Frequency Response Mismatch Research Articles

Frequency Response Mismatches in 4-channel Time-Interleaved ADCs: Analysis, Blind Identification, and Correction

This article proposes a novel adaptive architecture for blind identification and compensation of frequency response mismatches in 4-channel time-interleaved analog-to-digital-converters (TI-ADCs). Detailed frequency response mismatch modeling is first carried out elaborating in detail the interleaving mismatch spurs characteristics. Stemming from the established mirror-frequency crosstalk nature of the different mismatch spurs, the interleaving mismatch identification process is then carried out using complex second-order statistics based methods. The developed learning algorithm performs the mismatch identification and learns the mismatch compensation filter parameters in a blind manner for almost the full digital bandwidth of the 4 TI-ADC system. The proposed solution's efficiency and performance are verified and demonstrated using state-of-the-art RF-sampling TI-ADC hardware measurements with GHz range instantaneous bandwidth. In addition to this, the relationship between a four-channel TI-ADC and an I/Q sampling 2-channel TI-ADC is explored and an interesting link between the two is established in this work.

An Adaptive All-Digital Blind Compensation of Dual-TIADC Frequency-Response Mismatch Based on Complex Signal Correlations

This brief introduces an adaptive all-digital architecture for dual time-interleaved analog-to-digital converter (TIADC) frequency-response mismatch compensation based on a linear periodic time-varying correction. Parameters of the correction are estimated using correlations of the complex signal derived from the TIADC output. Simulation results of the compensation technique based on real and generated data demonstrate the efficiency of our method.

Correlation-Based Frequency-Response Mismatch Compensation of Quad-TIADC Using Real Samples

This brief proposes a new digital architecture to compensate for the frequency-response mismatch that is specific to four-channel time-interleaved analog-to-digital converters (quad-TIADCs) using a linear periodic time-varying correction and an adaptive feed-backward design. Estimation of the correction parameters is performed iteratively by solving two linear systems based on correlation values of the real signal from the TIADC output. Problem formulation is well detailed and hardware implementation results demonstrate the efficiency of our method.

Frequency Response Mismatch Analysis in Time-Interleaved Analog I/Q Processing and ADCs

This brief examines a novel method to increase the usable analog bandwidth (BW) of an analog-to-digital interface through the use of in-phase/quadrature (I/Q) downconversion or homodyne architecture, followed by time-interleaved analog-to-digital converters (TI-ADCs) in both I and Q branches. The increased analog BW comes with the inherent drawback of various spurious components, due to analog components' frequency response mismatches, which ultimately limit the dynamic range. In this brief, the impacts of different mismatch sources are modeled and analyzed. Actual measured hardware data of the considered time-interleaved homodyne architecture are also presented, verifying the modeling and analysis results. The analysis and modeling results of this brief thus provide new insight into the joint impact of different mismatch mechanisms and pave the way for future contributions on the correction of these mismatches, building on the derived composite behavioral model of the overall time-interleaved I/Q processing.

Analysis, Blind Identification, and Correction of Frequency Response Mismatch in Two-Channel Time-Interleaved ADCs

In this paper, novel blind identification and compensation architectures for the frequency response mismatch of a two-channel time-interleaved analog-to-digital-converter (TI-ADC) are proposed. First, detailed modeling of the frequency response mismatch is carried out, establishing a direct connection and similarity to the well-known in-phase/quadrature mismatch problem. Stemming from this modeling, the proposed blind mismatch identification and compensation architectures are then developed building on complex statistical signal processing. Compared to the existing methods in the literature, the proposed solutions can identify and correct the frequency response mismatch in a fully blind manner for the full digital bandwidth (BW) of the ADC system, and are also applicable in sub-sampling TI-ADC devices and RF sampling. The efficiency of the proposed solutions is verified and demonstrated using comprehensive measurements of actual RF-sampling TI-ADC hardware with gigahertz-scale instantaneous BW.

Introduction to the special issue on IEEE-MWSCAS 2013

It is our pleasure to introduce this special issue on the 56th International IEEE Midwest Symposium on Circuits and Systems (MWSCAS) that was held in Columbus, OH, August 2013. Out of the 436 paper submissions from 36 countries, 372 papers were accepted for presentation in ten special lecture sessions, 38 regular lecture sessions, and 27 poster sessions. The theme of the conference was on ‘‘Advancing the Frontiers of Green Technology’’. In addition to the typical analog, digital and mixed signal circuits sessions, power management and energy harvesting sessions were particularly tied to the conference theme, The paper entitled ‘‘Design of High-Performance Integrated Dimmable LED Driver for High-Brightness SolidState Lighting Applications’’ by Zhidong Liu and Hoi Lee, was selected from that session to present a high-voltage dimmable LED driver in 0.35 lm technology for highbrightness solid-state lighting applications. The driver presented in the paper achieves significant improvements in power efficiency (peak efficiency of 98.8 %) and current accuracy. The improvement in efficiency was realized by eliminating the power diode and the sensing resistor in the power stage, thereby significantly reducing conduction losses in these components. A simultaneous peak and valley current sensing scheme is introduced in the paper to improve current sensing accuracy. The proposed scheme minimizes LED current errors under a wide range of input voltages and LEDs. Analog computer aided design (CAD) and circuit synthesis is a topic of considerable importance to the circuits and systems community (CAS). The paper by Reyad ElKhazali on the Biquadratic Approximation of FractionalOrder Laplacian Operators, introduces an improved algorithm to approximate the fractional Laplace operator. The presented biquadratic transfer function shows a flat phase characteristics with the frequency band of interest, with a bandwidth of approximation that can be extended by cascading several biquadratic modules. In addition to the several numerical examples given, the novel algorithm is also used for synthesizing fractional-order inductors and capacitors. For Analog to Digital Converters, two papers were selected for this special issue. In the paper by Simran Singh, Mikko Valkama, Michael Epp, Lauri Anttila, Wolfgang Schlecker, and Elmar Ingber, entitled, ‘‘Digital Correction of Frequency Response Mismatches in 2-Channel TimeInterleaved ADCs Using Adaptive I/Q Signal Processing’’, the authors propose a novel adaptive compensation architecture to address the frequency response mismatch of 2-channel time-interleaved ADCs. Time interleaved ADC (TI-ADC) are gaining a lot of momentum given the technological limitations on having a single core ADC running at high sampling rate without sacrificing resolution. However, the analog component variations and temperature drift within the parallel ADCs in TI-ADC introduce its own frequency dependent amplitude and phase mismatch, limiting the effective resolution and spurious free dynamic range (SFDR) of the ADC. In the paper, an adaptive method is proposed to detect the frequency response mismatch inside the frequency band of interest by utilizing digital I/Q mismatch estimation and correction algorithms. M. Hella (&) Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180, USA e-mail: hellam@ecse.rpi.edu

Digital correction of frequency response mismatches in 2-channel time-interleaved ADCs using adaptive I/Q signal processing

A novel adaptive compensation architecture for the frequency response mismatch of 2-channel time-interleaved ADC (TI-ADC) is proposed for developing high-performance self-adaptive systems. The proposed approach overcomes the existing methods in the sense that the TI-ADC mismatch identification can be performed without allocating a region where only the TI-ADC mismatch spurs are present. This is accomplished via mapping the TI-ADC problem into an I/Q mismatch problem which allows deploying complex statistical signal processing. As proof of concept, the compensation architecture is demonstrated and tested on a 16-bit TI-ADC measured hardware data.

Prefilter-Based Reconfigurable Reconstructor for Time-Interleaved ADCs With Missing Samples

This brief proposes a reconstruction scheme for the compensation of frequency-response mismatch errors at the output of a time-interleaved analog-to-digital converter (TI-ADC) with missing samples. The missing samples are due to sampling instants reserved for estimating the channel mismatch errors in the TI-ADC. Compared with previous solutions, the proposed scheme offers substantially lower computational complexity.

A Novel Iterative Structure for Online Calibration of $M$-channel Time-Interleaved ADCs

This paper proposes a computationally efficient calibration structure for online estimation and compensation of offset, gain and frequency response mismatches in M-channel time-interleaved (TI) analog-to-digital converters (ADCs). The basic idea of the proposed approach is to reserve some sampling instants for estimating and tracking the mismatch parameters of sub-ADCs with reference to a known input. Since the estimation problem is analogous to a standard system identification problem, we propose two simple variable digital filter (VDF) based adaptive filter structures which are derived from the least mean squares (LMS) and normalized LMS algorithms. On the other hand, the reservation of some sampling instants in the normal operation of TI ADC implies that part of samples have to be sacrificed. Based on a general time-varying linear system model for the mismatch and the spectral property of a slightly oversampled input signal, we also propose a novel iterative framework to solve the resulting underdetermined problem. It not only embraces a number of iterative algorithms for the tradeoff between convergence rate and arithmetic complexity but also admits efficient update structure based again on VDFs. Therefore, thanks to the well-known efficient implementation of VDFs, the adaptability of both estimation and compensation algorithms allows us to combine them seamlessly to form an online calibration structure, which is able to track and compensate for the channel mismatches with low complexity and high reconstruction accuracy. Finally, we demonstrate the usefulness of the proposed approach by means of computer simulations.

A Self-Adaptive Frequency Response Compensation Method for a TIADC System

Time interleaving is one of the most efficient techniques employed in high-speed sampling systems. However, the frequency response mismatch among different channels will create distortion tones that degrade the system performance. In this paper, a self-adaptive frequency response mismatch compensation method is presented, where the design of compensation filter is optimized with a self-adapting strategy. This digital postprocessing technique realizes the compensation of frequency response effectively and also the increase of the digital bandwidth of the acquisition system. MATLAB-based simulation and an actual two-channel acquisition system test verify the effectiveness of the algorithm.

New Iterative Framework for Frequency Response Mismatch Correction in Time-Interleaved ADCs: Design and Performance Analysis

This paper proposes a new iterative framework for the correction of frequency response mismatch in time-interleaved analog-to-digital converters. Based on a general time-varying linear system model for the mismatch, we treat the reconstruction problem as a linear inverse problem and establish a flexible iterative framework for practical implementation. It encumbrances a number of efficient iterative correction algorithms and simplifies their design, implementation, and performance analysis. In particular, an efficient Gauss-Seidel iteration is studied in detail to illustrate how the correction problem can be solved iteratively and how the proposed structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. We also study important issues, such as the sufficient convergence condition and reconstructed signal spectrum, derive new lower bound of signal-to-distortion-and-noise ratio in order to ensure stable operation, and predict the performance of the proposed structure. Furthermore, we propose an extended iterative structure, which is able to cope with systems involving more than one type of mismatches. Finally, the theoretical results and the effectiveness of the proposed approach are validated by means of computer simulations.

Adaptive Blind Background Calibration of Polynomial-Represented Frequency Response Mismatches in a Two-Channel Time-Interleaved ADC

This paper introduces an adaptive calibration structure for the blind calibration of frequency response mismatches in a two-channel time-interleaved analog-to-digital converter (TI-ADC). By representing frequency response mismatches as polynomials, we can exploit slight oversampling to estimate the coefficients of the polynomials by using the filtered-X least-mean square (FxLMS) algorithm. Utilizing the coefficients in an adaptive structure, we can compensate frequency response mismatches including time offset and bandwidth mismatches. We develop an analytical framework for the calibration structure and analyze its performance. We show the efficiency of the calibration structure by simulations, where we include examples from the literature.

A Flexible and Scalable Structure to Compensate Frequency Response Mismatches in Time-Interleaved ADCs

In this paper, we present a flexible and scalable structure to compensate frequency response mismatches in time-interleaved analog-to-digital converters (TI-ADCs). The flexibility of the structure allows for designing compensation filters independent of the number of channels that can achieve any desired signal-to-noise ratio due to the scalability of the structure. Therefore, the compensation structure may be used to compensate time-varying frequency response mismatches in TI-ADCs, as well as to reconstruct uniform samples from nonuniformly sampled signals. We analyze the compensation structure, investigate its performance, and demonstrate application areas of the structure through numerous examples.

A Polynomial-Based Time-Varying Filter Structure for the Compensation of Frequency-Response Mismatch Errors in Time-Interleaved ADCs

This paper introduces a structure for the compensation of frequency-response mismatch errors in M-channel time-interleaved analog-to-digital converters (ADCs). It makes use of a number of fixed digital filters, approximating differentiators of different orders, and a few variable multipliers that correspond to parameters in polynomial models of the channel frequency responses. Whenever the channel frequency responses change, which occurs from time to time in a practical time-interleaved ADC, it suffices to alter the values of these variable multipliers. In this way, expensive on-line filter design is avoided. The paper includes several design examples that illustrate the properties and capabilities of the proposed structure.

A Least-Squares Filter Design Technique for the Compensation of Frequency Response Mismatch Errors in Time-Interleaved A/D Converters

This paper introduces a least-squares filter design technique for the compensation of frequency response mismatch errors in M-channel time-interleaved analog-to-digital converters. The overall compensation system is designed by determining M filter impulse responses analytically through M separate matrix inversions. The proposed technique offers an alternative to least-squares techniques that determine all filters simultaneously. Several design examples are included for illustration.

Digital Signal Processing with Interleaved ADC Systems

This paper addresses a problem associated with interleaved ADC systems from the digital signal processing algorithm design perspective. The output streams of an interleaved ADC system are inherently in parallel format. It would be nice if DSP algorithms can be designed to take advantage of the inherently parallel signal streams in the interleaved ADC system without the need of a high speed parallel-to-serial multiplexer. Frequency response of a parallel filter bank is derived. It is found that the overall frequency response is the average of each individual interpolated channel filter plus the aliasing components. The aliasing components come from the deviation of each individual channel from the average response.Results are applied to characterize the gain mismatch of ADC arrays. Sinusoidal response is also investigated. The results can be used to characterize the frequency response mismatch of ADC arrays.

Analysis of the uncertainty budget for the reflection and absorption coefficient given by the two-microphone method

The method for measurement of the reflection and absorption coefficient at normal incidence consists of a sound source at one end of an impedance tube, where the plane waves propagated are reflected from a sample that is at the other end of the tube. Those plane waves are generated by a random signal, and the decomposition of the standing wave pattern is carried out measuring the acoustical pressure at two-fixed microphone positions, from which it is possible to determine a transfer function to obtain the reflection and absorption coefficient. The systematic errors associated with the two-microphone technique using an impedance tube are analyzed, i.e., microphone-sample distance, microphone spacer, atmospheric measurement conditions, correction factors to the microphone sensitivity, and phase and amplitude mismatch in the microphones. These parameters constitute some of the sources to the measurement uncertainty of the measurand-reflection and absorption coefficient. The estimation of the measurement uncertainty for the reflection and absorption coefficient by the two-microphone method; likewise the analysis of the uncertainties sources and its sensitivity coefficients are discussed using a linear approach model. Furthermore, the influence of the correction factor due to the frequency response mismatch in the microphones in the calculation of the reflection and absorption coefficient is experimentally evaluated.