURE 9
Digital Circuit Hierarchy
Static Circuit:
In General, digital circuits are divided into two classes:
Combinational: The outputs are function of the inputs only.
Sequential: The outputs are a function of the inputs as well as the states of the circuit.
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Lecture#9 Overview
CMOS Combinational Logic
Shown in figure below, is the general structure of this family of circuits. It has two major
parts, the path to VDD, through the pull up network and the path to Vss through the pull
down network. The pull up is a pmos network, while the pull-down is an nmos network.
Each gate will take 2N transistors, where N is the number of inputs.
Simple Example: an inverter
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Lecture#9 Overview
 2-input NAND Gate
The NAND gate has two nmos transistors in series in the pull-down
and two pmos transistors in parallel in the pull-up network as shown
below.
The basic functionality of a 2-input NAND gate is given in the figure above Whenever
input A is ‘0’ and for any value of B, transistor A is active and will conduct, pulling the
output node high. Similarly, whenever input B is ‘0’ and irrespective of input A,
transistor B will drive the output node high. The only time that the output is low is when
both A and B are high, in which case the pull down network will become active at the
same time, pulling the output node low. This behavior is typical of ‘inverting logic’.
 3-input NAND Gate
Increasing the pull-down and the pull-up series and parallel networks transistors by
one as shown in the diagram the 3-input NAND is constructed.
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Lecture#9 Overview
 2-input NOR gate
2-input NAND Gate Sizing
Consider the following circuit
What will be the optimum size of the transistors which can optimize the circuit in terms
of power, delay and area?
The Aspect Ratio of an inverter is made to be Wp/Wn =µr (the mobility ratio) so that the
pull up and the pull down have the same drive strength, ie the same resistance.
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Lecture#9 Overview
The aim is to equalize rise and fall time, assuming that minimum width of an inverter is
Wp
Wnmin. for tr=tf ,
  r let Lp=Ln=Lmin. That is, if  r =3, then Wp = 3Wn. Then, the
Wn
sizing of Wn and Wp is shown in the figure above.
NOTE
This is an approaximate method. Approaximating PD and PU network by a single
transistor is wrong due to body effects of different regions of the circuit and internal
node capacitances.
Sizing of Transistors
Generally, assume Ln=Lp=Lmin unless otherwise stated,
For series pass transistors,
W
W
W
) effec  [( 1 ) 1  ( 2 ) 1 ]1 , that is we add the lengths together ie increase in
L
L1
L2
resistance. Please note this is an approximation method.
(
For parallel pass transistors,
W
W
W
) effec  ( 1 )  ( 2 ) , that is we add the
L
L1
L2
widths together. ie increase in
conductance.
(
VTC and the impact of transistor
sizing
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Lecture#9 Overview
With one input being ‘0’ or ‘1’, only one transistor is on while with two inputs being
“00”, two transistors become on, increasing the effective width to 2Wmin. Similarly, with
an input of “11”, the 2 NMOS transistors are on and this will divide the length by two
giving Weff=1/2.
Weff pull - up
2

4
Weff pull - down 1 / 2
To obtain the same VTC and noise margin as with an equivalent inverter, Wn and Wp
need to be adjusted so as to give equal rise and fall time or Wp =  r Wn effective.
2-input NOR Gate Sizing
Since the PMOS transistors are in series, the resistance adds up. As such, we need to
multiply the width in order to reduce resistance. That is, for Wn=Wn min in this circuit,
Wp=6Wmin, where 6 = 2x3, 2 for resistance and 3 for  r .
NOTE
Design Technique
NOR gates are costly. For the same performance (computation efforts), it results in
increased area, power, delay, output load capacitance (due to an increase in drain
diffusion capacitance) and increase in input capacitance presenting higher load to driver
circuits. Convert your circuit to NAND whenever you can and avoid use of large fanin
NOR.
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Lecture#9 Overview
Complex Gates Design
Implement the following Boolean function:
F  A  B  (D  C)
The general idea is to start with the pull down structure, using series transistors for
“AND” and parallel transistors for OR as shown below. Transistor sizing is done for the
pull up path and pull down path to be equal to the design inverter. In the circuit below we
have sized the transistors for r of 2.
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Lecture#9 Overview
Transistors sizing is performed, now we look at the transistors ordering!
By replacing the branches, we may obtain a better performance for the same function. In
this circuit, put the smaller drain capacitances nearer to the output node.
Now we have a better circuit implementation as there are less drain
capacitances at the output node.
Please also note that even a better circuit can be obtained if we place the
transistors according to the signal arrival, with the ltest arriving signal
nearer to the output. This will be covered later.
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Lecture#9 Overview
Ratioed Logic (Pseudo NMOS)
The circuit uses N+1 transistors to implement a function, where n is the number of the
inputs. The pull-up is a single pmos with the rest of the pull down consists of nmos
transistors, thus saving in area greatly.

2-input NAND Pseudo NMOS

2-input NOR Pseudo NMOS
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Lecture#9 Overview
Complex Gates Design
F  A  B  (D  C)
The same design methodology applies here. Select
an optimum pseudo NMOS inverter and optimize
your gate accordingly.
Design technique
Remember that this is a ratioed logic, therefore the pull-down transistor/pull-up resistance
has to be calculated to give Vol<Vtn, where the value could be Vtn/2.
R pd
V
*Vdd  tn
R pd  R pu
2
Advantages of using Pseudo NMOS are: Saving in area, faster depending on design.
Disadvantages: Static power dissipation, short circuit current, reduced noise margin.
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Lecture#9 Overview
Cascode Logic Family
Block diagram of a DCVS circuit (Differential Cascode Voltage Swing)
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Lecture#9 Overview
Example of Cascode Logic
A signal from one gate to the next is always transferred with its complement.
During switching a current spike takes place. This current is usually larger than that of a
complementary logic.
This logic is fully compatible with complementary logic because the output makes a full
swing between Vdd and Vss.
Both output and its complement are present.
The circuit uses mainly nmos transistors.
Slower than conventional complementary gate because during switching the pull-ups
have to “fight” the n pull-down trees.
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Lecture#9 Overview
A static Cascode (CVSL) complex logic gate
F  ( A  B)  C  ( D  E )
The load for a static DCVS
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Lecture#9 Overview
The DCVS trees for a full adder Sum and Carry Pull-Down Networks
S’(A,B,C) = A’BC’ + A’B’C + ABC + AB’C’
S (A,B,C) = A’B’C’ + A’BC + ABC’ + AB’C
C(A,B,C) = AB + BC + AC
END OF LECTURE #9
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Lecture#9 Overview