192 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 60, NO. 4, APRIL 2013 Two-Tone Phase Delay Control of Center Frequency and Bandwidth in Low-Noise-Amplifier RF Front Ends Bogdan Georgescu, Member, IEEE, Roghoyeh Salmeh, Member, IEEE, Michel Fattouche, Member, IEEE, and Fadhel Ghannouchi, Fellow, IEEE Abstract—This brief presents a two-tone system for controlling the center frequency and bandwidth of an RLC tank with an application to center frequency and bandwidth control in low noise amplifier (LNA) RF front ends. The circuit operates based on the fact that an RLC tank induces a phase difference with special properties between two frequencies. The system is demonstrated in hardware in the TSMC CMOS 0.18-μm process for a center frequency of 2.45 GHz and a bandwidth of 60 MHz. The LNA center frequency can be controlled with a precision of ≈0.2% while the bandwidth can be controlled with a precision of ≈8%. The tuning time is 3 μs multiplied by the number of tuning states. The tuning states are the circuit states set digitally and analyzed until the desired operating point is achieved. Index Terms—Bandwidth control, center frequency control, GPS receivers, low noise amplifier (LNA), Q-enhancement. I. I NTRODUCTION M OST RF front ends are based on a low noise amplifier (LNA) as shown in Fig. 1. With some exceptions, the LNAs usually perform amplification by driving an LC tank. Mainly because the inductor is not ideal, the LC tank is in fact an RLC tank. This RLC tank, R T , L T , and C T in Fig. 1, sets the bandwidth as well as the center frequency of the LNA. It is possible to avoid additional filtering and rely on the control of the RLC tank to remove out-of-band interferers. Recently, work has been done [1]–[4] to remove the preselect filter before the LNA and use the RLC filter for selectivity. This is necessary for GPS applications where the large insertion loss of the preselect filter makes the performance of the LNA in terms of noise figure unacceptable. The bandwidth can be reduced using active Q-enhancement if the Q value of the inductor is low as it is typically the case with on-chip inductors. By generating an active negative resistor R T in Fig. 1, the Q of the RLC tank and the gain of the LNA can be increased to high values. The associated decrease in the noise figure can be solved by using Q-enhancement as Manuscript received November 6, 2012; revised January 18, 2013; accepted February 2, 2013. Date of publication March 26, 2013; date of current version April 15, 2013. This brief was recommended by Associate Editor A. Bevilacqua. B. Georgescu is with the Topnotch Canada, Calgary, AB T3B 4W4, Canada (e-mail: bageorge@topnotchcanada.ca). R. Salmeh is with the ATCO Group, Calgary, AB T2R 1N6, Canada. M. Fattouche and F. Ghannouchi are with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Alberta. Color versions of one or more of the figures in this brief are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSII.2013.2251948 Fig. 1. Simple LNA. a second stage, and the decrease in linearity can be solved by using high Q only for small signals or blockers. If an external high-Q (≈100) inductor is used, the bandwidth may be controlled using passive Q-relaxation with a positive resistor R T without loss in linearity or noise performance. On the other hand, the center frequency of the RLC tank can be adjusted by tuning the capacitor value C T . In integrated circuit form, even if we assume that the simu- lations can predict the behavior of the circuit perfectly, process variations may cause 10% error in the capacitor value and as much as 25% error in the Q value. For a center frequency of 2.4 GHz and a bandwidth of 80 MHz, this represents a change in the center frequency of ±100 MHz and a change in the bandwidth of ±20 MHz. These large, undesired, and unpredictable variations affect the performance of the LNA drastically at least in terms of gain and selectivity. In this brief, we develop a method to eliminate postfabrication variations using circuit methods. II. STATE OF THE ART The bandwidth and center frequency control methods pro- posed in the past fall into two categories. The first category is the oscillator methods [5]–[7]. In this approach, the RLC tank is transformed into an oscillator, and from that circuit state, its bandwidth and center frequency are controlled. More specifically, after the RLC tank is brought into oscillation, the feedback is reduced until the oscillations 1549-7747/$31.00 © 2013 IEEE