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.