# Parallel-Coupled-Line Bandpass Filter with Notch for Ultra-Wideband (UWB) Applications
## 2 UWB Filter Design and Analysis
The electromagnetic simulated behavior for the parallel lines section with and without short-circuited stub is demonstrated in Figure 3.0 It can be noticed that the three parallel lines section without adding the stub exhibited a  
Figure 3.1 Microstrip structure for the presented UWB bandpass filter. Figure 3.2 Circuit model for the presented UWB filter without a notched band. passband with only a single transmission zero at the DC and a second transmission zero at double the midband frequency. For the purpose of enhancing the performance of this type of structure and to achieve a very high selectivity, more sections are required, which will increase the filter circuit size. Alternatively, a single shorted stub can be added at the end of the midline of the parallel lines section to exhibit two additional symmetric transmission zeros in the rejection bands and close to the passband boundaries as displayed in Figure 3.3 In order to locate the two transmission zeros at \(2.6\) GHz and at \(11\) GHz, the physical dimensions for the shorted stub parameters were selected as follows: \(W_{s}=0.4\) mm, \(L_{s}=4.2\) mm. As a result, an ultra-wideband passband with very high selectivity was obtained. The two transmission zeros not only increased the selectivity of the passband, but have also extended the rejection bands efficiently, as shown in Figure 3.4 At the upper rejection band, there is another additional transmission zero which is symmetrical to the transmission zero nearby the upper side of the passband. This transmission zero widened the upper rejection band effectively. Hence, the presented UWB filter with only one section of three parallel-coupled lines attained sharp passband skirts and wide rejection bands. As an advantage, the proposed filter achieved a very compact circuit size, which makes this filter attractive for filter design engineers. In order to minimize the physical circuit size of the presented UWB microstrip filter, the short circuit stub was folded, and its length and width were optimized in such a way that does not cause any unwanted coupling with the parallel-coupled line. The final microstrip layout of the presented UWB filter with folded stub is displayed in Figure 3.5 Figure 7 demonstrates the simulated insertion loss (S21) and return loss (S11) of the proposed microstrip filter. The insertion loss was better than \(25\) dB at the lower rejection band and more than \(15\) dB at the upper rejection band. The return loss showed four poles inside the desired passband with more than \(-15\) db. One advantage of adding the short-circuited stub is the control of the bandwidth of the bandpass filter. This can be achieved by changing the value of the characteristic impedance of the short-circuited stub without changing the other parameters of the coupled lines. Figure 3.6 Frequency response for the three parallel lines section without and with shorted stubs. Figure 3.7 The microstrip layout of the presented UWB bandpass filter with a folded stub. Figure 8 depicts the simulated insertion loss (S21) with different values of the characteristic impedance of the short-circuited stub. As demonstrated in Figure 8, the pair of transmission zeros at the lower and upper rejection bands can be generated at precise frequencies by changing the value of \(Z_{s}\). As can be noticed, the bandwidth is directly proportional to the value of the characteristic impedance of the shorted stub where higher impedance provides larger bandwidth and vice versa.