## 4 Design and Measurement
Take the dimensions, i.e., a, b, and g, if the simulated circuit exhibits the required preferable S-parameters, i.e., \(S_{21}\) at the attenuation pole location is less than \(-20\) dB. Therefore, to achieve the required parameters of the DGS section, i.e., a, b and g, a separate EM simulation was performed on the transmission line, TL2, of length \(2*l_{2}\), as shown in Figure 9, to get the approximate values of a, b, and g from the preferred results, as shown in Figure 8. Figure 9 shows the photographs of the fabricated one-pole Butterworth low-pass filter designed at 3 GHz with the DGS section under the TL2 microstrip line of length \(2*l_{2}\) for the approximation of the physical dimensions of the DGS section. The preferred isolation between Ports 2 and 3 is more than 20 dB, and the proposed WPDs are designed at 3 and 2 GHz. Therefore, to achieve this target, an equivalent low-pass filter with a dumbbell-shaped DGS etched in the ground plane below the transmission line TL2 of length \(2*l_{2}\) needs to be designed for each WPD. The dimensions a, b and g of the DGS are changed iteratively until the \(S_{21}\) is \(<\)\(-20\) dB. The preferred \(S_{21}\) of both WPDs are obtained, as illustrated in Figure 8. The figure shows that the \(S_{21}\) parameters of both WPDs are in the order of approximately equal to or more than \(-20\) dB. Hence, these results can be taken as adequate reference points for the preferred attenuation poles and  
Figure 7: Simulated S-parameters results of the proposed circuit with different substrates. the cutoff frequencies. The dimensions a, b and g of the DGS section are obtained from this EM simulation. To get the parameters of the DGS sections, Figure 8 clearly shows that the resonant frequency or attenuation pole location and cutoff frequency are 3 and 1.5 GHz, respectively, for WPD designed at 3 GHz and 2 and 1 GHz, respectively, for the WPD designed at 2 GHz. Thus, the approximated values of the preferred resonant frequency and cutoff frequency were plugged into Equations (14) and (15) to obtain the values of Capacitance and inductance of an equivalent circuit of the DGS for each divider. To achieve the required cutoff frequency and attenuation pole at a certain frequency, the simulation result should illustrate the characteristics of both low pass and bandstop filter responses simultaneously. To make an effective guess for the initial dimensions of the DGS section, this phenomenon is crucial, i.e., as the etched area, i.e., \(a\times b\) increases, the cutoff frequency and attenuation pole location move to lower frequencies. Although the variation in the gap distance g results in no change in the cutoff frequency, as the gap distance increases, the location of the attenuation pole shifts to higher frequency [14]. Thus, to attain the preferred result, these approximations are very helpful and are handy to tune and comprehend the best  
Figure 8: Simulated S–parameters results of the DGS sections for the approximation of the physical dimensions. Figure 9: Photographs of the fabricated one-pole Butterworth low-pass filter designed at 3 GHz with the DGS section under the transmission line of the length \(2*l_{2}\) for the approximation of the physical dimensions a, b and g of the DGS section. possible effect of each step. The calculated values of the equivalent lumped elements of the equivalent DGS circuits and their respective physical dimensions are shown in Table 3 for both WPDs. To check the validity of the proposed design technique, ANSYS High Frequency Structure Simulator (HFSS) was used. The design values and dimensions for the proposed circuit are calculated and entered using the values in Table 2, and S-parameter simulation was applied to the proposed circuits. The equivalent LC resonant circuit of the dumbbell-shaped DGS section and the isolation resistor were inserted between the TL2 transmission lines, as shown in Figure 10, to achieve an acceptable isolation.