Zero Phase Shift Research Articles

A Method for Eliminating the Wall Shift in the Atomic Hydrogen Maser

The wall shift of the hydrogen maser depends on the collision rate and the average phase shift per collision of the atoms in the storage bulb. By operating at the temperature where the average phase shift per collision is zero it is possible to remove the wall shift. The determination of this temperature is made by measuring the wall shift as a function of temperature for two similarly coated bulbs offering different collision rates to the stored atoms. The intercept of the wall shift vs. temperature curve for the two bulbs-occurs at the zero phase shift per collision temperature. To eliminate the possible differences in wall coatings the use of a flexible storage bulb is recommended.An experimental example of the technique is given using two separate bulbs. The data is in good agreement with a previous measurement of the unperturbed hydrogen hyperfine frequency by H. Hellwig et al.

General expressions for unsteady forces in a lattice of profiles

A large number of studies have been devoted to the unsteady flow of a viscid incompressible fluid past a lattice of thin profiles and the determination of the resulting aerodynamic forces and moments. For example, in the particular case of the motion of a lattice with stagger γ with zero phase shift α of the oscillations between neighboring profiles, Haskind [1] determined the unsteady lift force and moment. Popescu [2] suggested expressions for the force and moment in the case when α=0 and γ=0, using the method of conformal mapping. Samoilovich [3] obtained equations for the unsteady lift force and moment by the method of the acceleration potential for phase shift α=0 and α=π of the oscillations between neighboring profiles. Musatov [4] used an electronic digital computer to calculate the overall unsteady aerodynamic characteristics of a grid by the vortex method, taking into account the amplitude of the oscillations and the initial circulation for α=mπ (∥m∥≤1). Gorelov [5] determined the coefficients of the over-all unsteady aerodynamic force and moment of a profile in a lattice with the stagger γ and any value of α=mπ. He used a method based on the unsteady flow past an isolated profile with subsequent account for the interference of the profiles in the lattice.

Temperature compensation of the circadian oscillation in Drosophila pseudoobscura and its entrainment by temperature cycles

Detailed analysis of the effects of temperature on the circadian rhythm of eclosion in Drosophila pseudoobscura adults yielded results similar to those in similar studies of other poikilotherms: although the period, τ, of the free-running oscillation varies little with different constant temperatures, it can be phase shifted by changes (steps and pulses) and entrained by temperature cycles. Temperature steps-up generate only phase advances (+Δφ); steps-down generate only phase delays (−Δφ). Pulses, however, give both +Δφ and −Δφ. The size of Δφ generated depends on the point in the oscillation's cycle exposed to the temperature signal. An empirical relationship is found between temperature steps and pulses: to first approximation, the +Δφ or −Δφ generated by 12 hr pulses may be computed from the Δφ generated by the steps comprising that pulse. This finding justifies the assumption that the Δφ normally effected by the step is accomplished rapidly (within a few hours). An empirical response curve model for (square wave) temperature cycle entrainment of the eclosion rhythm is developed: from the Δφ response curves for single 12 hr pulses (high or low), the phase angle difference, Ψ, between 24 hr recurrent pulses (square-wave forcing oscillation) and the eclosion rhythm (driven circadian oscillation) is correctly predicted. From the response curves for a temperature step-up ( T 1 T 2 ) and a temperature step-down ( T 2 T 1 ) the Δφ response curves for single pulses ( T 1/T 2/T 1 ) of different duration were computed. These computed response curves differ in their zero phase shift points; that is, exposure of certain points in the oscillation's cycle to a temperature step-up will generate a +Δφ equal to the −Δφ generated by the step-down which comes n hr later, n being the duration of the pulse. Assuming the validity of the empirical response curve model for temperature entrainment, the variation in zero phase shift points of the computed pulse response curves predicts a parallel variation of Ψ between the eclosion peak and 24 hr recurrent pulses of different durations (different thermoperiods). Such an experiment thus tests both the validity of deriving pulse response curves from step response curves and the validity of the response curve model of entrainment; and indeed the agreement between observation and prediction is close. Most workers agree that this remarkable conjunction of properties—relative invariance of τ with different constant temperatures and entrainment by temperature cycles—implies some mechanism for temperature compensation of circadian oscillations. Possible mechanisms of temperature compensation are discussed, and a ‘temperature adaptation’ model—based on feedback inhibition—is proposed which readily describes the known effects of temperature on circadian oscillations. Present evidence does not exclude other possible mechanisms; the present model is intended only to show that what is known can be readily simulated by assuming a mechanism whose elements—oscillations and temperature adaptation—are known to occur in living systems.

Constant-Phase Electrically Controllable rf Attenuator using Permalloy Films at Resonance

A constant-phase, electrically controllable attenuator using Permalloy films has been investigated both analytically and experimentally. The well known behavior of the permeability as a function of bias field near resonance is utilized. The permeability of a Permalloy film can be expressed as μ=μ1−jμ2. In a film-loaded strip line, the attenuation constant is strongly affected by μ2 while the phase constant depends on the magnitude and sign of μ1. Controllable attenuation with net zero phase change can be realized with the following arrangement: Two film strips, identical in properties and geometry are used in a strip line and both are biased at H0, the resonance bias field, resulting in a maximum attenuation and zero phase shift. Super-imposed is a control field of opposite polarity on the two film strips. If the control field is set at ΔH, then the net bias field is H0−ΔH on one film strip and H0+ΔH on the other, yielding a permeability, −|μ1|−j|μ2| on one and +|μ1|−j|μ2| on the other. As a result, the phase change due to the reactive permeability components cancel each other out and only the attenuation due to the loss component remains. Such an attenuator has been built and tested successfully over a frequency range from 1 to 3 Gc/sec.

Imaginary part of the optical model potential in nuclear matter

The imaginary part of the optical model potential in nuclear matter has been calculated for various values of the energy, assuming Gammel-Thaler nucleon-nucleon interactions. The calculations were made using the separation method in which the interaction is separated into a short range and long range part, the former giving zero phase shift. To a good approximation, only the long range component contributes to the imaginary part of the optical potential.

RESOLVING POWER OF THREE ANTENNA PATTERNS DERIVED FROM THE SAME APERTURE

Three antenna patterns are derived from the same linear aperture and may be described in terms of an angular spectrum of spatial frequencies ranging from zero to a common cutoff frequency. The band passes according to the shape of the spectrum are rectangular, triangular, and cosinusoidal for the three patterns, and give resolving powers respectively of 1.33, 1.00, and 1.05, in terms of the cutoff period. The rectangular band pass gives rise to the optimum antenna pattern and allows the Fourier components of a source from zero to cutoff frequency to be received with equal intensity and zero phase shift. Scanning curves of two equally intense point sources and a uniformly bright line are investigated.

Sound Radiation from a Finite Cylindrical Shell with Rigid End Caps

Utilizing the concept of a point source omnidirectivity, two separate approaches are derived to the problem of far field sound radiation from a finite cylindrical shell source with rigid end caps vibrating in one of its normal modes. An additional approach is derived by taking the expressions of Laird and Cohen [D. T. Laird and H. Cohen, J. Acoust. Soc. Am. 24, 46 (1952)] and expending them into a shell band source on an infinite cylinder. For all three above approaches, three separate boundary conditions are considered. Case I, finite cylinder in a free field; case II, finite cylinder resting normal on a rigid plane reflector with zero phase shift between incident and reflected wave; case III, similar to case II except for a 180° phase shift between incident and reflected wave. All nine approaches are compared to one another, together with a case III comparison to experimental values.

Transformer Design for Zero Phase Shift

A design method for obtaining minimum phase shift between output and input of a transformer is described. The method is applicable to precision reference transformers employed in analog computers and servo loops where minimum quadrature voltages are mandatory. A rigorous analysis of the equivalent circuit of the transformer demonstrates that the transformer can be treated as a combination lead and lag network to yield zero phase shift. This is done by making the ratio of primary resistance to primary shunt reactance equal to the quotient of total leakage reactance and load resistance. The procedure consists of l) designing for theoretical zero phase.

The Radar Display as a Linear Filter

When an intensity-modulated cathode ray tube is fed by an electronic gamma-correction circuit to compensate for the tube power law, the over-all system may be interpreted as a linear filter. It is shown that if the electron distribution within the beam is Gaussian, then (for at least some applications) the corresponding equivalent filter has a Gaussian amplitude characteristic and zero phase shift. Thus, a recent radar tube, the 5FP14A, has a frequency response given by exp [-7.07f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ] when used on a range of 30 nautical miles. (Here f is expressed in megacycles.) A similar result applies to this tube when used as a flying-spot scanner. If the radar video amplifier is to produce no degradation of this display it must be flat to a frequency 1.2v/w, where v is the sweep velocity and w the spot size. The desirable pulse duration is equal to the time required to sweep past a spot. Simple modifications of these relations are necessary if ground-range sweeps are used.

Novel Circuit for a Stable Variable Frequency Oscillator

In the past, quartz crystals have been used extensively to control single frequencies. This paper describes a circuit where a quartz crystal exercises considerable control over a continuously variable frequency spectrum. The circuit is characterized by multiloop feedback, which enables oscillation to be maintained at three frequencies, with the corresponding voltages confined to certain branches of the circuit and coupled to each other through three mixers. The frequencies of oscillation, to be called f1, f2, and f3, are determined by zero phase shift conditions in the feedback loops and by one frequency condition, f1+f2 = f3. The frequency f3 is restricted by a quartz crystal resonator, whereas the frequencies f1 and f2 are tunable in such a manner, that as f1increases, f2 decreases and vice versa. The LC resonators which control f1 and f2 drift in the same direction when the ambient conditions change. Such a drift cannot influence f1 and f2, since the latter can change only when the LC resonators shift in the opposite direction. The presence of a quartz crystal in the feedback loop also improves the phase stability of the circuit. An experimental model has been tested, and shows a thirty to hundredfold reduction of the frequency drift with temperature, excellent short and long term stability and a remarkably small initial frequency drift with switching on.

Dielectric Potentiometers

The term "dielectric potentiometer" is used to designate a new type of controllable voltage divider employing a lossy liquid dielectric as the impedance medium. With proper design, the dielectric potentiometer may be operated over an extremely wide frequency range with a flat amplitude response and zero phase shift. Unlike conventional wire-wound and film type controls, the new device is readily capable of being perfectly compensated for broadband operation when operated into either resistive or capacitive loading, or a parallel combination of both. Other advantages include infinite resolution, long life, and adaptability to specific nonlinear requirements. Probable advantages such as a low noise figure and the capability of operation at high rotational speeds have yet to be experimentally investigated. Examples of designs for particular applications are given.