IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 36, NO. 12, DECEMBER 2001 1879 A Quadrature Data-Dependent DEM Algorithm to Improve Image Rejection of a Complex Modulator Lucien J. Breems, Member, IEEE, Eise Carel Dijkmans, and Johan H. Huijsing, Fellow, IEEE Abstract—A dynamic element matching (DEM) algorithm is presented that is controlled by the quadrature output data of a complex sigma–delta modulator. This DEM technique is used to correct the gain and phase errors between the circuits in the in-phase and quadrature-phase feedback paths of the modulator. The key feature of this DEM technique is that it does not cause leakage of high-frequency quantization noise in the signal band, as encounters with the periodic or pseudorandom DEM techniques. No test signal is required to measure the gain and phase errors, and as the DEM circuit is operating continuously, it compensates for changes in, e.g., temperature and supply voltage. A 0.35- m CMOS prototype chip has been designed to test the DEM circuit. A batch of 38 measured samples shows a typical mismatch-inde- pendent image rejection ratio of 63 dB with DEM. Index Terms—Analog-to-digital conversion, continuous-time fil- ters, dynamic element matching, image rejection, radio receivers, sigma–delta modulation. I. INTRODUCTION T HE DEMAND for digital implementation of analog func- tions in wireless communication receivers, such as filters and mixers, is pushing the requirements for analog-to-digital (A/D) converters toward higher resolution, higher linearity, and stronger rejection of image channels. For these reasons, modulation has become a very popular technique for A/D con- version in communication receivers. Fig. 1 shows a traditional heterodyne receiver architecture with a mixer in the front-end modulating the RF input to an intermediate frequency (IF). High linearity and high resolution can be achieved with the use of baseband modulators in a conventional heterodyne receiver architecture, while preserving the low-power require- ment inherent to wireless applications. Therefore, a second mixer stage in the receiver of Fig. 1 modulates the IF signal to a low offset frequency (low-IF) or dc (zero-IF). Because a single mixer is sensitive to both sidebands around the local oscillator (LO) carrier frequency, two mixers are employed that are driven by LO clocks having a 90 phase difference. By complex adding or subtracting the quadrature baseband output signals, the desired sideband can be selected while the undesired sideband (image) is suppressed. Depending on the Manuscript received March 31, 2001; revised July 17, 2001. L. J. Breems and E. C. Dijkmans are with the Philips Research Laboratories, 5656 AA Eindhoven, The Netherlands (e-mail: lucien.breems@philips.com). J. H. Huijsing is with Delft University of Technology, 2628 CD, Delft, The Netherlands. Publisher Item Identifier S 0018-9200(01)09320-9. Fig. 1. Heterodyne receiver architecture. choice of the second IF, the image rejection requirements may be in the order of 25 dB for zero-IF (e.g., QPSK-OFDM-QAM) or 80 dB for low-IF (e.g., AM/FM radio) applications [1], [2]. The image rejection performance is based on the gain and phase matching between the quadrature paths and is in the order of 40–50 dB in state-of-the-art designs [2], [3]. Another 40 dB of image rejection is provided by the IF channel filter to meet low-IF requirements. Alternatively, a bandpass modulator [4] can be used for direct digitization of an IF channel. This way, the problem of image interference is solved, as the second mixer stage is implemented in digital with perfect matching. However, dynamic range and linearity requirements are more difficult to meet at higher frequencies due to circuit nonidealities and parasitic effects, especially at low power consumption. As a consequence, one or more external ceramic or surface acoustic wave (SAW) filters are needed to protect the ADC against either large image channels (in low-IF receivers) or strong interference signals, whether a baseband or bandpass modulator is used. This paper discusses the image rejection performance of the second IF stage (dashed box in Fig. 1) implemented with two real continuous-time baseband modulators with integrated passive mixers [5]. This system will be referred to in this paper as a quadrature or complex IF modulator, as it has quadra- ture output signals. It was shown in [2], [5] that this IF system provides high-resolution A/D conversion with high linearity at very low power consumption. Section II will describe some de- sign issues of this complex IF modulator related to gain and phase mismatch. In Section III, the technique of dynamic element matching (DEM) will be discussed. A data-dependent algorithm used to drive the DEM switches will be presented. The implementation of the complex modulator with DEM cir- cuit will be described in Section IV. Measurement results will be presented in Section V, and conclusions will be drawn in Sec- tion VI. 0018–9200/00$10.00 © 2001 IEEE