Novel Low-Pass Filter Structures Using Spur-Lines to Generate Additional Attenuation Poles

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Low-pass filters (LPFs) are widely employed to suppress harmonics and spurious signals in communication systems.The performance of an LPF is defined by the characteristics of its skirt, passband insertion loss, and stopband attenuation.Therefore, incorporating measures to ensure excellent performance is the main goal of LPF design, which can be achieved by various methods.Among these, microstrip openstub LPFs (OSLPF) and stepped-impedance line LPFs are the most widely used types because of their ease of design and manufacturing.However, these structures generate harmonics and spurious responses based on the periodicity of the transmission-line length; this is one of the main reasons for limiting wide stopband implementation.Therefore, many studies have been conducted on suppression of unwanted signals, such as harmonics and spurious responses; LPF structures using a ground plane, such as PBG and DGS [1][2][3][4], and structures using coupled lines [5][6][7] are representative examples of such studies.In addition, several other studies have been conducted on various structures to generate additional attenuation poles in the stopband [8][9][10][11].In this study, to improve the stopband performance, we consider two novel structures of the LPF using spur-lines; the configurations of the two proposed LPFs are modified from the basic structure of the OSLPF.The first structure has the spur-line added to the serial lines of the OSLPF, and the second structure has the spur-line added to the parallel stub.We named the first configuration as serial spur-line LPF (SSLPF) and the second as parallel spur-line LPF (PSLPF).The equivalent structures for these two LPFs are presented, and the required design formulas are derived.Then, the two types of LPFs were fabricated and validated by theoretical analysis as well as the simulated and measured results

░ 2. SYNTHESIS OF THE SSLPF
The first proposed structure is the SSLPF, where the spur-line is added to the serial transmission line of the typical OSLPF structure.This structure allows improved stopband characteristics by generating additional attenuation poles in the stopband while maintaining the passband characteristics of the OSLPF using the spur-lines.If the spur-line structure of figure 2 were to be applied to the serial line of figure 1(a), then the equivalent structure can be expressed as figure 3(a), where X-X′ is the axis of symmetry.Therefore, the variables corresponding to the left and right sides about this axis are identical, and only the variables on left side of the central axis will be described from this point forward.In figure 3(a), the spur-line impedance is defined as the impedance (ZL1) of the serial line to simplify the calculation and minimize the of the serial transmission line; the length Φ1 is set to λ/4 at the desired frequency such that the attenuation pole can be generated at that frequency.Yinc in figure 3(a) is calculated as shown in equation (1).
Here, Yin2 is obtained using Z2 in figure 2.
The equivalent capacitance can be calculated using equation ( 2) under the condition that A1 and A3 are identical.
Using the Cp1 calculated with equation ( 2) and the required open-stub impedance, the modified length of the outermost open stub can be obtained as shown in equation (3).
As shown in figure 3, only the outermost open stubs are affected by the spur-lines but that in the middle is not affected; this means that in figures 1(a) and 1(b), Zc2 is Zp2 and θc2 is θp2. Figure 4 shows that when the length of the spur-line is changed, the passband characteristics remain similar to those of the OSLPF; however, it can be seen that the position of the attenuation pole changes according to the length of the spurline (Φ1), and θp2 is not affected by Φ1.Therefore, we see that the first attenuation poles are formed equally at the frequency where θp2 is equal to λ/4 in all cases.The second attenuation poles are formed at the frequency where the length of the spurline is λ/4.Accordingly, if the length of the spur-line is set correctly, the positions of the second attenuation poles can be adjusted with reference to the fixed first attenuation poles such that the stopband bandwidth and attenuation depth can be controlled partially.One of the notable features of this structure is that θp1 can be calculated as zero if Φ1 is selected appropriately; this means that the open stub can be removed if needed.

░ 3. SYNTHESIS OF THE PSLPF
The second proposed structure is the PSLPF, where the spurline is added to the parallel open stub of the typical OSLPF structure, as depicted in figure 5.   5).
Further, if Yin and Yin′ are the same in equation ( 6), then dotted boxes D in figure 1(a) and D′ in figure 5 are equivalent structures.
Equation ( 6) can be expressed as a polynomial of tanθ, as shown in equation (7).Here, the coefficients C1, C2, and C3 are as follows: From the solution of equation ( 7), we can obtain θ as in equation ( 8).

░ 4. FABRICATION OF THE FILTERS AND ANALYSIS OF THE RESULTS
with H = 0.7874 mm and εr = 2.2 were used for the simulation and fabrication.The passband return loss and insertion loss were measured to be more than 16.2 dB and less than 0.1 dB, respectively.Table 1 presents a summary of the characteristics related to attenuation poles.

░ Table 1. Summary of the results in figure 9
Frequency of Attenuation Pole The relative stopband bandwidth of the SSLPF is observed to be about 4.7 times better than that of the OSLPF but the absolute stopband bandwidth is not very large; nevertheless, it is clear that the proposed structure is advantageous for realizing strong attenuation.The passband return loss and insertion loss were measured to be more than 15.4 dB and less than 0.12 dB, respectively.The stopband bandwidth of the PSLPF is approximately 1.4 times better than that of the OSLPF.Although the PSLPF has a relatively small stopband bandwidth ratio compared to the SSLPF, it can suppress the third harmonic adequately.Therefore, if the frequencies of attenuation poles are appropriately arranged based on the length of the spur-line, it may be possible to implement a wider stopband or achieve greater attenuation.

Fabrication and evaluation of the PSLPF
The above results are limited to the fabricated sample SSLPF and OSLPF only and are not general; nevertheless, the above results sufficiently showed us that the two proposed structures were valid, and the design formulas were correctly derived.

░ 5. CONCLUSION
In this study, the SSLPF and PSLPF were designed as spurlines added to the OSLPF structure in serial and parallel, respectively, to improve the stopband performance.We derived the equations to calculate the design variables for the two structures, and the two LPFs were fabricated according to the design formulas and principles.By comparing the features and analyzing the measured and simulated results of the OSLPF as well as the two proposed LPFs, the validity of the proposed structure and derived equations were demonstrated.
From the analysis results, we observed that two proposed LPFs were advantageous for realizing a wide stopband.
It is convinced that an LPF design that simultaneously applies spur-lines to both the serial line and parallel open stub could produce stronger attenuation and wider stopband.In addition, it is believed that the proposed method could be applied similarly to more extended structures than N=5 as considered in this study.

Figure 2 .
Figure 2.Equivalent structure of the spur-line (SL) in figure 1(b)

Figure 3 .
Figure 3. (a) Structure with spur-line equivalent applied to the OSLPF; (b) changes Structural to the OSLPF to obtain the SSLPF Boxes A1, B1, and C1 in figure 3(a) correspond to boxes A1′, B1′, and C1′ in figure 3(b), respectively.Thus, when all the parts are matched, the structure in figure 1(a) is transformed to that in figure 1(b).In figure 3(a), the spur-line impedance is defined as the impedance (ZL1) of the serial line to simplify the calculation and minimize the of the serial transmission line; the length Φ1 is set to λ/4 at the desired frequency such that the attenuation pole can be generated at that frequency.Yinc in figure 3(a) is calculated as shown in equation (1).

Figure 5 .
Figure 5. Proposed PSLPF structure If the dotted box D in figure 1(a) is equivalent to the dotted box D′ in figure 5, then the passband characteristics of the LPF are the same.However, the structure in figure 5 can generate additional attenuation poles in the stopband compared to that in figure 1(a).Figure 6 shows the equivalent structure of the dotted box D′ from figure 5.

Figure 7 .
Figure 7. Characteristics of the PSLPF based on spur-line length

Figure 8 .
Figure 8. Fabricated SSLPF In the SSLPF shown in figure 8, we see that the outermost open stubs have been removed, as originally designed.Figure 9 shows the electromagnetic (EM) simulated and measured results of the fabricated SSLPF; the typical OSLPF characteristics are also presented to show the improved stopband performance.

Figure 10 .
Figure 10.Fabricated PSLPF Figure 11 shows the EM simulated and measured results of the fabricated PSLPF along with the OSLPF characteristics.

Table 2
presents a summary of the characteristics related to attenuation poles.