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.     

Unmanned scientific exploration throughout the solar system

Velocity requirements for scientific probe vehicles operating throughout the entire solar system are presented. Both direct flights and those using planetary swingby modes are considered. Launch-vehicle and payload sizes necessary to perform useful scientific missions are examined. Scientific investigation of the solar system is shown to be much less difficult than is commonly believed.     

Delay-Doppler Ambiguity Function for Wideband Signals

The conventional ambiguity function is extended to include the Doppler distortions of the modulation function. The distinctive features of the extension are the use of the complex notation for wideband signals, and inclusion of the Doppler effect on the signal amplitude. The result is an ambiguity function from which Woodward's form can be found by inspection. It is shown that the well-known volume constraint also applies, in unchanged form, to the generalized ambiguity function. For the volume to be constant, it is not required that the distortions of the modulation function be neglected. Rather, the volume constancy is related to the sinusoidal fluctuations of a modulated carrier-type signal and thus is strictly a matter of the percentage bandwidth of the signal.     

Random Characteristics of the Type II Phase-Locked Loop

The results of a study of the characteristics of the second-order Type II phase-locked loop with a Gaussian noise input, and obtained by digital computer simulation, are presented. The digital simulation is described and the random state variables are defined such that their characteristics can be interpreted in terms of existing phase portraits of autonomous phase-locked loops. The statistics associated with the state variables, which are phase error and a measure of frequency error, and those associated with the number of cycles skipped and the mean time to unlock, are given.     

Design of Zigzag FM Signals

Since no practical method is available for synthesizing radar waveforms, a sizable effort has been directed into studies of the matched-filter response, or ambiguity function, of many waveforms. In this paper, we investigate the class of FM signals whose instantaneous frequency varies in a zigzag pattern. The waveforms thus consist of linear FM segments and are relatively easy to generate and process. The paper discusses the relation between the characteristics of the waveform and the features of the associated ambiguity function. The effects studied include those of signal repetition, changes in the FM slope, phase-shift and frequency-shift coding, and staggering of frequency step and segment duration. Ambiguity functions of interesting waveforms illustrate the general results. These ambiguity functions are computer-plotted projections of the three-dimensional surface above the delay-Doppler plane.     

History of Time-Frequency Technology

Present-day collision avoidance systems (CAS) of the time-frequency variety employ modes of operation similar to those of airborne equipment which has been operating in military aircraft since 1959. A fleet operational evaluation of these systems began in 1961 in aircraft of U. S. Navy Helicopter Squadron HS-4, based on the aircraft carrier U.S.S. Yorktown. This equipment utilized a local clock in each aircraft, a separate time slot for each aircraft's interrogation signal, air-to-air coarse synchronization of all stations, and sufficient free-drift stability for time slot keeping. Operational use of one-way ranging with elimination of propagation delay offsets, higher clock stability for open-loop time keeping in the SNS-64 ... AN/APN-169 family of systems began in 1964 in U. S. Air Force C-130E turboprop aircraft. In 1965, use of the EROS I collision avoidance system began during flight testing of F-4 Phantom supersonic aircraft.     

A Test of the Effect of Satellite Spin on Two-Way Doppler Range-Rate Measurements

Analysis indicates that the rotation of a satellite can cause an error in the range-rate measurements of a two-way Doppler tracking system. The error is proportional to the rotation rate, and the constant of proportionality depends on the polarization of the satellite transponder antennas. Measurements made by ground-based simulation confirmed the analytical prediction.