Alexander Buhmann

A Comparative Study on Excess-Loop-Delay Compensation Techniques for Continuous-Time Sigma–Delta Modulators

Excess loop delay (ELD) is well known for its detrimental effect on the performance and stability of continuous-time sigma-delta modulators. A detailed analysis on the most recently published compensation techniques for single-stage modulators is performed in this paper, thus enabling their application to an arbitrary modulator. Based on different characteristics such as circuit complexity, achievable dynamic range, or requirements on the operational amplifiers, their advantages and disadvantages are investigated. Subsequently, the analysis is extended to cascaded modulators. Contrary to intuition, the results indicate that a compensation of ELD in every stage of the cascade is insufficient for optimal performance. Although not configured in a feedback configuration and as such not suffering from stability problems, each coupling network between two stages must additionally be compensated for ELD.

On the Implicit Anti-Aliasing Feature of Continuous-Time Cascaded Sigma–Delta Modulators

This paper deals with one of the most outstanding advantages of continuous-time (CT) sigma-delta modulators compared to their discrete-time counterparts: the implicit anti-aliasing feature (AAF). Although inherent in any CT architecture, analysis of anti-aliasing properties has mostly been restricted to single-stage modulators in the past. In this contribution, extensions on analysis methods for the study of the AAF of CT multistage noise-shaping architectures are covered. A theoretical model is introduced and confirmed through simulation results. Contrary to previous belief, the results indicate that usually all stages of a cascaded architecture are involved in the anti-aliasing behaviour and hence that it is not solely determined by the first stage.

Drive and sense interface for gyroscopes based on bandpass sigma-delta modulators

This paper demonstrates a MEMS gyroscope system with extensive use of sigma-delta (ΣΔ) modulation in both, primary and secondary modes. The primary loop has a bandpass ΣΔ-digital-to-analog converter (DAC) driving the primary mass into resonance, which is implemented on a field programmable gate array (FPGA). With this strategy of shifting the primary oscillation control into the digital domain, the analog circuit complexity is enormously reduced. A continuous-time (CT) fourth-order micro-electro-mechanical ΣΔ Modulator (ΣΔM) incorporating the secondary resonator is used to convert the Coriolis rate signal into a bit stream. This ΣΔM is implemented on PCB performing an in-band noise (IBN) below −60 dBFS.

A Method for the Discrete-Time Simulation of Continuous-Time Sigma-Delta Modulators

This paper presents a method for the discrete-time (DT) simulation of continuous-time (CT) sigma-delta modulators. Via the application of lifting, correction values for each state variable of a modulator are calculated, which subsequently are used to calibrate online these state variables during a DT simulation of the CT system. At the sampling instants, the values of the DT state variables are thus exactly equalized to those of the given CT modulator while the time consuming CT simulation itself has been replaced by an efficient and rapid DT one. A simple second order modulator serves as an example to illustrate the application of lifting not only to an ideal but also to a non-ideal modulator covering typical non-idealities such as finite opamp gain, finite gain-bandwidth, excess loop delay and even jitter.

A Continuous-Time Field Programmable Analog Array Using Parasitic Capacitance Gm-C Filters

Field programmable analog filters (FPAAs) often lack the necessary bandwidth for high performance applications. This paper presents an FPAA based on Gm-C filters, which achieves routing without the use of transmission gates. Not only can the parameters of these filters be tuned, but also their order and structure. No additional capacitor is used for integration, only the MOS parasitic capacitances. A maximum bandwidth of 164 MHz has been achieved in simulations based on a 130 nm 1.2 V CMOS process. Distortion performance is high with a HD3 of less than -70dB for a 50mV@1MHz signal. Influences of parasitic capacitances are simulated using a test chip with 49 Gm-cells arranged in a hexagonal array.

DISCO - A toolbox for the discrete-time simulation of continuous-time Sigma-Delta modulators using MATLAB™

This paper will present a MATLABTM toolbox for the discrete-time (DT) simulation of continuous-time (CT) sigma-delta modulators. Via the application of lifting, correction values for the state vector are calculated and used to correct the state vector of the DT simulation. Furthermore, several typical non-idealities of CT modulators, such as real opamp behavior, excess loop delay, and even jitter, are simulated with a tremendously speed up being for some simulation tasks up to a factor of 330. The introduced simulation algorithm is embedded in a CT sigma- delta design environment, which has a graphical user interface for a direct user interaction.

A GPS aided Full Linear Accelerometer Based Gyroscope-free Navigation System

This paper reports on a GPS aided, full linear accelerometer based, gyroscope-free inertial navigation system (INS), which permits an almost arbitrary placement and orientation of the acceleration sensors within the moving body. The objective of this approach is to reuse different accelerometers already existing in e.g. a car and thus reducing the costs of an INS. Besides navigation, this system can also be used for car safety applications like roll-over detection. In this field, calculation of the center of rotation in both, the body and the navigation frame of reference, is of great interest, which is an additional benefit of the system. The INS itself consists of at least 12 sensitive axes being necessary to calculate the entire body movement. In contrast to previous approaches, this is done by a simple matrix multiplication reducing the calculating effort. Simulations as well as measurement results verify this concept. Due to the sensor noise and the necessary integration steps, the variance of the position and orientation, meaning the uncertainty, increases with time. This problem is solved by coupling the INS with the long time stable GPS through a predictive filter. In contrast to a conventional gyroscope based INS, this approach offers additional information about the body movement, which is used in the filter to improve the overall performance. Due to the nonlinear behavior of the orientation, an Unscented Kalman Filter using a third order Wiener Process Acceleration Model is used. The adaptation of the covariance matrix is done by a fictive trajectory. With a GPS standard deviation of 10 m having a 1 Hz update, a sensor noise of 5 mg for a 100 Hz bandwidth and a simulation interval of slightly more than 4 minutes, the simulated position and orientation standard deviation are 4 m and 2°, respectively.

Microelectromechanical HF resonators fabricated using a novel SOI-based low-temperature process

This paper reports on a novel silicon-on-insulator (SOI) based low-temperature fabrication process to realize microelectromechanical high-frequency resonators. Key features of the devices are single-crystal silicon resonant beams, 400-nm or 600-nm thin transducer gaps, and gold electrodes. The fabrication process combines bulk silicon micromachining applying deep reactive ion etching, low-temperature deposition of a thin sacrificial oxide layer, and electroplating of the lateral electrodes. The resonant behavior of devices with resonance frequencies f/sub res/ between 420 kHz and 4.11 MHz was characterized as a function of the bias voltage V/sub bias/ applied to the beam. Measurements were performed at ambient pressures p between 5/spl times/10/sup -3/ Pa and 0.5 Pa. Q values up to 52000 at f/sub res/=420 kHz and 6000 at f/sub res/=4.11 MHz were obtained. The interaction of resonator and measurement setup were simulated using an electrical network simulation program combined with a finite element analysis using ANSYS.

Efficient Reliability-Based Design Optimization for Microelectromechanical Systems

The miniaturization of microelectromechanical systems (MEMS) makes cheaper products (due to less chip size consumption) and new applications, e.g., in chip cards, possible. With further miniaturization, however, the influence of manufacturing variances increases: hence it is more and more important to consider them already in the design optimization phase. The widely used Monte Carlo (MC) simulation is not suitable for the implementation in optimization algorithms, as a large number of required samples result in long simulation times. Instead we apply the Sigma-Point approach which enables the accurate calculation of the output variances, even for nonlinear functions with only few sample calculations. In conjunction with a MEMS resonator model the Sigma-Point approach turns out to be four orders of magnitude faster than an equivalent MC calculation. Therefore, it is optimally suited for an efficient reliability-based design optimization (RBDO). Furthermore, the Sigma-Point approach is simple to implement and matrix notation enables fast calculation, even for large models. A versatile analysis of the interaction between optimized sensor design, yield requirements, and manufacturing tolerances is feasible with the suggested RBDO methodology.

Low-Power, Continuous-Time Sigma-Delta Interface for Micromachined Gyroscopes Employing a Sub-Nyquist-Sampling Technique

In this paper a novel system concept for the implementation of low-power readout electronics for micromachined gyroscopes is described. The main innovation is a modified Chopper Stabilization (CHS) technique in a SigmaDelta loop based on an undersampling process. It enables the design of a full Continuous-Time (CT) SigmaDelta interface dissipating less power than its Discrete-Time (DT) counterpart without additional hardware effort for a flicker noise suppression. Further a systematic design approach for an interface employing this method and an architecture enabling this procedure is presented.