vlsi 2 unit.pdfvlsi unit 2 important notes for ece department

EC8095 – VLSI DESIGN
UNIT II: COMBINATIONAL MOS LOGIC CIRCUITS
Question and Answer
1. Draw the static CMOS logic circuit for the following expression
(a) Y=(A.B.C.D)’
(b) Y=(D(A+BC))’
2. Sketch a combinational function Z=[A(B+C)+DE]’ using
(i)Pseudo-nMOS logic
(ii) Static CMOS logic

3. Write short notes on i) Ratioedcircuits ii) Dynamic CMOS circuits.

ii) Dynamic CMOS circuits.
 Contention in Dynamic gate during Precharge mode is overcome by connecting
foot transistor between pulldown and ground potential.

4. Sketch a combinational function Y = (A(B+C+D)+ EFG) ’ using
(i)Domino logic
(ii)Cascode voltage switch logic.

5. Design a 2-input multiplexers using DPL, DCVSPG and CPL
circuit families.
6. List out the limitations of pass transistor logic. Explain any two
techniques used to overcome the drawback of pass transistor logic
design.
Pass transistor logic
 In the circuit families we have explored so far, inputs are applied only to the gate
terminals of transistors.
 In pass-transistor circuits, inputs are also applied to the source/drain diffusion
terminals.
 These circuits build switches using either nMOS pass transistors or parallel pairs of
nMOS and pMOS transistors called transmission gates.

CHARACTERISTICS OF PASS TRANSITORS
Techniques used to overcome the drawback of pass transistor logic
design.
 When an nMOS or pMOS is used alone as an imperfect switch, we sometimes call it a pass
transistor.
 By combining an nMOS and a pMOS transistor in parallel we obtain a switch that turns on
when a 1 is applied to g in which 0s and 1s are both passed in an acceptable fashion.
 We term this a transmission gate or pass gate.
7. Explain about CVSL logic with suitable example. What are the
drawbacks of this logic?
CVSL : Cascode Voltage Switch Logic
 Cascode Voltage Switch Logic seeks the benefits of ratioed circuits without the static
power consumption.
 It uses both true and complementary input signals and computes both true and
complementary outputs using a pair of nMOS pulldown networks.
 The pulldown network f implements the logic function as in a static CMOS gate, while f ’
uses inverted inputs feeding transistors arranged in the conduction complement.
 Cascode voltage switch logic (CVSL) eliminates the static power consumption of the
pseudo-nMOS design style.
 It has a pair of nMOS pull-down networks to compute an output and its complementary
value from associated input signals and their complementary values.
 The pull-down networks are complementary with one side having series transistors while
the other has a parallel combination.
 CVSL has the potential to improve switching speed since the gate input capacitance is
reduced.

8. Explain the domino and dual rail domino logic families with neat
diagrams.
 The monotonicity problem in dynamic gates can be solved by placing a static CMOS
inverter between dynamic gates.
 The dynamic-static pair together is called a domino gate.
 Example: Z=ABC

Dual-rail AND/NAND gate
Dual-rail XOR/XNOR gate

9. Explain the static and dynamic power dissipation in CMOS
circuits with necessary diagrams and expressions.
The sources of power dissipation in CMOS:
Power dissipation in CMOS circuits comes from two components:
 Dynamic dissipation due to
 charging and discharging load capacitances as gates switch
 “short-circuit” current while both pMOS and nMOS stacks are partially ON
 Static dissipation due to
 subthreshold leakage through OFF transistors
 gate leakage through gate dielectric
 junction leakage from source/drain diffusions
 contention current in ratioed circuits
Putting this together gives the total power of a circuit
Power can also be considered in active, standby, and sleep modes. Active power is the power
consumed while the chip is doing useful work. It is usually dominated by Pswitching. Standby
power is the power consumed while the chip is idle. If clocks are stopped and ratioed circuits are
disabled, the standby power is set by leakage. In sleep mode, the supplies to unneeded circuits are
turned off to eliminate leakage. This drastically reduces the sleep power required, but the chip
requires time and energy to wake up so sleeping is only viable if the chip will idle for long enough.
Dynamic Power dissipation:
The instantaneous power P (t) consumed or supplied by a circuit element is the product of the
current through the element and the voltage across the element
The energy consumed or supplied over some time interval T is the integral of the instantaneous
Power
The average power over this interval is
Power is expressed in units of Watts (W). Energy in circuits is usually expressed in Joules (J),
where 1 W = 1 J/s.
When the capacitor is charged from 0 to VC, it stores energy EC

The capacitor releases this energy when it discharges back to 0.
Figure 5.4 shows a CMOS inverter driving a load capacitance. When the input switches
from 1 to 0, the pMOS transistor turns ON and charges the load to VDD. According to EQ
(5.6), the energy stored in the capacitor is
The energy delivered from the power supply is
Observe that only half of the energy from the power supply is stored in the capacitor. The
other half is dissipated (converted to heat) in the pMOS transistor because the transistor has
a voltage across it at the same time a current flows through it. The power dissipated
depends only on the load capacitance, not on the size of the transistor or the speed at which
the gate switches. When the input switches from 0 back to 1, the pMOS transistor turns
OFF and the nMOS transistor turns ON, discharging the capacitor. The energy stored in the
capacitor is dissipated in the nMOS transistor. No energy is drawn from the power supply
during this transition. The same analysis applies for any static CMOS gate driving a
capacitive load.
Suppose that the gate switches at some average frequency fsw. Over some interval T, the
load will be charged and discharged Tfsw times. Then, according to EQ (5.3), the average
power dissipation is
This is called the dynamic power because it arises from the switching of the load. Because
most gates do not switch every clock cycle, it is often more convenient to express switching
frequency fsw as an times the clock frequency f. Now, the dynamic power

dissipation may be rewritten as
The activity factor is the probability that the circuit node transitions from 0 to 1, because
that is the only time the circuit consumes power. A clock has an activity factor of α = 1
because it rises and falls every cycle.
Short-circuit power dissipation:
Short-circuit power dissipation occurs as both pullup and pulldown networks are partially
ON while the input switches. Short-circuit power is typically about 2% or 10% of switching
power and has become almost negligible.
Static power dissipation:
Static power is consumed even when a chip is not switching. Static power arises from
subthreshold, gate, and junction leakage currents and contention current.
Subthreshold leakage current flows when a transistor is supposed to be OFF. It is given by
where Ioff is the subthreshold current at Vgs = 0 and Vds = VDD, and S is the subthreshold
slope
Gate leakage occurs when carriers tunnel through a thin gate dielectric when a voltage is
applied across the gate (e.g., when the gate is ON). It is given by
where A and B are technology constants.
Junction Leakage The p–n junctions between diffusion and the substrate or well form
diodes, as shown in Figure 2.22.
The well-to-substrate junction is another diode. The substrate and well are tied to GND or
VDD to ensure these diodes do not become forward biased in normal operation. However,

reverse-biased diodes still conduct a small amount of current ID. It is given by
where IS depends on doping levels and on the area and perimeter of the diffusion region and
VD is the diode voltage.
10. Describe the different methods of reducing static and dynamic
Power dissipation in CMOS circuits.
Various design technique to reduce power dissipation in CMOS:
Static Power Reduction Techniques:
1. Power Gating
The easiest way to reduce static current during sleep mode is to turn off the power supply to
the sleeping blocks. This technique is called power gating and is shown in Figure .The
logic block receives its power from a virtual VDD rail, VDDV.
When the block is active, the header switch transistors are ON, connecting VDDV to VDD. When
the block goes to sleep, the header switch turns OFF, allowing VDDV to float and gradually sink
toward 0. As this occurs, the outputs of the block may take on voltage levels in the forbidden
zone. The output isolation gates force the outputs to a valid level during sleep so that they do not
cause problems in downstream logic. Power gating was originally proposed as Multiple
Threshold CMOS (MTCMOS) because it used low-Vt transistors for logic and high-Vt header
and footer switches.
2. Multiple Threshold Voltages and Oxide Thicknesses:
Selective application of multiple threshold voltages can maintain performance on critical
paths with low-Vt transistors while reducing leakage on other paths with high Vt transistors.
A multiple-threshold cell library should contain cells that are physically identical savefor
their thresholds, facilitating easy swapping of thresholds. Good design practice starts with
high-Vt devices everywhere and selectively introduces low-Vt devices where necessary.
Using multiple thresholds requires additional implant masks that add to the cost of a CMOS
process. Most nanometer processes offer a thin oxide for logic transistors and a much
thicker oxide for I/O transistors that can withstand higher voltages. The oxide thickness is

controlled by another mask step. Gate leakage is negligible in the thick oxide devices, but
their performance is inadequate for high speed logic applications. Some processes offer
another intermediate oxide thickness to reduce gate leakage.
3. Variable Threshold Voltages:
Vsb modulates the threshold voltage through the body effect. Another method to achieve
high Ion in active mode and low Ioff in sleep mode is todynamically adjust the threshold
voltage of the transistor by applying a body bias. This technique is sometimes called
variable threshold CMOS (VTCMOS). For example, low-Vt devices can be used and a
reverse body bias (RBB) can be applied during sleep mode to reduce leakage .
Alternatively, higher-Vt devices can be used, and then a forward body bias (FBB) can be
applied during active mode to increase performance .Body bias can be applied to the power
gating transistors toturn them off more effectively during sleep. Too much reverse body
bias (e.g., < –1.2 V) leads to greater junction leakage through BTBT while too much
forward body bias (>
0.4 V) leads to substantial current through the body to source diodes. The body effect
weakens as tox becomes thinner, so body biasing offers diminishing returns at 90 nm and
below . Applying a body bias requires additional power supply rails to distribute the
substrate and well voltages. For example, an RBB scheme for a 1.0 V n-well process could
bias the p-type substrate at VBBn = – 0.4 V and the n-well at VBBp = 1.4 V.Figure shows a
schematic and cross-section of an inverter using body bias. In an n-well process, all nMOS
transistors share the same p substrate and must use the same VBBn. In a triple well
process,groups of transistors can use different p-wells isolated from the substrate and thus
can use different body biases.
4. Input Vector Control:
The stack effect and input ordering cause subthreshold and gate leakage to vary by up to
two orders of magnitude between best and worst cases. Therefore, the leakage of a block of
logic depends on gate inputs, which in turn depend on the inputs to the block of logic. The
idea of input vector control is to apply the input pattern that minimizes block leakage when
the block is placed in sleep mode. The vector can be applied via set/reset inputs on the
registers or via a scan chain. It is hard to control all the gates in a block of logic using only
the block inputs, but the best input vectors may save 25–50% of leakage as compared to
random vectors.

Dynamic Power Reduction Techniques:
Dynamic power consists mostly of the switching power:
Activity factors can be heavily dependent on the particular task being executed. For
example, a processor in a cell phone will use more power while running video games than
while displaying a calendar. CAD tools do a fine job of power estimation when given a
realistic workload. Low power design involves considering and reducing each of the terms
in switching power. As VDD is a quadratic term, it is good to select the minimum VDD that
can support the required frequency of operation. Likewise, we choose the lowest frequency
of operation that achieves the desired end performance. The activity factor is mainly
reduced by putting unused blocks to sleep. Finally, the circuit may be optimized to reduce
the overall load capacitance of each section. Dynamic power also includes a short-circuit
power component caused by power rushing from VDD to GND when both the pullup and
pulldown networks are partially ON while a transistor switches. This is normally less than
10% of the whole, so it can be conservatively estimated by adding 10% to the switching
power.
1. Activity Factor:
The activity factor is a powerful and easy-to-use lever for reducing power. If a circuit can
be turned off entirely, the activity factor and dynamic power go to zero. Blocks are
typically turned off by stopping the clock; this is called clock gating.
Clock Gating Clock gating ANDs a clock signal with an enable to turn off the clock to idle
blocks. It is highly effective because the clock has such a high activity factor, and because
gating the clock to the input registers of a block prevents the registers from switching and
thus stops all the activity in the downstream combinational logic. Clock gating can be
employed on any enabled register. Sometimes the logic to compute the enable signal is
easy; for example, a floating-point unit can be turned off when no floating-point
instructions are being issued. Often, however, clock gating signals are some of the most
critical paths of the chip. The clock enable must be stable while the clock is active (i.e., 1
for systems using positive edge-triggered flip-flops). Figure shows how an enable latch can
be used to ensure the enable does not change before the clock falls. When a large block of
logic is turned off, the clock can be gated early in the clock distribution network, turning
off not only the registers but also a portion of the global network. The clock network has an
activity factor of 1 and a high capacitance, so this saves significant power
2. Capacitance:
Switching capacitance comes from the wires and transistors in a circuit. Wire capacitance is
minimized through good floorplanning and placement (the locality aspect of structured
design). Units that exchange a large amount of data should be placed close to each other to
reduce wire lengths. Device-switching capacitance is reduced by choosing fewer stages of
logic and smaller transistors. Minimum-sized gates can be used on non-critical paths.

3. Voltage:
Voltage has a quadratic effect on dynamic power. Therefore, choosing a lower power supply
significantly reduces power consumption. As many transistors are operating in a velocity-
saturated regime, the lower power supply may not reduce performance as much as long-
channel models predict. The chip may be divided into multiple voltage domains, where
each domain is optimized for the needs of certain circuits. For example, a system on-chip
might use a high supply voltage for memories to ensure cell stability, a medium voltage for
a processor, and a low voltage for I/O peripherals running at lower speeds. Voltage also can
be adjusted based on operating mode; for example, a laptop processor may operate at high
voltage and high speed when plugged into an AC adapter, but at lower voltage and speed
when on battery power. If the frequency and voltage scale down in proportion, a cubic
reduction in power is achieved.
Voltage Domains: Some of the challenges in using voltage domains include converting
voltage levels for signals that cross domains, selecting which circuits belong in which
domain, and routing power supplies to multiple domains. Figure shows direct connection of
inverters in two domains using high and low supplies, VDDH and VDDL, respectively. A
gate in the VDDH domain can directly drive a gate in the VDDL domain. However, the gate
in the VDDL domain will switch faster than it would if driven by another VDDL gate. The
timing analyzer must consider this when computing the contamination delay, lest a hold
time be violated. Unfortunately, the gate in the V DDL domain cannot directly drive a gate
in the VDDH domain. When n2 is at VDDL, the pMOS transistor in the VDDH domain has
Vgs = VDDH – VDDL. If this exceeds Vt, the pMOS will turn ON and burn contention
current. Even if the difference is less than Vt, the pMOS will suffer substantially increased
leakage. This problem may be alleviated by using a high-Vt pMOS device in the receiver if
the voltage difference between domains is small enough
Dynamic Voltage Scaling (DVS): Many systems have time varying performance
requirements. For example, a video decoder requires more computation for rapidly moving
scenes than for static scenes. A workstation requires more performance when running
SPICE than when running Solitaire. Such systems can save large amounts of energy by

reducing the clock frequency to the minimum sufficient to complete the task on schedule,
then reducing the supply voltage to the minimum necessary to operate at that frequency.
This is called dynamic voltage scaling (DVS) or dynamic voltage/frequency scaling
(DVFS) Figure shows a block diagram for a basic DVS system. The DVS controller takes
information from the system about the workload and/or the die temperature. It determines
the supply voltage and clock frequency sufficient to complete the workload on schedule or
to maximize performance without overheating. A switching voltage regulator efficiently
steps down Vin from a high value to the necessary VDD.
4. Frequency:
Dynamic power is directly proportional to frequency, so a chip obviously should not run faster
than necessary. As mentioned earlier, reducing the frequency also allows downsizing transistors
or using a lower supply voltage, which has an even greater impact on power. The performance
can be recouped through parallelism), especially if area is not as important as power. Even if
multiple voltage supplies are not available, a chip may still use multiple frequency domains so
that certain portions can run more slowly than others. For example, a microprocessor bus
interface usually runs much slower than the core. Low frequency domains can also save energy
by using smaller transistors.

11. (i)Find the rising and falling propagation delays of fanout-of-one
NOT gate using the RC delay model.
(ii) Find the propagation delay of fanout-of-four inverter using
linear delay model. Assume τ =3ps.
The logical effort of the inverter is g = 1.
The electrical effort, h is 4 because the load is four gates of equal size.
The parasitic delay of an inverter is p = 1.
The total normalized delay is d = gh + p = 1 × 4 + 1 = 5 .
The propagation delay of fanout-of-four inverter, tpd = τd=3ps ×5=15 ps.

12. Draw the static CMOS circuit diagram, stick diagram and gate
Layout of four input NAND gate

vlsi 2 unit.pdfvlsi unit 2 important notes for ece department

13. Realize a 2-input XOR using static CMOS, transmission gate
and dynamic CMOS logic. Analyze the hardware complexity.

2-input XOR using transmission gate
2-input XOR using dynamic CMOS logic

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