Systematic design of double-sampling /spl Sigma//spl Delta/ A/D converters with a modified noise transfer function

Double-sampling /spl Sigma//spl Delta/ analog-digital converters (ADCs) are sensitive to path mismatch which causes quantization noise to fold into the signal band. A recent solution for this problem consists of modifying the noise transfer function (NTF) of the modulator such that it has one or several zeros at the Nyquist frequency, next to those in the baseband. In this brief, we present a systematic design strategy for such ADCs. It consists of finding optimal pole positions for the modified NTF. This can be combined with optimizing the zeros as well. Next, we introduce several efficient structures that have enough degrees of freedom to realize the optimized pole positions.     

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 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.     

A 250-kHz 94-dB double-sampling /spl Sigma//spl Delta/ modulation A/D converter with a modified noise transfer function

This paper presents a high-order double-sampling single-loop /spl Sigma//spl Delta/ modulation analog-to-digital (A/D) converter. The important problem of noise folding in double-sampling circuits is solved here at the architectural level by placing one of the zeros in the modulator's noise transfer function at half the sampling frequency instead of in the baseband. The resulting modulator is of fifth order but has the baseband performance of a fourth-order modulator. Through the use of an efficient switched-capacitor implementation, the overall circuit uses only four operational amplifiers and hence, its complexity is similar to that of a fourth-order modulator. An experimental 1-bit modulator was designed for an oversampling ratio of 96 and a bandwidth of 250 kHz at a 3.3-V supply in a conservative 0.8-/spl mu/m standard CMOS process. Due to the double-sampling, the sampling frequency is 48 MHz, although the circuits operate at a clock frequency of only 24 MHz. The circuit achieves a dynamic range of 94 dB. The peak signal-to-noise ratio and signal-to-noise-plus-distortion ratio were measured to be 90 and 86 dB, respectively. The power consumption of the complete circuit including clock drivers and output pad drivers was 43 mW. The analog blocks (opamps, comparators, etc.) consume 30 mW of this total.     

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.     

Efficient sampling of reference noise in switched capacitor /spl Sigma//spl Delta/ ADC

Efficient sampling of the reference leg noise within a bilinear switched capacitor /spl Sigma//spl Delta/ ADC is presented, resulting in improved thermal noise performance. Whenever a transition occurs in the feedback of a /spl Sigma//spl Delta/ ADC, implemented using bilinear integrators, zero charge is transferred from the reference leg. Consequently the average noise power added by the reference leg can be reduced substantially if the reference leg is only sampled when there is a corresponding charge transfer. For mid-scale inputs, the sampled noise from the reference leg is reduced by more than 6 dB.     

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.     

A novel noise efficient feedback DAC within a switched capacitor /spl Sigma//spl Delta/ ADC

Efficient sampling of the reference noise within a bilinear switched capacitor /spl Sigma//spl Delta/ analog-to-digital converter (ADC), resulting in improved thermal noise performance is presented. Bilinear integrators contain a zero at the Nyquist frequency, with the result that no charge is transferred from the reference when a transition occurs in the modulator output. The average noise power added by the reference digital-to-analog converter (DAC) can be reduced substantially if the reference DAC is sampled only when charge is to be transferred. For midscale inputs, the sampled noise from a single bit reference DAC is reduced by more than 5 dB. When multibit quantization and feedback is used the reference noise can be further suppressed, in the case of 5 bits of feedback the reference noise is reduced by more than 20 dB.     

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/.     

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.     

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.     

A 14-bit high-temperature /spl Sigma//spl Delta/ modulator in standard CMOS

Experimental verification is given for the use of /spl Sigma//spl Delta/ modulation for high-temperature applications (/spl ges/approximately 150/spl deg/C) in a standard CMOS process. Switched-capacitor circuits are used to implement a second-order single-stage and a third-order 2-1 MASH /spl Sigma//spl Delta/ modulator with single-bit quantization. The two modulators have an oversampling ratio of 256 with an input signal bandwidth of 500 Hz. The modulators were fabricated in a 1.5-/spl mu/m standard CMOS technology. A fully differential signal path and near minimum sized switches are used to mitigate the effect of large junction-to-substrate leakage current present at high temperatures. Experimental results show both modulators are capable of over 14 bits of resolution at 225/spl deg/C and over 13 bits of resolution at 255/spl deg/C. Results show that the single-stage modulator is more resistant to high-temperature circuit impairment than is the MASH cascaded structure.     

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.<>     

Cascade /spl Sigma//spl Delta/ modulator with digital correction for finite amplifier gain effects

A simple and fully digital solution to correct the effect of amplifier finite gain in cascade /spl Sigma//spl Delta/ modulators is presented. The main contribution of this study is a simple digital method to evaluate the integrator pole errors, which are further taken into account to modify the reconstruction filter. The method is applied to a 2-1 cascade modulator.     

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.     

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.     

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.     

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.     

Comparison frequency doubling and charge pump matching techniques for dual-band /spl Delta//spl Sigma/ fractional-N frequency synthesizer

The frequency synthesizer with two LC-VCOs is fully integrated in a 0.35-/spl mu/m CMOS technology. In supporting dual bands, all building blocks except VCOs are shared. A current compensation scheme using a replica charge pump improves the linearity of the frequency synthesizer and, thus, suppresses spurious tones. To reduce the quantization noise from a /spl Delta//spl Sigma/ modulator and the noise from the building blocks except the VCO, the proposed architecture uses a frequency doubler with a noise-insensitive duty-cycle correction circuit (DCC) in the reference clock path. Power consumption is 37.8 mW with a 2.7-V supply. The proposed frequency synthesizer supports 10-kHz channel spacing with the measured phase noise of -114 dBc/Hz and -141 dBc/Hz at 100-kHz and 1.25-MHz offsets, respectively, in the PCS band. The fractional spurious tone at 10-kHz offset is under -54 dBc.     

High-order electromechanical /spl Sigma//spl Delta/ modulation in micromachined inertial sensors

Analysis of second-order electromechanical sigma-delta (/spl Sigma//spl Delta/) inertial sensors shows that in-band quantization error introduces a resolution penalty, which cannot be eliminated by oversampling. In addition, a tradeoff between resolution and phase compensation forces such systems to operate with reduced phase margin. This paper introduces high-order electromechanical /spl Sigma//spl Delta/ modulation as an approach, which eliminates the quantization noise overhead and allows for increased phase compensation without degrading the resolution. Quasi-linear analysis is used to evaluate the contribution of the individual noise sources to the output of the system and to examine the effect of noise interaction on the behavior of electromechanical /spl Sigma//spl Delta/ modulators.