# A Novel Wideband Splitter for a Four-Element Antenna Array
## 4 Achieved Results and Discussion  
To estimate the parameters of the proposed power splitter, simulations were carried out in the MATLAB environment as well as using free-to-use software calculation tools for coplanar microstrip structures and their parameters [25; 26]. Based on a detailed analysis of the power splitter circuit, an analytical model was programmed in the MATLAB environment. The programmed analytical model in MATLAB allows for the calculation and verification of all important characteristics of the proposed antenna splitter. The analytical model created in MATLAB will be made available on Matlab Central File Exchange ([[https://www.mathworks.com/matlabcentral/fileexchange/](https://www.mathworks.com/matlabcentral/fileexchange/)]([https://www.mathworks.com/matlabcentral/fileexchange/](https://www.mathworks.com/matlabcentral/fileexchange/)) (accessed on 1 January 2020)). The model mainly concerns the calculation of the frequency dependence of the following quantities:  
Figure 3: Manufactured prototype of the proposed antenna splitter: (**a**) manufactured board; (**b**) final splitter in the shielding case. * A transmission coefficient for segment A;
* A transmission coefficient for segment B;
* A phase error between segments A and B. The calculation of these parameters was carried out based on input data. The essential input data for the correct calculation include:  
* The physical length of the used transmission lines;
* The frequency dependence of the attenuation of the used transmission lines;
* The speed of propagation of the electromagnetic waves at the used transmission lines;
* The impedance of the coupling elements;
* The mutual arrangement of the splitter structure and shielding cover. In the first step, the characteristic impedances \(Z_{0s}\), \(Z_{0a}\) and propagation constants \(\gamma_{s}\), \(\gamma_{a}\) of the used transmission lines were calculated. Since the proposed splitter is a passive reciprocal structure, the principle of reciprocity can be used for the required circuit analysis. The power source drives of the output port 5 and the response quantities on input ports 1 to 4 were analyzed. In accordance with the previous consideration, the parameters of the first fictive source, i.e., the internal voltage \(V_{f1}\) and internal impedance \(Z_{f1}\), located at the output of the asymmetrical transmission line, were calculated. Subsequently, it is possible to estimate the parameters of two fictive sources that are located in the individual antiphase segments:  
\[V_{f2A}=\frac{V_{f1}\times A}{2\times(Z_{Ca}+0.5\times Z_{f1}+A)}, \tag{2}\]  
\[V_{f2B}=\frac{V_{f1}\times A}{2\times(0.5\times Z_{f1}+A)}, \tag{3}\]  
\[V_{f2A,B}=Z_{C}+\frac{1}{B}. \tag{4}\]  
The quantities A and B in the equations above are artificial coefficients. These coefficients depend on the impedances \(Z_{f1}\), \(Z_{0s}\), \(Z_{c}\), and \(Z_{0}\), and are related to the division of voltage in the individual parts of the proposed structure. Subsequently, it is possible to calculate the voltages at the output load impedances. The voltage \(V_{12}\) for the first segment, i.e., the transmission line for port 1 and port 2, and voltage \(V_{34}\) for the second segment, i.e., the transmission line for port 3 and port 4, can be calculated as follows:  
\[V_{12} = \frac{V_{f2A}\times Z_{0}}{Z_{0}+Z_{f2A,B}}, \tag{5}\] \[V_{34} = \frac{-V_{f2B}\times Z_{0}}{Z_{0}+Z_{f2A,B}}. \tag{6}\]  
Based on the equations above, it is subsequently possible to calculate the scattering parameters for individual antiphase elements of the proposed splitter. In order to verify the design of the proposed splitter simulations, measurements were performed at the prototype of the proposed splitter. The results achieved in both the simulations and measurements of the proposed splitter are shown in the following figures.