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Design of Microstrip Symmetrical Dualband Filter Based on Wireless Sensor Network Nodes
EURASIP Journal on Wireless Communications and Networking volume 2019, Article number: 34 (2019)
Abstract
The microstrip antenna filter design of wireless sensor network nodes is usually used to improve the outofband suppression and frequency selectivity by increasing the order of the filters, but the filters are usually single band, not only the size is large, but also the inband characteristics of the filters are not ideal. This paper proposes a method to design a microstrip symmetric dualband filter in wireless sensor network nodes. Firstly, the coupling matrix of singlepassband filter is obtained by using the synthesis method of generalized Chebyshev filter function. Then, the coupling matrix of the dualpassband filter is generated according to the reflection zeros and the transmission zeros. Finally, the S parameters response curve is drawn by mapping the normalized frequency domain of the dualpassband to the actual frequency domain. According to the data analysis and experimental results, the method is feasible and effective to design a microstrip symmetrical dualband filter. It can not only provide a more guiding design method for the joint design of antenna and RF frontend circuit, but also realize the spread of singlepassband filter to multifrequency for a wireless sensor network node antenna.
Introduction
The traditional radio frequency (RF) transceiver system consists of antenna, filter, power amplifier, low noise amplifier, and other devices, which often work under a single communication standard. If multiple communication standards run at the same time, it requires multiple independenttransceiver systems to form a parallel working system which will be larger in size, high in power consumption and high in cost, and has been unable to meet the application needs of wireless sensor network nodes in the era of the big data, which has attracted the attention and widespread concern of researchers all over the world [1,2,3,4,5,6,7,8,9,10,11,12,13].
Microstrip filter is a very important component of wireless sensor network (WSN) nodes, which is used to select useful signals and suppress clutter interference signals. Multifrequency microstrip filters are required to effectively pick up the signals of each separate frequency band and prevent signal crosstalk between adjacent channels, which requires higher frequency selectivity and outofband rejection of the filters [4,5,6]. In recent years, scholars in various countries have carried out indepth research and proposed various design methods to solve the two core problems in the design of multiband microstrip filters [14,15,16,17,18,19,20]: Firstly, multipoint frequency selection can be realized, multifrequency can work in parallel, and each central frequency point has a certain capacity bandwidth; secondly, the signals in adjacent frequency bands must be effectively isolated and can not interfere with each other, and the outofband rejection performance of the filter is reliable. There are two main methods for designing multiband filters [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]: Firstly, based on the combination of multiband filters, including the cascade of broadband filters and notch filters, and the parallel connection of multiple filters in different frequency bands; secondly, based on the parasitic frequency of resonators, a multiband filter is designed.
Traditional Butterworth, Chebyshev, and elliptic function filters can increase the design order of the filter to improve the filter’s outofband suppression and frequency selectivity, but the designed filter is usually singleband, not only the size is large, but also the filter’s inband characteristics are not ideal [36]. Generalized Chebyshev filter (GCF) is also known as quasielliptic function filter. It is between Chebyshev and elliptic function filter, which has excellent inband characteristics and steep edge characteristics [37, 38]. The transmission zeros of generalized Chebyshev filter can be flexibly controlled, which can be used to improve filter selectivity and stopband isolation. In order to improve the inband and outofband performance of the filter, the communication band of the filter is extended from a single band to a dual band. Based on the synthesis theory of generalized Chebyshev filter, the frequency transformation is carried out with lowfrequency prototype, and the design from lowfrequency prototype to dualband filter is realized with a crosscoupling synthesis theory.
Methodology
Frequency conversion method of symmetrical dual band
The singleband filter model is transformed into a dualband filter and has to undergo two frequency conversion. Firstly, the normalized single lowpass filter is transformed into a normalized dualband filter, and then, the normalized dualband filter is transformed into a dualband filter of actual frequency by one transformation. Figure 1 shows that three frequency variables are applied in the frequency conversion process, one is the normalized lowpass frequency variable Ω, the other is the dualband normalized intermediate variable Ω^{′}, and the third is the actual frequency variable ω.
The transmission function of the generalized Chebyshev Norder lowpass filter [35] is shown as below
Among them, s = jΩ, ε is the ripple coefficients in the passband and C_{N}(s) is the characteristic function of the generalized Chebyshev lowpass filter.
The transmission zeros and reflection zeros of the generalized Chebyshev lowpass filter are described.
Among them, s_{pi} is the transmission pole, also known as the reflection zero, that is the filter power optimal transmission point and s_{zj} is the transmission zero.
It is assumed that the transmission function of the generalized Chebyshev lowpass filter is about Ω axis symmetry. The dualband frequency conversion process is shown in Fig. 1. Thus, the number of transmission zeros and reflection zeros of the generalized Chebyshev dualband filter obtained by frequency transformation is 2K and 2N, respectively. The low passband frequency range js' is −j to\( j{\Omega}_k^{\prime } \), and the high passband frequency range js' is \( j{\Omega}_k^{\prime } \) to j.
Firstly, the normalized frequency conversion from single passband to double passband is realized. The frequency conversion equations such as Eqs. (3) and (4) are given.
s^{′} is a frequency variable that is mapped from the prototype s plane. As shown in Fig. 1, when s changes from normalized frequency − 1 to 1 in the Ω domain, it maps to s^{′} from normalized frequency \( {\Omega}_k^{\prime } \) to 1 in the Ω^{′} > 0 domain; when s changes from normalized frequency − 1 to 1 in the Ω domain, it maps to s^{′} from normalized frequency \( {\Omega}_k^{\prime } \) to 1 in the Ω^{′} > 0 domain. Degenerate (3) into
The following Eq. (6) can be obtained by expression (5) of which s = jΩ.
When s = j, s^{′} = j or when \( s=j,\kern0.5em {s}^{\prime }=j{\Omega}_k^{\prime } \), the Eq. (7) can be obtained from the Eq. (6).
We can get s = j when s^{′} = j and \( {s}^{\prime }=j{\Omega}_k^{\prime },\kern0.5em s=j \) when s^{′} = − j and \( {s}^{\prime }=j{\Omega}_k^{\prime } \) from Fig. 1. Therefore, the following expressions can be obtained.
Thus, the normalized single passband to normalized dualband frequency conversion can be easily realized by expressions (7) and (8).
Secondly, the normalized dualband to the actual frequency of the dualband transformation, that is, the frequency transform domain from Ω^{′} domain to ω domain transformation. The transformation equation is
Among it, ϖ = jω. We can see that values of 1, \( {\Omega}_k^{\prime },\kern0.5em {\Omega}_k^{\prime } \), and − 1 in the Ω^{′} domain are mapped, respectively, to ω_{k4}, ω_{k3}, ω_{k2}, and ω_{k1} of the ω domain from Fig. 1.
We can get the expressions of l_{1}, l_{2}, and \( {\Omega}_k^{\prime } \).
Synthesis method of Norder crosscoupling matrix
With the development of communication technology, the spectrum is becoming more and more crowded, and the technical specifications of the filter, especially the rectangular requirements, are becoming more and more stringent. Traditional Butterworth and Chebyshev filters have been unable to meet the requirements. In order to improve the selectivity and outofband isolation of filters, transmission zeros are usually introduced into filters, which are generated by crosscoupling between nonadjacent resonators [30,31,32,33,34,35]. The crosscoupling filter with finite transmission zeros is the most common choice. Generalized Chebyshev function is usually used to implement it.
The lumped parameter equivalent circuit and equivalent network parameters of the coupling filter are shown in Fig. 2a and b, respectively. According to the Kirchhoff theorem that the sum of the voltage is zero along the loop, the voltage of each loop is described Eq. (11).
The specific method of treatment is shown in document [15], Eq. (11) which is expressed by matrix as Eq. (12).
[Z] is N × N impedance matrix. Each resonator of synchronous tuning filter has the same resonance frequency \( {\omega}_0=1/\sqrt{LC} \), and among it, L = L_{1} = L_{2} = ⋯L_{n}, C = C_{1} = C_{2} = ⋯C_{n}. FBW = Δω/ω_{0} is the relative bandwidth. The normalized impedance matrix is \( \left[\overline{Z}\right]=\left[Z\right]/\left({\omega}_0L\cdot FBW\right) \).
The external quality factor is defined as Q_{ei} = R_{i}/ω_{0}L(i = 1, N) and the coupling coefficient isM_{ij} = L_{ij}/L. While ω_{0}/ω ≈ 1 in the narrowband filter, there are
Among it, q_{ei} = Q_{ei} • FBW(i = 1.2), m_{ij} = M_{ij}/FBW, to I_{1} = i_{1}, I_{n} = − i_{n} in Fig. 2b, then we can get the Eq. (15).
After synthesizing the coupling matrix, the coupling matrix is deformed to correspond to the actual circuit model structure. This is advantageous to the actual physical circuit design, in which the negative coupling coefficient in the coupling matrix represents the capacitance coupling in the crosscoupling of the adjacent resonator circuit, and the positive coupling coefficient in the coupling matrix represents the inductive coupling in the crosscoupling of the adjacent resonator circuit.
Results and discussion
Basic parameters of dualband filter
Based on the previous generalized Chebyshev filter function synthesis theory of dualband filter, a symmetrical dualband filter (SDF) are designed. Assuming that the frequency range of the low passband is 2.9–2.95 GHz, the frequency range of the high passband is 3.05–3.10 GHz and the inband return loss is RL = 22 dB.
The dualband is symmetrical with respect to the center of ω_{0} = 3 GHz, and the four transmission zeros of the singlepass lowpass filter are 1.5j, − 1.5j, j∞, and −j∞.
ω_{k1} = 2.90, ω_{k2} = 2.95, ω_{k3} = 3.05, and ω_{k4} = 3.10 can be calculated from the conditions given above. According to Eq. (10), we can obtain \( {\Omega}_k^{\prime }=0.5 \). According to Eq. (8), we can obtain a_{1} = 0.5 and a_{2} = 1.
Design and simulation of symmetrical dualband filter
Based on the generalized Chebyshev filter synthesis method described in the previous section, we can obtain the roots of these functions P(Ω), F(Ω), and E(Ω), as shown in Table 1.
We can plot the response curve of the S parameter, as shown in Fig. 3. The coupling matrix [16] deduced from shortcircuit admittance parameters is:
Now, by using the frequency mapping equation, the reflection and transmission zeros of singlepassband normalized generalized Chebyshev function filters and a_{1} = 0.5, a_{2} = 1 are substituted in Eq. (6), we can obtain:
The transmission and reflection zeros of dualband filters are obtained by using Eq. (16). Then, the root of E(s^{′}) is obtained by using the generalized Chebyshev filter function synthesis of a symmetrical dualband. The roots of P(Ω^{′}), F(Ω^{′}), and E(Ω^{′}) are listed in Table 2.
Especially, the filter is a fourorder filter, with two finite transmission zeros, and two transmission zeros located at the positive and negative infinity. In the case of dualpassband transformation, the transmission zeros at infinity of single passband correspond to the transmission zeros at zero of dual passband. After the transmission and reflection zeros of the two passbands are obtained, the expressions of each polynomial of the two passbands can be obtained by using the synthesis method of the generalized Chebyshev filter function.
Thus, the normalized response curve of the dual bandpass filter can be obtained, as shown in Fig. 4.
Finally, Eq. (10) is used to calculate l_{1} and l_{2}, and the Eq. (17) are used to map the frequency domain from Ω^{′} to ω domain. Then, the S parameter curve in the actual frequency domain is obtained as shown in Fig. 5.
The coupling matrix obtained from the coefficients of P(Ω^{′}), F(Ω^{′}), and E(Ω^{′}) are then rotated to eliminate the element. The folded N + 2order, that is, the tenthorder coupling matrix is.
Conclusion
This paper presented an experimental study on the microstrip dualband filter based on wireless sensor network nodes. Firstly, according to the order, the position of the transmission zeros, and the ripple coefficients in the band of the filter to be designed, the generalized Chebyshev filter function synthesis method is applied to synthesize a singlepassband filter by combining the relationship between the shortcircuit admittance parameters. The coupling matrix of the singlepassband filter is obtained. Secondly, the generalized Chebyshev function polynomial is constructed according to the symmetrical frequency conversion equations from singleband to dualband, and the coupling matrix of the dualband filter is synthesized by the relationship between the generalized Chebyshev function polynomial and the shortcircuit admittance parameters. Finally, the normalized frequency domain is mapped to the actual frequency domain, and the S parameter response curve in the actual frequency domain is obtained. By flexibly controlling the transmission zeros of the generalized Chebyshev filter, the selectivity and stopband isolation of the filter can be effectively improved, and this method can design multiband filters with excellent performance and has a positive guiding role in the physical circuit design of microstrip filters based on wireless sensor network nodes.
Abbreviations
 GCF:

Generalized Chebyshev filter
 RF:

Radio frequency
 SDF:

Symmetrical dualband filter
 WSN:

Wireless sensor networks
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Acknowledgements
The research presented in this paper was supported by National Natural Science Foundation, Sichuan Provincial Education Department and Yibin University, China.
Funding
The authors acknowledge the Scientific Research Fund of Sichuan Provincial Education Department (Grant: 14ZA0269), Scientific Research Key Project of Yibin University (Grant: 2013QD02) and the National Natural Science Foundation of China (Grant: 61201266).
Availability of data and materials
The simulation code can be downloaded by contacting author after three years of publication. Mostly, I got the writing material from different journals as presented in the references. MATLAB tool has been used to simulate my concept.
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WBC is the main author of this manuscript. He conceived the novel ideas, designed the algorithms and experiments, and performed the analysis. He wrote the entire manuscript. He accomplished all the revisions provided during entire peer review process until publication. He conducted the final proof reading as well. This manuscript is the outcomes of the research activities carried out only by the main author. KD and WC checked, reviewed the manuscript, and gave valuable suggestions on the structure of the paper. All authors have read approved the final manuscript.
Corresponding author
Correspondence to Wenbo Cheng.
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Keywords
 Wireless sensor network nodes
 Symmetrical dualpassband technology
 Microstrip antenna
 Generalized Chebyshev function
 Crosscoupling synthesis theory
 Transmission zeros