Reducing multibit DAC circuits errors by a simplified dynamic element matching algorithm used in delta-sigma converters

Resolution of a multibit delta-sigma modulator (DSM) is limited by its internal digital-to-analog converter (DAC) nonlinearity that is usually caused by circuit mismatch errors while realizing. Recently, some dynamic element matching (DEM) methods were proposed for reducing mismatch errors. Two main difficulties of different dynamic element matching (DEM) techniques relate to instability and complexity of their algorithms. This paper provides a general method to simplify and to improve stability of high order dynamic element matching algorithms. It is shown that the proposed modifications can reduce necessary hardware for any order of sorting DEM algorithms and improve stability of the high order tree-structured DEM, without scarifying a considerable part of their ideal mismatchshaping function. Simulations are presented for different6 and 4 -order bandpass mismatch-shaping circuit, moved inside the feedback loop of a6-order bandpass delta-sigma modulator. However, it can also be used in lowpass DSM. I. I NTRODUCTION With increasing demand of ∆Σ modulators ( DSMs) with broader bandwidth and wider dynamic range ( DR), multibit architectures become attractive for this trend as [1], [2]: • theSNR directly increases by 6 dB for each extra quantization bit, resulting in lower OSR application possible, • multibit DSM’s loop possesses better stability resulting in additional loop gain for higher order structure, which in turn results indirectly in improvedSNR, • it is one of the best ways to reduce clock jitter noise resulting in high frequency application possible, • it possesses lower idle tone and lower out of band noise, • in multibit DSM, the first opamp needs lower input range and slew-rate resulting in lower power consumption. On the other hand, a multibit DSM needs a multibit-DAC on the feedback path which is usually a thermometric current steering DAC limited to 5-bits. Any feedback-DAC can suffer from inevitable mismatching occurred during fabrication process. This is a large disadvantage of the multibit DAC which seriously degrades its SNR, as it acts in the feedback path. Multibit architecture has no other sever inconvenience and its circuits’ complexity can be accepted if one needs such many advantages mentioned above. In order to integrate a multibit DSM, several error correction methods have been developed as trimming, calibration, digital correction, and dynamic element matching ( DEM ). The last one is widely used in high performance integrated modulators having a resolution over 10 bits. This technique can be realized in different ways. Randomization scheme whitens DAC’s mismatch errors over whole frequency range, so that input depended tones are diminished but its noise floor increases in the band of interest. Thus, better solution can be using a mismatch noise shaping technique. The well-known data weighted averaging method ( DWA) can effectively be used to shape mismatch errors reside in signal band. However, with the same frequency as in the quantizer, it can mainly be applied as a first order lowpass mismatch-shaping. For higher order mismatch-shaping, only two original methods have been introduced; feedback-vector or sorting algorithm (SDEM ) [3] and tree-structured scheme ( TDEM ) [4]. The SDEM suffers from lower hardware efficiency and clock rate limits, especially for higher number of quantization level. The TDEM suffers more from algorithm instability for high order mismatch-shaping. The authors have lately developed two new schemes, which are based on two mentioned original methods. The first one, calledMDEM , is a mixed structured of SDEM and TDEM [5]. The MDEM benefits of better stability nature of SDEM and hardware efficiency of TDEM. The second one, called STDEM , is a shortened tree-structured introduced in [6]. It is more stable than the pure TDEM with the same hardware efficiency. This paper tends to further generalize these schemas and introduces some examples of its related circuits, which are designed for a 3-bit feedback-DAC, in two next sections. II. SIMPLIFIED DYNAMIC ELEMENT MATCHING ALGORITHM The proposed algorithm is based on conventional TDEM [4] using an adapted segmenting strategy [7]. Figure 1 shows the general block diagram of a B-bit segmented tree-structured DAC, where each of thes segments employs an M-level sub dynamic element matching (Sub-DEM) algorithm. In order to explain the proposed algorithm, first we need to rewrite some basic equations for a TDEM algorithm [4], as in the left side of the schematic shown in figure 1. A conventional pure TDEM maps each digital input, supposed