Exponential Taper Research Articles

Frequency dependence of pulse distortions along an exponential microstrip taper

The propagation distortions have been numerically calculated for various signals based on a nonideal square pulse along an exponential microstrip taper. Numerical calculations have been performed for propagation distortions of various signals obtained by forcing the cutoff of the frequency components to be higher than some cutoff frequency in the spectrum of the nonideal square pulse. The mechanism in the pulse distortions has been clarified. The large and sharp spikes in the distorted pulse shape are caused by the delay time owing to the phase velocity in the high-frequency region, which is related to the slope part in the curve of the propagation time τL(ω)/2. These magnitudes depend on the magnitudes of spectra of the signal in that frequency region. The plateau distortions in the center and tail parts of the distorted pulse shape are mainly caused by multiple reflections in the low-frequency region below the angular frequency at the first zero point of the reflection coefficient, and occur in the terms of τL(0)/2−μ≤t≤3τL(0)/2+μ. The influence of the length of the taper on the distorted shape has been clarified. © 1999 Scripta Technica, Electr Eng Jpn, 129(4): 7–16, 1999.

Frequency dependence of pulse distortions along an exponential microstrip taper

The propagation distortions have been numerically calculated for various signals based on a nonideal square pulse along an exponential microstrip taper. Numerical calculations have been performed for propagation distortions of various signals obtained by forcing the cutoff of the frequency components to be higher than some cutoff frequency in the spectrum of the nonideal square pulse. The mechanism in the pulse distortions has been clarified. The large and sharp spikes in the distorted pulse shape are caused by the delay time owing to the phase velocity in the high-frequency region, which is related to the slope part in the curve of the propagation time τL(ω)/2. These magnitudes depend on the magnitudes of spectra of the signal in that frequency region. The plateau distortions in the center and tail parts of the distorted pulse shape are mainly caused by multiple reflections in the low-frequency region below the angular frequency at the first zero point of the reflection coefficient, and occur in the terms of τL(0)/2−μ≤t≤3τL(0)/2+μ. The influence of the length of the taper on the distorted shape has been clarified. © 1999 Scripta Technica, Electr Eng Jpn, 129(4): 7–16, 1999.

General theory of the modified Gutenberg-Richter law for large seismic moments

AbstractIt is well known that the Gutenberg-Richter power law distribution has to be modified for large seismic moments because of energy conservation and geometrical reasons. Several models have been proposed, either in terms of a second power law with a larger b-value beyond a crossover magnitude, or based on a “hard” magnitude cut-off or a “soft” magnitude cut-off using an exponential taper. Since large-scale tectonic deformation is dominated by the very largest earthquakes, and since their impact on loss of life and properties is huge, it is of great importance to constrain as much as possible the shape of their distribution. We present a simple and powerful probabilistic theoretical approach that shows that the gamma distribution is the best model given the two hypotheses that the Gutenberg-Richter power law distribution holds in absence of any condition and that one or several constraints are imposed, either based on conservation laws or on the nature of the observations themselves. The selection of the gamma distribution does not depend on the specific nature of the constraint. We illustrate the approach with two constraints: the existence of a finite moment release rate and the observation of the size of a maximum earthquake in a finite catalog. Our predicted “soft” maximum magnitudes compare favorably with those obtained by Kagan for the Flinn-Engdahl regionalization of subduction zones, collision zones, and midocean ridges.

Discussion on spikes and plateaus in pulse distortion shape along exponential microstrip taper

The propagation distortions of a nonideal square pulse along an exponential microstrip taper have been numerically calculated. Each part of the distorted pulse shape is related to either the frequency-dependent characteristics of the effective relative permittivity or to the frequency-dependent reflection coefficient characteristics. The components of signal spectra at frequencies below 9 Grad/s do not cause the ringing distortions, but cause the upward slope shift in the center part and the upward parallel shift in the sustained tail part to the distorted pulse shape for the case of no reflection (NR). The ringing distortions and the large spikes of the overshoot and undershoot distortions are caused by the components of the signal spectra in the frequency range 100/spl les//spl omega//spl les/200 Grad/s where the effective relative permittivity is changing very quickly with frequency.

Analytical solutions to a tapering multicylinder somatic shunt cable model for passive neurones.

A multicylinder somatic shunt cable model for passive neurones is considered in which one or more tapering equivalent cylinders emanate from a uniformly polarized soma. Each tapering equivalent cylinder approximates the loss of dendritic trunk parameter in the one or more dendritic trees that it represents, relaxing certain symmetry conditions necessary for the Rall equivalent cylinder concept and in particular allowing terminal branches to end at different electrotonic lengths. The case of exponential taper is considered in detail following the anatomical data on apical and basilar dendrites of CA1 and CA3 hippocampal pyramidal neurons obtained by Turner and Schwartzkroin [J. Neurophysiol. 44 (1980) 184; J. Neurosci. 3 (1983) 2381].

LLAMPÜDKEÑ: A high-current, low-impedance pulser employing an auxiliary exponential transmission line

The design and constructional aspects of a novel pulse power generator for use in dense plasma research presently under construction are presented. The generator consists of two Marx capacitor banks, each of 0.25 μF, 480 kV, and 28.8 kJ. Each Marx generator drives a water transmission line, in which the live electrode is the central conductor. The transmission lines consist of a constant impedance section followed by a multielectrode gas linegap followed by an exponential taper to the load section. The novel feature is the use of an auxiliary exponential line coupled at the load. This line controls both the voltage and the effective impedance at the load section. In addition, by leaving this line circuit open, energy not coupled to the plasma in the initial high-impedance phase may be reflected back and deposited into the discharge, increasing the peak current by 50%. Circuit simulations using a real-time-varying load impedance show that the current pulse rises in an approximately linear way to a maximum of 1.2 MA at 250 ns. The current falls to zero in the following 250 ns. The current waveform may be flattened simply by disconnecting the auxiliary line, giving a rectangular pulse of 350 ns with a maximum value of 950 kA. The overall impedance of the entire system may be adjusted by varying the separation between the conductors. The equivalent source impedance at the load is 0.8 Ω. This low value is by virtue of the auxiliary line, which limits the voltage at the load section and reduces the insulator constraints. We present simulations of the generator under real load conditions. The model also is checked against analytical solutions of exponential line behavior and against other published models of pulse power generators.

Seismic moment‐frequency relation for shallow earthquakes: Regional comparison

We determine the parameter values for the seismic moment‐frequency relation using Flinn‐Engdahl's regionalization of global seismicity and the Harvard centroid‐moment tensor data. The earthquake size distribution is approximated by the gamma law: a version of the Gutenberg‐Richter distribution with an exponential taper at the maximum moment. There is no statistically significant variation of the β value (the analog of the b value) for all seismic regions except for the midocean ridge systems. For the latter regions β=0.93, whereas for all other zones β=0.63. The maximum moment Mxg can be statistically evaluated only for subduction zones treated as a whole, Mxg = 1021 − 2 × 1022 Newton m, which corresponds to the worldwide Mxg value. For other regions, as well as for single subduction zones, Mxg is determined by comparing the number of events in each zone with the seismic moment rate calculated on the basis of the NUVEL‐1 model of plate motion. For subduction zones, we obtain the estimate of Mxg which agrees with the statistical value, giving evidence that most tectonic deformation is released by earthquakes. We test the hypothesis that no statistically significant variation in Mxg occurs in subduction and continent collision zones; the hypothesis cannot be rejected with available data. For the midocean ridges, the Mxg estimate cannot be unambiguously determined; it is quite possible that the estimate is significantly biased because only a small part of tectonic deformation at the ridges is released by earthquakes. These results have importance in evaluating seismic risk and may also lead to developing a physical theory for earthquake generation.

Earthquake size distribution and earthquake insurance

The distribution of earthquake seismic moment M is a Pareto (power-law) type with the exponent for shallow earthquakes. To ensure a finite total deformation energy, the distribution has to be modified for the largest earthquakes by introducing either a cutoff at or an exponential taper. Analysis of global seismicity suggests that both parameters do not change in a statistically significant way over continental areas and tectonic plate boundaries. Thus, very large earthquakes are possible in practically any urbanized areas. We present evidence that the statistical distribution of losses due to large earthquakes has a power-law (Pareto) tail with an exponent value less than 1.0: i.e., the distribution is heavy-tailed. If this statement is true, the earthquake average loss is controlled by the largest earthquakes. Neither the distribution of earthquake size at the maximum, nor the distribution of maximum losses is well known. This implies that insurance premiums can be determined only with significant uncertainty. We simulate the insurance ruin potential for three earthquake loss distributions: exponential, Pareto with exponent 3/2, and Pareto with exponent 2/3. The possibility of catastrophic losses due to great earthquakes suggests that the probabilities of the ruin of insurance companies are unacceptably high, unless the risk reserves are equal to or exceed the maximum possible loss. Although we do not give practical suggestions for earthquake insurance in the paper, these results point out the mathematical and geophysical constraints that insurance should operate within

Shaping a distributed-RC line to minimize Elmore delay

Euler's differential equation of the calculus of variations is used to determine the shape of a distributed-RC wire that minimizes Elmore delay. In two dimensions the optimal shape is an exponential taper. In three dimensions the optimal shape is a frustum of a cone.

Analysis of pulse dispersion distortion along exponential and Chebyshev microstrip tapers

The voltage and current transfer functions are shown for the tapered line. The dispersion distortion obtained by using these transfer functions are shown for the nonideal square pulse along the exponential taper and the Chebyshev taper. The great and sharp peak in the front of the distorted wave is caused due to the frequency dispersive characteristics of effective relative permittivity. The sustained tail and the ascent of gentle slope in the plateau in the distorted wave are caused due to the multi-reflection in the tapered line and are inherent characteristics in the configuration of taper. The sustained tail starts to vanish after the time of about one and half times of the echo time. >

Separation Filtering Applied to Aeromagnetic Data

Separation filtering of regional and residual gravity and magnetic fields has been the subject of extensive research. Wavenumber and spatial domain methods, variously described as matched filtering, layer filtering, depth slices etc. have been developedSeparation or layer filtering of magnetic data allows us to deconvolve the effects of causative sources occurring around a particular level. In practice, it is impossible to achieve a complete separation since the problem is non-linear. Separation filtering depends fundamentally on the concept of random distributions of sources within discrete layers and assumes that there is no statistical difference in response along each ideal layer and no correlation between the distribution in each layer.Interpretation of the log-power spectrum provides slope and intercept parameters for filter design. It is necessary to be able to recognise distinct linear segments of the spectrum corresponding to well separated depth ensembles in the data in order to deconvolve the effects of each depth ensemble with minimum contamination from sources at different levels. Non-linear spectra cannot be interpreted. It is important to apply a finite source width correction to the raw spectrum, otherwise indicated source depths will be too deep.Tests have been carried out on spectral matched filtering, differential upward continuation separation filtering, exponential taper filtering and a modified second vertical derivative filter. All filtering was performed in wavenumber domain. Spectral analysis of the test area suggested three depth ensembles with average depths of 1500 m, 300 m and 20 m below surface. The modified second vertical derivative technique provided the best representation of the shallow source ensemble being more stable and with a larger dynamic range than the matched filter residual filter. The spectral matched filter regional provided the best representation of the deep ensemble, although there was some contamination by shallower sources. The intermediate ensemble could not be extracted with any degree of confidence.Separation filtering can make a useful contribution to the enhancement of magnetic data, provided the limitations in the methods are recognised. Even where spatial source separation is reasonable, the filter will not manage to perform a complete rejection of shallow sources or deeper sources and will distort intermediate sources even more. The results should be used qualitatively to assist in source discrimination rather than used as input to analytical techniques.

Metal wave-guide to dielectric image guide transition using exponential taper

A unique metal wave guide to dielectric image guide transition has been developed using exponential taper in dielectric wave guide. The propagation characteristics have been computed theoretically and taper impedance for the different cross-sections have been evaluated, so as to match it with the metal wave guide for efficient mode conversion. Transmission loss and return loss for triangular and exponentail taper with frequency for same dimensional parameters have been measured.

A GaInAsP/InP tapered-waveguide semiconductor laser amplifier integrated with a 1.5 mu m distributed feedback laser

A GaInAsP/InP index-guided type tapered-waveguide traveling-wave semiconductor laser amplifier (TTW-SLA) with exponential taper structure was realized for the first time and its integration with a 1.5 mu m wavelength phase adjusted DFB laser was demonstrated. A reasonable amount of the single-pass gain, which was limited by the residual reflectivity at the output end of the amplifier region, was obtained with no serious problem with the lasing spectrum. A narrow beam divergence of FWHM=5.5 degrees and stable longitudinal mode operation were obtained with the output waveguide width of 20 mu m by adopting both a window structure and 7 degrees angled facets. This value agrees well with the theoretically calculated one and proves that single transverse-mode propagation can be attained by an exponentially tapered TTW-SLA with a very wide output end. >

Notch Filter Characteristics of Distributed Parameter C-R-NC Structures

The emergence of integrated circuitry has created interest in the study of distributed parameter C-R-NC structures. Three different configurations of distributed C-R-NC structures are analysed for their notch filter characteristics. The plots of amplitude and phase versus frequency of those networks are obtained under various loading conditions. The effects of exponential taper factor and resistive loads of various values on the shape of frequency response characteristics for one null network configuration of the exponential C-R-NC structure are displayed.

Parametric Transmitting Arrays: A Review and Some New Developments

Since Westervelt [J. Acoust. Soc. Amer. 32, 934–935(A) (1960); also 35, 535–537 (1963)] put forward the concept of parametric acoustic arrays, a great deal of effort has gone into extending his model of a line array with exponential taper to cover primary field distributions that can be realized in practice. Some of these models and their significances will be reviewed and the results of some new work in this field will be presented, with particular reference to the effects in the nearfield of parametric arrays. [Part of the work to be reported is being supported by the Office of Naval Research.]

Transition from 2-dimensional line analysis to 1-dimensional model

The transition from 2-dimensional line analysis to the 1-dimensional model is examined on the basis of a suitable series expansion of the voltage equation. It is shown that 1-dimensional equations can be derived from a 2-dimensional analysis with proper approximations for certain operators. A consistence procedure is outlined and applied to an exponential taper.

Coupled-mode description of a nonuniform transmission line

Coupled-mode analysis provides a conceptually simple technique for the analysis of nonuniform transmission lines and nonuniform coupled systems. The variable series and shunt elements couple backward and forward traveling waves. Reflection coefficients are derived for an exponential and linear taper by this technique.

On Some Three-Terminal Lumped and Distributed RC Null Networks

The selectivity characteristics of some three-terminal lumped and distributed RC null networks are examined. The lumped networks considered are the bridged and shunted ladders. In the symmetrical configuration, both networks are found to be less selective than the corresponding parallel-T. By tapering the ladder portion and increasing the number of sections, they can be made as selective as, or even more selective than the asymmetric parallel- T. The distributed networks are obtained as logical extensions of the lumped ones and are studied for exponential, proportional and parabolic types of tapering. Proportional tapering is found to offer no advantage over the untapered-line network. The other two types yield better selectivity; the maximum selectivity with parabolic taper is, however, less than that obtained with exponential taper. For both lumped and distributed networks, the selectivity is found to depend upon the direction of taper. For low source and high load impedances, a higher selectivity is obtained if the impedance level increases with distance from the source, while for high source and low load impedances, the reverse case yields a higher selectivity.

AN EXTENSION TO THE MODE THEORY OF VLF IONOSPHERIC PROPAGATION

The wave-guide mode theory of VLF propagation for a sharply-bounded homogeneous ionosphere is refined to include stratification at the lower edge of the ionosphere. The numerical results for a two-layer model are discussed in detail. By choosing the upper medium to have a conductivity with a factor of 10 greater than the lower medium, the attenuation vs frequency characteristic of the model is consistent with experimental data from 1.0 to 20 kc. The effect of the finite thickness of the E layer, important for frequencies less than 1.0 kc, is treated by an ionospheric model which has a sharp lower edge and an exponential taper to zero at greater heights.

Transmission Lines with Exponential Taper

Exponential lines, like exponential horns, are useful as impedance-matching devices. They are best inserted in a high-pass filter having the same cutoff frequency determined by the rate of taper. Unusual rules are derived for inserting the line in the filter with exact matching of iterative and image impedances. Design formulas are derived for the construction of exponential lines.