# Fractal Cardioid Slot Antenna for Super Wideband Applications
## 3 Experimental Results and Discussion  
The antenna is manufactured using a simple photolithographic process, with a small deviation from the desired dimensions. Figure 10. shows the produced antenna on an FR-4 substrate with a coaxial SMA connector [34] at the input of the CPW line, which is declared for frequencies up to 27 GHz. Figure 10: Realized fractal antenna in the form of a cardioid with overall dimensions of \(35\,\mathrm{mm}\times 47\,\mathrm{mm}\). Figure 9: Three-dimensional representation of the simulated radiation patterns. The antenna was measured using a vector network analyzer ANRITSU MS4647A. The reflection on the coaxial port of the antenna was obtained directly from the measurement results of the network analyzer. The maximum gain \(GR\) of the receiving antenna is obtained based on the Friis formula for the attenuation of free space:  
\[G_{R}=20 log_{10}d+20 log_{10}f+20 log_{10}4\pi/c-G_{T}-FSPL \tag{2}\]  
where \(FSPL\) denotes free space attenuation; \(d\) denotes distance in meters; \(f\) denotes frequency; \(c\) denotes the speed of light in a vacuum; \(GT\) denotes the gain of the transmitting antenna; and \(GR\) denotes the gain of the receiving antenna. A ridge-horn antenna was used as a transmitting antenna. The measured and simulated \(S_{11}\) parameters are shown in Figure 11.  
Some disagreement between measured and simulated results occur due to inaccuracies in manufacturing and because antenna simulations are performed without connectors. Moreover, the electromagnetic properties of a low-cost FR-4 laminate are not strictly controlled and may differ from one laminate board to another. In order to remove doubt about the influence of the SMA connector on an antenna reflection coefficient above 27 GHz, the simulation was performed with an ideal excitation (waveguide port) and then with an SMA connector [34]. It can be observed from Figure 11 that there are differences in the reflection coefficient above 20 GHz but the reflection coefficient is below \(-10\) dB with and without the connector. It is clear that the SMA connector, in this project, can be used up to 30 GHz without influencing the improvement of the reflection coefficient. Figure 12 shows the results of measurements and simulations of the gain calculated by expression (2). The gain was only measured up to 6 GHz because the transmitting antenna is declared in that band. The proposed antenna is compared with previously reported super wideband (SWB) antennas on FR-4 substrates in terms of operating bandwidth (BW), electrical dimensions and bandwidth dimension ratio (BDR). The results are shown in Table 1. The bandwidth  
Figure 11: Comparison of the measured and simulated reflection coefficients of the antenna with and without SMA connector. dimension ratio indicates how large the operating bandwidth is as a percentage per antenna electrical area unit [23]:  
\[BDR=\frac{BW_{\%}}{L_{f_{low}}\times W_{f_{low}}} \tag{3}\]  
where \(L_{f_{low}}\) represents the electrical length and \(W_{f_{low}}\) represents the electrical width of the antenna calculated at the lower-end of operating band that meets the \(-10\) dB return loss and \(BW_{\%}\) represents bandwidth in percentage calculated by the following formula:  
\[BW_{\%}=2\Big{(}f_{high}-f_{low}\Big{)}/\Big{(}f_{high}+f_{low}\Big{)}\cdot 1 00\% \tag{4}\]  
where \(f_{low}\) and \(f_{high}\) represent the lower and higher frequencies of operating bands, respectively. A larger BDR indicates that the designed antenna is smaller in dimension and wider in bandwidth. Figure 13 shows a comparison of simulated and measured radiation patterns in the E-plane and H-plane at the following frequencies: 1.8; 2.2; 2.4; 3.4, 5.8 and 10 GHz. \begin{table}
\begin{tabular}{c c c c c} \hline
**Reference** & **Freq.