A Miniaturize Bandpass Filter with Harmonic Suppression Using Meandered Quarter-Wavelength Resonators

A miniaturized bandpass filter with harmonics suppression is presented. The proposed filter consists of two quarter-wavelength microstrip resonators, which are meandered for circuit size reduction. An interdigital capacitor, loading at zero-voltage point, is employed to provide the desired coupling between the resonators at operating frequency, whereas the coupling coefficient at the third harmonic is realized to be zero. Besides, the second and fourth harmonics are suppressed since λ/4 resonators are adopted. Benefiting from these properties, a miniaturized bandpass filter with the second, third, and fourth harmonics suppression was designed and implemented. The final measured and simulated results show good consistence with the theoretical counterparts.


Introduction
The bandpass filter is one of the most important components in modern RF/microwave systems [1][2][3].Unfortunately, without special measures, most of the filters exhibit harmonic responses, which degrade the system performance [4][5][6][7][8][9].On the other hand, most mobile devices become smaller and leave limited space for the placement of filters.It is also of importance to miniaturize the required filter size.Therefore, bandpass filters with miniaturized size and harmonics suppression become more and more attractive [10][11][12][13][14][15][16].To reduce the circuit size, the designed filters with lower orders are preferred once the passband selectivity and outof-band rejection can reach the design requirements.One important method to improve the selectivity of the filters is to realize transmission zeros at finite frequencies.Moreover, the additional transmission zeros at harmonics can reject unwanted signals without sacrificing the performance of the passband [17,18].Therefore, a low-order filter with the help of transmission zeros may meet the stopband requirement that is usually achieved by higher-order filters.It still has challenges to design a lower order miniature bandpass filter with harmonic suppression.Various structures are proposed in [19][20][21][22][23][24][25][26][27][28][29][30][31], such as meandered parallel coupled-line structure [19][20][21][22][23][24][25][26], coupled/slot spur lines [27,28], fractal-shaped coupled lines [29], and triple-mode stub-loaded resonator [30,31].Recently, a novel coupling schematic is proposed in [32][33][34] that exhibits one transmission zero at a harmonic frequency.Thus, with this coupling scheme, one more transmission zero is added to the filter, which helps to improve the upper stopband performance.However, most of the filters mentioned above still occupy a fairly large space.
In this letter, a miniature two-order harmonicsuppressed microstrip bandpass filter using meandered quarter-wavelength resonators is presented.An interdigital coupling capacitor is placed on the zero-voltage point of the third harmonic along the resonators.With this benefit, a transmission zero appears at the third harmonic frequency.Besides, two additional transmission zeros located at the lower and upper skirts of the passband are obtained to enhance the selectivity.The circuit size reduction is realized by using two meandered quarter-wavelength resonators.With this structure, the proposed filter not only miniaturizes the circuit size but also extends the rejection band.To verify the performance, the proposed filter is implemented and measured.The active area of the filter is coupled-line structure only 8.9 mm × 12.2 mm (0.052  × 0.071  ;   is the guided wavelength at operating frequency), and the rejection band is extended to 4.2 0 .

Filter Design and Analysis
Figure 1 depicts the geometrical schematic of the proposed miniature harmonic-suppressed microstrip bandpass filter, which is operating at  0 = 1.13 GHz.This is a twoorder bandpass filter.The quarter-wavelength resonators are meandered and separated enough, as shown in Figure 1.The substrate in this design is the Rogers4350 substrate with a relative dielectric constant of 3.48 and a thickness of 0.762 mm.The physical dimensions are shown in Table 1.The coupling of the proposed bandpass filter is achieved only by the interdigital coupling capacitor, and the coupling coefficient is mainly determined by the location and value of interdigital coupling capacitor.With the meandered quarter-wavelength resonators, the circuit size can be reduced effectively.The input and output ports are connected with the resonators directly.The relation between the external quality and tapper position of input/output port has been investigated in [35].
The interdigital coupling capacitor and its equivalent circuit are shown in Figure 2.   and   represent the series and shunt capacitors of interdigital coupling capacitor, respectively [36].The value of interdigital coupling capacitor Figure 2: Interdigital coupling capacitor and its equivalent circuit. x

Coupling region
The fifth harmonic Fundamental frequency

Zero-voltage point
The third harmonic Quarter-wavelength resonator 1 Quarter-wavelength resonator 2 o  int can be adjusted by changing the parameters   ,   , and   .As the resonators separate away from each other, the coupling between them can be ignored when the interdigital coupling capacitor does not exist.Thus, the coupling is mainly realized by the interdigital capacitor, and the coupling coefficients can be calculated by [37] where V 1 () and V 2 () are normalized voltage wave functions along the two quarter-wavelength resonators and p represents a constant.As we know, the even-mode harmonics cannot be excited at the quarter-wavelength resonators.And thus, only the odd-mode harmonics existed, as shown in Figure 3.
When the center of coupling region is at the zero-voltage point of the third harmonic, V 1 () and V 2 () are nearly to zero for the third harmonic.With the very small length of coupling region  1 , the coupling coefficient  is close to 0. As a result, the third harmonic signals cannot pass through the coupling region and thus is suppressed.Therefore, combining the quarter-wavelength resonators and proper position of    the interdigital coupling capacitor, the rejection band can be extended to the fifth harmonic.
The proposed filter is simulated by the commercially available electromagnetic (EM) simulator of Ansoft HFSS.
Current distributions of the fundamental and third harmonic of the proposed filter are shown in Figure 4.It clearly shows how the fundamental frequency current is coupled from the input port to the output port, whereas the third harmonic is suppressed.This verifies the theoretical analysis stated above.
A parallel shorted coupled-line structure, shown in Figure 1, is adopted to enhance the selectivity.As shown in Figure 5, two additional transmission zeros are realized by the parallel shorted coupled-line structure.This structure is similar to the source-load coupling.Meanwhile, the location of transmission zeros is determined by the gap .The higher selectivity is achieved with the smaller gap s, which is shown in Figure 6.

Experiments
The proposed microstrip bandpass filter is fabricated using printed circuited-board (PCB) process and the photograph is given in Figure 7.The active area of the proposed filter is only 8.9 mm × 12.2 mm, which is about 0.052  × 0.071  , where   is the guided wavelength at operating frequency.Agilent network analyzer 8358E is used to test the performance.The simulated and measured results are illustrated in Figure 8 and show good agreements.The centre frequency of the passband is measured at 1.17 GHz against that of the simulated results at 1.13 GHz.Furthermore, the measured passband has a 3 dB bandwidth of 111 MHz or 10.6%.The insertion loss, including the loss from subminiature A (SMA) connectors, is only 1.3 dB compared to the simulated loss of 0.59 dB.From Figure 8, it is noted that there are two transmission zeros on the lower and upper skirts of the passband at 0.9 GHz and 1.61 GHz.Besides, another transmission zero is located at 3.1 GHz.Thus, the third harmonic is efficiently suppressed.It agrees with the theoretical analysis.Therefore, the 20 dB rejection band is extended to 4.96 GHz, which is about 4.2 0 .The proposed filter is compared with some previously published designs [26][27][28][29][30][31][32] in Table 2. Obviously from the table, the proposed filter has identical or even improved in-band performances.In addition, this work exhibits the smallest circuit size.

Conclusion
A miniature microstrip bandpass filter with harmonic suppression is presented in this paper.By utilizing the quarterwavelength and position of interdigital coupling capacitor, the second, third, and fourth harmonics are suppressed.The miniaturization characteristic is achieved based on the meandered quarter-wavelength resonator.Compared with the conventional approaches on designing miniature bandpass filter with harmonic suppression, the work in this paper exhibits a smaller circuit size and wider rejection band.

Figure 1 :
Figure 1: Schematic of the proposed miniaturized bandpass filter.

Figure 3 :
Figure 3: Voltage wave functions along the quarter-wavelength resonators.

Figure 4 :
Figure 4: Current distribution: (a) fundamental frequency and (b) the third harmonic.

Figure 5 :Figure 6 :
Figure 5: Response of proposed bandpass filter of different types.

Table 1 :
Dimensions of the proposed filter (unit: mm).

Table 2 :
Comparison with some previously published designs.