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Circuit measures phase error that exists in phase-locked loop between clock signal recorded in data on magnetic tape and reconstructed clock signal. Circuit presents error as digital word that can be compared with predetermined threshold to indicate lock status. With simple alterations, circuit can also be used as phase detector.
A spacecraft-to-spacecraft optical time-transfer simulation has been developed as a tool for informing NASA’s Surface Deformation and Change (SDC) mission architecture. The SDC mission will combine radar images from multiple spacecraft to improve understanding of the Earth’s sea-level and landscape changes. Spacecraft must be precisely synchronized in order to create sharp radar images. Simulation of multiple spacecraft time-synchronizing via laser communication can inform technology choices of a mission by providing a picosecond-precision level estimate of clock error. This timing and ranging simulation has been combined with a radar system performance analysis pipeline. The simulated timing errors are used to predict performance of bistatic SAR systems in the presence of oscillator noise and time synchronization in accuracy. This analysis includes both analytic approximation equations from existing literature, and a numerical radar simulation to extract key system performance parameters like phase error and signal-to-noise ratio (SNR)degradation. Precision time-transfer techniques facilitate the accurate synchronization of clocks between any combination of terminals. Most time-transfer technology for comparing two clocks at different terminals use radio frequencies (RF) to measure the time delay between the sending and receiving of signals. Laser technology offers the capability to transmit high data rates with systems that are of smaller size and lower power than comparable RF systems. The clocks on independent spacecraft will have some phase and frequency errors between them that result in clock drift. The two clock models that are included in this bi-directional MATLAB simulation are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC). The CSAC has flown as hardware for small satellite missions such as the University of Florida’s CHOMPTT mission. A study of example orbits, including that of NASA NASA-ISRO Synthetic Aperture Radar Mission (NISAR) mission, and lasing rates demonstrate the impact of flight configuration parameters on the synchronization error between two spacecraft. The MATLAB timing simulation uses a Runge-Kutta 4th-order method to propagate spacecraft orbits and computes the light-travel time estimate between them. The simulation outputs the estimated range and estimated clock error based on a user-defined spacecraft cluster configuration. The radar simulation and analytic approximations are applied to evaluate a potential future NASA bistatic SAR constellation architecture. In the proposed architecture, satellites follow each other in the same orbit at 800 km altitude, with a 210 km baseline. We also baseline the CSAC as an ultra stable oscillator, and use NASA’s NISAR for baseline radar system parameters to compute a clock-system introduced phase error of 5.6 degrees without synchronization by frequent time transfer. We build on this base case with a sensitivity analysis of radar performance over a proposed range of constellation and radar system parameters. With this analysis pipeline, we comment on which radar parameters should or should not be changed to minimize synchronization requirements. This analysis technique could be extended or modified to evaluate the timing requirements of other geometries for other future multistatic SAR missions, or other interferometric satellite missions.
Stationary phase error variance for second order phase locked loop for low signal to noise ratios
Central frequency synthesizer performance and voltage controlled oscillator static phase error
The system design, hardware construction, and predicted performance of a Costas loop is presented. Its expected performance regarding steady state phase error under assumed Doppler conditions, rms phase jitter, and their respective sensitivities with respect to variations in signal to noise ratios are discussed.
A concept for a solar power satellite antenna power combiner which utilizes solid state dc-rf converters is described. To avoid the power combining losses associated with circuit hybrids it is proposed that the power from multiple solid state amplifiers be combined by direct coupling of each amplifier's output to the radiating antenna structure. The selected power-combining antenna consists of a printed (metalized) microstrip circuit on a ceramic type dielectric substrate which is backed by a shallow lightweight aluminum cavity which sums the power of four microwave sources. The antenna behaves like two one-half wavelength slot-line antennas coupled together via their common cavity structure. A significant feature of the antenna configuration selected is that the radiated energy is summed to yield a single radiated output phase which represents the average insertion phase of the four power amplifiers. This energy may be sampled and, by comparison with the input signal, one can phase error correct to maintain the insertion phase of all solid state power combining modules at exactly the same value. This insures that the insertion phase of each SPS power combining antenna module is identical. An experiment verification program is described.
Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.
The standard method of magnetic core loss measurement was implemented on a high frequency digitizing oscilloscope in order to explore the limits to accuracy when characterizing high Q cores at frequencies up to 1 MHz. This method computes core loss from the cycle mean of the product of the exciting current in a primary winding and induced voltage in a separate flux sensing winding. It is pointed out that just 20 percent accuracy for a Q of 100 core material requires a phase angle accuracy of 0.1 between the voltage and current measurements. Experiment shows that at 1 MHz, even high quality, high frequency current sensing transformers can introduce phase errors of a degree or more. Due to the fact that the Q of some quasilinear core materials can exceed 300 at frequencies below 100 kHz, phase angle errors can be a problem even at 50 kHz. Hence great care is necessary with current sensing and ground loops when measuring high Q cores. Best high frequency current sensing accuracy was obtained from a fabricated 0.1-ohm coaxial resistor, differentially sensed. Sample high frequency core loss data taken with the setup for a permeability-14 MPP core is presented.
A received, suppressed carrier, quadraphase shift key modulated (QPSK)signal is demodulated with a phase locked loop including a variable frequency, coherent reference that drives first and second channels also responsive to the QPSK signal. The channels respectively derive first and second replicas of binary signals that modulated the suppressed carrier. The replicas are combined to derive a variable amplitude error signal for controlling the coherent reference frequency. The frequency of the coherent reference is dithered at a low rate so that there is derived a relatively low level tracking error phase from the locked loop. The frequency of the coherent reference is swept when the phase of the error signal differs from the dithering phase by a predetermined value that is appreciably less than 90 degrees.
Statistical behavior steady state phase error and time to cycle slip for phase lock loops
This paper describes an augmented Costas loop for use in low-cost avionics for the Navstar Global Positioning System. A standard loop has been augmented with supplementing feed-back to give a tracking error voltage proportional to the tangent of the phase error, rather than to the sine. The augmented loop yields increased performance in the presence of input phase acceleration and jerk, as caused by maneuvers of the GPS user vehicle. Many Monte Carlo simulation results are given.
A model that allows one to predict the tracking performance of the Block 4 receiver in the presence of a continuous wave radio frequency interference is discussed. Experimental and analytical results are provided for a typical Deep Space Network operational mode. Simulation and experimental results show good agreement with theoretical prediction for the static phase error and out-of-lock values. Predicted phase jitter is consistently lower than the experimental and simulated results by a factor of one-half for small interference to signal ratio (ISR) when the offset frequency is small. For large ISR, good agreement is observed. The analytical model assumes a noiseless condition, which is valid only when the loop is operated at strong signal levels. Experimental data indicate, however, that even at the minimum operating signal level of 10-dB carrier margin, reasonably good prediction can still be obtained. A curve of protection criteria that extends the current recommendation is also presented.
Variations in amplifiers and phase shifters can cause degraded antenna performance, depending also on the environmental conditions and antenna array architecture. The implementation of distributed phased array hardware was studied with the aid of the DISTAR computer program as a simulation tool. This simulation provides guidance in hardware simulation. Both hard and soft failures of the amplifiers in the T/R modules are modeled. Hard failures are catastrophic: no power is transmitted to the antenna elements. Noncatastrophic or soft failures are modeled as a modified Gaussian distribution. The resulting amplitude characteristics then determine the array excitation coefficients. The phase characteristics take on a uniform distribution. Pattern characteristics such as antenna gain, half power beamwidth, mainbeam phase errors, sidelobe levels, and beam pointing errors were studied as functions of amplifier and phase shifter variations. General specifications for amplifier and phase shifter tolerances in various architecture configurations for C band and S band were determined.
A probabilistic approach is used to obtain an analytical solution to the Fokker-Planck equation used in the transient analysis of the phase-locked loop phase error process of the first-order phase-locked loop. The solution procedure, which is based on the Girsanov transformation, is described.
Asymptotic formulas for the characteristic root errors as well as transfer function gain and phase errors are presented for a number of traditional and new integration methods. Normalized stability regions in the lambda h plane are compared for the various methods. In particular, it is shown that a modified form of Euler integration with root matching is an especially efficient method for simulating lightly-damped structural modes. The method has been used successfully for structural bending modes in the real-time simulation of missiles. Performance of this algorithm is compared with other special algorithms, including the state-transition method. A predictor-corrector version of the modified Euler algorithm permits it to be extended to the simulation of nonlinear models of the type likely to be obtained when using the discretized structure approach. Performance of the different integration methods is also compared for integration step sizes larger than those for which the asymptotic formulas are valid. It is concluded that many traditional integration methods, such as RD-4, are not competitive in the simulation of lightly damped structures.
This paper investigates the tracking performance of a Costas loop in the presence of single and multiple in-band pulsed RFI signals and receiver additive noise. It is shown that the loop's tracking performance is very sensitive to the pulse durations of the RFI signals, as well as their repetition rates and peak powers relative to those of the desired signal. The presence of in-band RFI can affect the loop's tracking performance in basically three ways. 1) The loop tracks the composite phase of the RFI instead of the phase of the desired signal when the effective RFI power is greater than that of the signal. 2) When the effective RFI power is not sufficiently large to capture the loop, there still will exist static phase error biases which cause the loop to lock at a phase between that of the desired signal and the composite RFI. 3) There is an increase in the rms phase jitter over the nominal design. These latter two effects degrade the bit error probability performance of the receiver. More significantly, if the nominal loop bandwidth is not designed properly to account for the increase in jitter phenomenon, frequency cycle slipping may result.
Simulation error compensation techniques for error reduction in analog computers
Phase-locked-loop (PLL) bit synchronizers often employ integrate-and-dump type phase detectors that provide phase error information only at discrete points in time. Usually these phase detectors are followed by sample-and-hold circuits to produce a stairstep error voltage as the input to a standard analog circuit loop filter. When the loop is configured in this manner, it is referred to as a hybrid PLL. Sampled-data analysis methods (Z transforms) are used to determine the stability and transient response of this loop.