Quadrature Mismatch Shaping with a Complex, Tree Structured DAC Stijn Reekmans, Jeroen De Maeyer, Pieter Rombouts and Ludo Weyten Ghent University (UGent) Electronics and Information Systems Laboratory (ELIS) Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium Email: Stijn.Reekmans@elis.ugent.be Abstract— Quadrature ΣΔ ADCs require a feedback path for both the I and the Q part of the complex feedback signal. If two separated multibit feedback DACs are used, mismatch among the unit DAC elements leads to additional mismatch noise in the output spectrum as well as an unbalance between the I and Q DAC. This paper proposes a new quadrature bandpass mismatch shaping technique. In our approach the I and Q DACs are merged into one complex DAC, which leads to near-perfect I/Q balance. To select the unit DAC elements of the complex, multibit DAC, the well-known tree structured element selection logic is generalized toward a complex structure and necessary conditions for its correct operation are derived. Finally, a very efficient first-order quadrature shaper implementation is proposed and simulations show the effectiveness of the quadrature bandpass mismatch shaping technique. I. I NTRODUCTION Nowadays, many wireless communication systems use low- IF receivers (Fig. 1) [1], [2]. Such receivers consist of an antenna, an analog part, an analog-to-digital converter (ADC) and a digital signal processor (DSP). The analog part is made up of a filter, an amplifier and two mixers that are driven by LO clocks having a 90 ◦ phase difference. The quadrature mixer demodulates the received radio frequency (RF) signal to an in-phase (I) and a quadrature (Q) signal at low intermediate frequency (IF). In order to end up with a flexible receiver, functions such as channel selection need to be shifted into the digital domain. Since the performance of the ADC will determine which functions are implemented with analog circuitry and what functionality is done in the DSP, the ADC is becoming a critical part of the receiver architecture. { Antenna RF ADC DSP I LO 0 ◦ 90 ◦ Q Analog part IF Filter Amp Fig. 1. Low-IF receiver architecture. II. MULTIBIT QUADRATURE BANDPASS ΣΔ ADC A quadrature bandpass (QBP) ΣΔ ADC is well suited for the use in low-IF receivers. Instead of digitizing the analog I and Q signals separately with two bandpass ADCs, it performs directly the complex analog-to-digital conversion of the analog I and Q signals. Moreover, in order to achieve the same performance, the QBP ΣΔ ADC uses only half the integrators compared to the traditional bandpass solution [2]. This results in power- and area saving. The architecture of most QBP ΣΔ modulators is shown in Fig. 2. It consists of a complex loopfilter, two real quantizers and two real feedback digital- to-analog converters (DAC I and DAC Q ). - - Complex DAC I DAC Q X I X Q Y I Y Q IF I IF Q loopfilter Fig. 2. A multibit quadrature bandpass ΣΔ ADC In many applications, multibit ΣΔ ADCs are used instead of single bit converters. On the one hand, multibit ADCs can achieve much higher performance because they allow a more aggressive noise transfer function. Also, since the output of the modulator more closely resembles the desired output, it contains much less out-of-band noise. On the other hand however, multibit ΣΔ ADCs need a multibit DAC in their feedback path. Since any feedback DAC error is added to the modulator input, the required matching precision is of the order of the desired precision of the overall data converter and this is often beyond the practical limits of present VLSI technology [3]. To reduce the negative effects of these mismatches, dynamic element matching is used in the DAC. These mismatch-shaped DACs use digital signal processing techniques to cause most of the error’s energy to reside outside the signal band. Although the implementation of Fig. 2 is used for multibit QBP ΣΔ ADC [1], [2], we will show in the next section that the use of a separate DAC for the I and Q path results in a major performance degradation. Therefore, in Section IV, the concept of a complex DAC is explained which paves the way 2969 ISCAS 2006 0-7803-9390-2/06/$20.00 ©2006 IEEE