Simulation technique for noise and timing jitter in electronic oscillators

Timing jitter is a concern in high frequency timing circuits. Its presence can degrade system performance in many high-speed applications. In this paper, a new method for efficiently measuring timing jitter due to phase locked loops is described. Two important parameters, absolute jitter and cycle-to-cycle jitter, used to describe jitter performance can be analyzed. Simulation results for the measurement of jitter in phase locked loop using MATLAB SIMULINK are presented. The methodology described is also applicable to other types of clock generator and oscillators such as LC oscillators, as well as other kinds of noise source such as power supplies.

The transmission of high-speed data over severely band-limited channels may be accomplished through the use of discrete multitone (DMT) modulation, a modulation technique that has been proposed for a number of new applications. While the performance of a DMT system has been analyzed by a number of authors, these analyses ignore the effect of timing jitter on system performance. Timing jitter becomes an increasingly important concern as higher data rates are supported and larger constellations are allowed on the DMT subchannels. Hence, in this paper, we assume that synchronization is maintained by using a digital phase-locked loop to track a pilot carrier, Given this model, we derive error rate expressions for an uncoded DMT system operating in the presence of timing jitter, and we derive an expression for the interchannel distortion that results from a varying timing offset across the DMT symbol. In addition, we investigate the performance of trellis-coded DMT modulation in the presence of timing jitter. Practical examples from the asymmetric digital subscriber line (ADSL) service are used to illustrate various results.

A time‐domain microwave imaging system with improved image quality is presented for early detection of breast cancer. The time‐domain system has the advantage of short scan time compared with the frequency‐domain system but suffers from low signal‐to‐noise ratio (SNR) due to high attenuation of the RF signal within the breast tissue. Signal averaging of repeated measurements can improve the SNR, but this method also smears the signal peaks due to the signal‐averaged jitter, which adversely affects the reconstructed image quality. An image enhancement method using Gaussian bandpass filtering (BPF) is proposed for a time‐domain imaging system. The results from the proposed method were compared with those from the deconvolution method, which is typically used to remove the effects of signal‐averaged timing jitter in short pulse measurements. Simulation results with a 3D hemispherical homogeneous breast model containing tumour cells revealed improvement of the reconstructed image quality with the proposed method in the presence of timing jitter. The signal‐to‐mean ratio was increased from 6.46 to 14.15 with BPF, whereas deconvolution resulted in an increase to 9.36. Simulation results with a non‐homogeneous realistic breast model also showed image enhancement with the proposed method.

Crystal oscillators are widely used in electronic systems to provide reference timing signals. Even though they are designed to be highly stable, their performance can be deteriorated by several types of random noise sources and deterministic interferences. This paper investigates the phenomenon of timing jitter in crystal oscillators induced by the injection of deterministic interferences. It is shown that timing jitter is closely related to the phase and amplitude modulations of the oscillator response. A closed-form variational macromodel is proposed to quantify timing jitter as well as to qualitatively explain the interference mechanism. Analytical results and efficient numerical simulations are developed to explore how timing jitter depends on the frequency of the interfering signal. The methodology is tested by a crystal Pierce oscillator.

Single-photon lidar is one of the important development directions of long-range lidar in the future. Since the detection mechanism of single-photon lidar is quite different from the traditional lidar detection system, it is necessary to measure the range walk error caused by its measurement. We analyzed the detection mechanism of single-photon lidar, established a mathematical model of laser echo signal and detector’s timing jitter, and deduced the relationship between the range walk error and timing jitter. Besides simulation, we set up a coaxial lidar and utilized three kinds of Geiger mode avalanche diode(GM-APD) detectors with different timing jitter to verify the simulation results. The results show that with the increase of the detector’s timing jitter, the range walk error of the system also increase, and the two are positively correlated. When the standard deviations of the detector timing jitter are 15ps, 350ps, and 1152ps, the range walk error are 0.88cm, 2.55cm, and 12.56cm, respectively. Finally, an evaluation model of ranging accuracy is established by using appropriate data fitting method, which provides an evaluation model for the ranging accuracy of single-photon radar and it has potential application value.

Many of today's applications require that a phase-locked loop (PLL) operate at high speeds, while maintaining reasonable phase noise and jitter performance. Voltage-controlled oscillators (VCO) are important building blocks in PLLs. More importantly, the VCO is the major contributor of phase noise in a PLL. The noisy environment, mainly due to the switching noise generated by the digital portion of these systems. imposes stringent constraints on the design of VCOs, especially phase noise or timing jitter. The switching noise originated in the digital portion of the systems are coupled to the supply and ground rails of the VCO of PLLs. Another important block of a PLL is the charge-pump, a block that is responsible for generating the control voltage to be applied to the VCO. The stability or fluctuation of the control voltage, can severely affect the phase noise performance of the VCO. The research in this thesis, centered on (i) the design considerations of CMOS charge-pumps, (ii) the timing jitter of the delay-cells of low-voltage CMOS ring-VCOs and (iii) the design of a high-speed ring oscillator. A PLL was designed using a new active inductor 6.3-GHz ring oscillator, with a tuning range of +/- 15% was designed in 0.18um CMOS technology. The ring oscillator employed active inductor loads that resulted in an improvement of about 42% in oscillation frequency when compared to the conventional resistor loaded ring oscillator.

In a ring oscillator, the behaviour in which the output voltage ramp (up/down) of its individual delay cell crosses the threshold, which triggers the next stage delay cell, is crucial in determining the timing jitter, and hence phase noise. Specifically, as the slew rate of the ramp decreases and/or the amount of noise contribution from the transistors in the delay cell increases, the voltage ramp (up or down) has a higher probability of crossing the threshold multiple times, before finally passing it at a time denoted as last passage time, which is more accurate than the conventional first passage time model. This multiple crossing results in a higher jitter. In the past, investigation in last passage time jitter model results in jitter expression that can only be calculated numerically and thus no design guidelines/insights are apparent. In this paper, a novel model is presented with a simple closed form formula, which shows the extra jitter, due to multiple crossing, adds a term that increases as a function of the fourth power of the noise strength/slew rate ratio. The formula is applied to a real life practical low slow rate/high noise ring oscillator which finds application, for example, in random number generator implementation. Corresponding transistor level simulation results agree reasonably well with the model. Furthermore, it is shown that, on example designs, the last passage time approach in this paper can lead to time jitter that is 100 % larger than that due to conventional first passage time model.

On-chip clock generation is an attractive alternative to external quartz oscillators for low-power sensing systems. LC and ring oscillators typically use less power, and can start and stop much faster than traditional quartz oscillators, allowing systems to spend more time in low-power sleep states. A hybrid on-chip clocking scheme is evaluated in which a ring oscillator is used as the reference clock for digital processing, and an LC oscillator is used when a more stable, accurate reference is needed for digital communication. Simulations show that the fast wakeup capabilities of the hybrid clock system lead to as much as 80% reduced power in interrupt-driven applications compared to a system using a crystal reference clock source. The on-chip clock generators of the WIMS series of microsystems are described to demonstrate the concept of the hybrid clock scheme.

Phase-locked loops (PLL) in radio-frequency (RF) and mixed analog-digital integrated circuits (ICs) experience substrate coupling due to the simultaneous circuit switching and power/ground (P/G) noise which translate to a timing jitter. In this paper. an analysis of the PLL timing jitter due to substrate noise resulting from P/G noise and large-signal switching is presented. A general comprehensive stochastic model of the substrate and P/G noise sources in very large-scale integration (VLSI) circuits is proposed. This is followed by calculation of the phase noise of the constituent voltage-controlled oscillator (VCO) in terms of the statistical properties of substrate and P/G noise. The PLL timing jitter is then predicted in response to the VCO phase noise. Our mathematical method is utilized to study the jitter-induced P/G noise in a CMOS PLL, which is designed and simulated in a 0.25-/spl mu/m standard CMOS process. A comparison between the results obtained by our mathematical model and those obtained by HSPICE simulation prove the accuracy of the predicted model.

Under the condition of the higher order effects, a propagation equation is established to investigate the way to suppress the soliton self frequency shift and timing jitter in the picosecond and femtosecond soliton communication system using a combined control method of time domain and frequency domain. By the use of the variational approach, the evolution of the chirping Gaussian quasi-soliton pulse is analyzed in the presence of the effects including third order dispersion, intrapulse Raman scattering (IRS), and self steepening. Considering the soliton evolution properties and the mechanism of the timing jitter under the higher-order effects, the combined control method is adopted to eliminate the influence from Raman scattering and self-steepening. The soliton central frequency is stabilized and the timing jitter is suppressed effectively. A 160 Gb/s long-haul soliton transmission system is designed and its performance is numerically simulated. The simulation results are in good agreement with our theoretical analysis.

For the localization of epileptic seizure, it has a guiding significance to detect high frequency oscillations (HFOs) which are novel biomarkers of the seizure onset zone. In this paper, a new method including Fuzzy entropy (FuzzyEn) and Fuzzy neural network (FNN) for automatic HFOs detection is proposed. FuzzyEn and short time energy which is calculated by mean square method are used as the inputs of the FNN classifier. The T-S interference model is applied to the consequent part of the fuzzy rules. The least squares estimation and error back propagation algorithms are used to adjust the consequent and antecedent parameters, respectively. The output of the FNN classifier is utilized to classify the signal as HFOs or as normal activity. The simulation results indicate that FuzzyEn can extract the HFOs features more effectively compared with approximate entropy. Besides, the sensitivity and specificity of the FNN classifier proposed in this paper are obviously higher than those of the artificial neural network (ANN) classifier which has the same number of hidden layers, neurons and epochs with the FNN classifier. It is clear that the classification performance of the FNN classifier is better compared with the ANN classifier.

As high-speed digital and radio-frequency mixed-signal integrated circuits become increasingly common in product designs in industry, it is important for VLSI designers to be familiar with the challenges of chip testing and the behavior of circuit elements, including on-chip interconnect, at high frequencies. Expensive, specialized test equipment and software simulation packages for high-frequency chip testing and design are not always accessible for student research. This thesis documents the setup and characterization of a best-possible environment for high-frequency chip testing and data acquisition using existing laboratory equipment and resources. Experimental methodologies and measurement results of on-chip interconnect signal integrity and delay, ring oscillator noise and timing jitter, and time-domain reflectometry (TDR) testing are presented. Methods of modeling on-chip interconnect at high frequencies using field solvers and equivalent circuits are discussed. Lastly, the designs of single-ended and differential ring oscillators, for use in future voltage-controlled oscillator (VCO) and phase-locked loop (PLL) test chip designs, are presented and analyzed.

Supply and ground noise sensitivity of a wide variety of ring and LC oscillators has been analyzed based on the perturbation projection vector (PPV) technique. The resulting PPV provides an understanding of how specific frequency content of supply/ground noise is converted to oscillator phase noise. Based on this analysis oscillators that are tolerant of supply/ground noise can be identified and used for low noise oscillator design.

Injection locking is a nonlinear dynamical phenomenon that is often exploited in electronic and optical oscillator design. Behavioral modeling techniques for oscillators that predict this phenomenon accurately are of significant scientific and practical importance. In this paper, we propose a nonlinear approach for generating small phase-domain oscillator/voltage-controlled oscillator (VCO) macromodels that capture injection locking well. Our nonlinear phase-domain macromodels are closely related to recent oscillator phase noise and jitter theories, and can be extracted efficiently by algorithm from SPICE-level descriptions of any oscillator or VCO. Using LC and ring oscillators as test cases, we confirm the ability of nonlinear phase macromodels to capture injection locking, and also obtain significant computational speedups over full SPICE-level circuit simulation. Furthermore, we show that our approach is equally effective for capturing the dynamics of transition to locking, including unlocked tones and phase jump phenomena.

The presence of timing jitter between the trigger signal and the sampling strobe in an equivalent-time sampling oscilloscope causes distortion of the recorded waveform. Two methods exist to estimate the waveform from the jittered measurements. One method, called the median method, is based on the calculation of the point-by-point median of a large set of waveform measurements. It is shown here that this method is asymptotically biased if noise is present and if the waveform is nonmonotonic. Another method, called the pdf deconvolution method, is based on an estimation of the jitter probability density function and on a technique to deconvolve this density function from the average of all recorded waveforms. To estimate the jitter probability density function, it is assumed that the waveform has a part which can very well be approximated by a ramp during a time span which is smaller than the standard deviation. It is shown that a significant asymptotic bias is introduced by the method when this assumption is violated. A novel approach is proposed, based on a parametric model of the jitter probability density function, which results in an asymptotic unbiased estimate of the jitter probability density function. The method is experimentally verified, and it is explained why this method is especially useful when one is interested in the Fourier spectrum of the recorded waveform. >