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Wave Iterative Method (WIM) is a numerical modeling for electromagnetic field analysis of microwave circuits. Theories of transmission line, four terminal network and boundary condition are applied to developing WIM simulation that the physical electromagnetic wave is described to a mathematical model using GUI function of MATLAB. In applying, the microstrip patch antenna was analyzed and implemented. The research result shows that the WIM simulation can be used correctly to analyze the electric field, magnetic field theory and return lose of sample patch antenna. The comparison of the WIM calculation agrees well with the measurement and the classical simulation.

Presently, numerical methods are important for scientists, engineers and researchers. The development and research are necessary for technical problem solving [

The WIM concept based on iterative method is to calculate amplitude and direction of incident wave, reflected wave and transmitted wave in the multi-layers planar structure. The electric field, magnetic field and network parameters of equivalent circuit are results that we want to solve and display.

Transmission line is represented by equivalent circuit, as shown in _{in} and I_{in} are the voltage and current variables at the input ports,

Considering the input port, as shown in

The relation equation base on the incident wave (A) and reflected wave (B) is presented by

and

where

Then, the input voltage and current equation can be written as

Rewrite the equations in the form of an electric field and current density that are as

Equation (9) and (10) are the electric field and current density (or magnetic field) in following the wave equation. The variable A (incident wave) and B (reflected wave) are the key parameters used in the WIM algorithm.

Considering, the scattering parameter (S) of a two ports network as shown in

The S parameters defined by the incident and reflected wave are expressed as

where A_{n}, B_{n} are the wave variables and

The parameters variable S_{ii} is called the reflection coefficients at port_{ij} is the transmission coefficients of two ports network, where

Wave propagation described by incident, reflected and transmitted waves is represented in the planar structure. We see that the waves will be reflected continuously, as shown in

In iterative procedure, the excited wave

dielectric region (i) 1 and 2, the wave

The WIM procedure, as shown in

1) Define the excited wave

2) Convert the waves in the real domain to the spectrum domain by the FFT:

3) Apply the reflection coefficient

4) Transform the waves in the spectrum domain to the real domain by the IFFT:

5) Calculate the reflected waves using the scattering parameters of planar circuit:

6) Repeat step 2 to step 5 until the convergence of the network parameters are obtained.

After testing the convergence at the k iterations, the tangential electric field and current density in the discontinuity using Equations (9) and (10), can be written as

Thus, the admittance parameter of two ports network are obtained as

also, the impedance parameter can be written as

Finally, the scattering parameter of planar circuit is given by

The detail of mathematical operator in the WIM procedure, as shown in

The excited wave

where

For simplify the calculation of the generalized TE_{m}_{,n}, TM_{m}_{,n} mode wave description, the Modal FFT pair permits movement the transverse filed components from the real domain to the spectrum domain, the modal wave equation in x direction can be defined as

And also, the equation in y direction is defined as

Thus, the modal transform matrix using WIM algorithm can be represented as

Similar, the Modal IFFT pair permits movement the modal filed components from the spectrum domain comeback to the real domain, the spatial wave equation in x direction can be defined as

And also, the wave equation in y direction is defined as

Thus, the spatial wave matrix using WIM algorithm can be represented as

where

The expression of reflection coefficient at the upper and bottom side of box in the spectrum domain is given by

where the TE_{m}_{,n}, TM_{m}_{,n} mode admittances in the metallic box are

At the printed surface of the discontinuity, the boundary conditions of fields, as shown in

Case 1, on the metal regions (M), we have the condition;

Case 2, on the dielectric regions (D), we have the conditions;

Case 3, on the planar source regions (P), we have the condition;

where E_{0} refers the excited electric field and the Z_{0} refers the source internal impedance, and

Finally, at the planar circuit in the real domain, the scattering parameters of wave equation are summarized on each printed surface region using Equations (23)-(25). The wave relation equation can be expressed as

where

When considering the condition of each region, on the dielectric region:

Computer aided design based on a graphical user interface (GUI) function of MATLAB^{®} is developed using the Wave Iterative Method (WIM) algorithm. The WIM scheme consists of four parts as 1) setup the initial values, 2) design the patch antenna structures, 3) calculate the waves propagated in the spectrum (Modes) and real domain (Pixel) using WIM algorithm, and 4) analysis the network parameters and electromagnetic distributions. The WIM simulation process can be presented in

The WIM simulation applied to simple patch antenna works in the following steps.

1) Start the WIM simulation program base on GUI function of the MATLAB, as shown in

2) Setup the usable values of calculation by using the “Setup” menu such as; operating frequency, desired printed circuit, dielectric constant value, characteristic impedance, etc.

3) Select the “Analysis” menu to design the microstrip patch antenna parameters using conventional antenna theories approach [

4) Select the “Scattering” or “Impedance” or “Admittance” menu to calculate the scattering parameters of two ports network using the WIM algorithm for designed antenna analysis, an example is shown in

5) Select the “E- Field” menu to represent the electric field distributions using the WIM algorithm on the printed interface of planar circuit, as shown in

6) Select the “H- Field” menu to represent the magnetic field or current density distributions using the WIM algorithm on the printed interface of planar circuit, as illustrated in

7) Select the “Exit” menu to quit form the program.

An example of simple microstrip patch antenna is presented using the electromagnetic simulation base on the proposed Wave Iterative Method (WIM) algorithm. In this topic, we will introduce an antenna design tool, an efficiently WIM simulated results to compare to the IE3D software and measurement.

The optimal parameters of the simple microstrip patch antenna are designed at 1.8 GHz operating frequency. The FR4 printed board was implemented with the relative permittivity

dielectric layer is 1.6 mm ., The analyzed results using the WIM simulation program can be obtained correctly to compare the conventional antenna theories approaches [^{2}, as shown in

The simulation program has been developed using the WIM algorithm. Determination of the input E-filed of source excitation on the planar circuit, the computing electromagnetic field distribution will be propagated gradually on the planar structure. The evaluation of the electric and magnetic field distributions in term of iteration number at 1, 5, 10 and 200 rounds is appeared on the antenna structure, as shown in

In the order to confirm the efficiency of the WIM simulation to compare the IE3D software and measurement, we will analyze and measure the return loss of the simple patch antenna using the N5230C network analyzer of

Agilent Technologies, as shown in

The WIM simulated result of return loss of the designed patch antenna as shown in

We have demonstrated the full wave analysis based on the developed Wave Iterative Method (WIM) algorithm to analyze the simple microstip patch antenna. The novel WIM algorithm can provide a reasonably good approximation to the correct values of circuit parameters, and its accuracy is dependent on usable pixel size and mode number. Additionally, this algorithm has the advantage of representing the electromagnetic field on circuit structure. Finally, the contribution in this paper indicates the development of the novel WIM algorithm based on iterative method that can be used to analyze effectively in arbitrarily inhomogeneous region formations.

In the future, the proposed WIM algorithm will be also applied to MMICs, various planar circuit structures, passive circuit in the waveguide, and the electromagnetic solving for EMI/EMC problems.