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In previous modeling works, the waveguide radiation in the free space is modeled using an infinite flange in aperture plan. In this paper, we propose a new formulation to analyze the radiation of twin rectangular waveguides in free space. Our formulation consists firstly in simulating the free space as rectangular waveguide and seeking the appropriate dimensions that do not affect scattering parameters. In the second step, we use the symmetry principle to reduce the coupling problem to single guide radiating in the free space. Moreover, for more simplification, we consider a concentric discontinuity to solve this latter. This approach is based on moments method combined to the generalized equivalent circuit method (MoM-GEC) in order to reduce the number of unknown problems and alleviate their computation. Obtained numerical results are presented and discussed. A good agreement with literature is shown and the boundary conditions are verified.

Open-ended rectangular waveguide is the elementary component for the millimeter wave’s propagation. Several kinds of design have been proposed (single, coupled, networked...) to be used to achieve several applications such as satellite communication, radar, medical systems, and geophysical applications [

In [

Some other authors have used the generalized network formulation, which is based essentially on the equivalence principle and MoM method. This formulation was applied to finite phased arrays [

There are many other methods which have been applied to solve the flanged waveguide problem. The correlation matrix method which is based on the energy conservation low has been applied in [

In [

Mongiado et al. [

In this paper, a new rigorous approach is proposed to model two opened waveguides radiating in free space. The concept consists, firstly, in using the symmetry principle to reduce structure to half, and simulate properly the free space by another rectangular waveguide. Secondly, it consists in studying electromagnetic coupling between these waveguides. For validity purpose, obtained results are compared to those in previous works, and good agreement is shown.

Basically, in electromagnetic study, problems are well described by Maxwell’s equations. But in order to alleviate their complexity, we always need to choose the appropriate method that can approximate environment and boundary conditions to compute it within a reasonable time [

In this paper, we propose a modular formulation, in other terms, we simplify the problem step by step.

As shown in

In the second time, we use the symmetry principle to reduce the number of NGs to one. Then, odd and even input impedance are determined respectively when we apply structures presented in

Finally, we propose to study the SG influence, and we will make sure that considered dimensions do not affect the results.

So, now the problem is reduced to study NG1 radiates in SG. For this, we present the new considered structure in

The excitation is brought back to discontinuity plan as a modal source of current, its value is the current density of the fundamental mode, and its internal admittance is

where

The modes contribution of SG is expressed in the discontinuity plane by admittance operator

where

Based on the equivalent circuit shown in

Using the equations system (4), we can write:

Then, we can deduce the current

Taking into account the expression

Applying the Galerkin’s method:

This equations system can be rewritten as:

where A is the excitation vector, and [y] is the admittance matrix:

By separating the admittance operators, we can rewrite [y] matrix as:

where the first term presents the projection of test functions on the evanescent modes of the same guide, and the second term their projection on the load operator.

Finally, we deduce the unknown problem:

Taking into account relations (8) and (12), we deduce the input impedance z:

And scattering matrix is given by:

where

To pass to total structure, we must replace

So, the total input impedance matrix

We note that z is the reduced matrix, and

The total scattering matrix

Here, the formulation gives us

In this section, we propose first a quantitative discussion about the radiation of a real opened waveguide (WR90) in the free space, in order to determine the appropriate model that simulates the free space. Second, we study the electromagnetic coupling between NG1 and NG2.

To set certain parameters of the problem, a convergence study is strongly recurred.

As shown in

First main target of this study is to determine the appropriate SG dimensions to simulate the free space. For this, we present in _{1} are respectively dimensions of SG and NG1.

We can consider that from D = 7d_{1} − 4.6λ there is no influence of SG on results. For a validation propose, we present in

The second main target of this study is to determine coupling effects between two NGs. For this we explore

We present in

At

Method | Re (S11) | Im (S11) | |S11| | E_{r} |
---|---|---|---|---|

Present method | 0.0768 | −0.2662 | 0.2771 | |

Serizawa, Hongo [ | 0.0713 | −0.2344 | 0.2450 | 13% |

Bird [ | 0.0706 | −0.2352 | 0.2456 | 12% |

Macphie [ | 0.0632 | −0.2403 | 0.2484 | 11% |

Baudrand [ | 0.0655 | −0.2709 | 0.2787 | 0.5% |

Mongiardo [ | 0.0803 | −0.2365 | 0.2498 | 10% |

We can notice that

If one considers the load operator

Moreover, we present the normalized electric field in the discontinuity plan, with

In this study, we apply a rigorous formulation based on MoM-GEC method to explore a radiation of twin open ended waveguides in the free space. The main idea is composed by two steps. First, we consider two waveguides with a simple concentric discontinuity in the propagation axis. One represents the radiating waveguide, and the other is the load waveguide; and we seek how this latter can properly simulate the free space. So, we determine its appropriate dimensions so that it no longer affects the scattering parameters. Second, we studied the electro- magnetic coupling between these two open ended waveguides and we present the electric field in the discontinuity plan. For a validation purpose, obtained results are compared to previous published works and boundary conditions are verified and a good agreement is shown. From the numerical results discussion, we can deduce that the load waveguide emulates the free space and no mismatch problem is shown from r = 7 and that the electromagnetic coupling for twin waveguides can be considered neglected from a coupling distance

AbdessalemKaddouri,MouradAidi,TaoufikAguili, (2015) A New Approach Based on MoM-GEC Method to Mutual Coupling Analysis of Symmetric Twin Waveguides for Antenna Applications. Journal of Electromagnetic Analysis and Applications,07,283-290. doi: 10.4236/jemaa.2015.712030