Reconstruction of oversampled band-limited signals fromΣΔ encoded binary sequences

Considers the application of ΣΔ modulators to analog-to-digital conversion. The authors have previously shown that for constant input signals, optimal nonlinear decoding can achieve large gains in signal-to-noise ratio (SNR) over linear decoding. The present paper shows a similar result for band-limited input signals. The new nonlinear decoding algorithm is based on projections onto convex sets (POCS), and alternates between a time-domain operation and a band limitation to find a signal invariant under both. The time-domain operation results in a quadratic programming problem. The band limitation can be based on singular value decomposition of a certain matrix. The authors show simulation results for the SNR performance of a POCS-based decoder and a linear decoder for the single loop, double loop and two-stage ΣΔ modulators and for a specific fourth-order interpolative modulator. Depending on the modulator and the oversampling ratio, improvements in SNR of up to 10-20 dB can be achieved     

Use of sigma-delta modulation to control EMI from switch-mode powersupplies

Conducted electromagnetic interference (EMI) is a major cause of concern in switch-mode power supplies (SMPSs) which commonly use standard pulsewidth modulation (PWM). In this paper, sigma-delta (ΣΔ) modulation is proposed as an alternative switching technique to reduce conducted EMI from an SMPS. The result of using ΣΔ modulation is a spread in the spectrum of the conducted emissions so that large concentrations of power at discrete frequencies are avoided. Experimental time-domain waveforms and spectra of the switching function of first-order and second-order ΣΔ modulators are presented to prove the viability of the scheme for EMI mitigation. These modulators are then applied to a DC-DC converter in an off-the-shelf computer power supply and experimental results show a reduction of roughly 5-10 dB·μV in EMI emissions over standard PWM modulators     

Mismatch shaping for a current-mode multibit delta-sigma DAC

Mismatch shaping allows the use of multibit quantization in delta-sigma analog-to-digital converters and digital-to-analog converters (DAC's) since it noise-shapes the error caused by static element mismatch in a multibit DAC. In this paper, mismatch-shaping techniques for low-pass delta-sigma (ΔΣ) modulators are reviewed, and a mismatch-shaping technique for bandpass ΔΣ modulators is described. The dynamic error caused by frequent element switching is identified as a major source of error in a current-mode DAC with a continuous-time output. Modifying the mismatch-shaping algorithm to account for this effect yields a continuous-time ΔΣ DAC that is insensitive to both element mismatch and element switching dynamics. Experimental results confirm the effectiveness of the proposed techniques     

Granular quantization noise in a class of delta-sigma modulators

The trend toward digital signal processing in communication systems has resulted in a large demand for fast accurate analog-to-digital (A/D) converters, and advances in VLSI technology have made ΔΣ modulator-based A/D converters attractive solutions. However, rigorous theoretical analyses have only been performed for the simplest ΔΣ modulator architectures. Existing analyses of more complicated ΔΣ modulators usually rely on approximations and computer simulations. In the paper, a rigorous analysis of the granular quantization noise in a general class of ΔΣ modulators is developed. Under the assumption that some input-referred circuit noise or dither is present, the second-order asymptotic statistics of the granular quantization noise sequences are determined and ergodic properties are derived     

Quadrature bandpass ΔΣ modulation for digital radio

A quadrature bandpass ΔΣ modulator IC facilitates monolithic digital-radio-receiver design by allowing straightforward “complex A/D conversion” of an image reject mixer's I and Q, outputs. Quadrature bandpass ΔΣ modulators provide superior performance over pairs of real bandpass ΔΣ modulators in the conversion of complex input signals, using complex filtering embedded in ΔΣ loops to efficiently realize asymmetric noise-shaped spectra. The fourth-order prototype IC, clocked at 10 MHz, converts narrowband 3.75-MHz I and Q inputs and attains a dynamic range of 67 dB in 200-kHz (GSM) bandwidth, increasing to 71 and 77 dB in 100- and 30-kHz bandwidths, respectively. Maximum signal-to-noise plus distortion ratio (SNDR) in 200-kHz bandwidth is 62 dB. Power consumption is 130 mW at 5 V. Die size in a 0.8-μm CMOS process is 2.4×1.8 mm²      

Architecture, design, and test of continuous-time tunableintermediate-frequency bandpass delta-sigma modulators

This paper examines the architecture, design, and test of continuous-time tunable intermediate-frequency (IF) fourth-order bandpass delta-sigma (BP ΔΣ) modulators. Bandpass modulators sampling at high IFs (~100 MHz) allow direct sampling of the RF signal-reducing analog hardware and make it easier to realize completely software programmable receivers. This paper presents circuit design of and test results from continuous-time fourth-order BP ΔΣ modulators fabricated in AlInAs/GaInAs heterojunction bipolar technology with a peak unity current gain cutoff frequency (f_T) of 80 GHz and a maximum frequency of oscillation (f_MAX) of about 130 GHz. Operating from ±5-V power supplies, a fabricated 180-MHz IF fourth-order ΔΣ modulator sampling at 4 GS/s demonstrates stable behavior and achieves 75.8 dB of signal-to-(noise+distortion)-ratio (SNDR) over a 1-MHz bandwidth. Narrowband performance (~1 MHz) performance of these modulators is limited by thermal/device noise while broadband performance (~60 MHz), is limited by quantization noise. The high sampling frequency (4 GS/s) in this converter is dictated by broadband (60 MHz) performance requirements     

Influence of the feedback DAC delay on continuous-time bandpassΣΔ coverter

An analysis of the effect of the feedback digital-to-analogue converter (DAC) delay on the synthesis results of continuous-time ΣΔ bandpass modulators is presented. It is shown that non-null values of the feedback DAC delay can be optimal with respect to the filter gain margin     

Design and realization of a digital ΔΣ modulator forfractional-n frequency synthesis

The basic operation of a fractional-n frequency synthesizer has been published, but to date little has been presented on the digital ΔΣ modulators which are required to drive such synthesizers. This paper provides a tutorial overview, which relates digital ΔΣ modulation to other applications of ΔΣ modulation where the literature is more complete. The paper then presents a digital ΔΣ modulator architecture which is economical and efficient and which is practical to realize with commercially available components in comparison with other possible implementations which require extensive custom very large-scale integration (VLSI). A demonstration is made of a 28-b modulator using the architecture presented, which provides a 25-MHz tuning bandwidth and <1-Hz frequency resolution. The modulator is demonstrated in an 800-MHz frequency synthesizer having phase noise of -90 dBC/Hz at a 30-kHz offset     

A switched-capacitor delta-sigma modulator with reduced sensitivityto op-amp gain

Low operational amplifier (op-amp) gain can degrade the performance of a switched-capacitor delta-sigma modulator (ΔΣM). A ΔΣM that incorporates a new gain-compensated switched-capacitor integrator is described. The resulting ΔΣM topology has reduced sensitivity to op-amp gain. Simulation and measurement results for an experimental ΔΣM that demonstrate the advantages of the new architecture are presented     

Deterministic analysis of oversampled A/D conversion and decodingimprovement based on consistent estimates

Discusses the deterministic analysis of oversampled A/D conversion (ADC), the properties derivable from such an analysis, and the consequences on reconstruction using nonlinear decoding. Given a band-limited input X producing a quantized version C, the authors consider the set of all input signals that are band-limited and produce C. They call any element of this set a consistent estimate of X. Regardless of the type of encoder (simple, predictive, or noise-shaping), they show that this set is convex, and as a consequence, any nonconsistent estimate can be improved. They also show that the classical linear decoding estimates are not necessarily consistent. Numerical tests performed on simple ADC, single-loop, and multiloop ΣΔ modulation show that consistent estimates yield a mean square error (MSE) that decreases asymptotically with the oversampling ratio faster than the linear decoding MSE by approximately 3 dB/octave. This implies an asymptotic MSE of the order of 𝒪(R/sup -(2n+2/)) instead of 𝒪(R/sup -(2n+1/)) in linear decoding, where R is the oversampling ratio and n the order of the modulator. Methods of improvement of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple ADC, predictive ADC, single-loop, and multiloop ΣΔ modulation     

A 10.7-MHz IF-to-baseband ΣΔ A/D conversion system forAM/FM radio receivers

ΣΔ modulation with integrated quadrature mixing is used for analog-to-digital (A/D) conversion-of a 10.7-MHz IF input signal in an AM/FM radio receiver. After near-zero IF mixing to a 165 kHz offset frequency, the I and Q signals are digitized by two fifth-order, 32 times oversampling continuous-time ΣΔ modulators. A prototype IC includes digital filters for decimation and the shift of the near-zero-IF to dc. The baseband output signal has maximum carrier-to-noise ratios of 94 dB in 9 kHz (AM) and 79 dB in 200 kHz (FM), with 97 and 82 dB dynamic range, respectively. The IM3 distance is 84 dB at full-scale A/D converter input signal. Including downconversion and decimation filtering, the IF A/D conversion system occupies 1.3 mm² in 0.25-μm standard digital CMOS. The ΣΔ modulators consume 8 mW from a 2.5-V supply voltage, and the digital filters consume 11 mW     

A 1.8-mW CMOS ΣΔ modulator with integrated mixer forA/D conversion of IF signals

In this paper, the design of a continuous-time baseband sigma-delta (ΣΔ) modulator with an integrated mixer for intermediate-frequency (IF) analog-to-digital conversion is presented. This highly linear IF ΣΔ modulator digitizes a GSM channel at intermediate frequencies up to 50 MHz. The sampling rate is not related to the input IF and is 13.0 MHz in this design. Power consumption is 1.8 mW from a 2.5-V supply. Measured dynamic range is 82 dB, and third-order intermodulation distortion is -84 dB for two -6-dBV IF input tones. Two modulators in quadrature configuration provide 200-kHz GSM bandwidth. Active area of a single IF ΣΔ modulator is 0.2 mm² in 0.35-μm CMOS     

Experimental analysis and comparison on a power factor controllerincluding a delta-sigma processing stage

Monolithic ICs allow simple and cheap single-phase power factor correction (PFC) systems to be implemented. They contain an analog multiplier, the transfer characteristic of which may be nonlinear. In this paper, the delta-sigma (ΔΣ) modulation technique is applied to fully implement the algebraic operations of a PFC system's multiplier block. A ΔΣ multiplier prototype was breadboarded and inserted in a PFC control loop based on a commercial IC. The experimental results regarding the AC line current distortion are reported and compared with those obtained from the built-in analog multiplier of the IC. The benefits on the total harmonic distortion (THD) on the AC side are highlighted     

A 1.95-V, 0.34-mW, 12-b sigma-delta modulator stabilized by localfeedback loops

The design of a low-power, low-voltage, 12-b 8-kHz bandwidth ΣΔ modulator for high-quality voice that consumes only 0.34 mW at 1.95 V supply is described. The modulator employs a special architecture in which a third-order modulator is stabilized by a local feedback loop around each integrator. Unlike multistage ΣΔ modulators, this architecture is very tolerant to the modest dc gain of low voltage op-amps. The architecture, together with special circuit techniques, permits a low-voltage switched capacitor implementation at 1.95 V-3.3 V supply using standard 1.2-μm CMOS technology     

Signal-dependent timing jitter in continuous-time ΣΔmodulators

A previously unpublished mechanism of signal-to-noise ratio (SNR) loss specific to continuous-time ΣΔ modulators is illustrated. It arises from increased quantiser resolution time for small-amplitude quantiser inputs, and is related to metastability     

Triangularly weighted zero-crossing detector providingΣΔ frequency-to-digital conversion

It is shown that for delta-sigma (ΣΔ) frequency-to-digital conversion (FDC) there is no need for a ΣΔ modulator, since a limited FM signal itself may be considered as an asynchronous ΣΔ bit-stream. By feeding the limited FM signal directly to a sinc² ΣΔ decimator, a triangularly weighted zero-crossing counter FDC is introduced, providing ΣΔ noise shaping. The results measured confirm the theory     

A GMSK modulator using a ΔΣ frequencydiscriminator-based synthesizer

This paper describes a new transmitter architecture suitable for wideband GMSK modulation. The technique uses direct modulation of ΔΣ frequency discriminator (ΔΣFD)-based synthesizer to produce the modulated RF signal without any up-conversion. Digital equalization is used to extend the modulation data rate far beyond the synthesizer closed-loop BW. A prototype 1.9-GHz GSM transmitter was constructed consisting of a ΔΣFD-based synthesizer and a digital transmit filter. The synthesizer consists of an 0.8-μm BiCMOS ΔΣFD chip, a digital signal processor FPGA, and an off-chip D/A converter, filter, and VCO. Measured results, using 271-kbit/s GSM modulation, demonstrate data rates well in excess of the 30-kHz synthesizer closed-loop BW are possible with digital equalization. Without modulation, the synthesizer exhibits a -76-dBc spurious noise level and a close-in phase noise of -74 dBc/Hz     

A 900-mV low-power ΔΣ A/D converter with 77-dB dynamicrange

The design of a low-voltage and low-power ΔΣ analog-to-digital (A/D) converter is presented. A third-order single-loop ΔΣ modulator topology is implemented with the differential modified switched op-amp technique. The modulator topology has been transformed as to accommodate half-delay integrators. Dedicated low-voltage circuit building blocks, such as a class AB operational transconductance amplifier, a common-mode feedback amplifier, and a comparator are treated, as well as low-voltage design techniques. The influence of very low supply voltage on power consumption is discussed. Measurement results of the 900-mV ΔΣ A/D converter show a 77-dB dynamic range in a 16-kHz bandwidth and a 62-dB peak signal-to-noise ratio for a 40-μW power consumption     

Effects of non-ideal Hadamard modulators on the performance ofΠΔΣ ADC

A non-ideal Hadamard modulator in the front-end of ΠΔΣ ADC can be modelled as an ideal Hadamard modulator with gain error in parallel with an offset error. The effects of non-ideal Hadamard modulators can be partially removed by using chopper stabilisation and adaptive channel gain equalisation     

标准数字工艺下16位精度低压低功耗ΣΔ模数调制器设计

针对输入信号频率在20 Hz～24 kHz范围的音频应用,该文采用标准数字工艺设计了一个1.2 V电源电压16位精度的低压低功耗ΣΔ模数调制器。在6 MHz采样频率下,该调制器信噪比为102.2 dB,整个电路功耗为2.46 mW。该调制器采用一种伪两级交互控制的双输入运算放大器构成各级积分器,在低电源电压情况下实现高摆率高增益要求的同时不会产生更多功耗。另外,采用高线性度、全互补MOS耗尽电容作为采样、积分电容使得整个电路可以采用标准数字工艺实现,从而提高电路的工艺兼容性、降低电路成本。与近期报道的低压低功耗ΣΔ模数调制器相比,该设计具有更高的品质因子FOM。