Input Admittance Research Articles

Analytical method of spiral line

AbstractThe spiral line shows promise for miniaturization of circuits because it has the characteristics of a strip line and has a nonlinear structure. However, analysis of this line is difficult because of nonperiodic coupling between the conductors. This paper proposes a theoretical analysis to determine the distributed parameters for a traveling‐wave mode along the line. Theoretical analysis and experimental investigation are performed for the propagation characteristics of the spiral line. the innovative feature of this method is that the series impedance and the parallel admittance due to the primary constants of the line are expressed as integrals of the current distributions. From these expressions the distributed parameters for the forward wave and the backward wave are given in a series form containing complete elliptic integrals. These distributed parameters comprise the relations between the line structure and the frequency and represent the nonperiodic coupling between conductors. Using this method, we obtain the input admittance of the spiral line with its end open or shorted. Since the results agree well with measured data, validity of the method is confirmed. It is also shown that the frequency characteristic of the distributed parameters express that of the input admittance.

The horizontal circular loop antenna near a planar interface

The horizontal circular loop antenna near a planar interface between two materials is analyzed theoretically for both the transmitting and the receiving cases. For the transmitting antenna the distribution of current, input admittance, and electric field in both media are obtained by applying a limiting process to the previously obtained results for the eccentrically insulated circular loop antenna. The receiving formulation is for an electromagnetic plane wave incident at an arbitrary angle from either side of the interface, i.e., incident from either the region that contains or the region that does not contain the loop. Parametric studies are used to investigate the effect of the interface on the input admittance of the loop and the directive properties for the electric field of the loop in both media. Measured input admittances and electric field patterns of model loop antennas above and below an interface between air and fresh water are in good agreement with the theoretical calculations.

Eigenmodes and quality of violins

From a Scandinavian violinmakers' competition, a number of 24 violins of different qualities were selected. Input admittances as function of frequency were recorded perpendicularly to the top plate at two positions on top of the bridge. The admittance curves at the side of the bass bar show three resonances at approximately 400, 500, and 700 Hz and a broad resonance around 3 kHz. Three “acoustical” quality criteria were extracted from these curves: (1) the average level of the three resonance peaks (high is favorable), (2) the summed discrepancies between single peak levels and the average level (small is favorable), and (3) steepness of upwards slope from 1500 to 3000 Hz (steep is favorable). The levels of input admittances of the bass bar and sound post sides are approximately the same. A fourth acoustical quality criterion was extracted from the two curves: (4) the level discrepancies between the two curves (small is favorable). Calculated “acoustical” quality points correlate well with given tonal quality ratings (a correlation coefficient of 0.92 with five violins with singular faults excluded).

Guitars: Steady state and transient response

Measurements of input admittance confirm that the guitar can be considered as a bass‐reflex enclosure with flexible sides. The effect of this is to increase the sound output without distortion below the first resonance of the top plate. The proposed equivalent circuit will be reviewed. New measurements on plucked notes using a digital analyzer show that the onset of sound contains two distinct parts. The main steady state resonances are shock excited at the beginning of the pluck, grow, and decay within the first few milliseconds of the onset. Simultaneously the harmonics of the string grow and remain as the sustaining vibration of the tone after the steady state resonances have died away. It appears that every played note of the guitar contains at its beginning sound representative of the steady state response which contains information about the type of instrument being sounded and its quality, and this is followed by the sustaining harmonics of the string. Experiments with the violin, cello, and harp s...

RADIATION AND SCATTERING FROM PARTIALLY BURIED VERTICAL WIRES

ABSTRACT The purpose of the present work is the numerical modeling of partially buried vertical wire-antennas and scatterers. Our interest is in an efficient computation of their electromagnetic properties. Analytically the problem is formulated in terms of an integro-differential equation over the wire current across the air-ground interface. This equation is then converted into a numerically solvable form by means of Galerkin's method together with the piece-wise linear functions. The inverse Bessel transforms, commonly called Sommerfeld integrals, appearing in the Kernel of the integral equation have been evaluated by numerical integration over the real axis. The resulting computer code“STAKE,” which permits the numerical simulations of partially buried vertical wires, proved to be efficient and accurate in comparison with other computation methods. First the problem of antenna grounding has been investigated for the cases of soil and sea water. The current distributions, input admittances and radiatio...

Mechanical and electrical mechanisms in the ear: Alligator lizard tales

The ear of the alligator lizard is similar in structure and function to mammalian ears, but somewhat simpler and more accessible to in vivo experimental studies. Our focus has been on signal transmission through the middle ear and the portion of the inner ear having hair cells with free-standing stereocilia. We have measured two-tone distortion products in the sound pressure and the input admittance at the tympanic membrane; velocity of the extrastapes, stapes, and basilar membrane; intracellular receptor potential of hair cells; and spike discharges of cochlear nerve fibers. Many features of these measurements have been represented by a model of the underlying mechanical and electrical mechanisms. Conclusions suggested by the experimental and theoretical work include: (1) Nonlinearities detected in the external and middle ear responses appear to be independent of mechano-electric transduction in the cochlea. (2) The nonlinearities observed in the receptor potential at low-stimulus levels are associated with hair-cell processes. (3) The frequency selectivity of the receptor potential is determined not only by the middle-ear—basilar-membrane mechanical system but also by stereociliary-tuft resonances whose frequencies depend on tuft morphology. [Supported by NIH and the Whitaker Health Sciences Fund.]

The pulsating elastic sphere

The elastic sphere is shown to develop catastrophic pressures at its center in response to a finite square pulse input. Also shown is an unusual driving point input admittance function.

Driving point impedances of thick homogeneous plates in flexure

The input admittance of a plate is derived, Mindlin's plate equation being used to take into account rotatory inertia and finite shear stiffness. It turns out that the real part of the admittance is very similar to the well-known result from Kirchhoff's plate theory; only at higher frequencies does one find differences depending on the size of the exciting area. The imaginary part of the admittance has a spring-like character; it is inversely proportional to the shear stiffness and becomes very large when the exciting area goes to zero. The calculated results are compared with measurements. The agreement is good.

Oboe normal mode adjustment via reed‐staple proportioning

We have analyzed a simple theoretical model of an oboe, having a truncated conical air column of variable length and a reed assembly consisting of a tapered neck leading to a closed, cylindrical cavity. Proportions are chosen for this assembly so that its input admittance at the bottom of the neck is very closely the same function of frequency as the admittance of the missing conical segment at the apex of the air column for frequencies below the tone‐hole cutoff. The most important requirements are that the reed assembly by itself possess the same volume and lowest‐mode frequency as the missing apex. The intervals between the first‐mode frequency and the below‐cutoff frequencies of the second, third, and fourth modes of the model instrument can be made harmonic to within five cents as the length of the air column is varied to sweep the first mode through an octave range. We have investigated the effects of small variations in the proportions of the reed assembly on the natural frequencies of the model instrument. The results provide practical guidance for adjustment of the reed structure of a real oboe to special features of its own not‐quite‐conical acoustical behavior.

Impedance measurement source and microphone proximity effects

The input impedance Zin as normally defined is the air column pressure response to a unit plane-wave flow excitation. The experimental measurement of Zin for an arbitrary air column is affected by the nearfield interactions between an excitory source (capillary, annulus, membrane, etc.) and microphone. In addition to the plane-wave component, the source produces a local disturbance (due to the evanescent modes) at the microphone. The net microphone pressure pm can be written in terms of the source strength us, the wave impedance R0 and radius a of the air column entryway, and wavenumber k: pm = usR0[(Zin/ R0)+jkaℰ]. The evanescent mode factor ℰ is real and independent of frequency for ka<1. Its value depends on the source and microphone geometry. Measured values agree with detailed calculation. Placement of one transducer along the center axis of the air column, with the other at R = 0.6a from the center eliminates all azimuthal mode coupling (Jm Bessel functions, m≳0), and minimizes the coupling to the lowest order J0 evanescent mode. If neither transducer can be placed at the center, 90° azimuthal separation will eliminate all J1 modes. Placing one or both at R = 0.6a from the center then minimizes J0 effects. These configurations make the ℰ contribution to pm negligible for ‖zin/R0‖≳2, but experimental study near Zin minima (i.e., input admittance maxima) still poses special problems whose reduction is discussed.

Middle-ear mechanics: Comparison of cat and alligator lizard

Although the middle ears of cat and alligator lizard have similar components [tympanic membrane (TM), middle-ear cavities, and ossicular system], there are clear differences such as the number of ossicles and the structure of the TM. Mechanical responses of these two types of middle ear were investigated with measurements of the input admittance at the TM with the cavities open (Yd). Comparisons are made over the 10 Hz–15 kHz range. For cat Yd is compliancelike below 1 kHz and approximately resistive at higher frequencies. In lizard Yd is also compliance dominated below 1 kHz, and resistive near 2 kHz, but is masslike above 3 kHz. Admittance was also measured with the cochlear load removed and interrupted or fixed ossicular systems. Preliminary conclusions are: (1) In cat and the cochlear load has a large effect on Yd, while in lizard Yd is relatively independent of the cochlea. (2) In the lizard Yd is primarily determined by the TM. (3) The ossicular systems, by themselves, contribute little to Yd in either species. [Work supported by NIH and the Whitaker Health Sciences Fund.]

On Solving Waveguide Junction Scattering Problems by the Conservation of Complex Power Technique

Normal mode expansions are used to mode match the tangential electric field at the transverse junction of two cylindrical waveguides. Instead of mode matching the tangential magnetic field the principle of conservation of complex power is invoked and leads, without a matrix inversion, to an expression for the junction's input admittance matrix, as seen from the smaller guide. Simple matrix algebra and the reciprocity theorem then provide the generalized scattering matrix of the two-port (with higher order modes included). It is also shown that the solution satisfies the continuity condition for tangential magnetic field in the junction's aperture. Numerical results are given for parallel plate waveguides with TEM, TE/sub 1/, and TM/sub 1/ incident fields, numerical convergence being achieved with about ten modes in the smaller waveguide.

Scattering Matrix Analysis of Surface Acoustic Wave Reflectors and Transducers

Absmcr-The phased periodic array scattering parameters [l] have been modified and corrected for use as a single electrode mixed units scattering matrix consisting of one electrical and two acoustic ports. These scattering parameter analytical expressions are functions of material constants, electrode geometry, and frequency. The threeport single-electrode scattering matrices are acoustically cascaded to produce a three-port device scattering mat&x which takes into account all finger interactions (acoustic and electric) for the combined effects of piezoelectric and mechanical scattering. The analysis agrees well with experimental measurements of input admittance, electroacoustic transfer function, and acoustic transmission and reflection coefficients as functions of frequency. Analysis results for the complete modeling of solid and split electrode transducers and transducers with floating electrodes are also presented.

A nonlinear impedance converter

It is shown that under reasonable assumptions a common op amp circuit operating under nonlinear conditions possesses a nonlinear input admittance operator <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y(.)</tex> . By an appropriate choice of parameters a negative admittance may be obtained in the vicinity of the origin. Bounds on the behavior of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y(.)</tex> and Its inverse are given.

Normal input admittance of a disk in a thin flat plate

The input admittance for a rigid, massless, circular disk undergoing uniform normal motion in a thin flat plate is found as a function of disk radius, within the limitations of the classical theory for thin-plate dynamics. A modal reciprocity theorem is derived which relates the real part of the input admittance, for any single mode of deformation of the source region, to the mean-square response velocity in that mode when it is excited by an isotropic, homogeneous, stochastic field of waves incident from the plate.

Impedance measurement source and microphone proximity effects

The input impedance Zin, as normally defined, is the air column pressure response to a unit plane wave flow excitation. The experimental measurement of Zin for an arbitrary air column is affected by the near-field interactions between an excitatory source (capillary, annulus, membrane, etc.) and microphone. In addition to the plane wave component, the source produces a local disturbance (due to the evanescent modes) at the microphone. The net microphone pressure pm can be written in terms of the source strength us, the wave impedance R0 and radius a of the air column entryway, and wavenumber k: pm = usR0[(Zin/R0) + jkaε]. The evanescent mode factor ε is real and independent of frequency for ka &amp;lt; 1. Its value depends on the source and microphone geometry. Measured values agree with detailed calculation. Placement of one transducer along the center axis of the air column, with the other at r = 0.6a from the center eliminates all azimuthal modes coupling (Jm Bessel functions, m &amp;gt; 0), and minimizes the coupling to the lowest order J0 evanescent mode. If neither transducer can be placed at the center, 90° azimuthal separation will eliminate all J1 modes. Placing one or both at r = 0.6a from the center then minimizes J0 effects. These configurations make the ε contribution to pm negligible for Zin(R0 &amp;gt; 2, but experimental study near Zin minima (i.e., input admittance maxima) still poses special problems. [Work supported by NSF.]

Analysis of a wire antenna in the presence of a body of revolution

The problem of an arbitrarily oriented thin-wire antenna located near a body of revolution is analyzed. The usual integrodifferential equation for a thin wire in unbounded space is generalized to account for scattering from the nearby body. The presence of the body is accounted for by a numerical dyadic Green's function. The modified wire equation is solved by standard numerical techniques to obtain the current distribution on the wire. The effects of various bodies on input admittance are compared with results for an isolated antenna. Measured and theoretical input admittance data for a monopole near several different bodies of revolution are found to be in good agreement.

Analysis of a Wire Antenna in the Presence of Sphere

An integro-differential equation is formulated for the problem of a thin-wire antenna in the presence of a sphere, and this equation is solved by the method of moments. The analysis is valid for an arbitrarily oriented and positioned wire relative to the sphere which may be either a perfect conductor or may be any simple homogeneous material. Input admittance of the wire antenna near a conducting sphere is determined from computed wire current and is corroborated by measured values of admittance. Also presented are calculated radiation patterns for the antenna/sphere structure.

Surface Charge and Field Distribution in a Finite SAW Transducer

Using the moment-method technique, closed-form expressions for the surface charge, potential and electric fields of a finite transducer over a low coupling substrate are derived. The influence of the end effects on the total capacitance of the transducer are studied and the field patterns of three different electrode sequences are computed. It is shown that for Y-Z lithium niobate, the surface-charge density is proportional to the normal component of the electric field under the transducer. The moment-method technique was also used to study the total input admittance of finite transducers on Y-Z lithium niobate as a function of the number of finger pairs. Numerical results indicate that the increase in capacitance and conductance with the number of finger pairs, when the number of finger pairs exceeds three, is approximately constant.

Calculated admittance of an idealized drill rod antenna in a lossy medium

Some calculated results for the input admittance of both insulated and uninsulated drill rods immersed in a lossy medium are given. The source can be either a voltage gap or a thin toroidal coil. For this input admittance calculation the drill rod is assumed to be of infinite length. Even a very thin insulating layer is found to greatly decrease the real part of the input admittance or the input power.