A Compensation Method for Magnitude Response Mismatches in Two-channel Time-interleaved Analog-to-Digital Converters Stefan Mendel Christian Doppler Laboratory for Nonlinear Signal Processing Graz University of Technology, Austria Email: stefan.mendel@tugraz.at Christian Vogel Signal Processing and Speech Communication Laboratory Graz University of Technology, Austria Email: c.vogel@ieee.org Abstract— Analog-to-digital converters (ADCs) are critical components of signal processing systems and one of the bottlenecks of modern telecommunication systems. Time-interleaved ADCs (TI-ADCs), in which multiple ADCs are combined, are an effective way to achieve high sampling rates in order to comply with modern telecommunication standards. The drawback of such TI-ADCs are additional errors that are due to mismatches among the channels, which degrade the overall per- formance. Several qualified methods have been proposed to compensate offset, static gain, and timing (or linear-phase) mismatches. However, an effective method to compensate frequency-dependent magnitude response mismatches is still missing. In this paper we consider the compensation of frequency-dependent magnitude response mismatches for a two-channel time-interleaved sampling system. A single linear-phase finite impulse response (FIR) filter cascaded by a single time-varying multiplier provides the magnitude response compensation so that the performance of a TI- ADC is no longer limited by linear channel mismatches. I. I NTRODUCTION In order to increase the sampling rate of an analog-to-digital converter (ADC) beyond a certain production process limit, time interleaving of ADCs has been proposed [1]. The analog input signal is successively sampled by different channel ADCs in a cyclic manner. Theoretically, the overall sampling rate of such a time- interleaved ADC (TI-ADC) scales with the number of ADCs in contrast to a single ADC. Ideally, the characteristics of all ADCs should be identical; in practice, however, various technology depen- dent imperfections cause component mismatches. These mismatch errors become evident as fluctuation of the sampled values in the time domain and as an increase of spurious spectral components in the frequency domain. Therefore mismatches degrade for example the signal-to-noise and distortion ratio (SINAD) [2]. Offset, static gain, timing (or linear-phase), and frequency response mismatches are four significant types of mismatch errors [3]. Several techniques to compensate for timing mismatch errors have been introduced, e.g., [4] or [5]. A prototype implementation considering offset, gain, and timing mismatch calibration has been presented in [6]. In [7] it has been pointed out that magnitude response mismatches are the remaining factor limiting the performance, after having compensated for offset, static gain, and linear-phase mismatches. The influence of nonlinear-phase response mismatches is significantly smaller than the error due to magnitude response mismatches. Thus, an open issue to compensate frequency response mismatches is the compensation of magnitude response mismatches. The author in [8] shows a method to compensate frequency-dependent mismatches based on a discrete Fourier transform (DFT). This approach is limited to a finite number of samples due to the DFT calculation and it is not shown how to extend this method to continuous processing of samples. In [9] measurements of each channel transfer function are used to design finite-impulse response (FIR) filters, which need large tap sizes for compensating linear mismatches. An estimation TI-ADC y 1 (t) y 0 (t) ADC 0 h 0 (t) ADC 1 h 1 (t) ∑ ∞ q=−∞ δ(t − (2 · q + 1) · T s ) ∑ ∞ q=−∞ δ(t − (2 · q + 0) · T s ) Impulse train to sequence converter y[n] y(t) x(t) Fig. 1. Time-interleaved ADC with two channels. Each ADC is modeled by a linear filter (h 0 (t), h 1 (t)) and a sampler, which has a sampling period of 2 · Ts and a constant time offset (0 · Ts, 1 · Ts). The TI-ADC output y(t) can be interpreted as the sum of the signal ˜ y(t) and an error signal e(t) introduced by mismatches between h 0 (t) and h 1 (t). equalizing technique to reduce the effect of linear and nonlinear mismatches in the transfer characteristic is applied in [10]. In this paper we propose a novel compensation structure for magnitude response mismatches in a two channel time-interleaved sampling system. Only a single FIR filter followed by a time- varying multiplier is used to compensate the magnitude response mismatches. Since many methods for compensating offset, static gain, and timing mismatches are known, we assume for the analysis that these errors have already been compensated and do not limit the TI-ADC performance. Nevertheless, in the simulation section we consider the influence of all mismatches. II. ANALYSIS Figure 1 depicts a linear two-channel time-interleaved ADC model, where the behavior of the channel ADCs is represented by linear filters with impulse responses h0(t) and h1(t). The output before impulse train to sequence conversion becomes y(t)= 1  m=0 x(t) ∗ hm(t) · ∞  q=-∞ δ(t − (2q + m) · Ts) =˜ y(t)+ e(t), (1) where δ(t) is the Dirac Delta function, Ts is the sampling period, and ∗ denotes the convolution operation. The TI-ADC output is y(t)= 1-4244-0395-2/06/$20.00 ©2006 IEEE. 712