# Parallel-Coupled-Line Bandpass Filter with Notch for Ultra-Wideband (UWB) Applications
## 3 Implementation of Notched Filter  
Since the specified UWB spectrum by the U.S. Federal communication commission covers a very large band, there are many existing radio signals with very narrow passbands that may produce interference with the UWB systems. Thus, the UWB bandpass filters should have the capability of rejecting those unwanted radio signals. To create a notched band filter to reject the unwanted radio signal that may appear inside the passband (such as a WLAN signal), a single stepped-impedance resonator was employed as illustrated in Figure 9. The stepped-impedance resonator contains two sections of low impedance separated by one element of high impedance. As demonstrated in Figure 10, the electrical length and the characteristic impedance of the low-impedance sections were defined by \(\theta_{L}\) and \(Z_{L}\). Moreover, the electrical length and the characteristic impedance of the high-impedance element were denoted by \(\theta_{H}\) and \(Z_{H}\), respectively. In order to determine the resonance frequencies of the stepped-impedance resonator, the following conditions should be met [21]:  
\[\theta_{0}=tan^{-1}\sqrt{K} \tag{10}\]  
where the impedance ratio of the stepped-impedance resonator is denoted by \(K\) and can be defined by (\(K=Z_{L}/Z_{H}\)). The entire electrical length for the stepped-impedance resonator is defined as follows:  
\[\theta_{SIR}=2(\theta_{L}+\theta_{h})=\pi/2 \tag{11}\]  
The impedance ratio \(K\) can be used to control the fundamental frequency and spurious resonance mode for the stepped impedance. For instance, when \(\theta_{H}=\theta_{L}=\theta_{0}\), the primary as well as the first spurious resonant frequencies (\(f_{0}\)) and (\(f_{s1}\)) are expressed as follows:  
\[f_{s1}=\left[\frac{\pi}{tan^{-1}\sqrt{K}}\right]f_{0} \tag{12}\]  
Figure 11 illustrates the microstrip layout of the UWB filter with a notched band. The length and width of the high-impedance part of the stepped-impedance resonator are defined by \(L_{h}\) and \(W_{h}\). In addition, the physical length and width of the low-impedance sections are represented by \(L_{L}\) and by \(W_{L}\), respectively. In order to produce the notch at a midband frequency ( \(f_{0}\)) of around 6.3 GHz to block the unwanted WLAN signal, the physical parameters for the stepped-impedance resonator were chosen to be as follows: \(W_{L}=0.95\) mm, \(L_{L}=1.7\) mm, \(W_{h}\)= 0.1 mm, \(L_{h}=4.1\) mm. The stepped-impedance resonator was folded for circuit size reduction as shown in Figure 11.  
Figure 12 depicts the EM-simulated performance (insertion loss) of the notched filter. The bandwidth of the notch can be controlled by the spacing (s) between the stepped-impedance resonator and the parallel lines section, as demonstrated in Figure 12. As can be noticed that the bandwidth is directly proportional to the spacing (s), which means increasing the spacing (s) extends the bandwidth and vice versa. For the purpose of producing a narrow notched band that has a fractional bandwidth (FBW) of approximately 5% at a 6.3 GHz mid-band frequency, the spacing (s) was selected to be 0.2 mm. The EM-simulated insertion (S21) and return (S11) losses of the microstrip layout, shown in Figure 11, for the presented bandpass filter with a notched band, is displayed in Figure 13. The presented filter exhibits a UWB passband with high selectivity, notched band, and wideband stopbands. Figure 14 demonstrates the current density of the proposed filter at  
Figure 10: The microstrip stepped-impedance resonator configuration. the transmission zeros, the notched band frequency, and the center frequency of the UWB passband. It can be noticed from the current distribution in Figure 14 that there was no transmission at the transmission zeros frequencies and the notched frequency. Figure 11: Microstrip layout for the filter with a notch. Figure 12: EM-simulated performance of the notch with various values of the spacing (s).