IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 54, NO. 4, APRIL 2007 293 Transformer-Based Dual-Mode Voltage-Controlled Oscillators Andrea Bevilacqua, Member, IEEE, Federico P. Pavan, Christoph Sandner, Member, IEEE, Andrea Gerosa, Member, IEEE, and Andrea Neviani, Member, IEEE Abstract—In this brief, we propose to use a transformer-based resonator to build a dual-mode oscillator, e.g., a system capable of oscillating at two different frequencies without recurring to switched inductors, switched capacitors, or varactors. The be- havior of the resonator configured as a one-port and a two-port network is studied analytically, and the dependence of the quality factor on the design parameters is thoroughly explored. These results, combined with the use of traditional frequency tuning tech- niques, are applied to the design of a wide-band voltage-controlled oscillator (VCO) that covers the frequency range 3.6–7.8 GHz. The performance of the designed VCO, implemented in a digital 0.13- m CMOS technology, has been studied by transistor-level and 2.5D electromagnetic simulation (Agilent Momentum). A typical phase noise performance at 1-MHz offset of dBc Hz has been predicted, while the power consumption ranges from 1 to 8 mW, depending on the VCO configuration. Index Terms—Feedback, microwave oscillators, reconfigurable architectures, transformers, voltage-controlled oscillators (VCOs). I. INTRODUCTION F ULLY integrated voltage-controlled oscillators (VCOs) capable of operating at several frequency bands while showing low phase noise are key building blocks in both emerging multiband, multistandard, and broad-band radios, as well as in wire-based communication systems [1]–[11]. LC VCOs have been preferred over ring and relaxation oscillators because of their better phase noise performance. In order to achieve a wide tuning range, several techniques can be used. Inversion- or accumulation-type MOS varactors support a large capacitance variation, at the price of higher tuning sensitivity, and, in the end, worse phase noise performance. Switched ca- pacitor banks suffer from the resistive and capacitive parasitics associated with the switches. A variable inductor is beneficial, since it results in both a smaller capacitance and a smaller capacitance variation requirements, improving tuning range, phase noise and power consumption simultaneously. Inductor switching has been proposed [8], [9], although this technique is severely limited by the switches. In this brief, we propose a different technique to extend the tuning range of LC VCOs. An oscillator built around a trans- former-based resonator is shown to feature two modes of os- cillation. By selecting the proper feedback mechanism either of Manuscript received April 4, 2006; revised November 15, 2006. This paper was recommended by Associate Editor P. P. Sotiriadis. A. Bevilacqua, F. P. Pavan, A. Gerosa, and A. Neviani are with Diparti- mento di Ingegneria dell’Informazione, Università di Padova, 35131 Padova Italy (e-mail: andrea.bevilacqua@dei.unipd.it). C. Sandner is with Infineon Technologies Austria AG, A-9500 Villach, Austria. Digital Object Identifier 10.1109/TCSII.2006.889734 the two modes of oscillation can be selected. This results in two bands of operation. Compared to the inductor switching tech- nique, the proposed approach does not require any switch con- nected to the LC tank that would degrade the resonator . By combining the dual-mode operation with capacitance variation a very wide tuning range is achieved. The brief is organized as follows. In Section II, the trans- formed-based resonator employed in this work is described. Sections III and IV discuss how a dual-mode oscillator can be built by using the resonator as a one-port or a two-port network, respectively. In Section V, the quality factor of the transformer-based resonator is analyzed. The design of a VCO which demonstrates the proposed technique is presented in Section VI, along with some simulation results. Finally, the work is wrapped up in Section VII. II. TRANSFORMER-BASED RESONATOR A transformer, made of two magnetically coupled coils with inductance and , respectively, and coupling coefficient is turned into a resonator by loading its primary and secondary ports with capacitors and , as shown in Fig. 1(a). The transformer is described by means of the impedence matrix (1) where the losses are simply modelled by means of the resis- tances and . The primary and secondary coil quality fac- tors are and , respectively. The resonator can be described as a two-port network by means of the impedance matrix (2) The use of a transformer as a resonator allows the possi- bility of having two modes of oscillation, as explained in the following. III. ONE-PORT OSCILLATOR The simplest oscillator configuration is obtained by loading either port of the transformer-based resonator by a negative con- ductance , as sketched in Fig. 1(b) for the primary port. The start-up condition is (3a) (3b) 1549-7747/$25.00 © 2007 IEEE