Mathematical Model Of Noise Research Articles

Studies on Phase Noise Profiles of Proportional-Integral-Derivative Controlled PLL

Phase noise in a phase-locked loop is originated from reference oscillator, phase detector, loop filter, voltage controlled oscillator and frequency divider which make the system unstable by generating high phase noise at the output spectrum. In this work, a mathematical linear phase noise model is therefore developed to investigate the effect of reference noise, phase detector noise, voltage controlled oscillator noise, frequency divider noise and specifically the loop filter noise. For this purpose, the conventional active or passive low pass filter of the phase locked loop is replaced by a proportional-integral-derivative controller during acquisition. The noise problem of each component is formulated as a transfer function derived from linear analysis of the proposed mathematical noise model. The simulation results show that the effect of noise attenuation of voltage controlled oscillator is -40dB/decade while the noise attenuation of the reference noise, phase detector noise, proportional integral derivative controller noise and frequency divider noise are approximately -20dB/decade each. The 6.21GHz proposed proportional-integral-derivative controlled phase-locked loop is also highly stable with fast switching speed of 0.238nS at damping factor of 0.625 and phase margin of 92° for minimum phase noise.

Noise and crosstalk models of the particle detector with zero-pole transformation charge sensitive amplifier

Abstract This paper presents design and mathematical noise model of front-end electronics for a silicon particle detector , considering the complete transfer function of a charge sensitive amplifier (CSA). The work includes the noise and crosstalk analysis of a pixel array with a conventional CSA and a zero-pole transformation CSA (ZPT–CSA) (Jaffari et al., 2011). The pixel array has been designed and simulated in a 180 nm CMOS technology with the supply voltage of 1.8 V and the substrate potential of –10 V. The comparative study for conventional and ZPT–CSA is performed with the circuit simulations. The study demonstrates a reduction of 30 % in output noise spectral density and 46 % in equivalent noise charge (ENC) for a frequency band of 100 kHz–100 MHz by using a zero-pole transformation technique. Further, the paper proposes systematic design criteria for a ZPT–CSA with a continuous reset mechanism for the noise reduction. The complete transfer function for the ZPT–CSA is derived and noise model is presented in the presence of interpixel capacitive crosstalk. The results of the mathematical model are compared with the circuit simulations. An average error of 3 × 1 0 − 10 V 2 ∕ Hz is seen in the output noise voltage spectral density for a frequency range of 100 kHz to 100 MHz. The comparison shows an average relative error of 1.8% for the crosstalk voltages. ENC from both the simulations has an average error of 2.91 aC ( ∼ 18 electrons) when plotted for a pixel capacitance range of 10 fF–100 fF in 100 kHz to 100 MHz frequency band.

A Mathematical Model of Noise in the Measuring Channels of Intelligent Systems

G.I. Volovich, South Ural State University, Chelyabinsk, Russian Federation, g volovich@mail.ru, E.V. Solomin, South Ural State University, Chelyabinsk, Russian Federation, nii uralmet@mail.ru, I.G. Topolskaya, South Ural State University, Chelyabinsk, Russian Federation, irina topol71@mail.ru, D.V. Topolsky , South Ural State University, Chelyabinsk, Russian Federation, topol69@mail.ru

Point Cloud Process of Laser Scanning with a Mathematical Noise Model

Considering the unreasonable noise of laser scanning point data during measuring, which causes the reconstructed curve and surface rough, some problems are analyzed to deal with noise. The mathematical noise model on scanning point cloud is proposed, which consists of deterministic and random noise error, and the random error mainly consists of geometric error and measurement one. The data process is proposed to reduce noise and to simplify data. The noise process consists of obvious noise removed, random filter algorithm and data fairing with an optimized correction value. Due to redundant data about mass point cloud, method of combining deviation parameters with allowed angle is proposed to simplify point cloud. The experiments show that the proposed method has many obvious advantages than a single algorithm of data processing, such as all sorts of noise data can be removed respectively, mass data can be streamlined. And the proposed algorithm has the advantages of high reservation of curve and surface reconstruction of point cloud.

Noise in a CMOS digital pixel sensor

Based on the study of noise performance in CMOS digital pixel sensor (DPS), a mathematical model of noise is established with the pulse-width-modulation (PWM) principle. Compared with traditional CMOS image sensors, the integration time is different and A/D conversion is implemented in each PWM DPS pixel. Then, the quantitative calculating formula of system noise is derived. It is found that dark current shot noise is the dominant noise source in low light region while photodiode shot noise becomes significantly important in the bright region. In this model, photodiode shot noise does not vary with luminance, but dark current shot noise does. According to increasing photodiode capacitance and the comparator's reference voltage or optimizing the mismatch in the comparator, the total noise can be reduced. These results serve as a guideline for the design of PWM DPS.

A mathematical model of noise in narrowband power line communication systems

This manuscript introduces a mathematically tractable and accurate model of narrowband power line noise based on experimental measurements. In this paper, the noise is expressed as a Gaussian process whose instantaneous variance is a periodic time function. With this assumption and representation, the cyclostationary features of power line noise can be described in close form. The periodic function that represents the variance is then approximated with a small number of parameters. The noise waveform generated with this model shows good agreement with that of actually measured noise. Noise waveforms generated by different models are also compared with that of the proposed model.