High-level synthesis of switched-capacitor, switched-current and continuous-time /spl Sigma//spl Delta/ modulators using SIMULINK-based time-domain behavioral models

This paper presents a high-level synthesis tool for /spl Sigma//spl Delta/ modulators (/spl Sigma//spl Delta/Ms) that combines an accurate SIMULINK-based time-domain behavioral simulator with a statistical optimization core. Three different circuit techniques for the modulator implementation are considered: switched-capacitor, switched-current and continuous-time. The behavioral models of these circuits, that take into account the most critical limiting factors, have been incorporated into the SIMULINK environment by using S-function blocks, which drastically increase the computational efficiency. The precision of these models has been validated by electrical simulations using HSPICE and experimental measurements from several silicon prototypes. The combination of high accuracy, short CPU time and interoperability of different circuit models together with the efficiency of the optimization engine makes the proposed tool an advantageous alternative for /spl Sigma//spl Delta/M synthesis. The implementation on the well-known MATLAB/SIMULINK platform brings numerous advantages in terms of data manipulation, processing capabilities, flexibility and simulation with other electronic subsystems. Moreover, this is the first tool dealing with the synthesis of /spl Sigma//spl Delta/Ms using both discrete-time and continuous-time circuit techniques.     

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/.     

Highly linear 2.5-V CMOS /spl Sigma//spl Delta/ modulator for ADSL+

We present a 90-dB spurious-free dynamic range sigma-delta modulator (/spl Sigma//spl Delta/M) for asymmetric digital subscriber line applications (both ADSL and ADSL+), with up to a 4.4-MS/s digital output rate. It uses a cascade (MASH) multibit architecture and has been implemented in a 2.5-V supply, 0.25-/spl mu/m CMOS process with metal-insulator-metal capacitors. The prototypes feature 78-dB dynamic range (DR) in the 30-kHz to 2.2-MHz band (ADSL+) and 85-dB DR in the 30-kHz to 1.1-MHz band (ADSL). Integral and differential nonlinearity are within /spl plusmn/0.85 and /spl plusmn/0.80 LSB/sub 14 b/, respectively. The /spl Sigma//spl Delta/ modulator and its auxiliary blocks (clock phase and reference voltage generators, and I/O buffers) dissipate 65.8 mW. Only 55 mW are dissipated in the /spl Sigma//spl Delta/ modulator.     

A triple-mode continuous-time /spl Sigma//spl Delta/ modulator with switched-capacitor feedback DAC for a GSM-EDGE/CDMA2000/UMTS receiver

Time jitter in continuous-time /spl Sigma//spl Delta/ modulators is a known limitation on the maximum achievable signal-to-noise-ratio (SNR). Analysis of time jitter in this type of converter shows that a switched-capacitor (SC) feedback digital-to-analog converter (DAC) reduces the sensitivity to time jitter significantly. In this paper, an I and Q continuous-time fifth-order /spl Sigma//spl Delta/ modulator with 1-bit quantizer and SC feedback DAC is presented, which demonstrates the improvement in maximum achievable SNR when using an SC instead of a switched-current (SI) feedback circuit. The modulator is designed for a GSM/CDMA2000/UMTS receiver and achieves a dynamic range of 92/83/72 dB in 200/1228/3840 kHz, respectively. The intermodulation distance IM2, 3 is better than 87 dB in all modes. Both the I and Q modulator consumes a power of 3.8/4.1/4.5 mW at 1.8 V. Processed in 0.18-/spl mu/m CMOS, the 0.55-mm/sup 2/ integrated circuit includes a phase-locked loop, two oscillators, and a bandgap.     

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.     

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.     

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.     

Integrated stereo /spl Delta//spl Sigma/ class D amplifier

A 2/spl times/40 W class D amplifier chip is realized in 0.6-/spl mu/m BCDMOS technology, integrating two delta-sigma (/spl Delta//spl Sigma/) modulators and two full H-bridge switching output stages. Analog feedback from H-bridge outputs helps achieve 67-dB power supply rejection ratio, 0.001% total harmonic distortion, and 104-dB dynamic range. The modulator clock rate is 6 MHz, but dynamically adjusted quantizer hysteresis reduces output data rate to 450 kHz, helping achieve 88% power efficiency. At AM radio frequencies, the modulator output spectrum contains a single peak, but is otherwise tone-free, unlike conventional pulse-width modulation (PWM) modulators which contain energetic tones at harmonics of the PWM clock frequency.     

A noise-shaped switching power supply using a delta-sigma modulator

A technique to reduce in-band tones in switch-mode power supplies is described. It takes advantage of the noise-shaping properties of the delta-sigma (/spl Delta//spl Sigma/) modulator to eliminate the spikes normally present in switching power supplies. A framework is introduced for comparing the conventional pulsewidth modulated (PWM) controller and this approach. A buck converter test circuit is constructed that is designed for a PWM controller clocked at 200 kHz and then substituted with a /spl Delta//spl Sigma/ modulator controller clocked at 400 kHz. The RMS noise power of the PWM controller is 14.9 mW compared to the rms noise power for the /spl Delta//spl Sigma/ modulator of 75.85 mW measured in a 2-MHz bandwidth. Although the /spl Delta//spl Sigma/ modulator rms noise power is higher, the noise floor is below the tones seen at the output of the PWM controller. A multibit /spl Delta//spl Sigma/ modulator controller, however, provides a significant reduction in the spectral output of the power supply. Values of 3.75 and 0.24 mW rms noise power are observed at the output of a 2-bit and 4-bit /spl Delta//spl Sigma/ modulator controller, respectively.     

Tunable continuous-time bandpass /spl Sigma//spl Delta/ modulators with fractional delays

An analytical design methodology for continuous-time (CT) bandpass (BP) /spl Sigma//spl Delta/ modulators is presented. Second- and fourth-order tunable continuous time BP /spl Sigma//spl Delta/ modulator design equations are presented. A novel /spl Sigma//spl Delta/ loop architecture, where the traditional CT BP loop filter function is replaced with the filter function with fractional delays, is proposed. Validity of the methodology is confirmed by mixed-signal behavioral simulations.     

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.     

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 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 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.     

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.     

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 1.5-V direct digital synthesizer with tunable delta-sigma modulator in 0.13-/spl mu/m CMOS

In direct digital synthesizer (DDS) applications, the drawback of the conventional delta sigma (/spl Delta//spl Sigma/) modulator structure is that its signal band is fixed. In the new architecture presented in this paper, the signal band of the /spl Delta//spl Sigma/ modulator is tuned according to the DDS output frequency. We use a hardware-efficient phase-to-sine amplitude converter in the DDS that approximates the first quadrant of the sine function with 16 equal-length piecewise second-degree polynomial segments. The DDS is capable of frequency, phase, and quadrature amplitude modulation. The die area of the chip is 2.02 mm/sup 2/ (0.13 /spl mu/m CMOS technology). The total power consumption is 138 mW at 1.5 V with an output frequency of 63.33 MHz at a clock frequency of 200 MHz (D/A converter full-scale output current: 11.5 mA).     

Single-chip per channel codec with filters utilizing /spl Delta/-/spl Sigma/ modulation

A single-chip per channel codec with filters, fabricated using a single poly-Si NMOS technology, is discussed. In the encoder, the analog signal is converted to a 2.048 M samples/s digital signal by a /spl Delta/-/spl Sigma/ modulator. Filtering necessary for the sampling rate 8 k sample/s and compression by the /spl mu/255 law are performed digitally. In the decoder, the 8 k samples/s PCM is successively resampled and converted into the 2.048 M samples/s /spl Delta/-/spl Sigma/ signal, which is then decoded by a /spl Delta/-/spl Sigma/ demodulator. All the high-frequency images, which appear around multiples of 8 kHz, are removed by digital filters. The chip has continuous-signal antialiasing and smoothing filters for the 2.048 Samples/s sampling rate. It also has reference voltage generators for /spl Delta/-/spl Sigma/ modulation/demodulation. Some of the observed characteristics are given. The NMOS /spl Delta/-/spl Sigma/ modulator requires only two on-chip matched capacitors as precision components, and does not require a linear amplifier. A deliberate quantization step imbalance is introduced to allow a low sampling rate. The main band limiting for the 8 k samples/s is done by the recursive filter. This is realized with the serial-parallel pipeline multiplier (SPPM) in four-phase logic. The whole system is integrated on a 296 mil/spl times/342 mil chip.     

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.     

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.