## 3 Results and Discussion  
In this paper, the T-shaped resonator is coupled to the basic ultra-wideband filter and the L-shaped defect microstrip structure is realized by etching an asymmetric L slot line whose width is \(W_{7}\). The T-shaped resonator is comprised of short-stub (\(L_{5}\), \(W_{5}\)) and open-stub (\(L_{6}\), \(W_{6}\)) with equal length and width (\(L_{5}=L_{6}\), \(W_{5}=W_{6}\)) so that the impedance ratio (\(K=Z_{2}/Z_{1}\)) only depends on their electrical length. The final size of the filter is optimized by using HFSS with 0.1 GHz sweep step. Optimized design parameters of the proposed ultra-wideband filter is given in Table 2. The simulated and fabricated results proved that the first notched band is adjustable by the parameters (\(g_{1}\), \(L_{6}\) and \(W_{6}\)) of the T-shaped resonator, while the second notched band is controlled by the parameters (\(L_{7}\), \(L_{8}\) and \(W_{7}\)) of the L-shaped defect microstrip structure. The simulation results of the T-shaped resonator and L-shaped defect microstrip structure is given in Tables 3 and 4. It can be concluded that the lower frequency notched band with a 3-dB bandwidth of 1.07 GHz was generated by the T-shaped resonator, and the higher frequency notched band with a 3-dB bandwidth of 0.61 GHz was realized by etching the L-shaped defect microstrip structure. It can be seen that the first notch band has a fractional bandwidths (FBW) of about 15.47% and the second notch band has a FBW of about 8.76%. Moreover, the measured results show that the dual notched bands are observed at 3.5 and 7.5 GHz with the rejection level of 25.2 dB and 17.3 dB, with a fractional bandwidths (FBW) of 15.91% and 9.63%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Notch Frequency (GHz)** & **3 dB Bandwidth (GHz)** & **Fractional Bandwidths (FBW) \%** & **Rejection Level (dB)** \\ \hline
3.5 & 1.09 & 15.91 & 25.2 \\
7.5 & 0.66 & 9.63 & 17.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized design parameters of the proposed ultra-wideband filter (The units are mm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Length** & **Length** & **Width** & **Width** & **Radius** & **Gap Length** \\ \hline \(L_{1}=15\) & \(L_{5}=5.3\) & \(W_{1}=1.95\) & \(W_{5}=0.5\) & \(R_{1}=0.15\) & \(g_{1}=0.1\) \\ \(L_{2}=5\) & \(L_{6}=10.6\) & \(W_{2}=3\) & \(W_{6}=0.3\) & \(R_{2}=0.15\) & – \\ \(L_{3}=4\) & \(L_{7}=9\) & \(W_{3}=0.3\) & \(W_{7}=0.1\) & – & – \\ \(L_{3}=4\) & \(L_{8}=0.1\) & \(W_{4}=1.4\) & \(W_{8}=0.3\) & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results of the dual notched bands. Figure 7: The photograph of the fabricated filter. Figure 8a shows the examination photo of the fabricated filter by Vector Network Analyzer Plannar 804/1 (Copper Mountain Technologies, Indianapolis, IN, USA) with the frequency range of 8 GHz. The simulation data and the measured data are imported into the Excel form, and the comparison between the simulation results and the measured results is drawn by Origin software (OriginLab Corporation, Northampton, MA, USA) as shown in Figure 8b. According to Figure 8b, the measured insertion loss is lower than 1.2 dB and the reflection coefficient is higher than 15 dB over the ultra-wideband passband. The measured and simulation results have the same resonant frequencies. The equivalent model of resonant elements composed of the T-shaped resonator and L-shaped defect microstrip structure is proven to be correct by the consistent resonant frequencies. Figure 9 illustrates the proposed filter performance with different parameters (\(g_{1}\), \(L_{6}\), \(W_{6}\)) of the T-shaped resonator. Figure 9a depicts that the proposed filter performance is adjusted by changing L6 of the T-shaped resonator under the condition of \(L_{6}\) = 2\(L_{5}\). As \(L_{6}\) increases from 9.4 to 10.6 mm, \(f_{01}\) decreases from 4 to 3.5 GHz, while \(f_{02}\) is still 7.5 GHz. It can be derived from the Equations (4) and (5) that this leads to the decreasing of \(f_{01}\).