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.     

On the design of high-performance wide-band continuous-time sigma-delta converters using numerical optimization

Continuous-time (CT) sigma-delta (/spl Sigma//spl Delta/) modulators are growing increasingly popular in wide-band analog-digital conversion. High orders of quantization noise shaping, and multibit quantizers, are used to compensate for the low oversampling ratios in wide-band applications. These, however, add circuit complexities and excess loop delay that are detrimental to the /spl Sigma//spl Delta/ control loop. This paper presents an exact mathematical analysis technique, based on the CT-discrete time equivalence, that can take these effects into account. A design-by-optimization approach based on that analysis is used to compensate for these effects, avoid intractability issues and to gain flexibility in the design. It is also shown that it is advantageous not to fix the position of the quantization noise-shaping zeros in the signal band.     

Resonant tunnelling delta sigma modulator suitable for high-speed operation

A resonant tunnelling logic gate, monostable-bistable transition logic element (MOBILE), was used to test high frequency operation of the /spl Delta//spl Sigma/ modulator based on a frequency modulated intermediate signal. This /spl Delta//spl Sigma/ modulator has no feedback loop and is promising for high-speed operation. Good noise shaping characteristics over four decades were measured. This ideal noise shaping demonstrated that the MOBILE can work as an ideal quantiser.     

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 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.     

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.     

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.     

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.     

Decimation schemes for /spl Sigma//spl Delta/ A/D converters based on Kaiser and Hamming sharpened filters

Cascaded-integrator-comb (CIC) filters are efficient anti-aliasing rate-conversion filters widely used for /spl Sigma//spl Delta/ A/D converters. High-order structures, attempting to increase the noise rejection within the folding bands, have the drawback of inserting multiple zeros in the same positions and increasing the edge-band attenuation. A combination of sharpened and CIC filters is proposed in the paper, with the goal of increasing the rejection of the /spl Sigma//spl Delta/ quantisation noise around the folding bands and reducing the pass-band drop of the designed decimation filters with respect to classic CIC structures. Design criteria, leading to optimised structures, and comparisons are given with respect to both classical and modified CIC filters.     

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 2.4-GHz monolithic fractional-N frequency synthesizer with robust phase-switching prescaler and loop capacitance multiplier

The design of a 2.4-GHz fully integrated /spl Sigma//spl Delta/ fractional-N frequency synthesizer in a 0.35-/spl mu/m CMOS process is presented. The design focuses on the prescaler and the loop filter, which are often the speed and the integration bottlenecks of the phase-locked loop (PLL), respectively. A 1.5-V 3-mW inherently glitch-free phase-switching prescaler is proposed. It is based on eight lower frequency 45/spl deg/-spaced phases and a reversed phase-switching sequence. The large integrating capacitor in the loop filter was integrated on chip via a simple capacitance multiplier that saves silicon area, consumes only 0.2 mW, and introduces negligible noise. The synthesizer has a 9.4% frequency tuning range from 2.23 to 2.45 GHz. It dissipates 16 mW and takes an active area of 0.35 mm/sup 2/ excluding the 0.5-mm/sup 2/ digital /spl Sigma//spl Delta/ modulator.     

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.     

A 10-300-MHz IF-digitizing IC with 90-105-dB dynamic range and 15-333-kHz bandwidth

An integrated low-noise amplifier, mixer, bandpass /spl Delta//spl Sigma/ analog-to-digital converter (ADC), decimation filter, and two synthesizers implement a general-purpose back-end for a narrow-band superheterodyne receiver. The /spl Delta//spl Sigma/ ADC is merged with the mixer and combines LC, active-RC, and switched-capacitor resonators to achieve low noise and robust operation with low power consumption. A variable full-scale feature adds an automatic-gain-control capability to the ADC while saving power and minimizing noise at low signal levels.     

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.     

Self-tuning algorithms for high-performance bandpass switched-capacitor /spl Sigma//spl Delta/ modulators

Switched-capacitor high-frequency bandpass /spl Sigma//spl Delta/ modulators could suffer from capacitor mismatch, finite opamp dc gain, and finite opamp bandwidth. These problems make the notch frequency and the quality factor of the zeros of the noise transfer function to deviate from their nominal values, strongly affecting the modulator dynamic range (DR). In order to avoid this situation, two sampled-data algorithms have been developed which allow to self-calibrate the bandpass /spl Sigma//spl Delta/ modulators. They use 3500 gate and 0.043 mm/sup 2/ area and consume power only when they are active, while, when the system is on, they are off and do not interfere with standard operation. The validity of the proposal is demonstrated by a silicon prototype in which the proposed solution allows to guarantee a 75-dB DR performance also under worst case conditions. In the particular case, it allows for the recovery of 3 dB in the SNR for the 200-kHz FM band (from 73 to 76 dB).     

K-band monolithic InGaP-InGaAs DCFET amplifier using BCB coplanar waveguide technology

A K-band (20 GHz) monolithic amplifier was developed and fabricated by adopting a low-/spl kappa/ benzocyclobutene (BCB) coplanar waveguide (CPW) line and InGaP-InGaAs doped-channel HFETs (DCFETs). This monolithic microwave integrated circuit (MMIC) utilizes a high impedance BCB CPW microstrip line (Z/sub 0/=70 /spl Omega/) for the biasing circuits, and a Z/sub 0/=50 /spl Omega/ line for the RF signal transmission. The low dielectric constant characteristic of the BCB interlayer is beneficial for a common-ground bridge process, which reduces the parasitics. The calculated loss tan/spl delta/ is 0.036 for the BCB at 20 GHz. The one-stage MMIC amplifier achieves an S/sub 21/ of 5 dB at 20 GHz, which is the first demonstration of the K-band InGaP-InGaAs DCFET monolithic circuit.     

A 92-MHz 13-bit IF digitizer using optimized SC integrators in 0.35-/spl mu/m CMOS technology

A feedforward compensation scheme with no Miller capacitors is proposed to overcome the bandwidth limitations of traditional Miller compensation schemes. The technique has been used in the design of an operational transconductance amplifier (OTA) with a dc gain of 80 dB, gain bandwidth of 1.4 GHz, phase margin of 62/spl deg/, and 2 ns settling time for 2-pF load capacitor in a standard 0.35-/spl mu/m CMOS technology. The OTA's current consumption is 4.6 mA. The OTA is used in the design of a fourth-order switched-capacitor bandpass /spl Sigma//spl Delta/ modulator with a clock frequency of 92 MHz. It achieves a peak signal-to-noise ratio of 80 and 54 dB for 270-kHz (GSM) and 3.84-MHz (CDMA) bandwidths, respectively and consumes 19 mA of current from a /spl plusmn/1.25-V supply.     

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.     

Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames

The K-level Sigma-Delta (/spl Sigma//spl Delta/) scheme with step size /spl delta/ is introduced as a technique for quantizing finite frame expansions for /spl Ropf//sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error where N is the frame size, and the frame variation /spl sigma/(F,p) is a quantity which reflects the dependence of the /spl Sigma//spl Delta/ scheme on the frame. Here /spl par//spl middot//spl par/ is the d-dimensional Euclidean 2-norm. Lower bounds and refined upper bounds are derived for certain specific cases. As a direct consequence of these error bounds one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/. When dealing with sufficiently redundant frame expansions, this represents a significant improvement over classical pulse-code modulation (PCM) quantization, which only has MSE of order 1/N under certain nonrigorous statistical assumptions. /spl Sigma//spl Delta/ also achieves the optimal MSE order for PCM with consistent reconstruction.     

A continuous-time sigma-delta modulator with 88-dB dynamic range and 1.1-MHz signal bandwidth

This paper presents the design and experimental results of a continuous-time /spl Sigma//spl Delta/ modulator for ADSL applications. Multibit nonreturn-to-zero (NRZ) DAC pulse shaping is used to reduce clock jitter sensitivity. The nonzero excess loop delay problem in conventional continuous-time /spl Sigma//spl Delta/ modulators is solved by our proposed architecture. A prototype third-order continuous-time /spl Sigma//spl Delta/ modulator with 5-bit internal quantization was realized in a 0.5-/spl mu/m double-poly triple-metal CMOS technology, with a chip area of 2.4 /spl times/ 2.4 mm/sup 2/. Experimental results show that the modulator achieves 88-dB dynamic range, 84-dB SNR, and 83-dB SNDR over a 1.1-MHz signal bandwidth with an oversampling ratio of 16, while dissipating 62 mW from a 3.3-V supply.