Study of Design Parameter Variations in Simple Grounded Active Inductor

This paper presents a fundamental active inductor topology named Simple Grounded Active Inductor (SGAI) for analyzing variations in Q factor and inductance. Design parameters like aspect ratios and biasing of the transistors are varied and the Q factor and inductance variations are measured at 2.4GHz. The SGAI structure is simulated using Cadence Virtuoso spectre using 180nm technology and a supply voltage of 3.3 V. For a biasing current of 500μA and aspect ratio of 5μm/0. 18μm, the Q factor is 2.45, inductance is 2.5nH, and the self resonating frequency is 23.47GHz at 2.4GHz. The designed SGAI circuit consumes a power of 3.3mW. Keywords— SGAI, SRF, Q factor, SCAI, Regulated Cascode, CMOS, RFIC INTRODUCTION In order to make Moore’s low pronouncing in radio frequency integrated circuits (RFIC), the RF components can no more be passive in nature. RFIC normally work between 300MHZ to 30GHZ. High Q factor inductor is a major parameter that determines the reliability and efficiency of CMOS RF blocks. Usually inductors are realized on chip as spiral inductors. But they consume a higher area and also has a limited Q factor due to various losses. The inductance and q factor of spiral inductors is determined by design parameters like total length, width, thickness of wire, number of loops, conductivity of the metal etc. Even though passive inductors are simpler to design, they possess a low Q factors in the range of 5 for bulk CMOS and 20 for SOI at GHz frequencies [1]. As the RFIC performance is mainly determined by the tank circuit, a reliable inductor design is inevitable. Active inductors are a promising solution in this scenario. They offer many advantages over their passive counter parts like small chip area, tunable inductance, high Q factor etc [2]. Even though there are several active inductor topologies in the literature most of them are based on gyrator-C configuration [3]. An ideal gyrator is a linear two port network that neither stores nor dissipates energy. BASIC ACTIVE INDUCTORS Usually active inductors are build on gyrator type configuration where two transistors are connected in a back to back fashion [5]. The topology utilizes the parasitic capacitance of the transistors in order to make the overall circuit to behave inductive. Simple Grounded Active Inductor (SGAI) is the fundamental topology that uses two transistors to mimic the inductive behavior [10]. However the Q factor that can be achieved is limited and for improving the same, Simple Cascoded Active Inductors (SCAI) can be used. Problem with SCAI is the reduction in the frequency range of the operation. To alleviate that drawback, regulated cascode active inductors [6] are there which provide a better performance compared to SGAI in terms of Q factor and SCAI in terms of frequency range. A. Theory of operation of SGAI Input voltage Vin is applied to the gate of M1 which converts the voltage into a current that charges Cgs2. The voltage across Cgs2 is then translated into current by M1 that maintain I2 as a constant [5]. Initially, Id2=I2. Increasing Iin causes voltage across Cgs1 to increase. This increases Id1 and since I1 is a constant current source, charges from Cgs2 is extracted out to meet the increased current demand of M1. Reduction in gate voltage along with increase in source voltage of M2 reduces Id2. Now to hold KCL, the increase in input current is utilized by I2 to remain constant. In this manner SGAI resist the changes in current thereby mimicking inductive behavior. International Journal of Engineering Research and General Science Volume 4, Issue 4, July-August, 2016 ISSN 2091-2730 235 www.ijergs. org Fig1: Circuit Schematic of SGAI illustrating parasitic capacitances. B. Figure of merits of inductors Frequency range A gyrator-C based active inductor exhibits inductive characteristics over a specific frequency range[8]. Lowest frequency bound is determined by the zero (ωz) and upper bound by the pole (ωo) of impedance transfer function. Gyrator-C network will be resistive when ω< ωz , inductive when ωz <ω< ωo and capacitive when ω> ωo. ωo is also referred to as Self Resonating Frequency (SRF) [4] where the magnitude of impedance is at its peak. Q factor The Quality factor or Q factor is a performance indicator that indicates the energy losses within a resonant element. It is dimensionless frequency dependent parameter and can be defined as the ratio of inductive reactance to resistance. Inductance Tunability Inductance value can be tuned by varying the transconductance and biasing currents [11]. Since aspect ratio of inductor cannot be tuned once it is fabricated, it is done with biasing currents. So active inductors are beneficial in reconfigurable systems [1]. Chip Area Active inductors being implemented with active devices, reduces the chip area to a greater extend when compared with their passive versions. Linearity Linearity defines the ability of active inductor to sustain a constant inductance and Q factor over a wide input power range [1]. Square law relationship followed by gate source voltage and drain current is the reason for nonlinearity in active inductors [11]. Noise Active inductors exhibit a higher noise level compared to their passive counterparts [1]. The dominant contributors of noise are thermal noise in the transistor channel and flicker noise due to dangling bonds near the surface [12]. International Journal of Engineering Research and General Science Volume 4, Issue 4, July-August, 2016 ISSN 2091-2730 236 www.ijergs. org C. Design considerations in SGAI When the transconductors used for the synthesis of AI has finite input and output impedance, there will be parasitic capacitive (parallel capacitance Cp) and resistive effects (parallel resistance Rp & series resistance Rs) which make the structure lossy. Fig2 below shows the equivalent structure of AI with parasitic effects. Applying KCL at nodes 1 and 2 gives Node1 => (sC1 + Go1)V1 − gm1V2 =0 (1) Node2 => −Iin +(sC2 + Go2)V2 − gm2(−V1)=0 (2) Admittance looking into node 2 is given by Y = = sC2 + Go2 + ( ) (3) Above equation can be represented by an equivalent RLC network (Fig2) with following parameters. Rp = (4) Cp = C2 (5) Rs = (6)