Miniature filters are essential for wireless communications systems although they often suffer from limited rejection bandwidths. However, through the use of a modified coupling structure for harmonic suppression, it has been possible to design a dual-mode filter capable of wide rejection bandwidth and 20-dB rejection through 8.5 GHz.

A number of dual-mode filters^{1-4} have been developed based on microstrip square loop resonators.^{5-7} The main drawback of these kinds of filters is the limited rejection bandwidth introduced by higher-order resonance of the microstrip loop resonators. Three techniques are often used to suppress harmonics in a microstrip loop-based filter. One is by using slow-wave structures to move the parasitic passband.^{8-10} The other two methods are by adding frequencynotched structures such as spur-line or defected ground structures at the input/output lines^{11-15} and using modified ring resonators with characteristic mode suppression or transmission zeros.^{16-20} However, these techniques add size and loss due to the additional circuit elements. Several improved coupling structures enhance coupling strength and reduce the insertion loss for single-mode and dual-mode resonators or filters.^{23-25}

* Figure 1(a)* shows the geometrical configuration of a square-loop resonator with conventional line-to-ring coupling structure. Theoretically, there are two second- order resonant modes in a side-coupled loop resonator, with orthogonal field distributions.

^{26}But for a resonator with coupling structure shown in

*, only one of the two modes, the transverse magnetic TM*

**Fig. 1(a)**_{210e}mode, will be excited. This mode has four electric field maximums at the middle of each side line of the square loop. The other mode, the TM

_{210m}mode, having four electric field maximums at the four corners of the loop, is suppressed due to the symmetry of the coupling structure with respect to the feed line. To suppress both modes, the conventional coupling structure is modified by bending and extending the coupling arms to form a pair of parasitic resonators

*; second harmonics can be suppressed by tuning open stub length, L*

_{s}.

* Figure 1(c)* shows another improved version of the coupling structure, where the bent coupling arms are placed inside the resonator with the input/output lines connected to the coupling arms by via holes. Based on these two line-to-ring coupling structures, a modified coupling structure was developed by rearranging the coupling arms

*. Resonators with different coupling structures were simulated on a substrate with a thickness of 0.635 mm and a relative dielectric constant of 10.2. The fundamental resonant frequency is assumed to be 3.4 GHz. Due to the resonant condition of these coupling structures, most of the energy transferred from the input port is concentrated in the coupling structure and little energy is transferred into the loop resonator. As a result, harmonic resonances at the resonant frequency are suppressed*

*.*

**(Fig. 2)***shows the differences in harmonic suppression of these different coupling structures. Due to its shorter coupling length, the resonator of coupling structure (c) achieves a slightly wider stopband compared to structure (b). For the resonator of the modified coupling structure, the coupling length is one-half that of (b).*

**Figure 3** The modified coupling structure in * Fig. 1(d)* was adapted to the design of a dual-mode filter (DMF)

*. A small square patch was attached to an inner corner of the loop for exciting and coupling a pair of degenerate modes. A dual-mode filter with conventional line-to-ring coupling structure was also designed for comparison*

*. These filters were fabricated on the same substrate described by the simulation of the resonators, and with the same loop dimension as the single-mode resonators. By tuning Ls, second-order harmonics can be effectively suppressed*

*. Because the coupling lines are arranged asymmetrically with respect to the feed lines, both of the second-order resonant modes will be excited at different frequencies when the stub length is not properly tuned*

**(Fig. 5)***. Thus, the stub length should be optimized to suppress both second-order resonant modes. The dimensions of the perturbation element, coupling gap, stub length and feed line offset can be optimized for different fractional bandwidths together with second-order harmonic suppression.*

**(Fig. 5)***shows simulated frequency responses for filters with different dimensions, with values for the filters listed in the table. For the same dimension of coupling gap s and nearly equal coupling length, the modified filter shows lower insertion loss and wider bandwidth. This is because the bent coupling lines with offset position enhance the coupling strength in the resonant mode. To get the same bandwidth as the dual-mode filter with modified coupling (filter 4), the gap distance s in a conventional filter must be less than 0.1 mm, at the limit of conventional printed-circuitboard (PCB) fabrication processes.*

**Figure 6** Another modified structure in * Fig. 4(c)* can be used to further improve the filter performance when fabrication tolerances are considered. When the open stub length is changed from 5.2 mm to 5.6 mm, the second-order harmonic suppression is degraded to 25 dB when coupling structure in

*is used*

**Fig. 4(b)***. By introducing another offset Lt between the feed line and the end of the coupling line in*

**(Fig. 7)***, there is no visible degradation when the open stub length is changed from 5 mm to 5.3 mm*

**Fig. 4(c)***. This is probably because in the modified structure the change of current strength at the junction of the feed line and coupling line is less compared to the structure without offset when the length of open stub is changed, then the harmonic suppression is less sensitive to the change of the open stub length. When Lt is changed within the values of fabrication tolerance, there is no visible degradation in second-order harmonic response*

**(Fig. 8)***.*

**(Fig. 9)** To verify the effectiveness of the harmonic suppression technique and demonstrate its application for filter and resonator design, three dualmode filters based on conventional and two modified coupling structures were designed using IE3D full-wave simulation software from Zeland Software and fabricated on a duroid substrate with relative dielectric constant of 10.2 and thickness of 0.635 mm * (Fig. 10)*. Figure 4 shows the dimensions of the three filters, while

*and*

**Figs. 11***plot the measured passband and wideband frequency responses of the filters. The measured center frequencies and frequency notches are slightly lower than the simulation results, due to fabrication tolerances and the sensitivity of the frequency notch to the open stub length, respectively. The filter with modified coupling structure based on*

**12***shows measured results closer to the simulations than the filter from*

**Fig. 4(c)***. Despite the discrepancies, the two modified filters exhibit a wide stopband with rejection better than 20 dB to 8.5 GHz and sharp frequency notch over 70 dB. Suppression at the second-order harmonic frequency (6.6 GHz) is better than 40 dB. The measured fractional bandwidth and passband insertion loss are 8.48 percent and 1.45 dB for the conventional filter, and 13 percent and 0.92 dB for the modified filters, respectively. Insertion loss includes a pair of SMA connectors.*

**Fig. 4(b)**REFERENCES

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