Gain Calibration Research Articles

A 10.1-ENOB, 6.2-fJ/conv.-step, 500-MS/s, Ringamp-Based Pipelined-SAR ADC With Background Calibration and Dynamic Reference Regulation in 16-nm CMOS

This work presents a single-channel, fully dynamic pipelined-SAR ADC with relaxed architectural tradeoffs thanks to the use of ring amplification and background calibration. It leverages a novel SAR quantizer and narrowband dither injection to achieve fast and comprehensive background calibration of DAC mismatch, interstage gain, and ring amplifier (ringamp) linearity and bias optimality. The ADC also includes an on-chip, wide-range, fully dynamic reference regulation system. Implemented in 16-nm CMOS, it consumes 3.3 mW at 500 MS/s (including regulation) and achieves 10.1 ENOB and 75.5-dB SFDR, resulting in Schreier and Walden figure-of-merit (FoM) values of 171.1 dB and 6.2 fJ/conv.-step, respectively.

A Self-Adapted Two-Point Modulation Type-II Digital PLL for Fast Chirp Rate and Wide Chirp-Bandwidth FMCW Signal Generation

Different from the conventional two-point modulation (TPM) type-II phase-locked loops (PLLs) requiring non-trivial gain calibrations and TPM type-III PLLs with loop stability concern and limited chirp rate, a self-adapting gain mismatch TPM type-II digital PLL is proposed in this article. It directly detects frequency error as its input signal, allowing frequency ramp tracking with zero steady-state frequency error using a type-II PLL. In addition, the maximum trackable slope in the case of the proposed TPM type-II PLL is intrinsically larger than that of the conventional TPM type-III PLL. A polarity navigator is embedded in the digital loop filter to improve the linearity at the chirp turning-around points (TAPs). Fabricated in a 28-nm complementary metal–oxide–semiconductor (CMOS) technology, the proposed PLL consumes 23 mW from a 1-V power supply and occupies 0.31 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The measurement results indicate that the proposed PLL can generate a precise triangular chirp with 2.27-GHz bandwidth (BW) and 18.2- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> period at 12.5 GHz. To the best knowledge of the authors, this work demonstrates the widest normalized Chirp-bandwidth and the fastest chirp rate simultaneously.

OTA-Free 1–1 MASH ADC Using Fully Passive Noise-Shaping SAR &amp; VCO ADC

We present an OTA-free 1–1 multi-stage noise-shaping (MASH) analog-to-digital converter (ADC) utilizing a fully passive noise-shaping successive approximation register (NS-SAR) as the first stage and an open-loop ring voltage-controlled oscillator (VCO) as the second stage. The key contribution of this work is to address the challenge of driving large sampling capacitors for high-resolution NS-SAR. The proposed architecture allows a low-resolution NS-SAR stage and leverages residue attenuation due to passive charge sharing in the NS-SAR to linearize the VCO. The MASH architecture suppresses quantization noise and SAR comparator noise at the ADC output, and the high pass shapes VCO thermal noise. In addition, we demonstrate a computationally inexpensive foreground inter-stage gain calibration algorithm for the proposed ADC architecture. The prototype ADC consumes 0.16 mW while achieving an SNDR/DR of 71.5/75.8 dB over a 1.1-MHz bandwidth and Walden FoM of 23.3 fJ/step, which is the lowest in 65-nm technology.

A time-interleaved ADC calibration technique for spectrum monitoring applications

A fully background estimation and calibration technique to reduce the spur powers caused by time-interleaved ADC architecture is presented. The estimations of mismatches are succeeded using easily generated calibration signals. The implementation details for the mismatch estimations and calibrations are provided using a 2.8 GSPS ADC and a FPGA device. Continuous operation of the spectrum monitoring applications is allowed while the mismatch estimation and the calibration process in progress. The offset mismatch calibration is realized using an adder circuit at the background and more than 10 dB spur power reduction is obtained from the proposed method. A digital multiplier circuit is used to realize the gain calibration. The timing skew calibration is fulfilled by the addition of a small offset to the DDS (Direct Digital Synthesizer) phase offset of DDC (Digital Down Converter). It is possible to get more than 6 dB power reduction at some critical spur signals after the application of proposed timing mismatch calibration technique when a single tone sine wave input is applied.

A 20 MHz Bandwidth 79 dB SNDR SAR-Assisted Noise-Shaping Pipeline ADC With Gain and Offset Calibrations

This article presents a second-order successive approximation register (SAR)-assisted noise-shaping (NS) pipeline analog-to-digital converter (ADC) with optimized noise transfer function (NTF) zeros, background inter-stage gain, and offset calibrations. The NS, realized with an error-feedback (EF) structure, takes place in the second stage of the pipeline. A single amplifier, utilized for residue handover, realizes the EF and the optimized zeros. Copies of the EF capacitors allow their rotation role for residue saving, feedback, and sampling operations, thus omitting the extra phase for the EF operation. While further incorporating a coarse SAR ADC and partial interleaving techniques, the prototype can run at high speed with low power and strong in- band noise suppression. A split-over-time architecture with level-shift-based gain calibration is introduced to ensure the robustness of the ADC, whose hardware also facilitates the offset calibration. Besides, the split second-stage ADCs also share a single comparator, thus enabling a mismatch error insensitive split-ADC architecture with a fast convergence speed of 4000 cycles. Fabricated in 28 nm CMOS, the ADC prototype runs at a 260 MHz sampling rate and retains 20 MHz bandwidth (BW) with a signal-to-noise-and-distortion ratio (SNDR) of 79.1 dB under a small over-sampling ratio (OSR) of 6.5. It consumes 3.1 mW power at a 1 V supply and yields a Schreier figure-of-merit (FoM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> ) of 177.2 dB.

Calibration of gain and timing mismatch for TI-ADCs with signals in all Nyquist zones using adaptive noise canceller

This paper presents a novel all-digital background calibration technique for general Time-Interleaved Analog-to-Digital Converters (TIADCs). Calibration of gain and timing mismatch of TIADCs using the estimation technique is designed based on the principle of the Adaptive Noise Canceller (ANC). In this ANC, there are two stages in gain, timing mismatch estimation in which a cascade structure of the correction and estimation is proposed to guarantee that our calibration achieves high performance. Besides the first Nyquit zone, the input signal at different Nyquist zones is also experimented. It is shown through the result that our calibration performs excellently on all chosen Nyquist zones. It achieves the SNDR (Signal to Noise Ratio) and SFDR (Spurious Free Dynamic Range) improvement of 19dB and 49dB, respectively. Moreover, the synthesized design with hardware co-simulation carried on the Xilinx Kintex-7 field-programmable gate array (FPGA) platform consumes only 7.36 % of the hardware resources of the FPGA chip and reduces the mismatch tone level to -87 dB. In addition, our convergence speed of SNDR during calibration is approximately 1/3 others.

Gain and Phase Calibration of Uniform Rectangular Arrays Based on Convex Optimization and Neural Networks

A calibration method based on convex optimization (CVX) and neural networks is proposed for the large planar arrays of phased array three-dimensional imaging sonar systems. The method only needs an acoustic calibration source at an unknown position in the far field, and the direction of arrival (DOA) and gain and phase error are jointly estimated. The method uses a CVX algorithm to solve an optimization problem and initially estimates the DOA of the calibration source robustly. Subsequently, according to the estimation results, a neural network is used for fitting to obtain off-grid DOA estimation of the calibration source. Thereafter, spatial matched filtering is performed to obtain the gain and phase residual estimations. The root mean square error (RMSE) of the beam pattern calibrated by the method for uniform planar arrays can reach a value of 4.9542 × 10−5. The experimental results demonstrate the efficiency of the proposed method for gain and phase calibration.

Fully Digital On-Chip Wideband Background Calibration for Channel Mismatches in Time-Interleaved Time-Based ADCs

This letter presents a fully integrated on-chip digital mismatch compensation system for time-based time-interleaved (TI) data converters. The proposed digital compensation features blind calibration of gain, offset, and timing mismatches. The implemented system uses time-based sampling clock mismatch detection, achieving convergence within 32K samples, which is on par with analog-assisted background methods. A specialized filter structure compensates for timing mismatches of magnitude up to 0.21 of the sampling period, nearly triple the range of other published digital compensation methods, and is effective for input signals up to 0.92 Nyquist bandwidth. The on-chip digital correction achieves suppression of all mismatch tones to levels below −60 dBc while running fully in the background. The operation is demonstrated with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times $ </tex-math></inline-formula> TI 2-GS/s analog-to-digital converter (ADC) prototype chip implemented in a 28-nm CMOS process.

A 529-μW Fractional-N All-Digital PLL Using TDC Gain Auto-Calibration and an Inverse-Class-F DCO in 65-nm CMOS

This paper presents an ultra-lower-power (ULP) digital-to-time-converter (DTC)-assisted fractional-N all-digital phase-locked loop (ADPLL) suitable for IoT applications. A proposed hybrid time-to-digital converter (TDC) extends the vernier-TDC input range with little power overhead in order to overcome the stability issue in the conventional architectures. The hybrid TDC also facilitates a background gain calibration to achieve a stable in-band phase noise insensitive to process, voltage, and temperature (PVT) variations. The implementation of a buffer-cascaded DTC simplifies the design complexity of the fractional-N operation. The ADPLL also features a 200<inline-formula> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> low-phase-noise inverse-class-F (class-F^&#x2212;1) digitally controlled oscillator (DCO) without the need of two-dimensional (2-D) capacitor tuning for frequency alignment of the fundamental and 2^nd-harmonic. Fabricated in 65-nm CMOS, the ULP ADPLL prototype achieves 868fs_rms jitter in a fractional-N channel when consuming only 529<inline-formula> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula>, corresponding to a figure-of-merit (FoM) of &#x2212;244dB.

Calibration of Siberian Radioheliograph antenna gains using redundancy

The paper describes application of standard gain calibration using redundancy for a 48-antenna prototype of Siberian Radioheliograph. Traditionally, for calibration, the visibilities were measured only between adjacent antennas since they have the highest signal-to-noise ratio and are sufficient for phase calibration. We have shown that this limited set of visibilities did not allow using the antenna array redundancy potential and obtaining images with a high dynamic range on a permanent basis. Images without amplitude calibration contain many artifacts and require special care when analyzed. The inclusion of visibility measurement between antennas with a double step made it possible to significantly increase the accuracy of solving the system of equations for amplitudes. Images constructed using both phase and amplitude calibrations do not have visible artifacts and are more reliable.

Измерение задержек в приемном тракте Сибирского радиогелиографа

To achieve the maximum dynamic range of solar radio images obtained using aperture synthesis in relatively wide frequency bands 0.1−0.5 % of the operating frequency, it is necessary to compensate the signal propagation delays in the antenna receive path before calculating visibility functions (hereinafter visibilities). When visibilities are corrected without delay compensation, the signal-to-noise ratio decreases due to residual phase slopes in the receiving system bandwidth. In addition to enhancing dynamic range, preliminary compensation for delays simplifies real-time imaging — no antenna gain calibration is required to get a first approximation image. The requirements for the accuracy of antenna placement are also reduced — in contrast to the measurement of the phase visibility error, the measurement of the delay is actually not so critical to the antenna position errors that are larger than the operating wavelength. The instantaneous frequency band of the Siberian Radioheliograph, which determines the minimum step for measuring the phase slope, and hence the accuracy of determining the delay, is 10 MHz. At the speed of light in an optical fiber of ~0.7c, a step of 10 MHz makes it possible to unambiguously measure the difference between electrical lengths of cables up to 20 m and to correct antenna positions by radio observations, even if the error in the position of the antennas exceeds the operating wavelength. Correction of the band phase slopes during the observation time adapts the radio telescope to the temperature drift of delays and decreases antenna gain phase spread. This, in turn, leads to more stable solutions to systems of equations containing antenna gains as unknowns.

Measurement of Siberian Radioheliograph cable delays

To achieve the maximum dynamic range of solar radio images obtained using aperture synthesis in relatively wide frequency bands 0.1−0.5 % of the operating frequency, it is necessary to compensate the signal propagation delays in the antenna receive path before calculating visibility functions (hereinafter visibilities). When visibilities are corrected without delay compensation, the signal-to-noise ratio decreases due to residual phase slopes in the receiving system bandwidth. In addition to enhancing dynamic range, preliminary compensation for delays simplifies real-time imaging — no antenna gain calibration is required to get a first approximation image. The requirements for the accuracy of antenna placement are also reduced — in contrast to the measurement of the phase visibility error, the measurement of the delay is actually not so critical to the antenna position errors that are larger than the operating wavelength. The instantaneous frequency band of the Siberian Radioheliograph, which determines the minimum step for measuring the phase slope, and hence the accuracy of determining the delay, is 10 MHz. At the speed of light in an optical fiber of ~0.7c, a step of 10 MHz makes it possible to unambiguously measure the difference between electrical lengths of cables up to 20 m and to correct antenna positions by radio observations, even if the error in the position of the antennas exceeds the operating wavelength. Correction of the band phase slopes during the observation time adapts the radio telescope to the temperature drift of delays and decreases antenna gain phase spread. This, in turn, leads to more stable solutions to systems of equations containing antenna gains as unknowns.

Калибровка амплитуд коэффициентов передачи антенн Сибирского радиогелиографа с использованием избыточности

The paper describes application of standard gain calibration using redundancy for a 48-antenna prototype of Siberian Radioheliograph. Traditionally, for calibration, the visibilities were measured only between adjacent antennas since they have the highest signal-to-noise ratio and are sufficient for phase calibration. We have shown that this limited set of visibilities did not allow using the antenna array redundancy potential and obtaining images with a high dynamic range on a permanent basis. Images without amplitude calibration contain many artifacts and require special care when analyzed. The inclusion of visibility measurement between antennas with a double step made it possible to significantly increase the accuracy of solving the system of equations for amplitudes. Images constructed using both phase and amplitude calibrations do not have visible artifacts and are more reliable.

A Nonlinear Observability Analysis of Ambient Wind Estimation with Uncalibrated Sensors, Inspired by Insect Neural Encoding.

Estimating the direction of ambient fluid flow is key for many flying or swimming animals and robots, but can only be accomplished through indirect measurements and active control. Recent work with tethered flying insects indicates that their sensory representation of orientation, apparent wind, direction of movement, and control is represented by a 2-dimensional angular encoding in the central brain. This representation simplifies sensory integration by projecting the direction (but not scale) of measurements with different units onto a universal polar coordinate frame. To align these angular measurements with one another and the motor system does, however, require a calibration of angular gain and offset for each sensor. This calibration could change with time due to changes in the environment or physical structure. The circumstances under which small robots and animals with angular sensors and changing calibrations could self-calibrate and estimate the direction of ambient fluid flow while moving remains an open question. Here, a methodical nonlinear observability analysis is presented to address this. The analysis shows that it is mathematically feasible to continuously estimate flow direction and perform self-calibrations by adopting frequent changes in course (or active prevention thereof) and orientation, and requires fusion and temporal differentiation of three sensory measurements: apparent flow, orientation (or its derivative), and direction of motion (or its derivative). These conclusions are consistent with the zigzagging trajectories exhibited by many plume tracking organisms, suggesting that perhaps flow estimation is a secondary driver of their trajectory structure.

A numerical study of 21-cm signal suppression and noise increase in direction-dependent calibration of LOFAR data

ABSTRACT We investigate systematic effects in direction-dependent gain calibration in the context of the Low-Frequency Array (LOFAR) 21-cm Epoch of Reionization (EoR) experiment. The LOFAR EoR Key Science Project aims to detect the 21-cm signal of neutral hydrogen on interferometric baselines of 50–250 λ. We show that suppression of faint signals can effectively be avoided by calibrating these short baselines using only the longer baselines. However, this approach causes an excess variance on the short baselines due to small gain errors induced by overfitting during calibration. We apply a regularized expectation–maximization algorithm with consensus optimization (sagecal-co) to real data with simulated signals to show that overfitting can be largely mitigated by penalising spectrally non-smooth gain solutions during calibration. This reduces the excess power with about a factor of 4 in the simulations. Our results agree with earlier theoretical analysis of this bias-variance trade off and support the gain-calibration approach to the LOFAR 21-cm signal data.

1/f noise analysis for FAST H i intensity mapping drift-scan experiment

ABSTRACT We investigate the 1/f noise of the Five-hundred-meter Aperture Spherical Telescope (FAST) receiver system using drift-scan data from an intensity mapping pilot survey. All the 19 beams have 1/f fluctuations with similar structures. Both the temporal and the 2D power spectrum densities are estimated. The correlations directly seen in the time series data at low frequency f are associated with the sky signal, perhaps due to a coupling between the foreground and the system response. We use singular value decomposition (SVD) to subtract the foreground. By removing the strongest components, the measured 1/f noise power can be reduced significantly. With 20 modes subtraction, the knee frequency of the 1/f noise in a 10-MHz band is reduced to $1.8 \times 10^{-3}\, {\rm Hz}$, well below the thermal noise over 500-s time-scale. The 2D power spectra show that the 1/f-type variations are restricted to a small region in the time-frequency space and the correlations in frequency can be suppressed with SVD modes subtraction. The residual 1/f noise after the SVD mode subtraction is uncorrelated in frequency, and a simple noise diode frequency-independent calibration of the receiver gain at 8-s interval does not affect the results. The 1/f noise can be important for H i intensity mapping, we estimate that the 1/f noise has a knee frequency (fk) ∼ 6 × 10−4 Hz, and time and frequency correlation spectral indices (α) ∼ 0.65, (β) ∼ 0.8 after the SVD subtraction of 30 modes. This can bias the H i power spectrum measurement by 10 per cent.

Development of a Real-Time Magnetic Field Measurement System for Synchrotron Control

The precise knowledge of the magnetic field produced by dipole magnets is critical to the operation of a synchrotron. Real-time measurement systems may be required, especially in the case of iron-dominated electromagnets with strong non-linear effects, to acquire the magnetic field and feed it back to various users. This work concerns the design and implementation of a new measurement system of this kind currently being deployed throughout the European Organization for Nuclear Research (CERN) accelerator complex. We first discuss the measurement principle, the general system architecture and the technology employed, focusing in particular on the most critical and specialized components developed, that is, the field marker trigger generator and the magnetic flux integrator. We then present the results of a detailed metrological characterization of the integrator, including the aspects of drift estimation and correction, as well as the absolute gain calibration and frequency response. We finally discuss the latency of the whole acquisition chain and present an outline of future work to improve the capabilities of the system.

PMT gain calibration and monitoring based on highly compressed hit information in KM3NeT

The cubic-kilometre neutrino telescope, which consists of large-scale 3D-arrays of photomultiplier tubes (PMTs) currently under construction on the Mediterranean seabed, relies on accurate calibration procedures in order to answer its science goals. These proceedings present the gain calibration method used in KM3NeT, which is based on highly compressed PMT hit information. In particular, it is shown that the PMT gains can be tuned to within 2% of the nominal value, based on the measured single photoelectron time-over-threshold distribution of each PMT.

Exploring sub-MeV sensitivity of AstroSat–CZTI for ON-axis bright sources

The Cadmium–Zinc–Telluride Imager (CZTI) onboard AstroSat is designed for hard X-ray imaging and spectroscopy in the energy range of 20–100 keV. The CZT detectors are of 5-mm thickness and hence have good efficiency for Compton interactions beyond 100 keV. The polarisation analysis using CZTI relies on such Compton events and have been verified experimentally. The same Compton events can also be used to extend the spectroscopy up to 380 keV. Further, it has been observed that about 20% pixels of the CZTI detector plane have low gain, and they are excluded from the primary spectroscopy. If these pixels are included, then the spectroscopic capability of CZTI can be extended up to 500 keV and further up to 700 keV with a better gain calibration in the future. Here we explore the possibility of using the Compton events as well as the low gain pixels to extend the spectroscopic energy range of CZTI for ON-axis bright X-ray sources. We demonstrate this technique using Crab observations and explore its sensitivity.

Improved NOAA-20 Visible Infrared Imaging Radiometer Suite Day/Night Band Image Quality by Upgraded Gain Calibration

Due to complex radiometric calibration, the imagery collected by the Day/Night Band (DNB) of the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar Partnership (Suomi-NPP) and the NOAA-20 follow-on satellite is subject to artifacts such as striping, which eventually affect Earth remote sensing applications. Through comprehensive analysis using the NOAA-20 VIIRS DNB prelaunch-test and on-orbit data, it is revealed that the striping results from flaws in the calibration process. In particular, a discrepancy between the low-gain stage (LGS) Earth view (EV) gain and the onboard calibrator solar diffuser view gain makes the operational LGS gain coefficients of a few aggregation modes and detectors biased. Detector nonlinearity at low radiance level also induces errors to the mid-gain stage (MGS) and high-gain stage (HGS) gain through the biased gain ratios. These systematic errors are corrected by scaling the operational LGS gains using the factors derived from the NOAA-20 VIIRS DNB prelaunch test data and by adopting linear regression for evaluating the gain ratios. Striping in the NOAA-20 VIIRS DNB imagery is visibly reduced after the upgraded gain calibration process was implemented in the operational calibration.