Lock Range Research Articles

Speed Control by Phase-Locked Servo Systems -- New Possibilities and Limitations

The operation of phase-locked servo systems is described and a linear discrete model is developed to describe their behavior. This model explains the observed phenomenon that the system becomes unstable at low speeds. Also discussed are the design problems, speed variations, and the extension of lock range by lag-lead networks.

Perturbation theory of injection locking for Josephson junction oscillator

The system consisting of a Josephson element inside a resonant cavity biased by a current source has been analyzed from the circuit point of view. The dynamical equations for an ideal Josephson element shunted by a resistance and an external linear circuit in series with a rf voltage source are solved by a systematic perturbation theory. When the rf voltage is zero, these solutions describe the cavity induced step and for a non zero rf voltage, these solutions indicate the phenomenon of phase locking. The lock range is obtained as a function of the cavity Q, the coupling of the element to the cavity, the critical junction current and the incident power. The results are compared with the Longacre and Shapiro theory of the magnitude of the cavity induced step, the general phase locking theory of Adler and the experimental results of Stancampiano and Shapiro.

Design characterization of a phase-locked v.h.f. land mobile receiver

A ‘long loop’ v.h.f. phase-locked a.m. receiver with synchronous detector is described. The effect of the narrow-band Chebyshev i.f. filter on receiver lock-in range, hold-in range and capture time is investigated as a function of carrier level, −60 to −120 dBV, for a range of low-pass filter time-constants. The transient response of the Chebyshev filter and instantaneous limiting in the i.f. strip are shown to play a crucial role in determining the time which the receiver takes to lock onto the carrier. The receiver is not significantly more complex or expensive than sets currently in use and has the advantage that it may also be used to demodulate double-sideband diminished carrier (d.s.b.d.c.) signals.

An application of acoustic surface wave devices to communication receivers

In this paper we present a new acoustic surface wave phase-locked loop FM demodulator. This device uses the nonlinear coupling characteristics of an insulating piezoelectric to an adjacent semiconductor to generate an electric field in the semiconductor. The low-frequency voltage resulting from the spatial integration of the electric field along the semiconductor is used as the controlling voltage of a voltage controlled oscillator. The above device acts as a phase-locked loop of either the first order or the second order, depending on the amplitude of the input waves, the characteristics of the coupling device, and the integration length of the electric field in the semiconductor. Both theoretical and experimental results relating to the lock range, frequency tracking, and FM demodulation characteristics of the novel device are described.

An automatic clarifier for s.s.b. speech communication

By introducing certain inaudible distortion into the audio wave-forms used to modulate an s.s.b. transmitter it becomes possible to detect any frequency translations in the system. Audio frequency circuits in the receiver generate an a.f.c. voltage proportional to any such translation, and and this is used automatically to correct the frequency of the local carrier generator without the need for pilot tones or carrier. At present the system has a lock-in range in excess of ± 200 Hz, and a locked-in error of a few hertz. It may make practicable s.s.b. operation at v.h.f, as well as simplifying the operation of h.f. equipment.

A Class of All Digital Phase Locked Loops: Modeling and Analysis

An all digital phase locked loop which tracks the phase of the incoming signal once per carrier cycle is proposed. The different elements and their functions, and the phase lock operation are explained in detail. The general digital loop operation is governed by a nonlinear difference equation from which a suitable model is developed. The lock range for the general model is derived. The performance of the digital loop for phase step and frequency step inputs for different levels of quantization without loop filter are studied. The analytical results are checked by simulating the actual system on the digital computer.

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 precised 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 exponential voltage-controlled oscillator improves the performance of a phase-locked loop

A design example is worked out to demonstrate how to stabilize a phase-locked loop containing an exponential voltage-controlled oscillator. It is shown that this kind of loop can be designed with an arbitrarily large capture range, a wide lock-in range, and a short transient receovery-time constant.

Distortion and Locking Range of a Pulse Synchronized Linear LC(t) Circuit

Exact conditions for the synchronization of the Oscillations of a linear resistanceless <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC(t)</tex> circuit to a harmonic/subharmonic of the frequency of the capacitance variation are derived for the case of a periodically pulsed capacitance. It is shown that the magnitude of the largest undesired spectral component relative to that of the desired output is given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-A_{0}(N) + 20 \log N_{\pi \nu} (dB)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{0}(N)</tex> is determined by numerical computation for several <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\nu</tex> is the fractional offset of the resonant frequency from the Nth harmonic of half the synchronization frequency.

Experimental Results for Phase-Lock Loop Systems Having a Modified nth-Order Tanlock Phase Detector

Two parameters which are important in the theory and design of phase-lock loop systems are lock range and threshold. In this paper these parameters are carefully defined and the results of an experimental study to determine the effects of the modified n thorder tanlock class of phase detector characteristics upon these parameters are presented. Lock range as a function of signal-to-noise ratio (SNR) is of particular interest. It is shown that when the SNR is high, the lock range of phase-lock systems with modified n th-order tanlock phase detector characteristics exceeds that of systems employing a sinusoidal phase detector. However, as threshold is approached, the lock range of the tanlock systems falls off faster than the lock range of conventional sinusoidal systems. When compared to systems with sinusoidal phase detectors and normalized with respect to equivalent noise bandwidth the tanlock systems are shown to exhibit a higher threshold, but when normalized to lock range the tanlock systems have a slightly lower threshold. The series of curves which summarize the study may be used as an aid in the design of phase-lock loop systems.

A feedback-stabilized vertical-deflection circuit

This paper describes a feedback-stabilized vertical-deflection circuit that makes use of a transistor oscillator to drive an output tube. The circuit possesses a few innovations that overcome some of the deficiencies that exist in conventional vertical-deflection circuits. These innovations include improved interlace over the lock-in range, increased independence from variations in output-tube characteristics, true height adjustment, and picture height regulation for color.

MiniaturizedRCFilters Using Phase Locked Loop

It is shown that an automatic phase-locked loop (APLL) can be used as a bandpass filter and FM discriminator while satisfying the circuit conditions imposed by microminiaturization techniques. It has the advantage over other methods of ease of adjustment and reduction in the number of circuit components. For this reason it is to be assumed that the APLL will be added to the few practical solutions of the frequency selection problem in microminiaturization available to date. In contrast to most other applications, no assumptions can be made here about the ratio of the natural undamped system frequency to the lock range of the loop. This is taken account of in an analysis of the APLL which enables design equations and considerations to be derived. An approximation of the so-called capture ratio, defined as the ratio of capture-to-lock range, is presented. It produces results that correspond very well with the equivalent measurements. The description of an APLL designed as RC channel filter and discriminator for a multichannel data receiver is presented. RC active circuits that are compatible with current microminiaturization techniques are employed exclusively. They are described in detail, and an analysis of the voltage-controlled oscillator used is included in the Appendix.

A Stable Tunable Microwave Source

This paper describes a prototype model of a phase-stabilized backward wave oscillator (BWO). The BWO is locked to a harmonic of a crystal oscillator by employing an automatic phase control loop. Tuning is accomplished by pulling the crystal oscillator and switching different crystals into the oscillator circuit. Power spectrum plots are taken in open-and closed-loop conditions, and methods of analyzing these plots are described. With the proper loop bandwidth, the BWO will assume the frequency stability of the reference oscillator. The phase-locked BWO is analyzed by a conventional feedback control technique. Each element in the loop is assigned a transfer function. From this the open-loop transfer function is determined. It is then shown that the improvement in short-term frequency stability is directly proportional to the open-loop transfer function and, hence, the open-loop gain. Utilizing plots of the absolute magnitude and phase angle of the open-loop gain vs. frequency, conclusions are drawn as to the maximum amount of gain which is possible while still maintaining system stability. Possible implementation of a series equalizer is considered in conjunction with this. Comments are also made on the relationship of the closed-loop bandwidth to the system lock-in range and system response to incremental changes in frequency.

A Servo-Stabilized Analogue-to-Digital Converter for High Resolution Pulse-Height Analysis

A 4096 channel pulse-height analyzer has been constructed to exploit the high resolution attainable with semiconductor junction charged particle detectors in the 0 to 40 Mev range. The use of so large a number of channels can only be justified if the drift in the system can be held to less than one channel. It was felt that, using conventional techniques, it would be very difficult to stabilize the linear amplifier gain, the converter gain and the converter zero to a part in 4000. A servo-stabilized system was therefore adopted which assures long term system stability without imposing unreasonable restrictions on component stability. A stable pulse generator produces two reference pulses, one 8 times as large as the other, and presents them alternately to the preamplifier input along with the detector pulses. Reference and detector pulses are amplified and measured by the same analogue-to-digital converter. The small reference pulses should fall in channel 512 and the large pulses in channel 4096. The amounts by which the reference pulses miss their intended channels constitute the error inputs to two integrating digital servos. The large-pulse servo controls the converter clock frequency and the small-pulse servo controls the converter zero setting. The servos have sufficient lock-in range to compensate perfectly for gain changes of ± 3% and zero changes of ± 1.5%.

Regenerative Fractional Frequency Generators

A new regenerative frequency divider circuit is presented which offers several advantages over other available circuits. These advantages are large lock-in or stability range, ability to produce either relatively constant output or amplitude modulated output, circuit simplicity and the fact that it is self-starting. An approximate nonlinear analysis is given which provides a reasonable prediction of the operation. This analysis is a quasi-linear, semigraphical technique which clearly shows the dependence upon diode characteristics and transistor input impedance. Results are also given for harmonic generation, in order to actually give a fractional frequency output and not merely a subharmonic.

A New Look at the Phase-Locked Oscillator

The uses of phase-locked oscillators are briefly reviewed. A simple automatic-phase-control (APC) system is analyzed as a servomechanism analog. Three major characteristics of the system are considered: the lock range, the capture range, and the filter bandwidth. The lock range is the total drift in the unlocked oscillator frequency which can be exactly compensated by the locked system. The capture range is the largest unlocked frequency difference at which synchronization, or lock-in, will occur. The filter bandwidth of the system expresses the performance of the system as a low-pass filter with respect to FM noise components existing in the input to the system and as a high-pass filter with respect to FM noise components generated within the output oscillator. The mutual interdependence of these characteristics and the various quantities affecting each one are discussed. The conditions for stable operation of the system are established. The unlocked, locking-in, and locked conditions of operation and the effects of the low-pass filter are discussed. Simple design criteria are established.