2892 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 46, NO. 12, DECEMBER 2011 Digital Approaches to ISI-Mitigation in High-Resolution Oversampled Multi-Level D/A Converters Lars Risbo, Member, IEEE, Rahmi Hezar, Member, IEEE, Burak Kelleci, Member, IEEE, Halil Kiper, Member, IEEE, and Mounir Fares, Member, IEEE Abstract—A new digital signal processing approach to shaping intersymbol interference (ISI) and static mismatch errors simul- taneously in oversampled multi-level digital to analog converters (DAC) has recently been proposed. In this paper, a mathematical framework is established for analyzing ISI errors as well as comparing the ISI sensitivities of different mismatch shaping algorithms. The framework is used to analyze the fundamental problems of popularly used algorithms such as data-weighted-av- eraging (DWA) in the presence of nonlinear ISI: Large-signal even-order distortion and frequency modulated harmonics at low signal levels. The new ISI-shaping algorithm results in significant improvement over previous schemes including the modified Mis- match Shaper (MMS) which also addresses ISI error. The new ISI shaper, while increasing the digital complexity, practically elim- inates the need for conventional ISI mitigation techniques such as time consuming, layout-critical, non-automated and process specific analog design methods. The advantages of ISI shaping is further verified on an experimental audio DAC with simple non-return-to-zero (NRZ) current steering segments implemented in a 45 nm CMOS process and running off a single-phase clock of only 3.072 MHz. Index Terms—Audio, current-steering DAC, DAC, data- weighted averaging, digital-to-analog conversion, dynamic ele- ment matching, frequency modulation, idle tones, intersymbol-in- terference (ISI), ISI-shaping, mismatch shaping, noise shaping, non-return-to-zero (NRZ), out-of-band noise, sigma-delta modu- lation, vector quantizer. I. INTRODUCTION T HE current trend in high-performance audio DACs is to use fine resolution quantization to reduce the out-of-band noise (OBN), reduce jitter sensitivity and simplify analog fil- tering. Recent techniques achieve this goal by using a mix of DAC elements with different weights, e.g., segmenting [1] or cascading [2]. Unlike 1-bit modulation, the multi-level DACs need mismatch shaping algorithms to compensate for the typ- ical 0.1–1% on-die static element mismatch. In addition to the Manuscript received April 08, 2011; revised June 30, 2011; accepted July 29, 2011. Date of publication October 03, 2011; date of current version November 23, 2011. This paper was approved by Guest Editor Yiannos Manoli. L. Risbo is with Texas Instruments Denmark A/S, DK-2800 Kgs. Lyngby, Denmark (e-mail: lri@ti.com). R. Hezar is with Texas Instruments Inc., Dallas, TX 75243 USA. B. Kelleci is with the College of Engineering and Architecture, Okan Univer- sity, Tuzla, Istanbul, 34959 Turkey. H. Kiper is with MediaTek, Woburn, MA 01801 USA. M. Fares is with Texas Instruments Inc., Dallas, TX 75243 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSSC.2011.2164965 element mismatch, dynamic error sources such as asymmet- rical switching, clock skew and parasitic memory are major hin- drances to achieve distortion and dynamic range targets. The re- sulting dependence of present symbol error to the past symbol is referred as intersymbol interference (ISI), and is a function of the switching activity of all the individual DAC-segments. The first digital processing approach to mitigate circuit errors is proposed in [3] with simple averaging of two current sources. Randomization [4] and individual-level-averaging (ILA) [5] are later introduced for multi-level DACs. The very popular data- weighted-averaging (DWA) forms are first described in [6] and [7]. These algorithms can be found in many multi-level DACs and ADCs today due to their simple digital implementation ei- ther as a barrel shifter [6] or tree-branching [7]. Unfortunately, all of these methods [3]–[7] are addressing only the static mis- match problem. In addition, DWA algorithms [6], [7] increase the switching activity, thus amplify ISI errors. Furthermore, the error comes often in the form of spurious tones with signal dependent frequency (FM modulation [8]) that ruins the low- amplitude performance (e.g., harmonics for a 60 dB signal) which is critical for the perceived sound quality. A common remedy is to add a digital DC offset to shift the tones out of band. However, this merely moves the problematic amplitude region, and does not solve the problem. Moreover, ISI errors often limit the large signal THD as a result of a strong signal dependent modulation of the element transition rate. One popular analog solution to reduce ISI errors is to use the return-to-zero (RTZ) approach which eliminates the de- pendence on the previous symbol, [9]. However, it leads to increased current consumption, more high frequency compo- nents and higher sensitivity to circuit timing/jitter. Another analog solution [1] is to use a track and hold circuit to deglitch the waveform. However, such sampling circuits are sensitive to aliasing of high frequency noise. The Pulse Width Modulation method in [2] forces a fixed transition rate of the DAC elements resulting in a significantly reduced sensitivity to ISI. However, this comes at the expense of a high clock rate which may not be available in the system. This is also the case for the highly interesting DEM scheme of [10] with a fixed transition rate but without the intrinsic nonlinearity of PWM. Unfortunately, this scheme puts severe restrictions to the noise shaper preceding the DEM [10]. Recently, the “ISI-Shaper” DEM algorithm was introduced [11]. This algorithm provides concurrent spectral high-pass shaping of static element mismatch and dynamic ISI errors. An 0018-9200/$26.00 © 2011 IEEE