A 5-MHz 11-bit delay-based self-oscillating ΣΔ modulator in 0.025 mm2

In this paper a self-oscillating Sigma Delta modulator is presented. By introducing this self-oscillation in the system, the loop filter operates at a speed significantly lower than dictated by the clock frequency. This allows for a simple and power efficient design of the opamps used in the loop filter. The self-oscillation is induced here by introducing a controlled delay in the feedback loop of the modulator. A second order CMOS prototype was constructed in a 0.18 um technology. A clock frequency of 850MHz generates a self-oscillation mode at 106.25 MHz. The modulator achieves a dynamic range (DR) of 66 dB for a signal bandwidth of 5 MHz. The power consumption is only 6mW and the chip area of the modulator core is 0.025mm^2

A rigorous approach to the robust design of continuous-time ΣΔ modulators

In this paper we present a framework for robust design of continuous-time Sigma Delta modulators. The approach allows to find a modulator which maintains its performance ( stability, guaranteed peak SNR, ...) over all the foreseen parasitic effects, provided it exists. For this purpose, we have introduced the S-figure as a criterion for the robustness of a continuous-time Sigma Delta modulator. This figure, inspired by the worst-case-distance methodology, indicates how close a design is to violating one of its performance requirements. Optimal robustness is obtained by optimizing this S-figure. The approach is illustrated through various design examples and is able to find modulators that are robust to excess loop delay, clock jitter and coefficient variations. As an application of the approach, we have quantified the effect of coefficient trimming. Even with poor trim resolution, good performance can be achieved provided beneficial initial system parameters are chosen. Another example illustrates the fact that also the out-of-band peaking behavior of the signal transfer function can be controlled with our design framework

The Nyquist criterion: a useful tool for the robust design of continuous-time ΣΔ modulators

This paper introduces a figure of merit for the robustness of continuous-time sigma-delta modulators. It is based on the Nyquist criterion for the equivalent discrete-time (DT) loop filter. It is shown how continuous-time modulators can be designed by optimizing this figure of merit. This way modulators with increased robustness against variations in the noise-transfer function (NTF) parameters are obtained. This is particularly useful for constrained systems, where the system order exceeds the number of design parameters. This situation occurs for example due to the effect of excess loop delay (ELD) or finite gain bandwidth (GBW) of the opamps. Additionally, it is shown that the optimization is equivalent to the minimization of H_infinity, the maximum out-of-band gain of the NTF. This explains why conventional design strategies that are based on H_infinity, such as Schreier’s approach, provide quite robust modulator designs in the case of unconstrained architectures

Delay analysis of a place reservation queue with heterogeneous service requirements

We study the delay performance of a queue with a reservation-based priority scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays for the best-effort packets. In our model, we consider a discrete-time single-server queue with general independent arrivals of class 1 (delay-sensitive) and class 2 (best-effort). The scheduling mechanism makes use of an in-queue reservation for a future arriving class-1 packet. A class-1 arrival takes the place of the reservation in the queue, after which a new reservation is created at the tail of the queue. Class-2 arrivals always take place at the end of the queue. Past work on place reservation queues assumed independent and identically distributed transmission times for both packet classes, either deterministically equal to one slot, geometrically distributed or with a general distribution. In contrast, we consider heterogeneous service requirements with class-dependent transmission-time distributions in our analysis. The key element in the analysis method for class-dependent transmission times is the use of a new Markovian system state vector consisting of the total amount of work in the queue in front of the reservation and the number of class-2 packets in the queue behind the reservation, at the beginning of a slot. Expressions are obtained for the probability generating functions, the mean values and the tail probabilities of the packet delays of both the delay-sensitive and the best-effort class. Numerical results illustrate that reservation-based scheduling mitigates the problem of packet starvation as compared to absolute priority scheduling

Session delay in file server output buffers with general session lengths

In this paper, we analyze the delay incurred by session-based traffic in the output buffer of a file server. Users can start and end sessions during which they are active and download information from the file server. Per time slot, each active user downloads a random but strictly positive number of information packets. Each session lasts for a random, yet again, strictly positive number of slots. We model the file server output buffer as a discrete-time infinite-capacity queueing system and we present an analytical technique to study the queueing delay for sessions in case of a general session-length distribution. The analysis method is based on the combination of a generating-functions approach with the use of an infinite-dimensional state description. As a result, a closed-form expression for the mean session delay is obtained. The analysis is illustrated with a numerical example, based on real traces of file server traffic

Analysis of a discrete-time queueing system with an NT-policy

In this paper, we analyse a discrete-time single-server queue operating under the NT-policy, which aims at clustering the service of customers in order to reduce the number of server activations and deactivations. Starting from an empty queue, the service of arriving customers is postponed until either of two thresholds is reached. Specifically, exhaustive service of customers is initiated only if either N customers have accumulated (space threshold) or if more than slots have passed since the arrival of the first customer. This way, the queue cycles between three states, i.e. an empty phase, an accumulating phase and a serving phase. A Bernoulli arrival process and deterministic service times are assumed. We derive the steady-state probabilities of the system's state as well as the distributions of the phase sojourn times and the customer delay. For the latter, we condition on the phase during the customer's arrival slot. The influence of the model parameters on the results is discussed by means of a numerical example

Performance analysis of buffers with train arrivals and correlated output interruptions

In this paper, we study a discrete-time buffer system with a timecorrelated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying J-state Markov process during that slot. First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a 2-state Markov process. Some numerical examples help to visualise the influence of the various model parameters