PERFORMANCE STUDY OF FIXED VALUE INDUCTORS AND THEIR OPTIMIZATION USING ELECTROMAGNETIC SIMULATOR Genemala Haobijam and Roy Paily VLSI and Digital System Design Laboratory, Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati, Assam 781039, India; Corresponding author: roypaily@iitg.ernet.in Received 21 September 2007 ABSTRACT: In this article, we present an extensive analysis of the dependence of quality factor, peak frequency, self resonance frequency, and area of a spiral inductor on its layout parameters, while keeping the inductance value constant as opposed to various studies reported. This performance trend study establishes the optimum metal width and number of turns for a specified inductance value and desired operating frequency. We propose here an algorithm for accurate design and opti- mization of spiral inductors using a 3D electromagnetic simulator with minimum number of inductor structure simulations, and thereby reduc- ing its long computation time. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1205–1210, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop. 23310 Key words: on chip inductor; optimization; inductance; electromagnetic simulation 1. INTRODUCTION On-chip spiral inductors are extensively used in CMOS radio frequency integrated circuits (RFICs). The design and optimization of inductor is one of the critical steps of the design cycle since the performance and cost of the RFIC will depend on the quality factor and area of the inductor [1]. The complexity on the design of spiral inductor lies in determining the optimum layout parameters for a given technology. The layout parameters are sketched in Figure 1, which includes the number of turns (N), spiral track width (W), spiral track spacing (S), outer diameter (D out ), and inner diameter (D in ). The dependence of the inductance, quality factor, and self resonance frequency on the layout and process parameters has been studied as in [2– 6]. In these studies, the layout parameters are systematically varied and the corresponding changes in the induc- tance, quality factor, and resonance frequency were reported. In applications where one has the flexibility of choosing from a range of inductance values, this approach is useful. However, if a de- signer targets to design a specified inductance value and optimize its layout parameters for a particular application, such studies give insufficient information, since the quality factor and the inductance follow an opposite trend with the layout parameters. For example, one may attempt to increase the quality factor by increasing the inner diameter that will minimize the eddy current effect. But this approach will alter the value of inductance. One can vary N, W, and S to get back to the desired inductance value. However, this will again alter the quality factor and need not be the optimum value at the desired frequency. Therefore, a study of the perfor- mance trend by varying the layout parameters keeping the induc- tance value constant would be more beneficial in applications where a fixed value of inductance is required. The design of spiral inductor involves determining all possible combinations of the layout parameters such as N, W, D out or D in , and S that results in the desired inductance value and identify the combination that will result the highest quality factor at desired frequency. An optimization problem of spiral inductor involves maximization of quality factor and/or minimization of area that are generally done using enumeration algorithms [7, 8] or numerical algorithms [9 –11]. Enumeration methods are inefficient because of its long computation time; however optimization may be per- formed efficiently by layout parameter bounding [12]. Numerical methods are faster and are generally based on lumped element model. Quality factor may also be enhanced using variable metal width [13] without extra processing step. Methods based on lumped element model are generally adopted since electromag- netic (EM) simulations are computationally expensive and time consuming even though it provides the most accurate design. In addition, a lumped element model gives only an approximate electrical characteristic and the result may be prone to errors. Verification of the design using a full wave EM simulator is therefore required before fabrication. Sometimes the designer may even be compelled to repeat the entire design when such errors are not tolerable. Optimization using an EM simulator would be more advantageous, if the optimized layout can be quickly identified from simulation results of few inductor structures as will be demonstrated later. This article addresses two aspects of inductor design. The first one is an extensive analysis of the dependence of quality factor (Q), peak frequency (f max ), self resonance frequency (f res ), and area of a spiral inductor on its layout parameters, while keeping the inductance value constant for a given technology as opposed to various studies reported. To incorporate the effects of the parasitics on the performance, investigation is done using a method of moment-based 3D EM simulator [14]. The effect of varying layout parameters is illustrated by characterizing 19 planar inductor struc- tures of different geometry keeping the inductance value constant at 10 nH. The area and quality factor is also compared with stacked inductor structure. The second aspect of this article is a proposal of an algorithm that consists of the minimum steps required to design and optimize a spiral inductor by simulating few inductor struc- tures using a 3D EM simulator for a given technology based on the insights obtained from performance trends. The algorithm is val- idated by optimizing 1, 6, and 10 nH at 5, 2, and 1 GHz, respec- tively. The article is organized as follows. In Section 2, the performance trend for a fixed inductance value is discussed. In Section 3, the optimization of quality factor and area of the spiral inductor using the performance trend information is illustrated. Finally conclusions are drawn in Section 4. Figure 1 Layout of a square spiral inductor DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 5, May 2008 1205