INTRODUCTION
Oscillator circuits produce continuous and periodic sinusoidal waveforms
of a particular frequency and work on the concept of positive feedback.
The active elements like transistors, operational amplifiers, MOSFET
etc. are used to provide the loop gain, however, the passive networks
(including the tank circuit) yields positive feedback. Whenever the
oscillator is excited by a dc source it responds by a steady state
signal. The designing of oscillators is classified into families based
upon the kind and number of memory elements in use [1-2]. The
Colpitts oscillator (CO) family is one wherein the tank circuit has two
capacitances and one inductor coil. It is employed for high frequency
applications and is a preferred topology since it is simple and devoid
of mutual inductance effects present between two inductors as in the
case of Hartley oscillator [3-4]. Oscillators are mostly realized by
integer order elements; however, recently researchers have shown a lot
of interest in fractional order elements, like fractional order
inductors and capacitors, due to various advantages of fractional order
elements (FOE). Fractional order circuits have been found to be more
accurate in reproducing the behavior of physical processes than the
conventional integer order systems. Modeling examples have been found in
rheology, mechanics, chemistry, physics, bioengineering, robotics and
many scientific fields [5-8]. Fractance devices provide an
additional degree of control over phase and frequency response due to
the presence of fractional order, α. Fractional order, α gives an extra
freedom due to which higher order systems can be represented using fewer
coefficients. The fractional order capacitors (FOC) and fractional order
inductors (FOI) are very important elements for fractional circuitry and
are known to behave like constant phase elements (CPE). Over wide range
of frequency the phase characteristics of systems designed using
fractional elements is known to be constant, thus generating constant
phase zones (CPZ). Mathematically, for an ideal resistor, capacitor and
inductor, α is ‘0’, ‘1’ and ‘-1’ respectively. For a fractional order
element, α ranges from -1 to 1 and the magnitude of impedance varies
with frequency according to α. However, the realization of fractional
elements using passive RC ladder circuitry results in increased circuit
complexity, more power consumption and noise compared to the
conventional integer order counterparts. Therefore, there is an
immediate need to address the issues of complexity and power consumption
in fractional order circuitry to retain its advantages [9-11,14-18].
The use of conventional complementary metal oxide semiconductor (CMOS)
technology to realize FOC is a good choice, as it is well known for low
power consumption, large noise margin (NM), large packing density etc.
However, CMOS technology has its own limitations, particularly when
scaled below 22 nm technology node. The MOS devices face severe short
channel effects, gate oxide tunneling, increase in leakage, increase in
sensitivity to process variations in integrated circuit manufacturing
and increased fabrication cost [12-13]. Therefore, the need of the
hour is to have new devices which can replace the existing silicon
MOSFET, with clear-cut advantages and enabling efficiently new low cost
applications. Carbon nanotube field effect transistor (CNTFET) is
considered as a future device with extra ordinary properties due to the
presence of CNTs in its channel. A CNTFET has large mobility, large
transconductance (gm) due to the ballistic transport
property in CNTs, low intrinsic capacitance, near ideal subthreshold
slope (SS) and its CV/I performance is 13× higher than the bulk MOSFET
[19-31].
In this paper, we design and simulate four types of Colpitts oscillators
based on multiple technologies and compared their performances. These
include integer order conventional MOSFET based CO, fractional order
MOSFET based CO, CNTFET based integer order CO and CNTFET based
fractional order CO, all based on 32 nm technology nodes. A rigorous
comparative analysis of the key performance measuring parameters has
been done for all the circuits. The LC oscillators used in the COs are
characterized by their tank circuits. Herein, both the integer order
capacitors and the fractional order based pseudo-capacitors have been
used for modelling the tank circuits. In conventional oscillators the
oscillation frequency depends upon the RC/LC time constant values,
however, in the case of fractional order oscillators it further depends
on α, thus providing a greater control and more design freedom. A
rigorous simulation study and comparative analysis of the four designed
COs have been done. It has been observed that the CNTFET fractional
order CO has shown significant improvement in performance measuring
parameters, like power consumption, larger constant phase zone, apart
from the advantages of being fractional order. The fractional topology
provides precise control over phase and frequency of oscillatory output.
To the best of our knowledge, this is the first work where CNTFET based
CO, both integer and fractional order, has been designed, simulated and
compared.
The paper is divided into VII sections. Section I gives introduction.
Section II describes the details about CNTFET. Section III explains the
fractional order circuitry. Section IV gives insights on the designing
of the fractional order topology. Section V lists the proposed
oscillator topologies and there analysis Section VI gives the noise
analysis of the CO’s. Section VII concludes the paper.