Transient behavior of a phase-locked loop in the presence of noise
Transient behavior of first order phase locked loop in presence of noise, solving Fokker-Planck equation for loop dynamics by numerical integration
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Transient behavior of first order phase locked loop in presence of noise, solving Fokker-Planck equation for loop dynamics by numerical integration
Radiation resistance of small filamentary loop antenna in cold collisionless uniform multicomponent magnetoplasma, assuming uniform current distribution along loop
The phase model for the generalized multifilter phase-lock loop (M PLL) is considered and state equations for this model are derived. A linear analysis is presented to aid in the preliminary design of an M PLL and to indicate the noise improvement over a conventional phase-lock loop (PLL). Performance characteristics are examined for an M PLL with low-pass and bandpass characteristics used in a specific FM communication system. Both single and double sinusoidal FM are used and a region of proper operation of the M PLL is determined in terms of modulation index and modulati ng frequency. These results are obtained from both analog and digital computer simulation of the nonlinear system.
Parameter regions for proper operation of multifilter phase-lock loops used for demodulation are determined utilizing digital and analog computers. Experimental models are used to study these regions of proper operation. Generalized state models are developed for the multifilter phase-lock loop.
Four very large, shell-shaped features are known from the surveys of radio emission from the Galaxy. It is suggested that the giant loops represent a class of nebulae, induced by supernova radiation as opposed to supernova ejecta. The model considered provides a qualitative explanation for the spectral and polarization properties of the radio emission from giant loops. The radio emitting electrons are part of the general cosmic ray gas and need not arise specifically in the supernova that produced the fossil Stroemgren sphere.
The first-passage time boundary value problem for first-order phase-locked loops (PLL) is analyzed, and spectral representations are developed for the probability density function (pdf), the distribution function, and the moments of the first time to passage (or cycle-slip). For the sinusoidal PLL, an asymptotic formula, that is surprisingly accurate even at low loop SNR's and large frequency offsets, is obtained for the pdf of the time to cycle-slip, in terms of the mean time to slip.
Bit-synchronizers utilize all-digital phase-lock loops that are referenced to a high frequency digital clock. Phase-lock loop of first design acquires frequency within nominal range and tracks phase; second design is modified for random binary data by addition of simple transition detector; and third design acquires frequency over wide dynamic range.
An analytical study was made of the stability of a closed-loop liquid-lithium temperature control of the primary loop of a conceptual nuclear Brayton space powerplant. The operating point was varied from 20 to 120 percent of design. A describing-function technique was used to evaluate the effects of temperature dead band and control coupling backlash. From the system investigation, it was predicted that a limit cycle will not exist with a temperature dead band, but a limit cycle will not exist when backlash is present. The results compare favorably with a digital computer simulation.
A nonlinear analysis which can be used to assess certain statistical characteristics of double-loop tracking systems is presented. It takes into account the mutual coupling effects of the loops in the system. Two approaches are taken to obtain steady-state probability density functions (pdf's) of the system phase errors. From these pdf's, important system performance statistics, e.g., the phase-error variances, can be calculated, thus illustrating the application and usefulness of the analysis. The analysis is applied to a satellite transponder as an example.
A digital simulation of an imperfect second-order hybrid phase-locked loop (HPLL) operating in radio frequency interference (RFI) is described. Its performance is characterized in terms of phase error variance and phase error probability density function (PDF). Monte-Carlo simulation is used to show that the HPLL can be superior to the conventional phase-locked loops in RFI backgrounds when minimum phase error variance is the goodness criterion. Similar experimentally obtained data are given in support of the simulation data.
The surface brightness of the Cygnus Loop in X rays was obtained on a scale of 0.25 sq deg. The X-ray emission shows strong limb brightening, implying a shell-like source structure. The shell exhibits several regions of enhanced emission. X-ray emission which was observed from a region near the center of the Loop may be from a remnant object. The correlation between X-ray and optical emission is not as good as the correlation between radio and optical emission.
Actual tests with second-order digital phase-locked loop at simulated relative Doppler shift of 1x0.0001 produced phase lock with timing error of 6.5 deg and no appreciable Doppler bias. Loop thus appears to achieve subcarrier synchronization and to remove bias due to Doppler shift in range of interest.
The determination of an error criterion which will give a sampling rate for adequate performance of linear, time-invariant closed-loop, discrete-data control systems was studied. The proper modelling of the closed-loop control system for characterization of the error behavior, and the determination of an absolute error definition for performance of the two commonly used holding devices are discussed. The definition of an adequate relative error criterion as a function of the sampling rate and the parameters characterizing the system is established along with the determination of sampling rates. The validity of the expressions for the sampling interval was confirmed by computer simulations. Their application solves the problem of making a first choice in the selection of sampling rates.
Round trip Mars missions combining a standard trajectory leg and a looping trajectory leg are suggested as an alternative to the more conventional trajectories. Looping trajectories are shown to make it possible to trade a slight increase in total mission time for a significant reduction in Mars stay time, with the possible added benefit of a decrease in energy requirements.
A closed-loop control scheme for the control of intra-aortic balloon pumping has been developed and tested in dog experiments. A performance index reflecting the general objectives of balloon-assist pumping is developed and a modified steepest ascent control algorithm is utilized for the selection of a proper operating point for the balloon during its pumping cycle. This paper attempts to indicate the feasibility of closed-loop control of balloon pumping, and particularly its flexibility in achieving both diastolic augmentation of mean aortic pressure and control of the level of end-diastolic pressure (EDP) an important factor in reducing heart work.
Precise measurement and spacecraft tracking are obtained by using phase-locked loops in cascade in two-way communications links. Statistics on cycle slip time are of vital importance in system planning and design. This paper presents: (1) results of a computer simulation study of the mean time to first cycle slip of cascade phase-locked loops preceded by bandpass limiters, and (2) the determination of probability distributions of cycle slip. Numerical results are obtained for a typical coherent communication system.
Nonlinear behavior of phase-locked loops with rapidly varying phase error is examined by using computer phase-plane analysis. The phase variation is modeled by a sinusoidal function. Threshold loop parameters are presented for both sinusoidal and sawtooth phase comparators.
Parameter estimation techniques are discussed with emphasis on unbiased estimates in the presence of noise. A distinction between open and closed loop systems is made. A method is given based on the application of external forcing functions consisting of a sun of sinusoids; this method is thus based on the estimation of Fourier coefficients and is applicable for models with poles and zeros in open and closed loop systems.