The main purpose of this thesis is to research High-Order Sigma-Delta Analog-to-Digital converter for precision measurement, a PI compensator and a third-order Sigma-Delta modulator has been proposed based on a second-order Sigma-Delta modulator. In accordance with the analysis result of frequency domain and time domain of system, we use third-order model because of better response with auxiliary software to simulate and implement the system, then measure modulator output variance for input variation. This converter circuit demonstrates that it can achieve the requirements of precision and linearity which the measure instrument demands.

A new low power, wideband wireless transmitter able to convert any RF signal into a constant envelope signal enabling the use of a nonlinear and efficient power amplifier is presented. In the transmitter architecture, two normalized phase signals and the envelope are separated and processed separately. A 1-bit 2nd order SD modulator codes the envelope. Quantization noise is attenuated by a S&H interpolator introducing notches at multiples of the sampling frequency. Phase and Envelope signals are recombined and upconverted directly to radio frequencies using a novel full-digital, wideband quadrature modulator. This mixer takes advantage of the 1-bit SD output. As both LOs and envelope signals are represented by two-level signals, the product of these signals (XOR function) leads to a two-level signal, which can be used as command signal in the multiplexors. Phase signals or theirs complements that are generated by a simple Inversion Block are passed through this multiplexor at the rate of driving signals. This enables to implement a high frequency, wideband mixer instead of a more complex three-input modulator. This IQ mixer is very simple to implementate as it uses only CMOS logic gates. The generation of the quadrature clock signals in the mixer is obtained by carefully design of two paths to avoid mismatch to assure an error less than 1º (only demonstrated in simulation) and the use of SR flipflops to generate correctly the complementary signal prior to the divide-by-two circuit. Two asynchronous 9-bit DACs eliminate the 10-bit high-speed digital adder at the output of the IQ modulator and the 10-bit DAC before the PA, saving power and relaxing adder design constraints. Each DAC is divided into two full binary-weighted DACs of 4 and 5 bits. This topology enables to reduce the size ratios between the most and least significant bits related to a classic 9-bit binary-weighted structure (16 instead of 256). To test the speed and the gain control of the standalone DAC over 45 dB, a prototype DAC is designed in 0.13 ;m BiCMOS technology from STMicroelectronics together with a 1.4 GHz 9-bit CMOS ROM-less direct digital frequency synthesizer (DDFS). Over the output power range, measurements show a SFDR>25 dB with a power dissipation of 25 mW at the maximum differential output power of -3 dBm (RL=50 @). The whole transmitter is designed and implemented and a prototype transmitter is built in 0.13 μm BiCMOS STMicroelectronics process. This low cost single chip digital radio transmitter demonstrates a data rate of 1.8 GHz. The image level is measured to be -12 dBc at this sampling frequency. Dynamic range in the transmitter is 35 dB for sampling frequencies lower than 800 MHz and 25 dB for higher sampling frequencies up to 1.8 GHz. For a two-tone signal, the maximum single-ended output power is -31dBm for each tone and the power dissipation is about 35 mW. This architecture enables flexible and software-defined transmitter. Sampling frequency in the SD coder can be varied to adapt to different communications standards in terms of in-band and outof-band noise requirements and variable LO frequencies can be used. Moreover, the transmitter can adapt dynamically the output power to the power amplifier depending of the required transmitted power at the output of the PA. The transmitter has demonstrated its potential for use as a universal transmitter for applications targeting any frequency band and modulation schema up to 900 MHz (carrier frequency) and occupies a die area of 300x320 ;m2. The generated differential signal can be easily amplified by a switched-mode Power Amplifier (PA) in an efficient way because it presents constant-envelope and the PA can work in the saturation zone, which represents its optimal operation point.

The thesis demonstrates a low-cost, low-bandwidth and low-resolution Analog-to- Digital Converter(ADC) in 0.35 um CMOS Process. A second-order Sigma-Delta modulator is used as the basis of the A/D Converter. A Semi-Uniform quantizer is used with the modulator to take advantage of input distributions that are dominated by smaller-amplitude signals e.g. Audio, Voice and Image-sensor signals. A Single-bit feedback topology is used with a multi-bit quantizer in the modulator. This topology avoids the use of a multi-bit DAC in the feedback loop – hence the system does not need to use digital correction techniques to compensate for a multi-bit DAC nonlinearity. High-Level Simulations of the second-order Sigma-Delta modulator single-bit feedback topology along with a Semi-Uniform quantizer are performed in Cadence. Results indicate that a 5-bit Semi-Uniform quantizer with a Over-Sampling Ratio of 32, can achieve a resolution of 10 bits, in addition, a semi-uniform quantizer exhibits a 5-6 dB gain in SNR over its uniform counterpart for input amplitudes smaller than –10 dB. Finally, this system is designed in 0.35um CMOS process.

The sigma-delta modulator is a popular signal amplitude quantization error (or noise) shaper used in oversampling analogue-to-digital and digital-to-analogue converter systems. The shaping of the noise frequency spectrum is performed by feeding back the quantization errors through a time delay element filter and feedback loop in the circuit, and by the addition of a possible stochastic dither signal at the quantizer. The aim in audio systems is to limit audible noise and distortions in the reconverted analogue signal. The formulation of the sigma-delta modulator as a discrete dynamical system provides a useful framework for the mathematical analysis of such a complex nonlinear system, as well as a unifying basis from which to consider other systems, from pseudorandom number generators to stochastic resonance processes, that yield equivalent formulations. The study of chaos and other complementary aspects of internal dynamical behaviour in previous research has left important issues unresolved. Advancement of this study is naturally facilitated by the dynamical systems approach. In this thesis, the general order feedback/feedforward sigma-delta modulator with multi-bit quantizer (no overload) and general input, is modelled and studied mathematically as a dynamical system. This study employs pertinent topological methods and relationships, which follow centrally from the symmetry of the circle map interpretation of the error state space dynamcis. The main approach taken is to reduce the nonlinear system into local or special case linear systems. Systems of sufficient structure are shown to often possess structured random, or random-like behaviour. An adaptation of Devaney's definition of chaos is applied to the model, and an extensive investigation of the conditions under which the associated chaos conditions hold or do not hold is carried out. This seeks, in part, to address the unresolved research issues. Chaos is shown to hold if all zeros of the noise transfer function lie outside the unit circle of radius two, provided the input is either periodic or persistently random (mod delta). When the filter satisfies a certain continuity condition, the conditions for chaos are extended, and more clear cut classifications emerge. Other specific chaos classifications are established. A study of the statistical properties of the error in dithered quantizers and sigma-delta modulators is pursued using the same state space model. A general treatment of the steady state error probability distribution is introduced, and results for predicting uniform steady state errors under various conditions are found. The uniformity results are applied to RPDF dithered systems to give conditions for a steady state error variance of delta squared over six. Numerical simulations support predictions of the analysis for the first-order case with constant input. An analysis of conditions on the model to obtain bounded internal stability or instability is conducted. The overall investigation of this thesis provides a theoretical approach upon which to orient future work, and initial steps of inquiry that can be advanced more extensively in the future.

A dual-mode second-order Multirate Multibit Sigma Delta (MM-SD) modulator is implemented in a 90nm digital CMOS process for application in the baseband path of RF receivers. Low power consumption is achieved through a new integrator structure and a dedicated timing scheme along with aggressive capacitor scaling in the second stage of the modulator loop. Fabricated prototype achieves 68.6dB peak Signal-to-Noise and Distortion ratio (SNDR) in the 200 kHz GSM band and requires 1.1mA of total current from a 1.5V supply. This dual-mode design also achieves 42.8dB SNDR in the 1.94 MHz WCDMA band with only 1.9mA of total current consumption.

The thesis proposes a third order continuous-time sigma delta modulator used in GSM. We used a special 1.5bit quantizer, and to use its three different states to reach a differential feedback path. That can improve the resolution of our circuit. Oversampling and noise shaping are two keys of sigma delta modulator. In structure, the continuous-time features can reduce power consumption. The proposed sigma delta modulator uses TSMC 0.35 m CMOS process and its sampling frequency is 10.8MHz, bandwidth is200KHz and oversampling ratio is 32.

Continuous-time filters are critical components in the implementation of large bandwidth, high frequency, and high resolution continuous-time (CT) sigma-delta (ΣΔ) analog-to-digital converters (ADCs). The loop filter defines the noise-transfer function (NTF) and hence the quantization noise-shaping behavior of the ΣΔ modulator, and becomes the most critical performance determining part in ΣΔ ADC. This thesis work presents the design considerations for the loop filter in low-pass CT ΣΔ ADC with 12-bits resolution in 25MHz bandwidth and low power consumption using 0.18μm CMOS technology. Continuous-time filters are more suitable than discrete-time filters due to relaxed amplifier bandwidth requirements for high frequency ΣΔ ADCs. A fifth-order low-pass filter with cut-off frequency of 25 MHz was designed to meet the dynamic range requirement of the ADC. An active RC topology was chosen for the implementation of the loop filter, which can provide high dynamic range required by the ΣΔ ADC. The design of a summing amplifier and a novel method for adjusting the group delay in the fast path provided by a secondary feedback DAC of the ΣΔ ADC are presented in detail. The ADC was fabricated using Jazz 0.18μm CMOS technology. The implementation issues of OTAs with high-linearity and low-noise performance suitable for the broadband ADC applications are also analyzed in this work. Important design equations pertaining to the linearity and noise performance of the Gm-C biquad filters are presented. A Gm-C biquad with 100MHz center frequency and quality factor 10 was designed as a prototype to confirm with the theoretical design equations. Transistor level circuit implementation of all the analog modules was completed in a standard 0.18μm CMOS process.

The emergence of bandwidth-intensive services has created a need for high speed and high resolution data converters. Towards this end, system level design of a continuous-time sigma-delta modulator achieving 11 bits resolution over 100 MHz signal bandwidth by using a feed-forward topology is presented. The system is first built in the Simulink environment in MATLAB. The building blocks in the loop filter are modeled with non-idealities, and specifications for these blocks are obtained by simulations. An operational transconductor amplifier (OTA) with 100 mS transconductance, 70 dB linearity, and 34.2 mW power dissipation is designed to be used in the loop filter. Simulation results indicate that the 5th order loop filter implemented in the feed-forward architecture in transistor level shows lower power consumption, 105 mW, compared to the loop filter implemented by feedback architecture, 152 mW.

Bandpass sigma-delta modulators combine oversampling and noise shaping to get very high resolution in a limited bandwidth. They are widely used in applications that require narrowband high-resolution conversion at high frequencies. In recent years interests have been seen in wireless system and software radio using sigma-delta modulators to digitize signals near the front end of radio receivers. Such applications necessitate clocking the modulators at a high frequency (MHz or above). Therefore a loop filter is required in continuous-time circuits (e.g., using transconductors and integrators) rather than discretetime circuits (e.g., using switched capacitors) where the maximum clocking rate is limited by the bandwidth of Opamp, switch’s speed and settling-time of the circuitry. In this work, the design of a CMOS fourth-order bandpass sigma-delta modulator clocking at 500 MHz for direct conversion of narrowband signals at 125 MHz is presented. A new calibration scheme is proposed for the best signal-to-noise-distortion-ratio (SNDR) of the modulator. The continuous-time loop filter is based on Gm-C resonators. A novel transconductance amplifier has been developed with high linearity at high frequency. Qfactor of filter is enhanced by tunable negative impedance which cancels the finite output impendence of OTA. The fourth-order modulator is implemented using 0.35 mm triplemetal standard analog CMOS technology. Postlayout simulation in CADENCE demonstrates that the modulator achieves a SNDR of 50 dB (~8 bit) performance over a 1 MHz bandwidth. The modulator’s power consumption is 302 mW from supply power of ± 1.65V.

In this thesis, a switched-current integrator with active amplifier feedback and dummy switch is proposed to increase the operation speed and reduce the non-ideal effects in traditional switched-current circuit. The active amplifier is designed in low gain and high bandwidth so that the oscillation can be avoided. We improve the operation speed and transmission error by the active amplifier feedback and reduce the CFT error by the dummy switch so that high resolution can be achieved. Then we apply the proposed integrator to the switched-current sigma-delta modulator. The sigma-delta modulator is simulated using TSMC 0.35£gm CMOS process with 3.3V power supply. We obtain 67dB PSNR, 66dB dynamic range(DR), and 40KHz bandwidth. The sampling frequency is 10.24MHz, the power supply is 3.3V and the power consumption is 19mW.