Johannes Wagner

STF engineering in CT sigma-delta modulators using www.sigma-delta.de

This paper presents a straightforward method of STF engineering in continuous-time ΣΔ modulators within the web-based design tool www.sigma-delta.de. There are already different well known methods to obtain the STF depending on constraints given by the designer. One possibility is the analytical derivation of the high-level coefficients yielding a certain STF. Further, the ΣΔ modulator can be embedded into a filter with the desired characteristic or vice versa. However, as the NTF and STF are dependent upon each other, they cannot be chosen independently. The web-based design tool for continuous-time ΣΔ modulators relies on a heuristic search based on a genetic algorithm that is able to determine a STF complying to given constraints while maximizing the signal-to-noise ratio of the chosen modulator architecture at the same time. This paper shows the capabilities of the publicly available design tool in regard of STF engineering and gives corresponding examples.

Designing CT ΣΔ modulators with shaped feedback waveforms using www.sigma-delta.de

This paper describes an automated design approach to obtain continuous-time ΣΔ modulators with non-rectangular and even multiple DAC feedback waveforms using www.sigma-delta.de. There already exist well known techniques to calculate the necessary high-level coefficients for DAC waveforms other than non-return-to-zero. However, these calculations require expert understanding of ΣΔ modulators and get more challenging if two or even more different waveforms are utilized within one modulator. The design approach proposed in this paper allows an easy-to-use integration of multiple feedback waveforms in a rapid design process without further calculations and sophisticated knowledge on system theory or modulator design. This work presents the capabilities of the freely available design tool with regard to DAC waveforms and gives corresponding examples. Moreover, to emphasize the different characteristics of the individual waveforms, the sensitivity to ELD variations of all modulators is shown.

Phase noise vs. jitter analysis in continuous-time LP and BP ΣΔ modulators with interferers

Continuous-time (CT) ΣΔ modulators are well-known for their sensitivity to jitter. This paper intends to compare and clarify the effect of both colored phase noise and white jitter as measures for non-ideal clocks on the performance of CT ΣΔ modulators, which becomes of utmost importance under the influence of strong out-of-band (OOB) interferers. The jitter-induced noise is shown to be a convolution in the frequency domain between the clock phase noise and the CT derivative of the modulator output. Simulations on lowpass and bandpass modulators show that depending on the shape of the phase noise, the SNR of the modulator is limited by the input signal or the quantization noise. In the scenario where the SNR is limited by the input signal, techniques regarding feedback DAC waveforms cannot reduce the impact of jitter, and the SNR is further reduced in the presence of OOB interferers. Consequently, a realistic clock phase noise should be specified to allow frequency-domain analysis and thus an accurate estimation on the output spectrum and performance of CT ΣΔ modulators. Moreover, interferer attenuation techniques should be applied to reduce the clock jitter influence.

Designing CT bandpass ΣΔ modulators with arbitrary STF shapes

In this paper the automated design of continuous-time bandpass ΣΔ modulators with arbitrary signal-transfer-functions is described. State-of-the-art design methodologies rely on multiple transformations to obtain continuous-time bandpass modulators. Moreover, they are mainly focused on the NTF in order to achieve the required SNR. A design approach, which allows to realize a specified signal-transfer function is not known in the state-of-the-art. In contrast to that the web-based design tool www.sigma-delta.de allows STF engineering for bandpass modulators as first of its kind. The STF is optimized with regard to user defined specifications while the signal-to-noise ratio of the modulator is maximized. This work gives a general introduction to the tool and explains the features concerning bandpass modulators in detail together with corresponding examples.

Digital interferer suppression and jitter reduction in continuous-time bandpass ΣΔ modulators

Clock jitter sensitivity is a well-known drawback of continuous-time ΣΔ modulators. Although there exist various methods to alleviate the jitter influence, most are only effective in reducing noise incurred by out-of-band quantization noise. However, due to the steadily increasing signal frequency in receiver applications, the dominant jitter influence rather originates from the mixing between the close to in-band interferers and the close-in clock phase noise, either in a mixer or in the DAC of a bandpass ΣΔ modulator. This mixing results in additional in-band noise which cannot be reduced by existing solutions. In this paper, we use a reconfigurable digital filtering method for close to in-band interferer suppression in bandpass ΣΔ modulators, and demonstrate its effectiveness in improving phase noise tolerance through simulation. Additionally, a technique to simplify the implementation of the digital filters is proposed.

Using www.sigma-delta.de to rapidly obtain ELD compensated CT ΣΔ modulators

For two decades, Excess-Loop-Delay (ELD) is known to degrade the performance of continuous-time (CT) ΣΔ A/D converters. Many methods have been proposed to compensate for this effect, but for their implementation sophisticated knowledge in loop-filter design is necessary. The web-based design tool for CT ΣΔ modulators www.sigma-delta.de offers a straightforward integration of commonly used ELD compensation techniques in an early stage of the design process without the need of in depth knowledge of ΣΔ loop-filters. As the tool uses a heuristic search, based on a genetic algorithm within a parallel implementation on a GPU, it provides results with a very short response time. This paper presents the compensation techniques which are commonly implemented within the state of the art and shows their automatic application on architectural level by the design tool. Exemplary modulators are created and evaluated in a circuit level simulator. Further, the calculation of device parameters for a circuit-level simulator model, based on the coefficients obtained by the tool, is illustrated. Thereby, the usage of the developed and publicly available design tool for CT ΣΔ modulator is practically shown.

Finite GBW in single OpAmp CT ΣΔ modulators

This paper presents a comparison study on single-OpAmp resonators applied in ΣΔ modulators under the influence of nonidealities. In the recent state-of-the-art, single amplifier resonators have been proposed for the loopfilter to reduce hardware and thus power and area. The question arises if the effort for this single amplifier approach is indeed lower compared to the two amplifier approach, or if the single OpAmp has to fulfill much higher requirements, which would make the approach counterproductive. To answer this question, we compare the traditional dual amplifier approach, namely the CRFF and CRFB topology, to two single amplifier approaches for the resonator under the influence of amplifier nonidealities and mismatch. It is shown that the single amplifier resonator can come with significant drawbacks, but when compensated for carefully, can still be advantageously applied.

Designing CT ΣΔ modulators with www.sigma-delta.de

Due to a high performance and its inherent filtering capabilities, continuous-time (CT) ΣΔ modulators are the state-of-the-art for many different applications. In this demo, it is shown how to use www.sigma-delta.de for the design of these modulators. Moreover, the visitors are assisted to try the tool themselves on their own devices (e.g. notebooks, tablets, smartphones).

A study on op-amp nonlinearity in a single-bit CT ΔΣ modulator employing GBW compensation

This work investigates the nonlinear effect of the 1st operational amplifier (op-amp) in a CT ΔΣ modulator with finite gain-bandwidth product (GBW) compensation. A behavioral op-amp model employing a hyperbolic tangent expression has been created and verified to approximate the op-amp nonlinear characteristics. In analyzing transient simulations of ΔΣ modulators compensated for different GBWs, the influence of the 1st op-amp nonlinearity has been studied, indicating that more stringent linearity requirement on the 1st op-amp must be satisfied in the modulator compensated for lower GBW. This issue can be addressed by increasing the op-amp DC gain, or by employing a mixed feedforward/feedback (FF/FB) architecture, which outperforms the cascade of integrators with feedback (CIFB) topology concerning linearity due to the reduced internal swing, thus allowing both GBW compensation and relaxed linearity requirements.