Comments on “Anomalous mutual coupling between microstripantennas” [and reply]

The paper by Haddad and Pozar (see ibid., vol.42, no.11, p.1545, 1994) contains important observations about the mutual coupling between printed antennas. It presented the oscillatory behavior of the mutual coupling between two printed dipoles as the separation between elements is increased. The authors used a closed form asymptotic Green's function to evaluate the mutual impedance between the elements. The oscillatory behavior of the mutual coupling is supposed to be a consequence of the interference between the surface waves and the space waves. The authors of the aforementioned paper stated that this behavior was previously unreported. Rosales here comments that the "anomalous" oscillatory behavior of the mutual coupling between microstrip antennas was in fact reported in a paper presented at the Ninth Computing Conference on the Computation of Electromagnetic Fields, and by Haddad and Pozar in their paper, almost simultaneously. The results and conclusions of both papers confirm each other. Haddad and Pozar reply to the Comment     

Analysis of finite arrays of axially directed printed dipoles on electrically large circular cylinders

Various arrays consisting of finite number of printed dipoles on electrically large dielectric coated circular cylinders are investigated using a hybrid method of moments/Green's function technique in the spatial domain. This is basically an "element by element" approach in which the mutual coupling between dipoles through space as well as surface waves is incorporated. The efficiency of the method comes from the computation of the Green's function, where three types of spatial domain Green's function representations are used interchangeably, based on their computational efficiency and regions where they remain accurate. Numerical results are presented in the form of array current distributions, active reflection coefficient and far-field pattern to indicate the efficiency and accuracy of the method. Furthermore, these results are compared with similar results obtained from finite arrays of printed dipoles on grounded planar dielectric slabs. It is shown that planar approximations, except for small separations, can not be used due to the mutual coupling between the array elements. Consequently, basic performance metrics of printed dipole arrays on coated cylinders show significant discrepancies when compared to their planar counterparts.     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function     

Mutual coupling between reduced surface-wave microstrip antennas

An investigation of the mutual coupling between reduced surface-wave microstrip antennas is presented and compared with that for conventional microstrip antennas. Numerical results are presented from a theoretical analysis of the mutual coupling along with confirming experimental results. It is shown that for electrically thin substrates, the space-wave coupling, not the surface-wave coupling, is predominant for typical element spacing, for both the conventional and reduced surface-wave antennas. In addition, the mutual coupling behavior is examined using an asymptotic analysis, which demonstrates how the coupling falls off much faster with patch separation for reduced surface wave antennas compared to conventional microstrip patch antennas     

Properties of a phased array of rectangular waveguides with thin walls

The radiation impedance of an infinite array of open rectangular waveguides has been calculated by a function-theoretic method forHplane and quasi-Eplane beam scanning directions. The mutual coupling between columns has also been obtained. The amplitudes of the coupling coefficients decay asymptotically asr^{-3/2}while the phase difference between successive coupling coefficients approaches that to be expected from free space wave propagation. This asymptotic behavior is independent of waveguide dimensions for both planes of scan. It is similar to the asymptotic behavior of a line-source-excited wave propagating over a lossy surface. This suggests that the interface between an array and free space may in general be treated as such a surface. The coupling coefficients are used to determine the properties of an array, which has a finite number of active elements surrounded by an infinite passive array. Also, the edge effect due to the finiteness of an array is evaluated.     

Asymptotic Green's function of a surface magnetic current elementon a perfect electric conductor plane covered by a lossy dielectricsubstrate

Published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical. This paper proposes exact analytical asymptotic expressions of the far-field Green's functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness. From these expressions, the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped-slot antenna structure can be calculated, provided the source distribution across the slot is known. The potentials used in the analysis are defined and their boundary conditions are expressed. The Helmholtz equation is solved in the Laplace domain and the solutions are transformed into the space domain using the inverse Hankel transform and steepest descent method. The influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions. The model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator     

Corner effects on the mutual impedance between edge slots

An analysis for calculating the mutual impedance between two edge slots in a linear slotted waveguide array is presented. The analysis uses a 90° wedge Green's function to account for the influence of the waveguide corners on the evaluation of the external mutual coupling. A novel asymptotic formula for the 90° wedge Green function's is derived to expedite the numerical analysis for slots with large separation. Numerical results show that the phase of mutual impedance retards linearly with slot separation and the magnitude decays as the separation is increased. However, the mutual impedance of edge slots is larger and decays more slowly than that of longitudinal slots or other slots in a large ground plane. The distinguished characteristics can be attributed to the energy guiding effect of the waveguide corners, which is discovered and verified mathematically and numerically. Also shown in the numerical calculations are the incremental conductances of the individual slots in a linear edge slot array, which are compared, and found to be in good agreement, with the available experimental data     

Efficient analysis of planar microstrip geometries using aclosed-form asymptotic representation of the grounded dielectric slabGreen's function

A newly developed closed-form asymptotic representation of the grounded dielectric slab Green's function is used in a moment-method formulation to calculate the propagation constant of an infinite microstrip transmission line and the input impedance of a finite-length, center-fed printed dipole. In these problems, source and field points are laterally rather than vertically separated with respect to the substrate. The conventional Sommerfeld integral and the plane wave spectral integral (PWS) representations of the microstrip Green's function converge very slowly in this case. However, the asymptotic closed-form representation of the Green's function does not have this limitation, and it remains accurate even for very small lateral separation between source and observation points. A modified form of the Sommerfeld integral representation is used only for observation points in the immediate vicinity of the source, while the asymptotic form is used elsewhere. Some numerical results based on this approach are presented and are shown to compare very well with previous results based on the corresponding exact-integral or PWS forms of the Green's function     

A dynamic model for microstrip-slotline transition and relatedstructures

An analysis of microstrip-to-slotline transition is presented. The method of moments is applied to the coupled integral equations. In the formulation, the Green's function for the grounded dielectric substrate, which takes into account all the radiation, surface wave, and substrate effects, is used. Meanwhile, all the mutual coupling effects are included in the method of moments solution. Certain related structures, such as slotline and microstrip discontinuities, a slot fed by a microstrip line, and a printed strip dipole fed by a slotline, can also be solved with this analysis. This approach may find applications to other related transitions in MIC (microwave integrated circuit) design     

A theoretical and experimental study of mutual coupling inmicrostrip antenna arrays

Each microstrip antenna element in the array is replaced by an equivalent magnetic current source distribution over a grounded dielectric slab derived from the electric field on the walls of the element as given by the cavity model. A dyadic Green's function is developed for a grounded dielectric slab, using the rectangular vector wave functions. The function is used to calculate the magnetic field due to the magnetic current distributions. The formula for mutual impedance based on the reaction concept is used to calculate the mutual coupling in arrays of antenna elements. Some measurements have been conducted for mutual coupling between two rectangular patches in the C-band. Calculated results are in excellent agreement with measurements, including those of other authors     

Measured mutual coupling between microstrip antennas

Mutual coupling betweenL-band rectangular, nearly square, and circular microstrip antennas has been investigated experimentally by a series of measurements of theS-parameters. The mutual coupling level decreases monotonically with increasing separation between elements with theE-plane coupling down 20 dB and theH-plane coupling down 25 dB for typical adjacent element spacings. For 1/16 in and 1/8 in substrates atL-band the predominant coupling mechanism is via the space wave since the surface wave is shown experimentally to be small.     

Input impedance and mutual coupling of rectangular microstrip antennas

A moment method solution to the problem of input impedance and mutual coupling of rectangular microstrip antenna elements is presented. The formulation uses the grounded dielectric slab Green's function to account rigorously for the presence of the substrate and surface waves. Both entire basis (EB) and piecewise sinosoidal (PWS) expansion modes are used, and their relative advantages are noted. Calculations of input impedance and mutual coupling are compared with measured data and other calculatious.     

An asymptotic closed-form representation for the groundeddouble-layer surface Green's function

An efficient closed-form asymptotic representation for the grounded double-layer (substrate-superstrate) Green's function is presented. The formulation is valid for both source (a horizontal electric dipole) and observation points anywhere inside the superstate or at the interfaces. The asymptotic expressions are developed via a steepest descent evaluation of the original Sommerfeld-type integral representation of the Green's function, and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points. The asymptotic solution is shown to agree with the exact Green's function for lateral distances even as small as a few tenths of the free-space wavelengths, thus constituting a very efficient tool for analyzing printed circuits/antennas. Since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena, it provides physical insight into the field behavior, as shown by examples     

Analysis of circular waveguide arrays on cylinders

An analysis is given of the mutual coupling effects in a finite array antenna of circular waveguide elements on a conducting cylinder. The array is described in terms of a scattering matrix and the multimode aperture fields of the elements are solved for by moment methods. Mutual coupling through wave propagation along the surface is treated according to GTD, since for most cases of interest the surface curvature is small in terms of wavelength. Appropriate asymptotic expansions for the magnetic field Green's function are derived for the two basic cases of an axial and a circumferential magnetic current element on the cylinder, the latter being a new case. The method, which allows the array elements to be nonuniformly spaced, applies to cylinders with radii>2lambdaand thus also includes planar arrays. Illustrative numerical examples and comparisons with infinite cylindrical and planar arrays are included.     

The RCS of a cylindrical array antenna coated with a dielectric layer

The scattering properties of dielectric coated waveguide aperture antennas mounted on circular cylinders are investigated. Both the single element antenna and the array case are treated. The array antenna consists of 4 /spl times/ 32 rectangular apertures placed in a rectangular grid on the surface of an infinitely long circular cylinder. The problem is formulated in terms of an integral equation for the aperture fields which is solved with the method of moments using rectangular waveguide modes as basis and test functions. An efficient uniform asymptotic technique is used to calculate the excitation vector and the backscattered far-field. The asymptotic solution is valid for large cylinders coated with thin dielectric layers away from the paraxial (i.e. near axial) region. A similar asymptotic solution is used to calculate the mutual coupling in the nonparaxial region. For the self coupling terms and for the mutual coupling in the paraxial region a planar approximation is used with a corresponding spectral domain technique. Numerical results are presented as a function of frequency, angle of incidence, cylinder radius, and electrical thickness of the coating.     

Efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders

An efficient and accurate hybrid method, based on the combination of the method of moments (MoM) with a special Green's function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders. The efficiency and accuracy of the method depend strongly on the computation of the Green's function, which is the kernel of the integral equation that is solved via MoM for the unknown equivalent currents representing only the antenna elements. Three types of space-domain Green's function representations are used, each accurate and computationally efficient in a given region of space. Consequently, a computationally optimized analysis tool for conformal microstrip antennas is obtained. Input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method.     

Scan blindness phenomenon in conformal finite phased arrays of printed dipoles

Scan blindness phenomenon for finite phased arrays of printed dipoles on material coated, electrically large circular cylinders is investigated. Effects on the scan blindness mechanism of several array and supporting structure parameters, including curvature effects, are observed and discussed. A full-wave solution, based on a hybrid method of moments/Green's function technique in the spatial domain, is used to achieve the aforementioned goals. Numerical results show that the curvature affects the surface waves and hence the mutual coupling between array elements. As a result, the array current distribution of arrays mounted on coated cylinders are considerably different compared to similar arrays on planar platforms. Therefore, finite phased arrays of printed dipoles on coated cylinders show different behavior in terms of scan blindness phenomenon compared to their planar counterparts. Furthermore, this phenomenon is completely different for axially and circumferentially oriented printed dipoles on coated cylinders suggesting that particular element types might be important for cylindrical arrays.     

A Generalized Spectral-Domain Green's Function for Multilayer Dielectric Substrates with Application to Multilayer Transmission Lines

A generalized full-wave Green's function completely defining the field inside a multilayer dielectric structure due to a current element arbitrarily placed between any two layers is derived in two-dimensional spectral-domain form. It is derived by solving a "standard" form containing the current element with two substrates on either side of it, and using an iterative algorithm to take care of additional layers. Another iterative algorithm is then used to find the field in any layer in terms of the field expressions in the two layers of the "standard" form. The locations of the poles of the Green's function are predicted, and an asymptotic form is derived along with the asymptotic limit, by use of which the multilayer Green's function can be used in numerical methods as efficiently as the single-layer grounded-dielectric-substrate Green's function. This Green's function is then applied to a few multilayer transmission lines for which data are not found in the literature to date.     

Minimising mutual coupling in thick substrate microstrip antennaarrays

A new method based on the reaction concept, is used to assess the mutual coupling experienced by two adjacent circular microstrip antennas on a thick substrate. The coupling owing to surface waves is separated out from that due to the direct radiation and the large interference effects exhibited by the former create deep nulls in the overall mutual coupling characteristic: the nulls being dependent on the given choice of substrate geometry and element separation distance. Finally, the application of this coupling minimisation technique to practical arrays having many elements is briefly commented on