A 1.5-V 12-bit power-efficient continuous-time third-order /spl Sigma//spl Delta/ modulator

This paper presents the design strategy, implementation, and experimental results of a power-efficient third-order low-pass /spl Sigma//spl Delta/ analog-to-digital converter (ADC) using a continuous-time (CT) loop filter. The loop filter has been implemented by using active RC integrators. Several power optimizations, design requirements, and performance limitations relating to circuit nonidealities in the CT modulator are presented. The influence of the low supply voltage on the various building blocks such as the amplifier as well as on the overall /spl Sigma//spl Delta/ modulator is discussed. The ADC was implemented in a 3.3-V 0.5-/spl mu/m CMOS technology with standard threshold voltages. Measurements of the low-power 1.5-V CT /spl Sigma//spl Delta/ ADC show a dynamic range and peak signal-to-noise-plus-distortion ratio of 80 and 70 dB, respectively, in a bandwidth of 25 kHz. The measured power consumption is only 135 /spl mu/W from a single 1.5-V power supply.     

Continuous-time /spl Delta//spl Sigma/ modulators using distributed resonators

We derive a method for using distributed resonators in /spl Delta//spl Sigma/ modulators and demonstrate these /spl Delta//spl Sigma/ modulators have several advantages over existing /spl Delta//spl Sigma/ modulator architectures. Like continuous-time (CT) /spl Delta//spl Sigma/ modulators, the proposed /spl Delta//spl Sigma/ modulators do not require a high-precision track-and-hold, and additionally can take advantage of the high-Q of distributed resonators. Like discrete-time /spl Delta//spl Sigma/ modulators, the proposed /spl Delta//spl Sigma/ modulators are relatively insensitive to feedback loop delays and can subsample. We present simulations of several types of these /spl Delta//spl Sigma/ modulators and examine the challenges in their design.     

Resonator-based multi-stage /spl Sigma//spl Delta/ modulator for wideband applications with improved dynamic range

A new design methodology for wideband, multi-stage, multi-bit /spl Sigma//spl Delta/ modulators (/spl Sigma//spl Delta/Ms) with improved dynamic range, is presented. The key to improving dynamic range is to have the first stage oscillated, then the coarse quantisation noise vanishes and hence circuit non-linearities do not cause a leakage quantisation noise problem. Based on the proposed methodology, a fourth-order four-bit /spl Sigma//spl Delta/M can achieve the dynamic range of 80 dB at the OSR of 8 without using additional calibration techniques.     

Adaptive order reduction scheme for high-order single-bit /spl Delta//spl Sigma/ Modulators

A scheme for achieving adaptive reduction in the order of the loop filter of usual high-order, single-stage, single-bit Delta-Sigma (/spl Delta//spl Sigma/) modulators is proposed in order to improve their performance. The resulting /spl Delta//spl Sigma/ modulators can recover from instability effectively, having also an extended input signal range in comparison to that of the corresponding conventional /spl Delta//spl Sigma/ modulators.     

A 10.7-MHz self-calibrated switched-capacitor-based multibit second-order bandpass /spl Sigma//spl Delta/ modulator with on-chip switched buffer

A second-order multibit bandpass /spl Sigma//spl Delta/ modulator (BP/spl Sigma//spl Delta/M) used for the digitizing of AM/FM radio broadcasting signals at a 10.7-MHz IF is presented. The BP/spl Sigma//spl Delta/M is realized with switched-capacitor (SC) techniques and operates with a sampling frequency of 37.05 MHz. The input impulse current, required by the SC input branch, is minimized by the use of a switched buffer without deteriorating the overall system performance. The accuracy of the in-band noise shaping is ensured with two self-calibrating control systems. In a 0.18-/spl mu/m CMOS technology, the device die size is 1 mm/sup 2/ and the power consumption is 88 mW. In production, the BP/spl Sigma//spl Delta/M features at least 78-dB dynamic range and 72-dB peak SNR within a 200-kHz bandwidth (FM bandwidth). The intermodulation (IMD) is -65 dBc for two tones at -11 dBFS. The robustness of the aforementioned performance is demonstrated by the fact that it has been realized with the BP/spl Sigma//spl Delta/M embedded in the noisy on-chip environment of a complete mixed-signal FM receiver.     

The tiling phenomenon in /spl Sigma//spl Delta/ modulation

The theoretical error signal analysis of a sigma-delta (/spl Sigma//spl Delta/) modulator is a difficult problem due to the presence of a nonlinear operation (the amplitude quantization) in a feedback loop. In this paper, new deterministic knowledge on the transfer function of a /spl Sigma//spl Delta/ modulator is established, thanks to some recently observed properties of its state variables. For a large class of typical /spl Sigma//spl Delta/ modulators with constant inputs, the state variables appear to remain in a tile. We show what characteristics in a /spl Sigma//spl Delta/ modulator are specifically responsible for this property and give some initial proof of it. Under a constant input, the tiling phenomenon has as fundamental consequence that the output is a fixed and memoryless modulo function of n successive integrated versions of the input. This gives the theoretical knowledge that the modulator has an equivalent feedforward circuit expression. We give some immediate theoretical consequences on error analysis including the case of time-varying inputs.     

A time-delay jitter-insensitive continuous-time bandpass /spl Delta//spl Sigma/ modulator architecture

In this paper, we present a new continuous-time bandpass delta-sigma (/spl Delta//spl Sigma/) modulator architecture with mixer inside the feedback loop. The proposed bandpass /spl Delta//spl Sigma/ modulator is insensitive to time-delay jitter in the digital-to-analog conversion feedback pulse, unlike conventional continuous-time bandpass /spl Delta//spl Sigma/ modulators. The sampling frequency of the proposed /spl Delta//spl Sigma/ modulator can be less than the center frequency of the input narrow-band signal.     

Quasi-equivalent feedforward system in asymptotic /spl Sigma//spl Delta/ modulation

It was previously shown that sigma-delta (/spl Sigma//spl Delta/) modulators of "asymptotic" type theoretically yield an equivalent feedforward system where the recursive nonlinear mechanisms are extracted from the feedback loop and reduced to a memoryless function. With time-varying inputs, we show in this paper, partially by mathematical derivations and partially by experiment, that this system is quasi-equivalent to the original modulator in a sense that we explain. This reduction of the nonlinear mechanisms should permit more refined modeling of the /spl Sigma//spl Delta/ errors in future research, with a better account of the original nonlinearities of asymptotic /spl Sigma//spl Delta/ modulation.     

Numerical method for determining the quantization error PDF of single-bit /spl Sigma//spl Delta/ Modulators

Existing models for the quantizer of /spl Sigma//spl Delta/ modulators make assumptions on the probability density function (pdf) of the quantization error, or some other convenient signal of the modulator. In this paper, a method for the determination of this pdf for single-bit /spl Sigma//spl Delta/ modulators is presented. First, a numerical method is proposed in order to solve the simplified equation for the quantization error pdf for first-order systems considering noiseless and noisy dc input signals. Then, it is shown how most practical high-order (>2)/spl Sigma//spl Delta/ modulators, resulting from well-established design methods, can be modeled as first-order systems plus an additive noise source at the input. Hence, their quantization error pdf is analyzed using the proposed method. Simulation results are shown to be in considerable agreement with those of the proposed method.     

80-MHz bandpass /spl Delta//spl Sigma/ modulators for multimode digital IF receivers

Three fully differential bandpass (BP) /spl Delta//spl Sigma/ modulators are presented. Two double-delay resonators are implemented using only one operational amplifier. The prototype circuits operate at a sampling frequency of 80 MHz. The BP /spl Delta//spl Sigma/ modulators can be used in an intermediate-frequency (IF) receiver to combine frequency downconversion with analog-to-digital conversion by directly sampling an input signal from an IF of 60 MHz to a digital IF of 20 MHz. The measured peak signal-to-noise-plus-distortion ratios are 78 dB for 270 kHz (GSM), 75 dB for 1.25 MHz (IS-95), 69 dB for 1.762 MHz (DECT), and 48 dB for 3.84 MHz (WCDMA/CDMA2000) bandwidths. The circuits are implemented with a 0.35-/spl mu/m CMOS technology and consume 24-38 mW from a 3.0-V supply, depending on the architecture.     

Design of double-sampling /spl Sigma//spl Delta/ modulation A/D converters with bilinear integrators

Double-sampling techniques allow to double the sampling frequency of a switched capacitor /spl Sigma//spl Delta/ analog-to-digital convertors without increasing the clock frequency. Unfortunately, path mismatch between the double sampling branches may cause noise folding, which could ruin the modulator's performance. The fully floating double-sampling integrator is an interesting building block to be used in such a double sampling /spl Sigma//spl Delta/ modulator because its operation is tolerant to path mismatch. However, this circuit exhibits an undesired bilinear filter effect. This effectively increases the order of the modulator by one. Due to this, previously presented structures don't have enough freedom to fully control the modulator pole positions. In this paper, we introduce modified topologies for double-sampling /spl Sigma//spl Delta/ modulators built with bilinear integrators. We show that these architectures provide full control of the modulator pole positions and hence can be used to implement any noise transfer function. Additionally, analytical expressions are obtained for the residual folded noise.     

Breaking the feedback loop of a class of /spl Sigma//spl Delta/ A/D converters

/spl Sigma//spl Delta/ modulation is the currently successful technique used to perform high resolution analog-to-digital conversion. In spite of its practical success, its theoretical signal analysis has remained limited because a /spl Sigma//spl Delta/ modulator contains of a feedback loop that includes a nonlinear operation, i.e., the amplitude discretization or quantization. The feedback allows us to use oversampling to compensate for the limitations of the quantizer in resolution and in precision, which are typical of analog circuits. However, because of the lack of signal analysis, it is still not clear how much resolution of conversion can be gained as a function of the oversampling. We show that for a large class of /spl Sigma//spl Delta/ modulators, the feedback loop theoretically yields an equivalent feedforward signal flow graph, at least for constant inputs. This is possible thanks to remarkable modulo properties of these modulators. This equivalence can be asymptotically extrapolated to time-varying inputs with increasing oversampling. Although the exact components of the equivalent graph are not currently known in general, the theoretical structure of the feedforward graph is sufficient to point out misconceptions in the current knowledge on the final resolution of an nth-order /spl Sigma//spl Delta/ modulator. Specifically, except when the modulator is "ideal", the global resolution of conversion increases by n bits per octave of oversampling, instead of the currently believed rate of n+(1/2) bits/octave.     

A vertically integrated tool for automated design of /spl Sigma//spl Delta/ modulators

We present a tool that starting from high-level specifications of switched-capacitor (SC) /spl Sigma//spl Delta/ modulators calculates optimum specifications for their building blocks and then optimum sizes for the block schematics. At both design levels, optimization is performed using statistical techniques to enable global design and innovative heuristics for increased computer efficiency as compared with conventional statistical optimization. The tool uses an equation-based approach at the modulator level, a simulation-based approach at the cell level, and incorporates an advanced /spl Sigma//spl Delta/ behavioral simulator for monitoring and design space exploration. We include measurements taken from two silicon prototypes: (1) a 16 b @ 16 kHz output rate second-order /spl Sigma//spl Delta/ modulator; and (2) a 17 b @ 40 kHz output rate fourth-order /spl Sigma//spl Delta/ modulator. Both use SC fully differential circuits and were designed using the proposed tool and manufactured in a 1.2 /spl mu/m CMOS double-metal double-poly technology.<>     

A time-interleaved continuous-time /spl Delta//spl Sigma/ modulator with 20-MHz signal bandwidth

This paper presents the first implementation results for a time-interleaved continuous-time /spl Delta//spl Sigma/ modulator. The derivation of the time-interleaved continuous-time /spl Delta//spl Sigma/ modulator from a discrete-time /spl Delta//spl Sigma/ modulator is presented. With various simplifications, the resulting modulator has only a single path of integrators, making it robust to DC offsets. A time-interleaved by 2 continuous-time third-order low-pass /spl Delta//spl Sigma/ modulator is designed in a 0.18-/spl mu/m CMOS technology with an oversampling ratio of 5 at sampling frequencies of 100 and 200 MHz. Experimental results show that a signal-to-noise-plus-distortion ratio (SNDR) of 57 dB and a dynamic range of 60 dB are obtained with an input bandwidth of 10 MHz, and an SNDR of 49 dB with a dynamic range of 55 dB is attained with an input bandwidth of 20 MHz. The power consumption is 101 and 103 mW, respectively.     

IF-sampling fourth-order bandpass /spl Delta//spl Sigma/ modulator for digital receiver applications

Bandpass modulators sampling at high IFs (/spl sim/200 MHz) allow direct sampling of an IF signal, reducing analog hardware, and make it easier to realize completely software-programmable receivers. This paper presents the circuit design of and test results from a continuous-time tunable IF-sampling fourth-order bandpass /spl Delta//spl Sigma/ modulator implemented in InP HBT IC technology for use in a multimode digital receiver application. The bandpass /spl Delta//spl Sigma/ modulator is fabricated in AlInAs-GaInAs heterojunction bipolar technology with a peak unity current gain cutoff frequency (f/sub T/) of 130 GHz and a maximum frequency of oscillation (f/sub MAX/) of 130 GHz. The fourth-order bandpass /spl Delta//spl Sigma/ modulator consists of two bandpass resonators that can be tuned to optimize both wide-band and narrow-band operation. The IF is tunable from 140 to 210 MHz in this /spl Delta//spl Sigma/ modulator for use in multiple platform applications. Operating from /spl plusmn/5-V power supplies, the fabricated fourth-order /spl Delta//spl Sigma/ modulator sampling at 4 GSPS demonstrates stable behavior and achieves a signal-to-(noise + distortion) ratio (SNDR) of 78 dB at 1 MHz BW and 50 dB at 60 MHz BW. The average SNDR performance measured on over 250 parts is 72.5 dB at 1 MHz BW and 47.7 dB at 60 MHz BW.     

A 3.3-mW /spl Sigma//spl Delta/ modulator for UMTS in 0.18-/spl mu/m CMOS with 70-dB dynamic range in 2-MHz bandwidth

A quadrature fourth-order, continuous-time, /spl Sigma//spl Delta/ modulator with 1.5-b quantizer and feedback digital-to-analog converter (DAC) for a universal mobile telecommunication system (UMTS) receiver chain is presented. It achieves a dynamic range of 70 dB in a 2-MHz bandwidth and the total harmonic distortion is -74 dB at full-scale input. When used in an integrated receiver for UMTS, the dynamic range of the modulator substantially reduces the need for analog automatic gain control and its tolerance of large out-of-band interference also permits the use of only first-order prefiltering. An IC including an I and Q /spl Sigma//spl Delta/ modulator, phase-locked loop, oscillator, and bandgap dissipates 11.5 mW at 1.8 V. The active area is 0.41 mm/sup 2/ in a 0.18-/spl mu/m 1-poly 5-metal CMOS technology.     

A 1-V 10.7-MHz switched-opamp bandpass /spl Sigma//spl Delta/ modulator using double-sampling finite-gain-compensation technique

A 1 V switched-capacitor (SC) bandpass sigma-delta (/spl Sigma//spl Delta/) modulator is realized using a high-speed switched-opamp (SO) technique with a sampling frequency of up to 50 MHz, which is improved ten times more than prior 1 V SO designs and comparable to the performance of the state-of-the-art SC circuits that operate at much higher supply voltages. On the system level, a fast-settling double-sampling SC biquadratic filter architecture is proposed to achieve high-speed operation. A low-voltage double-sampling finite-gain-compensation technique is employed to realize a high-resolution /spl Sigma//spl Delta/ modulator using only low-DC-gain opamps to maximize the speed and to reduce power dissipation. On the circuit level, a fast-switching methodology is proposed for the design of the switchable opamps to achieve a switching frequency up to 50 MHz. Implemented in a 0.35-/spl mu/m CMOS process (V/sub TP/=0.82 V and V/sub TN/=0.65 V) and at 1 V supply, the modulator achieves a measured peak signal-to-noise-and-distortion ratio (SNDR) of 42.3 dB at 10.7 MHz with a signal bandwidth of 200 kHz, while dissipating 12 mW and occupying a chip area of 1.3 mm/sup 2/.     

Hybrid /spl Sigma//spl Delta/ modulators with adaptive calibration

This paper describes an architecture for stable high-order /spl Sigma//spl Delta/ modulation. The architecture is based on a hybrid /spl Sigma//spl Delta/ modulator, wherein hybrid integrators replace conventional analog integrators. The hybrid integrator, which is a combination of an analog integrator and a digital integrator, offers an increased dynamic range and helps make the resulting high-order /spl Sigma//spl Delta/ modulator stable. However, the hybrid /spl Sigma//spl Delta/ modulator relies on precise matching of analog and digital paths. In this paper, a calibration technique to alleviate possible mismatch between analog and digital paths is proposed. The calibration adaptively adjusts the digital integrators so that their transfer functions match the transfer functions of corresponding analog integrators. Through behavioral-level simulations of fourth-order /spl Sigma//spl Delta/ modulators, the calibration technique is verified.     

Design of low-voltage MOSFET-only /spl Sigma//spl Delta/ modulators in standard digital CMOS technology

A design strategy of low-voltage high-linearity MOSFET-only /spl Sigma//spl Delta/ modulators in standard digital CMOS technology is presented. The modulators use substrate-biased MOSFETs in the depletion region as capacitors, linearized by different compensation techniques. This work shows the design, simulation and measured results of a number of MOSFET-only /spl Sigma//spl Delta/ modulators using different implementations of so called compensated depletion-mode MOS capacitors. The modulators are designed for the demands of speech band applications. The performance of the modulators proves the capability of compensated depletion-mode MOS capacitors to fulfill analog circuit requirements at low supply voltages with reduced processing efforts.     

Hexagonal /spl Sigma//spl Delta/ modulators in power electronics

Design techniques for /spl Sigma//spl Delta/ modulators from communications are applied and adapted to improve the spectral characteristics of high frequency power electronic applications. A high frequency power electronic circuit can be regarded as a quantizer in an interpolative /spl Sigma//spl Delta/ modulator. We review one dimensional /spl Sigma//spl Delta/ modulators and then generalize to the hexagonal sigma-delta modulators that are appropriate to three-phase converters. A range of interpolative modulator designs from communications can then be generalized and applied to power electronic circuits. White noise spectral analysis of sigma-delta modulators is generalized and applied to analyze the designs so that the noise can be shaped to design requirements. Simulation results for an inverter show significant improvements in spectral performance.