Super High-Selectivity Fifth-Order Bandpass Filter with Twelve Transmission Zeros

A fifth-order bandpass filter (BPF) with super high selectivity using three pairs of coupled lines and two open stubs is proposed. Twelve transmission zeros (TZs) from 0 to 2f0 (f0 denotes center frequency of the passband) and five transmission poles (TPs) in the passband can be obtained to realize good out-of-band suppression and sharp roll-off skirts. For demonstration, a simple BPF prototype centered at 2.04 GHz is designed, fabricated with measured 3-dB fractional bandwidth of 18% and very high transition band roll-off rates of over 567 dB/GHz. Good agreement between the simulations and measurements validates the design method.


Introduction
High-selectivity bandpass filters (BPFs) with low insertion loss in the passband and high rejection in the stopband are drawing increasing attentions to meet the requirement of the modern wireless communication systems [1].Recently, some works have been reported on introducing transmission zeros (TZs) to improve the out-of-band suppression of BPFs [2][3][4][5][6][7][8][9][10][11][12][13].In [2][3][4], signal interference techniques have been invented for the generation of multiple TZs due to the construction of multiple transmission paths.In [5], a new source-load cross coupling type with both capacitive and inductive coupling is introduced to obtain multiple TZs for suppressing the undesired harmonics.Moreover, the concept of TZ resonator pair is proposed in [6], where four TZs are located at the resonant frequency points of the two resonator pairs.However, the lower stopband cannot reject very well because of its intrinsic limitation of the scheme.In [7], a BPF with four TZs using two open coupled lines and several stubs is proposed, where two TZs can be introduced with the help of the two shorted stubs to improve the frequency selectivity.
In this paper, a super high-selectivity fifth-order BPF using three pairs of coupled lines and two open stubs is proposed.Based on our previously reported work [8], two half-wavelength open stubs are loaded on the first and third pairs of coupled lines, respectively, to generate four more TZs at the out-of-band.Thus, the total number of TZs is increased to 12 at the frequency range from 0 to 2f 0 (f 0 is the required center frequency), which is the most number in the previously reported literature to the best of our knowledge.For demonstration, a filter example with center frequency of 2.04 GHz is fabricated, whose simulated and measured results are in good agreement to validate the design idea.

Proposed BPF Design
The ideal circuits of the proposed fifth-order BPF with twelve TZs, which consists of three pairs of coupled lines and two open stubs, is shown in Fig. 1.The middle (second) pair of λ g /4 coupled lines (even/odd-mode charac- Open stub Open stub teristic impedance Z 0e2 , Z 0o2 , electrical length θ) are connected to the first and third pairs of 3λ g /4 coupled lines (even/odd-mode characteristic impedance Z 0e1 , Z 0o1 , electrical length 3θ), and two λ g /2 open stubs are loaded on the first and third pairs of coupled lines, respectively.
Figure 2 shows the simulated S-parameter comparisons between the proposed BPF (i.e., BPF with open stubs) and the BPF in [8] (i.e., BPF without open stubs).As seen in Fig. 2(a), four more TZs (f tz2 , f tz5 , f tz8 , f tz11 ) can be introduced by adding the two open stubs, and their positions are mainly determined by the characteristic impedance of the open stubs Z 1 .For the previously generated eight TZs, the four TZs f tz1 , f tz4 , f tz9 and f tz12 keep unchanged whose positions can be expressed as More importantly, the positions of the two TZs f tz6 and f tz7 are closer to the passband than the ones of BPF without open stubs.Thus, the roll-off skirt of the passband will become sharper to further improve frequency selectivity.

Analysis of the Proposed BPF
This filter circuit can also be analyzed by using impedance matrix deduction similarly to the method in [8].From Fig. 1, we can obtain that [Z] a and [Z] b denote the impedance matrices of the 3λ g /4 and λ g /4 parallel-coupled lines, respectively.The overall impedance matrix [Z]' and TZs of the filter can be calculated as Finally, twelve finite TZs in the stopband at the frequency range from 0 to 2f 0 can be obtained through calculation by setting transmission coefficient S 21 = 0, where S 21 is expressed as For transmission poles (TPs), they can be calculated by setting reflection coefficient S 11 = 0, where S 11 can be expressed as Through calculation, five TPs can be obtained, as illustrated below The positions of these five TPs are the same as those of the BPF without open stubs.This result can also be verified from the simulation comparison as shown in Fig. 2(b).
In addition to the TPs and TZs, the concerned BPF characteristics mainly include the 3-dB fractional bandwidth (Δf), maximal out-of-band |S 21 | (T s ), maximal in-band |S 11 | (T p ) [4] and transition band roll-off rate (ξ ROR ) [14] referring to the responses in Fig. 3(a).Figure 3(b), (c) and (d) show the corresponding variations of Δf, T s and T p against the parameters Z 1 , k 1 and k 2 , respectively, where  As plotted in Fig. 3(b), T s and T p will both decrease but Δf will rise up when Z 1 increases.The maximum Δf will be 18.7% when Z 1 increases to 180 Ω under the return loss condition of over 10 dB within the passband.On the other hand, as k 1 increases in Fig. 3(c), T s will grow up slightly but T p will decrease and then rise up, while the bandwidth Δf will fall down directly.In contrast, as k 2 increases, T s will almost remain unchanged but T p will reduce and then go up, while Δf will rise up simultaneously as seen in Fig. 3(d).

Simulation and Measurement
Based on the above analysis, the final parameters of the designed ideal circuit model filter with center frequency 0.45 0.46 0.47 0.48 0.49 0.50 13  4 illustrates a verified physical layout of this wideband BPF as well as its photograph fabricated on the F4B substrate with relative permittivity of 2.65 and thickness of 1 mm, where the loss tangent of dielectric is tan = 0.006, the conductivity and thickness of copper conductor are 5.8  10 7 S/m and 35 μm, respectively.
The measured S-parameters are plotted in Fig. 5 along with the simulation using Ansoft HFSS for comparisons.The simulated lower and upper transition band roll-off rates are better than 567 dB/GHz, while the measured counterparts are also over 567 dB/GHz.Table 1 tabulates the performance comparisons of the proposed BPF with some previous works, and it can be seen that the presented study has enhanced transition band roll-off skirts to realize super high frequency selectivity with the most number of TZs.

Discussion
For the ideal BPF circuit model in Fig. 1, the performance of the passbands and lower/upper stopbands must be ideal with symmetrical curves as seen in Fig. 2 by using the theoretically mathematical calculation or commercial soft-ware simulation (e.g., Ansoft Designer or ADS).For the physically realized geometry such as the layout in Fig. 4, however, the simulated or measured results will be deteriorated due to many discontinuities at the corners of two connected microstrip lines or meandering lines in the fullwave electromagnetic simulation, compared with the theoretically calculated results.Generally, at higher frequency, the discrepancy between full-wave simulated results and theoretically calculated results will be larger than that at lower frequency in the circuit design as seen in Fig. 5. Therefore, it is reasonable that the simulated and measured results of the physically realized geometry are different with the simulation of the ideal BPF circuit model.The upper stopband rejection level is worse than the lower stopband rejection level.The work in [8] also has the same situation as seen in Tab. 1.

Conclusion
This paper has presented a compact super high-selectivity fifth-order BPF with twelve TZs using simple circuit structure.The design idea and calculations on TZs and TPs are also provided.Due to its sharp roll-off skirts, multiple TPs and TZs, and ease of fabrication and integration with other circuits, the proposed BPF is promising in application of modern wireless communication systems.
04 GHz are taken as: