Five-order Equal Ripple Wideband Bandpass Filter with Minimized Variation in Group Delay

Equiripple design of low‐pass filter using stub‐loaded Z‐shaped coupled‐line section

“…The TFs in Table 1 are similar to those in [8,9]. Therefore, a similar design approach can be employed to demonstrate the filtering performance.…”

“…Therefore, a similar design approach can be employed to demonstrate the filtering performance. Here, the field of definition (x) is [−1, 1], much narrower than that (−∞, +∞) in [8,9], which brings a challenge in function matching. Since θ varies in [0, 2π], the cut-off frequency (x c ) or angle (θ c ) must be smaller than 1 or π/2 to realize an LPF.…”

“…Naturally, the solved impedance set, as well as the circuit response, depends on the selection of x ri . In other words, there is a new design freedom as in our previous works [8,9]. Without loss of generality, the first ripple x r1 is employed here for solving (6).…”

“…Coupled lines can be widely found in microwave-distributed circuits [1], such as filter [2][3][4][5][6][7][8][9], coupler [10][11][12], phase shifter [13,14] and impedance transformer [15][16][17], due to its controllable coupling strength and ease of planar implementation [1]. In practical circuits, coupled lines appear generally as 'sections', which can be categorized by the number of ports, connecting topology, and ending condition [18].…”

“…Figure 1 illustrates the three mostly used CLSs for a filtering application. The first two can be widely found in bandpass filter designs from narrowband [2] to ultra-wideband [3,[6][7][8][9]. The third is well known as the Schiffman unit [13], which can be used for phase equalization [14] or coupling enhancement [12].…”