Driving-point Impedance Research Articles

Numerical Design of Patch Radiator Arrays

ABSTRACT An electromagnetic analysis technique for probe–fed patch radiator phased arrays is presented that accurately models their driving point impedances and radiated electric fields. The use of this analysis methodology to both predict the behavior of and to design patch radiators is discussed. Salient features relevant to radiator synthesis are discussed, including radiator asymmetries due to multiple probe feeds and the realization of matching networks for wideband radiator operation. Key effects relevant to radiator performance, such as feed–network related resonances and surface wave effects, are elucidated and design examples are cited.

Numerical modelling technique for the radiation of wire antennas near conducting surfaces

Radiation of wire antenna structures in the vicinity of conducting surfaces is analysed using an entire-domain Galerkin formulation. A method is developed for modelling those conducting surfaces by interconnected rectangular plates. The singular integrals involved in the matrix elements due to the junctions between the plates are treated by a new series of co-ordinate transformations and evaluated with the aid of specially constructed quadrature formulas. Numerical results are presented for surface currents on the reflectors and for driving-point impedances and radiation patterns of the antennas. Several problems with different configurations are solved. Results show good agreement with those obtained by other methods.

Computer-aided design of two dimensional electric-type hyperthermia applicators using the finite-difference time-domain method

A hyperthermia applicator design tool consisting of a finite-difference time-domain (FDTD) technique in combination with a graphical display of electric fields and normalized linear temperature rise is described. This technique calculates, rather than assumes, antenna current distributions; it includes mutual interactions between the body and the applicator, and it calculates driving-point impedance and power delivered to the applicator. Results show that the fundamental limitation of 2-D electric-type applicators is overheating of the fat by normal components of the electric field, which exist because of near fields and capacitive coupling with the muscle. Two factors which contribute to the capacitance are the muscle conductivity and the small antenna size in air. Two examples of applicators designed to avoid fat overheating are described: a 27-MHz segmented dipole for heating large tumors to 7 cm depth, and a 100-MHz dipole for small tumors to 5 cm depth. The first uses a water bolus, and the second uses a water bolus with low-permittivity strips to reduce normal fields at the antenna ends. The results of this study describe fundamental limitations of electric field applicators, and illustrate the use of a powerful applicator design tool that allows rapid evaluation of a wide range of ideas for applicators which would require months and years to test experimentally.

A simplified absolute method for point impedance measurement

A previous work has indicated that an electromechanical transducer, i.e., an electrodynamic‐type or piezoelectric‐type vibration exciter, can be used for determining the point impedance by the reciprocity principle, and a general formula was given [L.‐F. Ge, J. Acoust. Soc. Am. Suppl. 1 87, S208 (1990)]. The present study develops a simplified and practical method. It is only needed to measure four complex electrical impedances of the exciter, W1, W2, W3, and Wx, corresponding to three known different mass loads, M1, M2, M3, and an unknown structure or material coupled successively on the exciter table while it is vibrated at a frequency of interest. The driving point impedance of the structure or material at the frequency f can be found from the equation: Zx = jω(M2M31W2Wx1 − M1M32W31Wx2)/(M31W32Wx1 − M32W31Wx2), where j2 = −1, ω = 2πf, double subscripts mean differences, such as M31 = M3 − M1, Wx1 = Wx − W1. The equation would be further simplified by the selection of M1 = 0, i.e., no‐load, to: Zx = jωM...

The resonant circular array of electrically short elements

Different resonant distributions of current in circular arrays with N=60, 72, and 90 elements are investigated theoretically with the method of symmetrical components and a two-term representation of current in each element. The arrays studied have only one driven element. The remarkable results—which are displayed in a sequence of graphs—indicate that the relative currents in the elements can be distributed in triplets, triplets alternating with singlets, two independent sets of singlets, or one set of singlets. The driving-point impedance of this last distribution is a pure resistance, the Q of the 90-element array is over 30 000, and the half-power beamwidth of each of the 90 sharp peaks in the power pattern is 2°.

Computationally efficient estimation of frequency response and driving point impedances in wide-band analog amplifiers

An alternative to traditional dominant and lumped-pole mathematical models of a linear analog circuit is proposed for estimation and sensitivity analysis of bandwidth, phase angle, and driving point impedances in wide-band signal processors. The proposed mathematical model, which accounts for transmission zeros and dominant complex pole pairs, is accurate to errors that are usually less than 15%, regardless of the relative densities of poles and zeros in the complex frequency plane. Although practical implementation of the model requires a personal computer or workstation, the results are computationally efficient since estimates of I/O frequency and phase responses, as well as the frequency response of driving point impedance at any circuit port, derive from only one solution of the circuit equilibrium equations. These results are design-oriented in that the realistic effects on high-frequency performance of potentially large uncertainties in any circuit or model parameter are accurately revealed. >

Steady-state response of rotating disks with internal damping, driven harmonically at one point.

The steady-state response of damped disks rotating at a constant angular velocity was analyzed subjected to the external harmonic force at one point fixed in space. The distribution of the internal stress was obtained analytically from the equilibrium equation of radial force which was expressed by the space coordinate. The equation of motion of the rotating disk with the internal damping expressed by the complex Young's modulus was derived by use of Galerkin's method. The driving-point impedance, the mode shape, and the relationship among the angular velocity, the harmonic exciting frequency and the maximum amplitude have been calculated numerically.

The effects of acceleration on whole-body vibration response in the primate model

A three degree-of-freedom model is proposed to predict the biodynamic responses of the seated human body of different masses. A baseline model is initially derived to satisfy both the mean apparent mass and seat-to-head transmissibility responses proposed in ISO/DIS 5982:2000 applicable for mean body mass of 75 kg. The validity of the resultant generic mass dependent model is verified by comparing the apparent mass and driving-point mechanical impedance responses computed for total body masses of 55, 75 and 90 kg with the range of idealized values proposed for body masses within the 49–93 kg range. Considering the lack of data that could be found to define the apparent mass/mechanical impedance of subjects with different body masses when applying the experimental conditions defined in ISO/DIS 5982:2000, an attempt is made to adapt the parameters of the base model to fit the measured apparent mass data applicable to groups of automobile occupants within different mass ranges. This is achieved through constrained parametric optimization which consists of minimizing the sum of squared errors between the computed response and the mean apparent mass data measured for automobile occupants within four mass groups: less than 60 kg, 60·5–70·5 kg, 70·5–80 kg and above 80 kg. The results show a reasonably good agreement between the model responses and the measured apparent mass data, particularly at frequencies below 10 Hz. The results suggest that the proposed mass dependent model can effectively predict the apparent mass responses of automobile occupants over a wide range of body masses and for two different postures: passenger (hands-in-lap) and driver (hands-on-steering wheel) postures.

Effect of Operating Frequency on Driving-Point Impedance and Radiation Characteristics of Helical Array

A rigorous theoretical method has been developed for the calculation of driving-point impedances and far-field radiation patterns of helical array of staggered half-wave dipole radiators at different operating frequencies. The method is based on induced E M F theory. The radiators of the array are considered to be thin, linear and centre-driven. The broad-band performance for the theoretically helical array has been investigated both in respect of driving-point impedances and far-field radiation characteristics.

Simplified design guidelines for dominant pole amplifiers peaked actively by emitter or source followers

The author discusses active inductance realization using time moment theory to determine the effective dominant zero and dominant pole of the driving point impedance seen at the emitter of a bipolar junction transistor (or source of a MOSFET) operated as a two-terminal circuit element. The analyses produce sufficient conditions for inductance realization, the value of the effective inductance actually realized, and the signal frequency range over which the effective inductance is nominally constant. Complementary benefits of the analyses include circuit design guidelines that eliminate output inductance in emitter and source followers. This latter information is useful when impedance buffering is required to couple amplifier outputs to capacitive loads. These results are interpreted and applied to the design of an actively peaked, broad-banded integrated circuit amplifier. >

Null double injection and the extra element theorem

The extra element theorem (EET) states that any transfer function of a linear system can be expressed in terms of its value when a given 'extra' element is absent, and a correction factor involving the extra element and two driving-point impedances are seen by the element. In the present work, the EET is derived and applied to several examples in a manner that has been developed and refined in the classroom over a number of years. The concept of null double injection is introduced first, because it is the key to making easy the calculation of the two driving-point impedances needed for the EET correction factor. The EET for series and parallel elements is then considered, and attention is also given to the EET as an analysis tool, to the symmetry of the two forms of the EET, and to return ratios and sensitivity. >

Steady state response of laminated FRP cantilevered rectangular plates.

The steady state response problem is solved for cantilevered rectangular plates made of symmetrically laminated FRP (fiber reinforced plastic) composites. The bending rigidities are obtained by using the thin-plate laminate theory, and the governing equation of motion for generally orthotropic plates is solved by the Ritz approach. In numerical study, driving point impedance is calculated for three types of FRP materials, and the effects of various parameters (material, number of layers, fiber orientation) upon the responses are discussed.

Steady-state response of a damped cantilever annular sector plate with curved radial edges.

A steady-state response is presented for a damped cantilever annular sector plate with curved radial edges by the Ritz method. The plate is transformed into a regular sector plate with a unit outer radius by a transformation of variables. The transverse displacement of the transformed plate is approximately expressed in terms of the power functions, and the driving-point impedance is derived analytically. By the application of the present method, the response curves of the cantilever annular sector plate with curved radial edges, driven at an arbitrary point, are calculated numerically. The effects of the shifting angle, damping factor and the location of the driving point on the steady-state responses are clarified quantitatively for the cantilever annular sector plate with curved radial edges.

Diffraction of plate waves at a fixed point

Rectilinear bending waves at a fixed frequency travel along an infinite thin plate in vacuo. One point on the plate is fixed: its displacement is zero, but the plate rotates about the point. Waves are scattered from the fixed point, and contours of the rms displacement near the fixed point are given. Next the fluid-loaded case is computed by evaluating numerically a complicated integral. The energy scattered to the farfield is calculated from the real part of the driving point impedance at various frequencies below coincidence for a steel plate, 1 cm thick, loaded with water on one side. The impedance in vacuo is real and independent of frequency, but, for the fluid-loaded plate, it is complex and frequency dependent. Charts of the pressure contours are given for the nearfield, both on the plate and in the water.

A technique for simulating the amplifier-to-eardrum transfer function of an in situ hearing aid.

There are numerous articles wherein mathematical models of various parts of an in situ hearing aid have been reported. Such parts include, for example, the microphone, receiver, cylindrical tubes carrying sound to the eardrum and out through the earmold vent, and the external path from the vent back to the microphone. This article extends these earlier works to include the hearing-aid amplifier. In particular, a mathematical technique for characterizing the amplifier in combination with the receiver is reported. Cascade parameters of a two-port model of one particular amplifier/receiver combination are obtained by this method. The cascade-parameter data and the method of obtaining this data are verified by two different experimental procedures. One procedure involves both computing and measuring the input driving-point impedance of the amplifier/receiver combination. In the second procedure, the amplifier-to-eardrum transfer function of a hearing aid incorporating this same amplifier/receiver combination and mounted on an artificial ear is both computed and measured. Experimental and computed values of this transfer function for three different earmold geometries are in reasonably close agreement. The amplifier/receiver model reported herein will be used in future studies of acoustic feedback in hearing aids.

The four-frequency process for coupled-duals using error-corrected S-parameter measurements

Although the four-frequency measurement process has been used successfully on coupled dual crystals from 9.4 MHz to 21.4 MHz, discrepancies between the crystal data and filter data at 45 MHz and 57.5 MHz suggested an error problem associated with the measurement system. To eliminate the errors, a twelve-term error model was chosen and the equations were derived for use with an automatic network analyzer. The details of the direct deviation of the four-frequency measurement process are given in which the two resonator frequencies and the synchronous peak separation frequency (SPSF) of a coupled dual crystal are calculated from the two frequencies of the zeros of the short-circuit driving point impedance, and the two frequencies of the zeros of the open-circuit driving point impedance. Determination of the four frequencies from the error-corrected S parameters is discussed, as well as the analysis of an external capacitor placed across the output circuit to obtain a more convenient distribution of the four frequencies. A comparison is made between data taken on the original fixture and data taken on an automatic network analyzer using error-corrected S parameters.

Response of a damped quadrilateral cantilever plate

The steady state response of an internally damped quadrilateral cantilever plate to a sinusoidally varying point force is determined by means of the Ritz method. An arbitrary quadrilateral plate is conveniently transformed into a unit square plate by a transformation of variables. The transverse deflection of the transformed square plate can be approximately expressed in a series of beam eigenfunctions, and the driving point impedance can be derived analytically. The present method is applied to the response calculation of a skew cantilever plate driven at an arbitrary point, and natural frequencies and corresponding mode shapes are also calculated. The effects of the aspect ratio, skew angle, damping factor and location of the driving point on vibrations of a skew cantilever plate are determined quantitatively.

On Complex-Normalized Reflection Coefficients

The paper presents a consistency theorem on the complex-normalized reflection coefficients of a terminated lossless reciprocal two-port network. It is shown that the reflection coefficient defined for the one-port source impedance normalizing to the driving-point impedance at the input port of the two-port network is equal to the reflection coefficient at the output port normalizing to the load impedance times the square of a real regular all-pass function. Examples are given to illustrate the theory.

Calculation of the driving-point impedance of a two-terminal network by the dual variational method

Describes how the input impedance of two-terminal networks can be calculated by a rapid, simple variational method, in which one of Kirchhoff's laws is relaxed while currents or voltages are distributed in accordance with the unrelaxed law, the deviation from compliance with the relaxed law being used to calculate the distribution of current or voltage to be used in the next iteration.

A model of eddy-current probes with ferrite cores

A model of a three-dimensional axisymmetric probe coil with a ferrite core in the presence of a conducting half-space (the workpiece) is developed. The half-space is accounted for by computing the appropriate Green's function by using Bessel transforms. Upon introducing equivalent Amperian currents within the core, we derive a volume integral equation, whose unknown is either the magnetic induction field, or induced magnetization, and whose kernel is the Green's function that was previously derived. The integral equation is transformed via the method of moments into a vector-matrix equation, which is then solved using a linear equation solver. This allows the computation of the magnetic induction field within the core, the driving-point impedance of the coil-core combination, and the induced eddy currents within the workpiece.