Pull-In Behavior of Third-Order Generalized Phase-Locked Loops

This paper analyzes third-order phase-locked loops with an arbitrary phase-detector characteristic and imperfect integration by the quasi-stationary approach with a suitable linearization of the non-linear differential equation deseribing the loop behavior; ideal integration is also considered. The main feature of this technique is the use of an easy mathematical approach which allows a direct physical insight into acquisition behavior and the development of simple expressions for the time and pull-in range.     

Statistical Analysis of Digital Phase-Locked Loops Fading Channiels

Statistical analyses of zero-crossing sampling first- and second order digital phase-locked loops in fading channls (DPLFC) are presented. A DPLFC is defined as one where the incoming signal is not only corrupted by additive Gaussian noise channel (AGN) but also by a fading communication channel. The three fading channels considered are the log-normal, Rayleigh, and Rician channels. The performance degradation of the DPLFC operation is characterized by the steady-state phase-error process probability density function and phase-error variance. Approximate analytic expressions for the phase-error statistics of a first-order DPLFC for both phase-step and frequency-step inputs are obtained by solving the Chapman-Kolmogorov equation associated with the phase-error process. The second-order DPLFC is analyzed for a frequency-step input. Numerical and simulation results are provided confirming the analyses presented for the three fading channels considered.     

On First Cycle Slip Time of Phase-Locked Loops in Cascade

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.     

A Comparison of Second, Third, and Fourth Order Phase-Locked Loops

This paper presents data describing various performance characteristics of phase-locked loops, which were obtained for the purpose of determining an optimum selection of system order in view of typical operating conditions. With the functions optimized with respect to particular performance characteristics, calculations of the integrated square error and peak error with polynomial inputs are presented in terms of the noise bandwidth; and the generalized error coefficients are also provided in terms of the bandwidth with consideration for the use of both perfect and imperfect integrators. With specific input functions as provided by signals transmitted from earth satellites, an improved performance is demonstrated with the use of the higher order loops, and experimental results verify the calculations and also demonstrate the feasibility of the fourth order loop design.     

Gated Phase-Locked Loop Study

The objectives of this paper are threefold. The first is to obtain a sampled data model of a gated phase-locked loop. Data from measurements made on an actual loop constructed in the laboratory are included, and the good agreement between measured and calculated results serves as a verification of the model. Second, with the aid of the model, some of the basic operating properties of the system will be presented. Third, comparisons will be made between gated and continuous loop operation.     

Threshold Investigation of Phase-Locked Discriminators

This paper is primarily an investigaton of a second-order phased-locked loop in the threshold region, with the loop filter chosen as (1/1+?s) or (1+?1s/1+?s). First-order loop results are also given. Effects of loop parameters, detuning error, and modulation are studied. It is shown that the loop with filter (1+?1s/1+?s) can be built two ways with same bandwidth and damping. One loop gives much better threshold than the other. The analytical results are supported by computer simulation as well as experimental work obtained by hardware simulation of the loop.     

Phase-Frequency Detection in Sampled Phase-Locked Frequency Mlultipliers

Phase-locked high-frequency multipliers which do not have powergreedy frequency dividers in the feedback loop, but which do have a sample-and-hold circuit as a phase detector are hard to design, due to conflicting requirements which determine the choice for loop gain and loop bandwidth. A circuit is described that acts as a frequency control if the loop is not locked and as a phase control once the loop can be locked. The loop filter has to be optimized for the locked condition only, and the allowable preset error is more than 80 percent of the sample frequency. The circuit also indicates whether the oscillator frequency is an odd or an even multiple of the sample frequency. Pull-in is at least an order of magnitude faster than with phase control alone.     

Longitudinal Waves in Coronal Loops

Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers.     

Statistical Measurements of Phase-Locked Receivers

Test instrumentation is described for use in the measurement of threshold sensitivities and noise bandwidths of narrow-band phase-locked receivers. The method is statistical in nature with the data being recorded digitally by a counter and printer. Scale factors can be selected for convenient relation of the data to the standard deviations, 1,2, or 3 sigma. Curves are included showing the results of a typical experiment.     

Phase-Locked Loop Behavior near Threshold

The phase-locked loop behavior is analyzed following the quasilinearization Booton's method. When the loop is locked on an unmodulated input signal with a static phase error, the phase detector nonlinearity produces an interaction between the static phase error and the voltage-controlled-oscillator (VCO) noise phase fluctuations. Formulas allowing one to compute the static phase error increase and the VCO phase variance increase are derived. When the input signal is phase modulated, there is an interaction between the static phase error, the VCO noise phase fluctuations, and the input signal phase modulation. Formulas are obtained that allow one to compute the loop loss of performances (static phase error increase and VCO phase variance increase) and the coherent phase demodulator output signal-to-noise ratio decrease. Finally, a slight modification to Booton's procedure is proposed, leading to results in better agreement with experimental data.     

Interference in Frequency-Locked Doppler Tracking Loops

The effects of interference on frequency-locked Doppler tracking loops are investigated. Conditions for jump from locking on the desired signal to locking on the interfering signal are established. Parasitic frequency modulation of the desired signal results when the other signal interferes with it. The index of this parasitic modulation as a function of the interference-to-desired signal amplitude ratio is computed. Both critical amplitude ratio and critical parasitic modulation index at the occurrence of jump are derived. Comparing frequency-locked loops with phase-locked loops with phase-locked loops in the presence of interference shows the former performs better for most cases of practical importance in Doppler tracking systems.     

Phase-Locked Demodulator Threshold: A New Approach

In this paper the dependence of the threshold CNR of a simple phaselocked demodulator on the frequency deviation of an FM signal has been evaluated by the concept of quasi-stationary approximation. Experimental findings have been presented in support of the theoretical conclusion.     

Graphical Analysis of a Digital Phase-Locked Loop

Under the assumption of negligible quantization error effect and no noise, a nonuniform sampling first-order digital phase-locked loop (DPLL) is analyzed by a graphical method which displays limit cycles and the cycle slipping phenomenon. The analysis suggests an upper bound to the model gain and, consequently, to the pull-in range. Moreover, this method enables one to obtain a closed-form expression of the acquisition time, accurate enough for the cases of practical interest.     

Frequency Tracking Characteristics of Split-Loop Phase-Locked Receivers

The excess time delay introduced by the incorporation of the intermediate frequency (IF) stage within the phase-locked loop (PLL) causes serious deterioration in the acquisition and tracking performance of the loop. The split-loop phase-locked system suggested by McGeehan and Sladen considerably reduces the effect of time delay on the acquisition and tracking performance of the loop. The frequency acquisition characteristics of the split-loop phase-locked receiver is investigated, and the effect of possible asymmetry in the arms of the loop on the acquisition range is examined. Closed-form approximate formulas are derived, and a comparison between split-, long-, and short-loop acquisition performance is presented.     

Transverse Oscillations of Coronal Loops

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.     

Noise Performance of a Gated Phase-Locked Loop

The objectives of this paper are two. The first is to show that a gated phase-locked loop (GPLL) is a tracking device whose operation approximates that of a maximum likelihood estimator of the phase of a pulsed sinusoid imbedded in noise. The second is to determine the behavior of theb loop in the presence of noise. It is found that the loop performance is equivalent to that of a continuous phase-locked loop driven by the same noise, plus a continuous sinusoid which has the same power as the pulsed sinusoid at the input of the GPLL.     

M-ary CPSK Detection with Noisy Reference and Interferences

A general expression of the error probability on an M-ary coherent phase-shift-keyed (MCPSK) signal purturbed by a noisy reference carrier, multiple interferences, and additive Gaussian noise is presented taking into account the frequencey divider in the carrier recovery circuit. First, a new expression for the probability density function (pdf) of the phase of a composite wave of signal, multiple interferences, and additive Gaussian noise is derived. Then this result and a pdf of the phase error modified from the Tikhonov distribution are used to obtain the erro probability of an MCPSK detector. In addition, the comparison between the error probabilities with and without the frequency divider is given, and it is found that the estimation is more pessimistic when the frequency divider is included.     

粘性高超声速激波—激波碰撞的计算和分析

本文用特片变量型的隐式ＮＮＤ格式计算了五种类型的高超声速激波－激波干扰流场，得到了清晰的流场结构图画。激波和剪切层等分辨得很清楚。计算的物面压力与实验甚为吻合。借助于激波极曲线，对第４类激波干扰结构进行了分析，解释了干扰引起物面压力增高的原因。     

Pull-In Performance of a Piecewise Linear Phase-Locked Loop

This is part of a study concerned with the analysis of phase-locked loops (PLL's). The broad objective throughout this work is to improve upon our general understanding in this important area. More particularly, ly, we are seeking quantitative results indicative of the pull-in behavior of PLL's. In the present paper, we point out some results in foreign publications and focus attention on a paper by Kapranov [1] which is devoted to the study of the pull-in frequency of second-order PLL's with a symmetric phase comparator. We apply the same approach and present results, in closed form, in the more general case where the phase comparator possesses an asymmetric triangular characteristic. Special cases of this phase comparator are the sawtooth and symmetric triangular comparators. It can also be viewed as an approximation to the Tanlock phase comparator. The RC filter case is treated.     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.