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Reverberation chambers have been used for quite some time for EMC measurements. Some early work was also done in antenna measurements, but the achieved accuracy was not sufficient for the method to be accepted. The paper describes the development of a reverberation chamber for antenna measurements and the applications for which it can be used. The disadvantage of using a reverberation chamber for measurement of small antennas and wireless terminals is that it is not possible to generate radiation diagrams. In some cases these are needed to fulfil specifications or by customers used to seeing the diagram as the only way of specifying their products. We know that some would like to use MEG to specify radiation, and this is not easily achieved in a totally uniform multipath environment. On the other hand we have met a growing understanding that this method is suitable for most of the measurements that have to be done throughout the development and evaluation of small wireless terminals: measurement of antenna characteristics (passive unit or cable fed terminal); total radiated power; head loss and prequalification of SAR values; receive sensitivity; spurious radiation.

There is an increasing interest in combining several antennas into a multi-function system, thus incorporating multiple frequency bands into a single antenna. Multi-band phased arrays are potential candidates for this purpose, allowing several frequency bands to operate from the same array aperture, i.e. aperture reuse. Such arrays may be realized by using compact narrowband elements in an array sufficiently sparse for intermediate compact elements operating at other frequencies to be embedded or superposed over the same array aperture. Hence, there is a need for miniaturized elements that are very small in terms of wavelength. The paper investigates miniaturized open-ended rectangular waveguides for use as array elements. We show that operating dielectric-loaded rectangular waveguide elements of an infinite planar array within the vicinity of the TEM frequency gives rise to the best transmission. In addition, it is seen that miniaturization in E-plane is better than in H-plane. For a large degree of miniaturization, the reflection coefficient is large and needs to be reduced by incorporating matching layers or similar. The results have been verified by using two independently developed codes. One of these has also been validated in other works.

We describe how to measure the radiation efficiency, correlation, diversity gain and capacity of a six-monopole antenna array in a reverberation chamber in order to characterize it by these parameters for a MIMO system. We show how these measurements can be used to find the channel capacity when a particular antenna array is used in a MIMO system. We also explain how numerical modeling of the MIMO array in a commercial code can be used to find the channel capacity.

Transversely corrugated surfaces are widely used in the design of hybrid-mode horn antennas. The authors propose referring to such surfaces and their relatives by the common name 'soft' surfaces. The reasons for this are that (1) these surfaces have the same characteristics relative to electromagnetic waves as the so-called acoustically soft surfaces have relative to acoustic waves, i.e., that the density-of-power flux along the surface is zero at the surface, and that (2) there also exists so-called artificially hard surfaces in electromagnetics, along which the power flux has a maximum for any polarization of the electric field. The authors define hard and soft surfaces in terms of an anisotropic surface impedance. Characteristics and possible applications of soft and hard surface are described. >

An approach is presented by which synthesis of offset dual-reflector antennas is reduced to solving nondifferential equations. This is made possible by approximating a known solution for the geometrical optics (GO) field reflected from a surface, and using local parabolic expansions of the reflector surfaces. The advantages of this approach are that the calculation is easy to carry out, the condition of low cross-polarization is included, and the question of existence clearly can be answered. The synthesis method can also readily be extended to the synthesis of multireflector antennas. >

The antenna of the radio observatory in Arecibo is currently fed by line feeds that correct for the spherical aberrations of the reflector. To improve the bandwidth and the sensitivity of the radiotelescope the line feeds will be replaced with a dual-reflector feed system. A computer code is described that is based on an efficient geometrical optics (GO) ray tracing technique. The code, called the TRT code, is related to the procedure of dynamic ray tracing used in seismics, which means that the complete complex ray field amplitude (and polarization for EM waves) is traced. The code also makes use of the paraxial-ray approximation, applied by considering each individual ray as an axis. In addition to the GO analysis, the code gives asymptotic information about the diffraction losses. This is obtained by the diffraction tracing techniques of the transition region theory (TRT). The characters of the TRT code are noted. >

A cheap alternative to the swan-neck feed, which can obtain low sidelobes even without an absorbing cylinder is presented. This feed is called the rectangular hat feed. The ideas of soft and hard surfaces have been used to optimize the performance of this linearly polarized feed. It can give low sidelobes and has broader bandwidth than the circular hat feed. >

The authors present a method, referred to as the cylindrical-wave-spectrum method, to determine the radiation pattern and self-admittance of a waveguide slot. where the region exterior to the waveguide may be a cylindrical structure of, in principle, any cross-sectional shape. Some examples of applications of the method are described, namely, arbitrary cylindrical geometry, baffles and finite ground plane, and slot-admittance determination. >

In recent years, the need for omnidirectional (in the azimuthal plane) antennas with narrow beams in the elevation plane, for wireless applications increased considerably. The antennas are used in amny frequency bands anywhere from 0.8 to 6 GHz. In a variety of configurations. The different collinear-array configurations are designed using back-to-back wide-beam elements or by simply using radiating elements with an intristic omnidirectional pattern. The motivation for this work was to devise a radiation element which (a) has an omnidirectional pattern in the azimuth plane, (b) allows for the design and fabrication of arrays, that can be easily integrated with other collinear arrays to generate a multitasking omnidirectional antenna. The element proposed in this paper is patch, which was built in a cylindrical geometry rather than a planar one, and which generates an omnidirectional pattern in the azimuthal plane.

The radio telescope of the Arecibo Observatory has a large primary reflector of 300 m diameter and with spherical shape. The old line feeds are now being replaced by a dual-reflector feed, referred to as the Gregorian feed, consisting of two sub reflectors (the tertiary and the secondary reflector) and several feed horns. The present paper presents a study in which the analysis techniques have been extended to study focusing of the beam at low altitudes in the ionosphere. The study is of general interest as it contains definitions of near-field gain and efficiency. Also, an algorithm is described from which the focus location can be calculated directly from the aperture field. This is used to study the displacement of the feed, or the tertiary or both at the same time to obtain as good focusing as possible at a certain altitude.

Reflector antennas with self supported waveguide feeds of swan-neck type are often used in radio link systems. If there are requirements for very low sidelobes, it is common to attach an absorbing cylinder to the rim of the reflector. Both the cylinder and the feed are expensive to manufacture. The paper describes a so called hat antenna which is cheap to manufacture, compact, light-weight and in addition has very low sidelobe performance. An experimental model with 43 cm reflector diameter has been built and measured at 15 and 30 GHz.

The paper gives a summary of the work that have been performed in the Antenna group at Chalmers University of Technology on measuring antennas for mobile phones in reverberation chambers. Reverberation chambers were originally developed for EMC measurements. We have shown that it also can be used to measure performance of antennas that are designed for use in multipath propagation environment, as well as the performance of complete phones. The antennas and phones can be measured with or without the presence of a head phantom or other objects. The antenna measurements give both radiation efficiency and reflection coefficient at different positions relative to an object such as a head phantom, as they would appear if the antenna and the head phantom were located in free space. The phone measurements give the total radiated power, which we refer to as the telephone communication power (TCP), also at different positions relative to an object. The present summary includes results from both antenna and phone measurements., Rad prikazuje rezultate istraživanja provedenih na Chalmers University of Technology o mjerenjima antena za pokretne telefone u malim ječnim komorama. Ječne su komore razvijene ponajprije za mjerenja na području elektromagnetske kompatibilnosti. Pokazali smo da se ječne komore mogu koristiti i za mjerenje osobina antena koje su predviđene za rad u uvjetima višestaznog rasprostiranja kao i za mjerenja osobina cjelokupnih pokretnih telefonskih uređaja. Antene i telefoni mogu se ispitivati sa ili bez prisutnosti fantoma ljudske glave ili drugih objekata. Mjerenjem se za antene može odrediti djelotvornost zračenja i koeficijent refleksije za različite položaje antena u odnosu na vanjske objekte kao što je npr. fantom ljudske glave. Rezultati mjerenja su jednaki kao u slučaju kad se antena i fantom nalaze u slobodnom prostoru. Mjerenjima na cjelokupnom pokretnom telefonu određuje se ukupna zračena snaga, koju nazivamo komunikacijska snaga telefona. Ova se snaga također određuje za različite položaje telefona u odnosu na vanjske objekte. U radu su prikazani rezultati mjerenja na antenama i telefonima.

A conical horn with a hard wall section realised by longitudinal grooves filled with dielectric is analysed. The analysis is based on stepwise representation of the conical surfaces and on the use of the method of generalised scattering matrices. The eigenmodes for the corrugated sections are determined by the asymptotic boundary condition. It is shown that the horn can provide high aperture efficiency (above 85%) and low cross-polarisation level (below -30 dB) in some frequency band, but the horn performance strongly depends on the hard section configuration because of wave reflections between the throat and aperture.

The authors of the original paper wish to thank Prof. Skobelev for complimenting their work and for his comments. Their response to the two points made in the Comment are provide.

The possibility of reducing the radiation from mobile phones into the human body by using a directive antenna is studied. The antenna analyzed is a Huygen's source, that is, a theoretical directive antenna consisting of an incremental electric dipole perpendicular to an incremental magnetic dipole. The relative power absorption is calculated for three different models of the human head. The simplest head model is a lossy dielectric half space, a somewhat less rough model is an infinitely long lossy cylinder of circular cross section and the most exact head model is a homogeneous lossy dielectric sphere. A comparison with a Hertzian dipole, i.e. an incremental electric dipole, at the same positions is done. The different head models are used in order to investigate to what extent it is possible to simplify the model of the human head while still getting useful results. The results show that the relative power absorption for the Huygen's source is substantially lower than that for a Hertzian dipole. When the antenna is placed 2 cm from a lossy dielectric homogeneous sphere of radius 10 cm, the relative absorption is 5 dB lower for the Huygen's source compared to a Hertzian dipole. It is also shown that when the antenna is placed close to the head, the results for the different head models are fairly similar, especially when the antenna is a Hertzian dipole.

The antenna and radome activities at Ericsson were initially related to the development of military airborne radar. Under Olof Dahlsjo's leadership, they also developed into other types of radar, as well as communications for ground, airplane, and space applications. The activity became world leading with a solid scientific foundation, examples of which are polarization-twisting, satellite antennas for scientific pro grams, and phased arrays. The latter were initially done together with the research group of Prof. Folke Bolinder at Chalmers, and several people from his group later started to work for Olof Dahlsjo.

A rotationally symmetric cellular phone with a monopole antenna is comprehensively analysed. The radiation efficiency is studied as a function of the size of the phone body and of the antenna length. Further, the possibility of shortening the monopole by coating it with a highpermittivity dielectric at the monopole is investigated. All calculations are performed both with and without a model of a human hand holding the phone. The Method of Moments is used for the simulations and the results are confirmed by measurements. A very good agreement is observed.

Recently it has been shown that so-called gap waveguides can be generated in the gap between parallel metal plates. The gap waveguides are formed by metal ridges or strips along which local waves propagate, and parallel plate modes are prohibited from propagating by providing one of the surfaces with a texture that generates an artificial magnetic conductor (AMC) or an electromagnetic bandgap (EBG) surface on both sides of the ridges or strips. The bandwidth of the gap waveguide is determined by the cut-off bandwidth of a parallel-plate waveguide where one surface has such a texture (and no ridges or strips). This paper studies the bandwidths (or stop bands) of such parallel-plate cut-offs when the AMC or EBG is realised by a metal pin surface, corrugations or a mushroom surface. It is shown that cut-off bandwidths of up to 4:1 are potentially available, and thereby similar bandwidths should be achievable also for gap waveguides.

This paper give an introduction to the concept of artificially soft and hard surfaces in electromagnetics. The soft and hard surfaces are defined from the boundary conditions of the E-field by an analogy with soft and hard surfaces in acoustics. The electromagnetic soft and hard surfaces have polarisation-independent boundary conditions (at the centre frequency), in contrast to a metallic conductor that has different boundary conditions for the tangential and normal components of the E-field. This makes the soft and hard surfaces desirable in many practical antennas, in particular when dual or circular polarisation is required. The soft and hard surfaces are realised by providing a metal conductor by an anisotropic surface impedance. This can be obtained by providing it with corrugations, or with a strip-loaded dielectric layer. The most known application of the soft surface is in hybrid-mode horns, more commonly known as corrugated horns. The corrugated "soft" surface is also often called "chokes" and used to reduce coupling and sidelobes in particular directions (e.g. choke-horn). The hard surface has only been known a few years. Two of the most important applications of the hard surface are described in the present paper. The first is to design hard horns which have very high aperture efficiency for application in cluster feeds and arrays. The second is to reduce scattering from masts or struts that block the aperture or radiation fleld of an antenna. The paper also describes how known calculation methods now are extended to analyse these types of loaded surfaces.

Resonators are traditionally characterised by their quality factor Q, which is inversely proportional to the relative bandwidth. Small antennas are often resonant, so they can be characterised by a Q, except for the fact that the correct quality measure of an antenna is the inverse Q, that is the relative bandwidth, rather than Q. Still, it has become common to study fundamental size limitations of small antennas in terms of a so-called radiation Q (or antenna Q). This study explains how this intrinsic radiation Q relates to: (i) the bandwidth-efficiency product of small single-resonance-type antennas, (ii) the gradual cut-off of spherical waves for wideband gradual-transition-type small antennas and (iii) the number of resonances needed to cover a certain frequency band for wideband cascaded-resonance-type small antennas. The study also introduces one intrinsic radiation Q for basic single TE and TM spherical mode sources, and another for combined TE and TM sources.

This study presents Green's functions of parallel-plate structures, where one plate has a smooth conducting surface and the other an artificial surface realised by a one-dimensional or two-dimensional periodic metamaterial-type texture. The purpose of the periodic texture is to provide cut-off of the lowest order parallel-plate modes, thereby forcing electromagnetic energy to follow conducting ridges or strips, that is, to form a gap waveguide as recently introduced. The Green's functions are constructed by using the appropriate homogenised ideal or asymptotic boundary conditions in the plane-wave spectral domain, thereby avoiding the complexity of the Floquet-mode expansions. In the special case of a single ridge or strip, an additional numerical search for propagation constants is needed and performed in order to satisfy the boundary condition on the considered ridge or strip in the spatial domain. The results reveal the dispersion characteristics of the quasi-transverse electromagnetic modes that propagate along the ridges or strips, including their lower and upper cut-off frequencies, as well as the theoretical decay of the modal field in the transverse cut-off direction. This lateral decay shows values of 50-100 dB per wavelength for realisable geometries, indicating that the gap waveguide modes are extremely confined. The analytical formulas for the location of the stopband of the lowest order parallel-plate modes obtained by small-argument approximation of the dispersion equation are also shown. To verify the proposed analysis approach, the results are compared with the results obtained with a general electromagnetic solver showing very good agreement.

The calculation of the equivalent admittance of a longitudinal slot radiating between baffles of finite height is discussed. A general method for analysis of waveguide slot antennas with arbitrary outer cross sections was introduced by Kildal et al. (1991). It was stated that, for large k/sub z/ values (wavenumber in z-direction), the slot cannot 'see' the environment around it and the problem can be considered equivalent to that of a slot radiating in an infinite ground plane. It is noted that, by using this concept, it becomes much easier to perform the inverse transform. To find the slot admittance, the H-field between the baffles is found by using a spectrum of 2-D solutions. An integral equation is then formulated and solved for the slot E-field. The equivalent shunt admittance of the slot is then calculated. The normalized 2-D field solution at the transverse location of the slot is shown as a function of k/sub z/ for an isolated waveguide slot radiating into three different outer geometries: in an infinite ground plane, between baffles of infinite height, and between baffles of finite height. >

Strip-loaded surfaces and corrugated surfaces can be efficiently analysed using asymptotic boundary conditions that are valid in the limit of vanishing strip and corrugation period, respectively. An even simpler boundary condition is obtained by assuming that the surfaces are ideally soft or hard. This corresponds to a curvilinear grid of quasi-parallel perfect electric conducting (PEC) and perfect magnetic conducting (PMC) strips of incremental width and period, referred to as a PEC/PMC strip grid. Such a simple model for soft/hard surfaces speeds up the design process and provides the proper object parameters under the ideal soft or hard conditions. After reaching the designed characteristics, one can study the bandwidth of realisations of the surface using the asymptotic boundary conditions and finally make a complete and detailed study of all characteristics of the realisations by including even the finite period of the strips and corrugations. The ideal PEC/PMC strip model is used here as an example applied to bodies of revolution (BOR) such as soft horns with transverse corrugations and hard horns with longitudinal corrugations. The longitudinally corrugated horn is not a BOR, but both the asymptotic boundary condition and the ideal PEC/PMC strip model make it possible to analyse it as a BOR with an anisotropic wall and this reduces the computer time enormously compared to a full wave analysis for a finite corrugation period. It is shown that the PEC/PMC strip grid can predict the radiation patterns well at the centre frequency, but the bandwidth cannot be determined.

The spherical reflector antenna of the Arecibo Observatory will be provided with a new dual-reflector feed. The author discusses how to synthesize this dual-reflector feed to provide an illuminated aperture with an elliptical shape. It is shown that an elliptical aperture can give 0.85 dB more gain than a circular aperture. >

An efficient code for the analysis of beam waveguides and multireflector antennas by PO (physical optics) integration is presented. In the ELAB PO-code, there is no restriction on the number of reflectors, each reflector can be numerically specified to any shape, and the reflectors may be plane or parts of ellipsoids, with elliptical contours. The code has been applied to analyze a beam waveguide with six reflectors. The computer time was 177 s on a CRAY supercomputer. A comparison is made with Gaussian multimode analysis. >

A longitudinally corrugated circular waveguide with dielectric-filled grooves of alternating depths is considered. The dispersion equation for determining the waveguide eigenmode parameters is derived for the small corrugation period. The waveguide is shown to support two quasi-transversal electromagnetic (TEM) modes, associated with each of the two frequencies at which the TEM condition is realised. Some features of these quasi-TEM modes are revealed. The potential performance of a dual-band conical horn is presented, and some future studies are discussed here.

Corrugated and strip-loaded soft surfaces are characterised in the same way the electromagnetic bandgap (EBG) surfaces are characterized, that is, in terms of the bandgaps in their dispersion diagrams. The strip-loaded surfaces are provided with metalised via holes, and both central and lateral locations of these are investigated. It is found that strip-loaded surfaces with vias have the same bandgaps as mushroom-type EBG surfaces of the same period. It is also found that the strip-loaded surface can be designed to have the bandgap appearing at lower frequency than the mushroom surface, by locating the vias at the edge rather than in the middle and by optimising the period of the vias along the strips.

For original paper see Ziolkowski and Kipple (IEEE Trans. Antennas Propag., vol.51, no.10, p.2626-40, 2003 October). The results of the commented paper are of no value for evaluating the performance of small antennas surrounded by double negative material. The characterizing parameter "radiated power gain" is misleading and turns out to be a relative input resistance rather than a gain.

Arrays of rectangular single and stacked-patch antennas embedded in a multilayer spherical structure are analysed using the spectral-domain approach and the moment method. The patch current is transformed to the spectral domain using the vector-Legendre transformation, which simplifies the analysis procedure since the electromagnetic field excited by one spectral source component has the same angular variation as the source. In order to avoid numerical difficulties appearing when analysing structures with large radius, a modified vector-Legendre transformation and normalized Legendre functions are defined and applied to the solution procedure. Furthermore, the asymptotic formulas for the field distribution of higher order spectral modes are implemented into the algorithm for calculating Green’ s functions. The effect of deviation from the spherical symmetry and the influence of the structure radius on self and mutual impedance are studied. A laboratory model is built to test different configurations of spherical patch antennas and to validate the developed program.

A six-monopole circular antenna array for use in a MIMO system is considered. The authors show how to calculate the embedded element patterns, both by classical analytical modeling and by the method of moments. Thereafter, these are used to calculate the radiation efficiency of each embedded element, correlation and diversity gain, as well as the maximum average capacity of the MIMO system when the array is located in a rich scattering environment. The theoretical value for the capacity is obtained by numerically distributing many plane wave sources statistically uniformly over 4/spl pi/, letting them illuminate the calculated embedded element pattern and using Shannon's capacity formula on the received wave amplitudes. The calculated results are compared with measurement in a reverberation chamber, representing a similar scattering environment. The agreement is good.

The asymptotic field expression, in the spectral domain, of a conducting patch on a multilayer dielectric substrate is derived. It is shown that the corresponding field solution in the spatial domain is equal to that of a patch in a homogeneous region with an effective permittivity. This allows the infinite double integral of the asymptotic part of the method of moments matrix elements to be computed in a homogeneous spatial domain. As a result, the computation time can be reduced considerably. It is shown that a spatial domain MoM code for conducting patches and lines in homogeneous regions can easily be modified to include a multilayer dielectric substrate by adding a correction factor to the matrix elements.

A finite element formulation combined with an asymptotic strip boundary condition is used for an analysis of the electromagnetic plane wave scattering from struts loaded with strips periodically displaced along the axial direction. The periodicity of the strips is supposed as being small when compared with the wavelength. The enforcement of this approximate boundary condition reduces the periodic vectorial problem to two coupled scalar finite element problems leading to an efficient numerical code.

The synthesis and analysis of a dual-reflector feed (DRF) for the radiotelescope in Nancay is presented. The telescope has an elongated spherical main reflector. The synthesis is done by geometrical optics (GO) based on the methods developed for the Gregorian feed of the radiotelescope in Arecibo. The DRF is diffraction-controlled in the vertical plane. Still, GO synthesis is possible by replacing the spherical reflector by an auxiliary one with an empirically determined shape in the vertical plane. The analysis is done by physical optics (PO) integration with the actual spherical primary reflector present. The results show that it is possible to correct for the spherical aberrations in the horizontal plane and to obtain a narrow diffraction-controlled beam in the vertical plane, as intended. The design is based on using corrugated sector horns as feeds. They provide high aperture efficiency of the telescope over the frequency band between 1-4 GHz. The sector horns have the same inner dimensions (height 28 cm, width 48 cm and length 30 cm), but the wall thicknesses are different due to the different corrugation depths.

We develop the Green's functions for different realizations of planar soft and hard surfaces by using the asymptotic boundary conditions and the spectral domain approach. The considered geometries are the ideal PEC/PMC strip surface, the strip-loaded grounded dielectric slab and the corrugated surface. In all cases the strips and corrugations are straight. The asymptotic boundary conditions are valid in the limiting sense, when the period of the strips or corrugations approaches zero. The developed Green's functions have poles corresponding to surface waves. These are of three types: an ordinary surface wave in the grounded dielectric slab propagating radially out from the source, a strip wave propagating along the strips of the strip-loaded dielectric slab and also along the strips of the PEC/PMC strip surface, and surface waves occurring due to the corrugated surface. The fulfillments of both the soft and hard boundary conditions are discussed in both the near and far field regions. The strip wave of the strip-loaded dielectric slab prevents the boundary conditions in the near-field from being fulfilled, and is thus undesired. The other two surface waves are needed in order to realize the hard boundary condition. This paper is done while Zvonimir Sipus was a Ph.D. Student at Chalmers University of Technology, Gothenburg, Sweden

The paper presents a study of some elementary antennas, such as a dipole, a waveguide aperture, a microstrip patch, a spiral and a helix, when they are mounted on a ground plane with circular corrugations acting as a soft surface. The results of both experiments and calculations are described. The latter have been done either by the uniform geometrical theory of diffraction (UTD) or by the moment method (MM), and are in good agreement with the measurements. It is found that the corrugated soft ground plane makes the radiation patterns of all the antennas more rotationally symmetric with lower sidelobe levels and lower crosspolarisation when compared to using a smooth conducting ground plane.

A compact flare angle controlled corrugated horn antenna with a 60° half beamwidth is optimised by using a moment method for bodies of revolution. The horn has corrugations with simple rectangular cross-sections and is excited by a smooth wall circular waveguide. The resulting 15 dB beamwidth varies by

A numerical parametric study is presented, of a circularly polarised square hard horn realised by dielectric-filled longitudinal corrugations. The horn is analysed as an open waveguide. The attenuation introduced by losses in the dielectric material is calculated from the characteristic equation of the modified TE/sub 10/ mode. The far field including radiation from the walls, is found from the electric vector potential. The attenuation, aperture efficiency and crosspolar sidelobe level are presented for different dielectric linings and waveguide sizes, and are compared with the performance of the smooth-walled horn.

An asymptotic theory is presented with which the reduction in aperture efficiency caused by diffraction from a subreflector edge can be calculated for any dual-reflector system. The theory is applied to conventional Cassegrain antennas, for which approximate analytical effieiency formulas are derived. These formulas show that subreflector diffraction may represent a significant efficiency loss even for subreflector diameters as large as 20 wavelengths. The formulas are used to obtain an optimum subreflector size which represents the best trade-off between losses due to subreflector diffraction and geometrical shadowing.

The feed efficiency, a first approximation to the aperture efficiency of a paraboloid or a conventional Cassegrain antenna, is used to define uniquely a combined E - and H -plane phase center of the feed pattern. A formula for numerical calculation of the combined phase center is presented, as well as theoretical results of the feed position tolerances and the efficiency loss due to differences in the principal plane phase patterns.

The first approximation to the aperture efficiency of a paraboloidal reflector antenna is called the feed efficiency. The factorization of the feed efficiency into subefficiencies which account for losses due to spillover, cross polarization, nonuniform aperture illumination, and phase errors is considered. The relations between the radiation patterns of circularly and linearly polarized feeds are also derived.

In the paper by V. Galindo-Israel and R. Mittra it is claimed that a dual shaped subreflector (DSS) feed can be used to upgrade the efficiency of classical Cassegrain antennas. In this comment it is shown that upgrading is not possible unless the diameter of the DSS feed is extremely large. In fact, if the Cassegrain antenna at Goldstone, CA, used as an example in the above paper, is fed by the DSS feed, the efficiency in X -band will be about the same as or less than if it is fed directly by an optimized scalar horn. The low efficiency is caused by diffraction. Instead, the efficiency can be upgraded by using a scalar horn with shaped lens.

In a symmetrical reflector antenna the feed system and its support struts block the aperture and thereby deteriorate the radiation characteristics. Simple design curves are presented for the efficiency reduction, the sidelobe levels, and the cross polarization caused by strut blockage. The results are obtained from an analytical study that includes the induced field ratio (IFR) of the struts. The most significant IFR values for struts with circular cross section are calculated and plotted in a way which makes them easy to use as design curves. The use of the design curves is demonstrated by an example. >

A study of the radiation characterisitics of the European Incoherent Scatter Association (EISCAT) cylindrical reflector antenna in Tromso Norway is presented. The radiation patterns are computed with attention given to such effects as blockage and reflection from the supports of the line feed as well as direct radiation from the feed. The computer programs are time-efficient and accurate. They are based on mathematical formulations given in this and three companion papers. The calculated patterns agree well with measured drift scans of the exterrestrial radio source Cassiopeia A.

The computer-aided optimization of a small five-wavelength diameter reflector antenna with a center-supported dipole-disk feed is described. The primary radiation is controlled by using a patented beamforming ring to give low cross polarization and low sidelobes due to spillover. The efficiency is maximized by controlling and taking advantage of the multiple reflections between the feed and the reflector. This has inspired the name "resonant reflector antenna." The gain from the feed reflector resonances is so large that it compensates almost completely for the about 1 dB loss due to center blockage of the aperture.

The element patterns of the circularly polarized line feeds for the spherical reflector in Arecibo are calculated, showing strong endfire radiation. The radiation fields of the line feeds are then obtained by adding up the contributions from all elements. The optimum excitation of the feed is found by an approximate stationary-phase solution of the radiation field. This shows that the element pattern gives a large phase contribution to the excitation, because of the finite diameter of the feed. If not corrected for, this phase error can cause losses up to 1.5 dB. The excitation is optimized further by cutting and trying. The validity of the analytical models is checked by calculation of the radiation pattern of the existing 96.6 ft 430 MHz feed. The excitation is modeled from measured phases along the feed. The calculated radiation patterns show good agreement with the measurements, including the phase errors and the dip in the center. By using the proposed new excitation it should be possible to increase the efficiency of the 96.6 ft feed by 0.7 dB and to increase the efficiency of the 40 ft feeds at higher frequencies by even more.