Sigma Delta Modulation Research Papers

A 280 mW, 0.07% THD+N class-D audio amplifier using a frequency-domain quantizer

2026, Analog Integrated Circuits and Signal Processing

Pulse Density Modulation-(PDM-) based class-D amplifiers can reduce nonlinearity and tonal content due to carrier signal in Pulse Width Modulation -(PWM-) based amplifiers. However, their low-voltage analog implementations also require a... more

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Experimental Demonstration of MASH Based Sigma Delta Radio over Fiber System for 5G C-RAN Downlink

by Giovanni Tartarini

2025, Journal of Optical Communications

Sigma Delta Radio over Fiber (S-DRoF) systems are looked upon as an enabling technology due to their advantages that comes due to combination of analog and digital radio over fiber (RoF) systems. In this paper, we have proposed and... more

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A 280 mW, 0.07% THD+N class-D audio amplifier using a frequency-domain quantizer

by Tino Copani

2025, Analog Integrated Circuits and Signal Processing

Pulse Density Modulation-(PDM-) based class-D amplifiers can reduce nonlinearity and tonal content due to carrier signal in Pulse Width Modulation -(PWM-) based amplifiers. However, their low-voltage analog implementations also require a... more

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Design of a low‐voltage op‐amp‐less ASDM to linearise VCO‐ADC

by Pieter Rombouts

2024, Electronics Letters

We present a very simple ASDM design for linearization of VCO ADC's. The circuit only consists of a passive feedback filter and a schmitt trigger. By proper sizing, the nonlinearity error can be reduced to well below 0.12% for input... more

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Using a Second Order Sigma-Delta Control to Improve the Performance of Metal-Oxide Gas Sensors

by Lukasz Kowalski

2024, Sensors (Basel, Switzerland)

Controls of surface potential have been proposed to accelerate the time response of MOX gas sensors. These controls use temperature modulations and a feedback loop based on first-order sigma-delta modulators to keep constant the surface... more

Figure 6. Experimental results in which 1st and 2nd order controls are used to obtain a given sequence of target chemical resistances Ry. (a) Time evolution of the chemical resistance (Left) and of the average temperature provided by the 1st order loop (Right); Ry, was set to 376, 385, 375, 381, 377, 382, and 380 kO in 15 min intervals; Thien = 280 °C, Tow = 200 °C, 6 = 25%, and Ts = 1 s; (b) same results when 2nd order control was applied to set Rehem to 341, 348, 335, 346, 337, 344, and 339 kO. in 60 min intervals; Thigh = 280 °C, Tio = 200 °C, x = 2 kO, 6 = 20% and Ts = 2s. In left plots, the grey lines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 200 samples. the control loop applies more BIT1s (T),;g, dominant), increasing the oxygen adsorption in the sensing ayer, until Rejem = Ry, is reached; from then on, the bit stream /temperature average slowly tends to the value necessary to keep Reje Constant. However, two “plateau events”, labeled as I and II in Figure 6a, are also observed. During these events, the average temperature injected into the sensor becomes locked to 240 °C (which corresponds to the same average number of BIT1s and BITOs, i.e., by = 0.5 or the temperature value (Thigh + Tiow)/2), and, in practice, the system behaves as in open-loop, thus losing control on the value of Reyer.

Figure 1. (a) First-order sigma-delta modulator topology to control the chemical resistance of the metal-oxide sensing layer. At each sampling time Ts, depending on whether the chemical resistance Rehem, measured at the reference temperature T);j.1,, is below (or above) the desired value Rj, a BIT1 (or BITO) temperature waveform is applied to the sensor during the next sampling period; (b) parameters of the BITO and BIT1 waveforms. The control proposed in [23] is shown in Figure la. It achieved the constant SP operation by applying an adequate sequence of temperature waveforms to the sensor. These waveforms, called BITO and BIT1, can be seen in Figure 1b. By periodically sampling the conductivity of the sensing layer, at the end of each sampling period, it is possible to monitor changes in Vs, since both waveforms end with the same temperature value Tjj.;. The control is designed to apply, for the following sampling period [nT;,(n +1)T;)], a BIT1 waveform if G[nT;] > Gtarget or a BITO if G[nTs] < Gtarget. This way, it is possible to change the average temperature in the sensor, while making decisions based on the conductivity of the sensing layer, measured at the same temperature. Renem, measured at the reference temperature T),jg,, is below (or above) the desired value Ry, a BIT1 (or

Figure 10. Experimental results in which either a 1st or a 2nd order control loop has been used to set Rehem to 155 kQ. when a sequence of small steps of ethanol of 25 ppb concentration was applied to the sensor in 10 min intervals. Tyjgn = 290 °C, Tiow = 160 °C, 5 = 25%, and Ts = 1s in both cases; « = 3 kO in the 2nd order case. (a) Evolution with time of the ethanol concentration (Top), the averaged bit stream provided by the control loop (Middle), and the chemical resistance (Bottom) when 1st order control was used; (b) same results when 2nd order control was used. In bottom plots the grey lines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 200 samples. Figure 10. Experimental results in which either a 1st or a 2nd order control loop has been used to set

Figure 5. Description of the experimental setup.

Figure 4. (a) XRD results obtained for typical tungsten oxide nanowire films. Tungsten oxide is single crystalline and belongs to the monoclinic phase; (b) low magnification micrograph showing the AACVD grown film on top of the electrode area of a sensor within the 4-element transducer (Left). Higher magnification micrograph showing the typical microstructure of the AACVD grown tungsten nanowire films (Right). The morphology and crystalline phase of the gas sensitive films were analyzed using an Environmental Scanning Electron Microscope (ESEM) and X-Ray Diffraction (XRD). Figure 4a shows typical XRD results for the films grown. These results indicate that a slightly oxygen-defective tungsten oxide is obtained, which corresponds to WO) 72 nanowires that have a P2/m belonging to the monoclinic system, in accordance to the JPCD card no. 73-2177. Figure 4b shows ESEM results. The lower magnification micrograph shows one membrane with interdigitated electrodes and, in light grey, the sensing layer composed of WO3 nanowires. The higher magnification micrograph shows a closer view of the nanowire film. grey, the sensing layer composed of WO3 nanowires. The higher magnification micrograph shows a

Figure 8. Experimental results in which 1st and 2nd order controls are applied to set Rene, to 340 kO, for 3 h. In both cases, Thign = 290 °C, Tiow = 200 °C, 6 = 25%, and Ts = 0.5 5; « = 1.4 kO in the 2nd order case. (a) Chemical resistance of the sensing layer (Top) and averaged temperature provided by the 1st order loop (Bottom); (b) same results as provided by the 2nd order loop; (c) power spectrum densities after 16,384 samples of the bit streams, obtained with standard P-Welch MatLab estimation. In top (a,b) plots, the grey lines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 200 samples.

Figure 2. Block diagram (Top) and equivalent sampled circuit (Bottom) of the 2nd order sigma-delta topology designed to control the chemical resistance of the MOX sensing layer.

Figure 9. Experimental results in which either a 1st or a 2nd order control loop is used to set Reje, to 300 kQ while a step of ethanol concentration was applied to the sensor. Tyjg, = 290 °C, Tigw = 160 °C, 5 = 25%, and Ts = 1s in both cases; « = 3 kO in the 2nd order case. (a) Evolution with time of the ethanol concentration (Top), the average temperature provided by the control loop (Middle), and the chemical resistance (Bottom) when 1st order control was used; (b) same results for 2nd order control. In bottom plots the grey lines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 60 samples.

Figure 7. Experimental results in which 1st and 2nd order controls are used to obtain the same sequence of target chemical resistances Ry, = 370, 382, 372, 358, 368, 388, 372, and 352 kO in 60 min intervals. In both cases, Thign = 280 °C, Tiow = 200 °C, 6 = 20%, and Ts = 2s; « = 2 kO in the 2nd order case; (a) time evolution of the chemical resistance (Left) and of the average temperature provided by the 1st order loop (Right); (b) same results when 2nd order control was applied. In left plots, the grey lines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 50 samples. This means that even by doubling the sampling frequency of the experiment in Figure 6, first order controls may still produce plateaus (Figure 7). However, using the 2nd order control method allows for the avoidance of these plateau-related events, thereby improving the performance of the sensor as a system.

Figure 3. Artistic view inside of the hot wall reactor during the AACVD process. A nitrogen flow carries the aerosol droplets of solvent containing the organic precursor.

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Active control of the surface potential of nanostructured layers

by Lukasz Kowalski

2024, IEEE Sensors Journal

The objective of this paper is to show the first results obtained with a control designed to keep constant the average surface potential of a nanostructured layer. This condition is equivalent to keeping constant the resistivity of the... more

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An Inherently Linear Transducer Using Thermal Sigma-Delta Modulator

by Amauri Oliveira

2024

The aim of this article is to describe a feedback circuit with thermoresistive sensor based on thermal sigma-delta modulator. The circuit uses 1-bit first order sigma-delta modulator in which a considerable part of conversion functions is... more

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A bulk-micromachined soil moisture probe with a mixed-signal interface

by Carlos Couto

2024

This paper presents a Multi-Chip-Module based (MCM) microsystem for irrigation management suitable for greenhouse environmental control. The proposed microsystem includes a soil moisture microsensor, analog interface and sigma-delta... more

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Synthesis of binary test sequences with good spectral properties using an evolutionary algorithm

by Paolo Carbone

2024, Measurement

This paper describes a novel method for the digital synthesis of high quality signals by means of one-bit digital-toanalog converters. The aim of the work is the analysis of the best binary sequences for signal generation, obtained using... more

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Binary Sequences With Good Spectral Properties Obtained by Genetic Algorithms

by Paolo Carbone

2024, IEEE Transactions on Instrumentation and Measurement

This paper describes a novel method for the digital synthesis of high quality signals by means of 1-bit digital-to-analog converters. The aim of this paper is the identification of the best binary sequences for signal generation and the... more

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Towards a narrowband photonic sigma-delta digital antenna

by Phillip Pace

2023

A narrow-band photonic sigma-delta digital antenna is described as a system intended to provide a proof of concept for the use of photonics technology in the sampling of wideband radio frequency (RF) signals.

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Digitally controlled sigma-delta modulated direct matrix converter for high frequency AC-AC Conversion

by Zoza Travels India Immigration Services

2023, Indian Journal of Engineering and Materials Sciences

In recent times, several digitally controlled modulation techniques (MTs) have envisioned for generating pulse width modulation (PWM) trigger pulses to improve the quality of the output (o/p) produced [in terms of reduced total harmonic... more

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A Describing Function Study of Saturated Quantization and Its Application to the Stability Analysis of Multi-Bit Sigma Delta Modulators

by Ludo Weyten

2023, IEEE Transactions on Circuits and Systems I: Regular Papers

This document is an author's draft version submitted for publication to IEEE Trans. Circ. Syst.-I. The actual version was published as [1].

Fig. 4. (a) Best fit gains Kg and Ky with (b) a close in view and (c) the RMS value og of the linearization error vs. the magnitude of the DC signal for the oe of a 9-level quantizer (n = 8) with a Gaussian noise RMS value 2 oN = 775°

Fig. 7. Equivalent describing function model of a MB SA modulator: (a) system diagram corresponding to the signal component and (b) system diagram corresponding to the noise component.

Fig. 12. Describing function prediction of the sinusoidal overloading level (marked with “x”’) as well as the simulated value (marked with “o”) vs. hoo results for maximally flat modulators of order 3,4 and 5. Fig. 11. Iterative algorithm to find Ky, Kg, 7Q, on and Ax fora sinusoidal input signal.

Fig. 15. | Modulator overloading level vs. hoo results for maximally flat modulators with a 17-level quantizer (n = 4): describing function pre- diction (marked with “x”) and experimental value (marked with “o”) for the sinusoidal case, describing function prediction (marked with “+’’)and experimental value (marked with “o”) for the DC case and Kenney and Carley’s bound [15], [16] (marked with “<”). Fig. 14. Modulator overloading level vs. hoo results for maximally flat modu- lators with a 3-level quantizer (n = 2): describing function prediction (marked with “x”) and experimental value (marked with “o”) for the sinusoidal case, describing function prediction (marked with “-++”)and experimental value (marked with “o’”) for the DC case and Kenney and Carley’s bound [15], [16] (marked with “<”’).

Fig. 9. Describing function results for a maximally flat 3rd-order modulator with hoo = 4 for the case of a 9-level quantizer (n = 8) vs. the modulator DC input level: (a) Best fit gains Kg and Ky with (b) the RMS noise level on in front of the quantizer and (c) the RMS value og of the linearization error.

Again we had to evaluate the integrals numerically, but it turns out that this can be done efficiently. Just as for the DC-case, the best fit gains Ky, Kg and the variance 0% of the linearization error all depend both on the amplitude of the quantizer input signal Ax and on the Again we were unable to find an analytical solution of the above integrals, but also here it is easy to obtain an efficient numerical evaluation (see e.g. the appendix). This way, Kg can be evaluated for any given n and oy and we can say that Kg sin(on,7) is a known function:

Fig. 6. (a) Best fit gains Kg and Ky with (b) a close in view and (c) the RMS value og of the linearization error vs. the magnitude of the DC signal for the ae of a 9-level quantizer (n = 8) with a Gaussian noise RMS value 2 oO = 7 N ~ V7

Fig. 13. Modulator overloading level vs. hoo results for maximally flat modu- lators with a 9-level quantizer (n = 8): describing function prediction (marked with “x”) and experimental value (marked with “o”) for the sinusoidal case, describing function prediction (marked with “++’’)and experimental value (marked with “o’’) for the DC case and Kenney and Carley’s bound [15], [16] (marked with “<”’).

It is important to realize that the best fit gains Ky, Kg and the variance ora) of the linearization error [Eqs. (9), (10) and (12)] all depend both on the magnitude of the quantizer input signal Xpc and on the variance 03, of the quantizer input noise. To illustrate this, some results for the case of This can be cast in closed form as: Here erf(-) is the error function. Finally the variance ray of the linearization error can be evaluated as well:

Fig. 1. (a) Block diagram of a MB SA modulator with (b) the input-output behavior of its nonlinear quantizers.

Fig. 10. Describing function prediction of the DC overloading level (marked with “x”) as well as the simulated value (marked with “o”) vs. hoo results for maximally flat modulators of order 3,4 and 5 for the case of a 9-level quantizer (n = 8).

Fig. 3. (a) Best fit gains K's and Ky and (b) the RMS value og of the linearization error vs. the magnitude of the DC signal for the case of a 9-level quantizer (n = 8) with a Gaussian noise RMS value oy = A,

and finally those in Eq. (20) into: All these integrals can efficiently be evaluated by discretiz- ing the integrandum in a few 100 data points.

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Calibration of DAC Mismatch Errors in $\Sigma\Delta$ ADCs Based on a Sine-Wave Measurement

by Ludo Weyten

2023, IEEE Transactions on Circuits and Systems II: Express Briefs

This document is an author's draft version submitted for publication to IEEE Trans. Circ. Syst.-II. The actual version was published as [1].

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Experimental characterization of Sigma Delta Radio over fiber system for 5G C-RAN downlink

by Giovanni Tartarini

2023, ICT Express

Radio over Fiber is a promising technology for the 5G Cloud Radio Access Network. We demonstrate experimentally Sigma Delta Radio over Fiber by means of Sigma Delta Modulator (SDM) subsequently replacing expensive digital to analog... more

M.U. Hadi, PA. Traverso, G. Tartarini et al. / ICT Express xxx (xxxx) xxx Fig. 7. ACLR performance for varying RF input power and fiber lengths.

Fig. 8. EOP performance for varying fiber lengths for 0 dBm.

Fig. 2. Structure of the SD modulator utilized in this paper. The integrators Y,; and Y2 combination yields second order SD modulator. Resolution of quantizer is one bit.

Parameters utilized in experimental setup. Table 1

Fig. 6. EVM performance for 10 km at (a) 20 Mbd and (b) 100 Mbd. Fig. 5. EVM for varying symbol rate for varying fiber lengths.

Fig. 1. Basic C-RAN architecture showing optical fronthaul. at the transmitter side applicable to 5G sub-6 GHz band. The paper is organized as follows. Section 2 discusses the proposed SDM. Section 3 describes the experimental setup. In Section 4, performance analysis of S-DRoF is presented in terms of Error Vector Magnitude (EVM), Adjacent to Channel Leakage Ratio (ACLR) and Eye-Opening Penalty (EOP). Section 5 concludes the paper.

Fig. 4. EVM for varying fiber lengths vs. input powers. Fig. 3. Experimental Bench for setup for Sigma Delta Radio over Fiber system. SDM: Sigma Delta Modulation. SMF: Single Mode Fiber. PPG: Pulse Pattern Generation. BPF: Band Pass Filtering. VSG: Vector Signal Analyzer. LNA: Low Noise Amplifier.

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SNDR sensitivity analysis for cascaded ΣΔ modulators

by Takazi Okuda

2023, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353)

Cascade, single and multi-bit, ZA architectures provide stable, high order quantization noise shaping used in high resolution A/ D conversion. One major disadvantage of cascaded EA topologies is the extreme SNDR sensitivity to gniit... more

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Low-Voltage CMOS Temperature Sensor Design Using Schottky Diode-Based References

by Curtis Cahoon

2023, 2008 IEEE Workshop on Microelectronics and Electron Devices

This paper presents the design of a fully differential sigma-delta temperature sensor using Schottky diode-based current references as a replacement for the traditional PN junction diode-based current references. This sensor was designed... more

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Control of MEMS Vibration Modes With Pulsed Digital Oscillators—Part II: Simulation and Experimental Results

by MANUEL CARRILLO DOMINGUEZ

2023, IEEE Transactions on Circuits and Systems I: Regular Papers

The aim of this paper is to show that it is possible to excite selectively different mechanical resonant modes of a MEMS structure using pulsed digital oscillators (PDOs). This can be done by simply changing the working parameters of the... more

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Custom integrated circuits for audio processing and signalling in vehicular units

by Giovanni Chiappano

2023, European Transactions on Telecommunications

The circuitry for the audio signal and subaudio signalling processing on the new vehicular unit for Italian Mobile Radio System is described. The overall system was realized with two different kinds of CMOS custom circuits and a few other... more

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Practical Approach of Producing Delta Modulation and Demodulation

by Anindita Sinha

2023

Engineers working in the field of Speech Coding have been actively searching for methods to reduce the bandwidth consumed by quantized speech signals. Human ear has a build in ability to become more or less sensitive to audible signals.... more

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Analysis of Non-Uniform Polar Quantisers in a Sigma Delta Transmitter Architecture

by Mike Faulkner

2023, IEEE Transactions on Circuits and Systems I: Regular Papers

The drive signals for radio frequency switch mode amplifiers can be directly generated by digital circuits using pulsewidth modulation and pulse position modulation. The quantisation noise that occurs when the pulsewidths are quantised to... more

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A 8 mW 72 dB ΣΔ-modulator ADC with 2.4 MHz BW in 130 nm CMOS

by Maarten De Bock

2022, Analog Integrated Circuits and Signal Processing

A double-sampling split Σ∆-ADC with bilinear integrators and a 7-level quantizer is presented. It achieves third order noise shaping with a second order modulator through quantization noise-coupling. The modulator is integrated in a 130... more

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Short Word-Length Entering Compressive Sensing Domain: Improved Energy-Efficiency in Wireless Sensor Networks

by Zahir M Hussain

2022

This work combines compressive sensing and short word-length techniques to achieve localization and target tracking in wireless sensor networks with energy-efficient communication between the network anchors and the fusion center.... more

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High Speed Continuous-Time Bandpass Σ∆ADC for Mixed Signal VLSI Chips

by Harsha Vardhini

2022, International Journal of VLSI Design & Communication Systems

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Closed-loop Compensation of Charge Trapping Induced by Ionizing Radiation in MOS Capacitors

by Gema Lopez Rodriguez

2022, IEEE Transactions on Industrial Electronics

The objective of this work is to explore the capability of a charge trapping control loop to continuously compensate charge induced by ionizing radiation in the dielectric of MOS capacitors. To this effect, two devices made with silicon... more

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Digital Radio Frequency Transport over Optical Fiber for 5G Fronthaul Links

by Giovanni Tartarini

2022, Journal of Optical Communications

Radio over fiber (RoF) is an empowering technology for the next-generation wireless networks including fifth generation cloud radio access networks. In this paper, we propose a new fronthaul interface which has been demonstrated for a... more

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Sigma-delta modulation of multi-phase high frequency converters

by Jonathan W Kimball

2022, 2010 Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC)

A power conversion control architecture is proposed that merges advanced digital modulation techniques, high frequency resonant converters, and multi-phase converters. If a converter's switching frequency is high enough, the converter may... more

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Use of Feedforward and Feedback in Oversampled Analog to Digital Converters to Bypass Performance Co

by Anthony Constantinides

2022, 1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990.

system performance of an oversampled Analog to Digital Converter (ADC) with feedback noise shaping is limited by the precision of the Digital to Analog Converter (DAC) in the feedback path as well as by the number of integrators in the... more

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A bulk-micromachined soil moisture probe with a mixed-signal interface

by Raul Morais

2022

This paper presents a Multi-Chip-Module based (MCM) microsystem for irrigation management suitable for greenhouse environmental control. The proposed microsystem includes a soil moisture microsensor, analog interface and sigma-delta... more

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High Speed Continuous-Time Bandpass Σ∆ Adc for Mixed Signal Vlsi Chips

by Harsha Vardhini

2022

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High Speed Continuous-Time Bandpass Σ∆ Adc for Mixed Signal Vlsi Chips

by Harsha Vardhini

2021

With the unremitting progress in VLSI technology, there is a commensurate increase in performance demand on analog to digital converter and are now being applied to wideband communication systems. sigma Delta (Σ∆) converter is a popular...