Cycle slip performance of digitally implemented phase detectors onAWGN channel

Cycle slip performance of digitally implemented phase detectors on additive white Gaussian noise (AWGN) channel is investigated. The performance measure evaluated is the mean cycle slip time of a first-order phase-locked loop. An equivalent phase detector model with state-dependent loop noise is employed. It is shown that this working basis is vital to arrive at correct results. Numerical results for triangular and saw-tooth type phase detectors are reported and compared with those for the multiplier phase detector     

Phase Detector Data Distortion in Phase-Lock Loop Receivers

The nonlinear characteristic of a sinusoidal phase detector can create an additional loop suppression factor and cause distortion of any phase-modulated data that is to be extracted in a phase-lock loop receiver. The distortion caused by the phase detector's sinusoidal characteristic will degrade the phase-lock loop parameters and decrease the amplitude of the phase-modulated data.     

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.     

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.     

S频段小数分频锁相环频率合成器实现与应用

传统的整数分频锁相环频率合成技术无法在单个环路实现高频率、低分辨率和低相噪的目标,小数分频锁相环在提高鉴相频率的同时减小分频计数值,从而降低相位噪声。针对USB统一测控系统的需要,本文提出基于单片小数分频锁相环的微波频率合成方法。实验结果表明,小数分频锁相环频率合成器具备良好的信号输出特性,可以为测控系统提供低成本频率合成方案。     

Double Dither Loop for Pseudonoise Code Tracking

A new type of phase detector for pseudonoise code tracking is introduced and analyzed in comparison with the delay lock loop (DLL) and tau-dither loop (TDL) configurations. It is shown that the double dither loop (DDL) combines the best features of the DLL and the TDL in that the DDL is insensitive to gain and offset imbalances and does not suffer the 3-dB degradation in noise performance typically associated with the TDL. The double dither concept is applicable to other dual channel detectors such as in a Costas-type carrier tracking loop.     

Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

Optimum Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

Pontryagin's maximum principle is applied to minimize the time for a phase-locked loop to lock to a step change in frequency. In particular, a Type II phase-locked loop is considered in detail. Phase control and frequency control of the input signal are analyzed with the nonlinearity of the phase detector taken into consideration. It is shown that application of Pontryagin's maximum principle offers a decided advantage in shortening this time by proper control.     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.     

Carrier loop architectures for tracking weak GPS signals

The performance of various carrier recovery loop architectures (phase lock loop (PLL), Doppler-aided PLL, frequency lock loop (FLL), and Doppler-aided FLL) in tracking weak GPS signals are analyzed and experimentally validated. The effects of phase or frequency detector design, oscillator quality, coherent averaging time, and external Doppler aiding information on delaying loss of lock are quantified. It is shown that for PLLs the metric of total phase jitter is a reliable metric for assessing low C/N performance of the tracking loop provided the loop bandwidth is not too small (~> 5 Hz). For loop bandwidths that are not too small, total phase jitter accurately predicts carrier-to-noise ratio (C/N) at which loss of lock occurs. This predicted C/N is very close to the C/N predicted by bit error rate (BER). However, unlike BER, total phase jitter can be computed in real-time and an estimator for it is developed and experimentally validated. Total phase jitter is not a replacement for BER, since at low bandwidths it is less accurate than BER in that the receiver loses lock at a higher C/N than predicted by the estimator. Similarly, for FLLs operating at small loop bandwidths, it is found that normalized total frequency jitter is not a reliable metric for assessing loss of lock in weak signal or low C/N conditions. At small loop bandwidths, while total frequency jitter may indicate that a loop is still tracking, the Doppler estimates provided by the FLL will be biased.     

带通限幅器对锁相环噪声性能的影响

锁相环路中,在鉴相器前加上AGC（自动增益控制）,可以使环路性能在输入信噪比发生变化时保持稳定,带通限幅器也可以起到类似作用。尽管有一些文章对限幅器的性能作了研究,但是在PLL（锁相环）闭环条件下,鲜有文章分析其对环路噪声性能的影响。因此,文章以基本PLL环路的数学模型为基础,推导出PLL中分别加入相干AGC和带通限幅器后新的环路数学模型,以一阶PLL为例,计算和比较不同控制方式下环路相位误差均方值的变化,最后说明应当根据飞行任务的不同选择对环路更有利的控制方式。     

Pull-In Time and Range of Any Order Generalized PLL

The general pull-in range and pull-in time expressions are derived versus the relevant system parameters and the initial detuning for any order loop with any type of phase detector by the quasistationary approach. Even though the pull-in time expression becomes more accurate as the loop's order becomes larger, it is correct also for second-and third-order loops provided that the initial detuning, supposed large, is approaching the pull-in range value.     

Acquisition Time of Second-Order Aided PLL

The analysis of a second-order tracking loop operating in the frequency-search mode is carried out by the quasi-stationary approach. An arbitrary phase detector characteristic is assumed and perfect or imperfect integrating filters are considered. The theory leads to a closed-form expression of the acquisition time versus the relevant system parameters, the initial detuning, and the search rate. The limitations of this analysis concern the absence of noise and the hypothesis of large initial detuning.     

Modeling and analysis for the GPS pseudo-range observable

In this paper, a digital system for the Global Positioning System (GPS) pseudo-range observable is modeled and analyzed theoretically. The observable is measured in a GPS receiver by accurately tracking the pseudorandom noise (PRN) code phase of the input GPS signal using a digital energy detector and a digital delay lock loop (DDLL). The following issues are presented: (1) mathematical modeling of the digital PRN code acquisition and tracking system, (2) the closed-form expression derivation for the detection and false-alarm probabilities of the acquisition process and for the variance of code phase tracking error, and (3) the linear and nonlinear performance analysis of the DDLL for optimizing the receiver structures and parameters with tradeoff between the tracking errors due to receiver dynamics and due to input noise     

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.     

热激励谐振式硅微结构压力传感器温度场研究

针对一种以方形硅膜片为一次敏感元件、硅梁谐振子为二次敏感元件 ;采用电阻热激励、压敏电阻拾振的压力微传感器 ,分析了其工作机理 ;依幅值、相位条件讨论了该谐振式微传感器的闭环自激系统 ;建立了微传感器的温度场模型和热应力模型 ,并进行了仿真计算与分析     

Synthesis and Analysis of Tracking Systems with Optimal Acquisition

The behavior of a tracking system during its acquisition phase is studied in the case where the input signal is a frequency step. The tracking system considered is a generalization of a type-II phase-lock loop where the phase detector characteristic is a general function. In order to improve the acquisition characteristics, the natural evolution of the local oscillator is modified by a command signal chosen in order to minimize the acquisition time, on the one hand, and, on the other hand, to maximize the lock-in range and the capture range of the tracking system. The influence of the different parameters (input, damping, natural frequency, pha e characteristic,command signal) on the acquisition of the resulting systems has been précised by means of a theoretical study of the trajectories in the phase plane and by an analog simulation. A simple criterion adopted in order to characterize the acquisition of a system disturbed by noise permits the study of the influence of S/N ratio on acquisition time.     

An Adaptive MTI for Weather Clutter Suppression

A digital realization of an adaptive clutter-locking loop is presented. The purpose of the loop is to estimate the mean Doppler frequency of the clutter. The clutter spectrum is then shifted toward the zero Doppler by this estimate. A fixed moving target indicator (MTI) canceler following the loop suppresses the shifted clutter. Experimental simulations illustrate the feasibility of the loop. Results indicate that the proposed canceler works significantly better than a fixed canceler, while not as well as the 10-pulse moving target detector (MTD) processor. However, the complexity of the MTD is significantly more than the relatively simple adaptive processor presented here.     

PAM approach to weak CPM and its application to flight termination receivers

A method for computing the PAM representation for weak continuous phase modulation (CPM) is presented and applied to the modulation defined in the enhanced flight termination system (EFTS) standard. The pulse-amplitude modulation (PAM) representation was used to formulate a reduced-complexity detector whose performance is within 0.7 dB of maximum likelihood detection and 5.6 dB better than limiter-discriminator detection in the additive white Gaussian noise (AWGN) environment. The complexity of the reduced-complexity detector is less than 25% that of the maximum likelihood detector but, unlike the limiter-discriminator detector, requires a carrier phase PLL. In the presence of phase noise, the reduced-complexity detector outperforms limiter-discriminator detection when the RMS frequency deviation due to phase noise is less than 10% of the bit rate.     

On Higher Order Discrete Phase-Locked Loops

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.