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Compact and wideband bandpass filters with analysis of the CRLH-TL characteristics based on stepped impedance resonator
Int. J. Electron. Commun. (AEÜ) 108 (2019) 96–106
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International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular paper
Compact and wideband bandpass filters with analysis of the CRLH-TL characteristics based on stepped impedance resonator Seyyed Mohammad Mehdi Moshiri, Maryam Khodadadi, Najmeh Nozhat ⇑ Department of Electrical Engineering, Shiraz University of Technology, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 6 March 2019 Accepted 12 June 2019
Keywords: Bandpass filter Composite right/left handed (CRLH) structure Coupled-shorted stub (CSS) Wideband (WB) Stepped impedance resonator (SIR)
a b s t r a c t In this paper, we have investigated two unique wideband (WB) bandpass filters (BPFs) based on composite right/left-handed (CRLH) structure that have high performance in C-band. The proposed filters have been implemented with stepped-impedance resonator (SIR) section and interdigital capacitors on it with a parallel coupled-shorted stub (CSS). High selectivity, high out-of-band rejection, low loss and two transmission zeroes at the lower and upper passband/stopband edges have been observed. The out-of-band rejection levels in two filters are better than 17 dB and 20 dB at the lower and upper band edges, respectively. In addition, the return loss and insertion loss of the proposed CSS filter are greater than 17 dB and less than 0.7 dB, respectively. Also, the return loss and insertion loss of the proposed spiral CSS (SCSS) filter are greater than 20 dB and less than of 0.5 dB, respectively. The presented structures have been investigated analytically and experimentally in order to verify balance between the results of the full-wave simulation and the equivalent circuit model with the experimental ones. The dimensions of the suggested filters are 21.6 3.06 mm2 and 14.6 4.2 mm2. The specifications and compact size of the filters make them suitable for wideband wireless communication systems. Ó 2019 Elsevier GmbH. All rights reserved.
1. Introduction Nowadays there is a necessity of a wide transmission bandwidth for wireless communication systems, which the frequency band is from 3.1 to 10.6 GHz. Therefore, wideband (WB) devices like filters in C-band (4–8 GHz) play a significant role in modern wireless local area networks (WLANs) and Bluetooth transceivers [1]. Since the federal communication commission (FCC) authorized the unlicensed use of ultra-WB (UWB) in 2002 [2], several surveys have been performed to develop wideband BPFs with different methods and structures [3–20]. Researches have proposed many different topologies for designing UWB filters such as stubloaded resonators [3], cascaded ring resonators filters that suffer from physical size but have good frequency response [4–8], UWB BPF with a notched band that suffers from poor skirt selectivity at both passband edges [7], TETRA band filters [11] and steppedimpedance slotline resonators [12]. Some of these structures have poor out-of-band rejection, narrow band transmission and complex design methodology. Recently, electromagnetic metamaterials have been used to design high performance filters [13–20]. The resonant-types of ⇑ Corresponding author. E-mail address: [email protected] (N. Nozhat). https://doi.org/10.1016/j.aeue.2019.06.011 1434-8411/Ó 2019 Elsevier GmbH. All rights reserved.
metamaterial structures that consist of split ring resonators (SRRs) and complementary split ring resonators (CSRRs) have been more used for the design of microwave filters [16,17]. Left-handed transmission lines (LH-TLs) with representing an abrupt transition pole at the lower or upper edge of the passband can improve the sharp attenuations near the passband and increase the bandwidth simultaneously [17–20]. The review of these articles [1,3–20] summarizes and mentions three main advantages in design of a filter. (1) Dimension: the size of the filter should be small enough so that the proposed filter is able to operate as a compact WB filter. (2) Simplicity of the fabrication process: the most microwave-integrated circuits have intricate structures due to the complex construction technology, which results in expensive and difficult fabrication process. However, this novel WB BPF has simple planar geometry and so can be succeeded in facing up to fabrication problems. (3) Improving the performance: a wideband filter must be devised with a high controlled passband selectivity and suitable out-of-band rejection. Hence, it has been suggested to utilize composite right/left handed transmission line (CRLH-TL) and high-low-high stepped-impedance resonator (SIR). It is worth to note that one of the specific features of the CRLH-TL is reduction of the loss [19,20]. In this paper, two unprecedented CRLH-TL wideband BPF topologies have been proposed based on SIR with introducing
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interdigital capacitors on it. In recommended structures the coupled-shorted stub (CSS) has been used to generate the transmission zeroes. The CRLH transmission lines have been applied to enhance the performance of the WB BPF and decrease the loss, effectively. According to these sketching, the prototype filters would have high selectivity with sharp skirt at the upper and lower band edges, high out-of-band rejection and low return loss. To achieve the desired wide band (4–8 GHz for the CSS filter and 5–9 GHz for the SCSS filter) and high out-of-band rejection, we can change the length and width of the SIR section. On one hand, in order to develop the sharp skirt at the upper band edge of the proposed filters, the spiral defected SIR structure has been used. On the other hand, the sharp skirt at the lower band edge and high out-ofband rejection of the bandpass filters can be controlled by the CSS section. Furthermore, in two structures, the left-handed (high-pass nature) section of the filter has been introduced by series interdigital capacitor and shorted shunt inductive line that the length of the section is smaller than kg/4, where kg is the guided wavelength. Also, the right-handed (low-pass nature) characteristic has been rendered by effective inductance of the middle transmission line (TL) section and the effective capacitance nominated by SIR section. As a result, the proposed layouts act as CRLH structures. The structures have been analyzed analytically and numerically by the finite element method (FEM). Moreover, the equivalent circuits of suggested filters are derived to obtain an insight into the working principle and calculate the dispersion diagram to show the CRLH performance of the filters. In addition, the results of the fabricated structures have been compared with the simulated results. The fractional bandwidth of the recommended filters is 66%. The insertion loss of the CSS filter is less than 0.7 dB and the return loss is greater than 17 dB. Furthermore, the insertion loss of the SCSS filter is less than 0.5 dB and the return loss is greater than 20 dB. The most important specifications of our suggested WB BPFs are wide bandwidth, multi-transmission poles, sharp lower and upper edges, compact size, high selectivity, higher outof-band rejection, flat group delay, simple design procedure and low cost. This paper is organized as follows. In Section 2, the fundamental aspects of the proposed filters are studied. In Section 3, design and analysis of two proposed filters are presented. In Section 4, the CRLH-TL characteristics are analyzed. In Section 5, the fabrication and measurement results are shown and compared with the previous works. The paper is concluded in Section 6. 2. Fundamental aspect of the proposed filters 2.1. Multi-mode resonance (MMR) feature The initial bandwidth is determined by high-low-high steppedimpedance resonator section that plays an important role as a multi-mode resonator structure. The schematic view of the SIR is depicted in Fig. 1. The middle TL section in Fig. 1 has the most
Fig. 1. High-low-high stepped-impedance multi-mode section.
important effect to create a wideband filter. The characteristic impedances of the low and high SIR are introduced by Z1 and Z2, respectively, and the electric lengths are defined by h1 and h2 . Two high impedance sections are used to couple with the input and output feed lines [15]. Particularly, one approach to calculate the resonance frequency is to obtain and analyse a circuit model of the coupling. However, for higher multimode microstrip resonator filters, this method is sometimes difficult. The other way to find the resonance frequency is utilizing the transmission line theory. The MMR is considered without the input and output coupling and the input admittance equals to zero. However, because of the reflection symmetry plane in the principle section of the proposed filters (MMR), according to Fig. 1, we should use two benefit strategies: 1. When the symmetry plane M-M0 is short-circuited, it illustrates even mode:
YL þ YR ¼ 0
ð1Þ 0
2. When the symmetry plane M-M is open-circuited, it shows odd mode:
ðY L þ Y R Þ ! 1
ð2Þ
where YL and YR are the input admittances from the middle of the MMRs and given by:
Y L ¼ jY 1
Y 1 tanh1 þ Y 2 tanh2 RZ tanh1 þ tanh2 ¼ jY 1 ¼ YR Y 1 Y 2 tanh1 tanh2 RZ tanh1 tanh2
ð3Þ
where the impedance ratio of the high and low lines is defined as RZ ¼ YY 12 ¼ ZZ21 ¼ k. The odd and even mode analysis is useful for calculating the the resonance frequencies of any multi-mode resonators. Generally, the resonance frequencies can be calculated by considering an appropriate proportion of the electric lengths of the MMR structure ðh1 and h2 Þ [15]. When h1 ¼ h2 , the resonance frequencies are defined as [15]:
f1 ¼
c pffiffiffi tan1 k 2p l
ð4aÞ
f2 ¼
c 4l
ð4bÞ
f3 ¼
c pffiffiffi p tan1 k 2p l
ð4cÞ
f4 ¼
c 2l
ð4dÞ
According to Eq. (4), it should be noted that these calculated resonance frequencies are dependent on the value of k. This dependency represents a relation between the resonant mode frequencies and the fundamental mode [16]. Consequently, the resonant mode frequencies get closer together for k > 1 [15,16]. In our initial proposed filters the correlation of h1 and h2 is considered as 3h1 ¼ h2 and four resonance frequencies are defined as:
c f1 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3ðk þ 1Þ n 2
c f2 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi kþ3 3k þ 1
c f3 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3ðk þ 1Þ þ n 2
ð5aÞ
ð5bÞ
ð5cÞ
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0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 pffiffiffi c @p tan1 3ðk þ 1Þ þ nA f4 ¼ 2pl 2
ð5dÞ
2
n ¼ 9k þ 14k þ 9 According to the Eq. (3) and considering the conditions of Eqs. (1) and (2), we can obtain Fig. 2(a) that illustrates the electric length ratio versus the resonance frequency ratio with k = 4.62. In addition, the relation between the impedance ratio and resonance frequency ratio with 3h1 ¼ h2 is shown in Fig. 2(b). It is observed that the bandwidth of the proposed WB bandpass filter can be controlled by the electric length and impedance ratio of the stepped-impedance line in the first three resonance frequencies.
the effective dielectric constant and transmission line length, respectively.
2.2. Interdigital capacitor on MMR
2.3. Coupled-shorted stub (CSS) section
In design of wideband filters, despite the importance of the bandwidth, the sharpness of the upper and lower edges is also important. Therefore, in order to obtain sharp upper edge, an interdigital capacitor on SIR is used. The schematic view of the interdigital capacitor and its equivalent electrical circuit are depicted in Fig. 3. There are several benefits for using this structure. One of them is the ability to control the location of the transmission zeros by changing the number, length and distance between the digits on the SIR, because of changing the values of capacitance and inductance in its equivalent circuit. The other one is the absence of undesirable parasitic mode in the stopband. In Fig. 3(b), C and L are operated as an interdigital capacitor that we can calculate its resonance frequency as:
Definitely, one of the most significant features in design and construction of a filter is a high out-of-band rejection. As mentioned in pervious section, the SIR creates undesirable modes in stopband and these modes prevent from increasing the out-ofband rejection. Hence, in this paper, in order to achieve an appropriate out-of-band rejection and omit the unfavourable modes, the CSS section is used. This technique generates two transmission zeros, which one of them is used to provide sharp lower band edge and the other one is utilized to increase the bandwidth of the outof-band rejection from 8 GHz to 16 GHz. This advantage is undeniable because of decreasing the effect of deterministic undesirable modes. The schematic view of the CSS section and its equivalent electrical circuit are shown in Fig. 4. The resonance frequency of the CSS can be obtained as:
1 f ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 C ðLP þ LS Þ
ð6aÞ
Fig. 3. The schematic view of (a) the interdigital capacitor and (b) its equivalent electrical circuit.
1 f ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 LðC P þ C S Þ
ð7Þ
The location of the resonance frequency of sharp upper band edge can be controlled by Eq. (6) as a transmission zero. Moreover, by considering that the transmission line length of the filter is shorter than the wavelength, the desired values of the capacitor and inductor are calculated as [21]:
C¼
l
ð6bÞ
v Z0
Lp;s ¼
lZ 0
ð6cÞ
v
where Z0 and
v ¼ pcffiffiffiffiffi are the characteristic impedance and phase e eff
velocity of the transmission line, respectively. Also,
eeff and l are
Fig. 4. The schematic view of (a) the coupled-shorted stub and (b) its equivalent electrical circuit.
Fig. 2. (a) Normalized resonance frequency versus the electric length ratio with k = 4.62. (b) Normalized resonance frequency as a function of the impedance ratio with 3h1 = h2 .
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The location of the resonance frequency of sharp upper band edge can be controlled by Eq. (7). Combining the MMR, interdigital capacitor and CSS constructs the principle of the introduced filters specifications. In the next sections, the design, performance improvement and selectivity of the suggested filters are described. 3. Filter design and analysis 3.1. Wideband bandpass filter based on CSS (CSS filter) The configuration of the suggested microstrip WB bandpass filter and its physical parameters are illustrated in Fig. 5. For optimizing the dimensions of the recommended filter, the FEM is used. In essence, the main advantage of this structure is its sharp band edges. The upper and lower band edges are sharpened and enhanced by applying interdigital capacitors on SIR and CSS sections, respectively. We have confirmed that in the proposed structure, two resonance frequencies are observed and can be controlled by changing the dimensions of the structural parameters such as L4 and g6. The effect of variation of L4 on jS21 j parameter is plotted in Fig. 6 (a) and it is shown that how this parameter can change the location of the upper zero. Also, by moving the via in an arm of the CSS, the upper transmission zero can be controlled as depicted in Fig. 6(b). Furthermore, as shown in Fig. 6(c), by varying g6, the lower zero is shifted more than the upper zero that illustrates the lower zero can be controlled by g6. In essence, considerable tuning can be achieved by three degrees of freedom for precise location of the transmission zeros. 3.2. Wideband bandpass filter based on spiral CSS (SCSS filter) The configuration of the second suggested microstrip wideband bandpass filter and its physical parameters are illustrated in Fig. 7. For optimizing the dimensions, the FEM method is used. The schematic view of the high coupling CSS and its equivalent electrical circuit are depicted in Fig. 8. The location of the resonance frequency of the band edges have been controlled by Eq. (7). One of the most achievements in this recommended structure is its compactness. The size of the proposed SCSS filter
99
(14.6 4.2 mm2) is smaller than the size of the CSS filter (21.6 3.06 mm2) that is introduced in the previous subsection. Moreover, decreasing the size of the filter is possible with utilizing unexampled spiral coupling method. In the SCSS filter, the function of this new coupling method causes the high coupling between the feed line and the other parts of the filter in comparison to the CSS filter and improves the performance of the suggested filter. In addition, design of the SCSS filter in the range of 5–9 GHz indicates that we can control the passband of the proposed filter by changing the dimensions of the SIR. Furthermore, the tunability of this filter is as an important factor for design and fabrication of a novel and efficient filter in the communications industry. This proposed structure can be affected the sharp skirt at the lower and upper band edges by utilizing the transmissions zeros that introduced in Fig. 7. The simulated frequency responses for different values of L4, L5 and g1 are shown in Fig. 9. It can be seen that there are five main resonance modes, namely, fm1, fm2, fm3, fm4, and fm5 in the range of 4–16 GHz. As shown in Fig. 9(a), by increasing the parameter L4 from 4.1 to 4.7 mm, the odd resonance modes of fm1 and fm5 tend to slowly shift descending and the other modes remain stable and fixed. On the other hand, as Fig. 9(b) depicts, by changing the length of L5 from 2.75 to 3.35 mm, only even resonance mode of fm4 moves towards the lower frequency. In nutshell, by changing the lengths of L4 and L5 we can control the location of the transmission zeros and passband of the proposed filter. It can be seen from Fig. 9(c), as the length of g1 varies from 0.1 to 0.4 mm, just the resonance modes of fm2 and fm3 tend to move towards the lower and higher frequencies, respectively. As a result, the five resonance modes confirm the superiority of the SCSS filter to make a wideband BPF with increased coupling degree. From Figs. 2 and 9, it is obvious that the modes properties of the resonator depend on the stub length and it verifies that we are able to get a significant WB BPF that covers the frequency range of 3.1–10.6 GHz for wideband systems.
3.3. Frequency response of the proposed filters To verify the performance of each part of the introduced filters, the scattering parameters of the MMR, CSS, and interdigital capacitor sections are studied. It is mentioned in Section 2 that the role
Fig. 5. (a) Configuration of the proposed WB filter and (b) physical parameters of the unit cell. L1 = 8.00, L2 = 8.00, L3 = 7.00, L4 = 6.02, 2 L5 = 3.15, g1 = 0.20, g2 = 0.20, g3 = 0.15, g4 = 0.20, g5 = 0.15, g6 = 0.40, g7 = 0.20, g8 = 0.20, g9 = 0.30, g10 = 0.20, g11 = 2.50 (All dimensions are in mm).
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Fig. 6. Simulated jS21 j of the CSS filter for different values of (a) L4, (b) location of via in L3 and L4 and (c) g6.
Fig. 7. (a) Configuration of the proposed WB filter and (b) physical parameters of the unit cell. L1 = 1.55, L2 = 1.25, L3 = 4.3, L4 = 4.20, 2 L5 = 3.55, L6 = 1.65, L7 = 1.10, L8 = 1.55, L9 = 2.05, L10 = 1.80, g1 = 0.20, g2 = 0.15, g3 = 0.15, g4 = 0.50, g5 = 0.20, g6 = 0.30, g7 = 0.20, g8 = 0.10, g9 = 1.00, g10 = 0.10 (All the dimensions are in mm).
of the MMR without utilizing the CSS and interdigital capacitor is creating desired bandwidth, as shown in Fig. 10. In order to enhance the sharpness of the filter, the CSS and interdigital capacitor are used in the microstrip section to add two transmission zeros. As illustrated in Fig. 11(a), the
coupled-shorted stub section is used to add a transmission zero at the lower edge of the CSS filter. Moreover, Fig. 11(b) confirms that by utilizing high coupling CSS in the SCSS filter, not only the lower edge becomes sharpness, but also a transmission zero at the out-of-band rejection near the upper edge creates. Finally,
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the effect of interdigital capacitor on the MMR is investigated. As demonstrated in Fig. 12, utilizing the interdigital capacitor creates transmission zero at the upper edge of the suggested filters. 4. CRLH-TL characteristics
Fig. 8. The schematic view of (a) the coupled-shorted ring stub and (b) its equivalent electrical circuit.
The equivalent circuit of the proposed filters based on the CSS is depicted in Fig. 13 and the parameters values of the suggested filters are given in Table 1. According to Fig. 13, the horizontal section (a) consists of LR1 and series CL1-LR2 resonator and models the effect of the feed line and high impedance of the SIR section. The vertical section (b) includes two identical parallel structures that each one shows a transmission zero created by the CSS. CL3
Fig. 9. Simulated jS21 jof the SCSS filter for different values of (a) L4 (b) L5 and (c) g1.
Fig. 10. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSS filters to show the MMR function without the CSS section and interdigital capacitor.
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Fig. 11. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSS filters to show the CSS function without the interdigital capacitor on the MMR.
Fig. 12. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSSs filter to show the interdigital capacitor function without the CSS section.
Fig. 13. Equivalent circuit of the proposed filters of Figs. 5 and 7.
and CL4 are used for showing the coupling between the feed line and CSS that are in series with a parallel LL1-CR2 resonator. This parallel resonator models the CSS in the equivalent circuit of Figs. 5 and 7. The horizontal section (c) shows the equivalent circuit of the coupling between the low impedance of SIR and the interdigital capacitor on it. The shunt capacitances of CR1 and CR4 are parasitic and they cannot be omitted. In a nutshell, the proposed structures are composed of series inductance of LR and shunt capacitance of CR, and also series capacitance of CL and shunt inductance of LL that act as right-handed and left-handed topology, respectively. Therefore, the proposed filters are known as a CRLH-TL structure.
To understand the operating principle of the CRLH filters, the ABCD-matrix is used to analyse the circuit properties such as dispersion characteristic. The dispersion relation is calculated by [20–23]:
cosðbpÞ ¼
A þ D A¼D ! cosðbpÞ ¼ A 2
ð8Þ
where p is the unit-cell length. Indeed, as shown in Fig. 13, the equivalent circuit is symmetric. Hence, for analysis of the properties of the proposed filters, the parameter A can be used [20–23]. If the matrix element A sets equal to 1 and the roots are solved, the cutoff frequencies are calculated. These frequencies show the cutoffs of
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S.M.M. Moshiri et al. / Int. J. Electron. Commun. (AEÜ) 108 (2019) 96–106 Table 1 The parameters values of the equivalent circuit of Fig. 13. Parameter
Value (CSS filter)
Value (SCSS filter)
Parameter
Value (CSS filter)
Value (SCSS filter)
LL1 LL2 LR1 LR2 LR3 LR4 CL1
1.11 nH 0.43 nH 0.92 nH 1.83 nH 0.56 nH 0.33 nH 0.78 pF
0.62 nH 0.18 nH 1.00 nH 2.81 nH 0.43 nH 0.31 nH 0.25 pF
CL2 CL3 CL4 CR1 CR2 CR3 CR4
0.39 pF 0.83 pF 0.35 pF 0.40 pF 0.73 pF 0.15 pF 0.56 pF
0.41 pF 0.43 pF 0.86 pF 0.46 pF 0.95 pF 0.23 pF 0.51 pF
the passbands at the left-handed and right-handed edges, respectively [23]. The dispersion is computed with introducing parameter A by S-parameters as [20–23]:
bp ¼ cos1
1 S211 þ S221 2S21
! ð9Þ
The dispersion diagrams of two proposed filters according to the equivalent circuit model and the FEM are illustrated in Fig. 14. The simulation results guarantee the credibility of the proposed equivalent circuit for recommended filters. It is obvious that the left-handed high-pass cutoff frequencies are fCL = 7.69 GHz and fCL = 7.55 GHz for Fig. 14(a) and (b), respectively. The right-handed low-pass cutoff frequencies occurs at fCR = 4.67 GHz and fCR = 5.41 GHz for the CSS and SCSS filters, respectively. Moreover, the phase constant of b is zero when the resonator works at the CRLH region. Therefore, at this resonance mode, the electromagnetic wave can propagate without the phase shift [24].
As shown in Fig. 14 (a) and (b), the frequency changes from RH to LH occurs at 6.20 GHz and 6.31 GHz for the CSS and SCSS filters, respectively. Hence, the proposed filters act as a balance CRLH structures, because in the balance case, the series resonance (xse) is equal to the shunt resonance (xsh) [23]. 5. Fabrication and measurement The photographs of the fabricated proposed filters are shown in Fig. 15 that the CSS and SCSS filters resonate at 6 GHz and 6.5 GHz, respectively. These filters have been fabricated on the RogersRT4003 substrate with 0.5 mm thickness. The dielectric constant of RogersRT4003 at 10 GHz is 3.38 ± 0.05. The sizes of the CSS and SCSS filters are 21.6 mm 3.06 mm (about 0.4kg by 0.07kg ) and 14.6 mm 4.2 mm (about 0.32kg by 0.1kg ), respectively, where kg is the central guided wavelength. The comparison between the frequency response of the simulation and measurement S-parameters of two proposed filters are depicted in Fig. 16. The simulated results come from the fullwave simulation based on FEM method and equivalent circuit
Fig. 14. Dispersion diagram of the proposed (a) CSS and (b) SCSS filters.
Fig. 15. The photographs of the fabricated WB bandpass filters. (a) CSS filter and (b) SCSS filter.
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Fig. 16. The comparison between the simulated, circuit model and measured results of |S11| and |S21| for (a) CSS filter and (b) SCSS filter and the group delay of (c) CSS filter and (d) SCSS with zoomed-in view of the passband.
Fig. 17. Current density distributions for the CSS filter at (a) 3.85 GHz and (b) 8.1 GHz and for the SCSS filter at (c) 4.9 GHz and (d) 9.1 GHz.
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S.M.M. Moshiri et al. / Int. J. Electron. Commun. (AEÜ) 108 (2019) 96–106 Table 2 Comparison of the proposed filters and reported wideband filters. References
f0
FBW (%)
Size kg kg
RL
IL
TZ
HS
CRLH-TL
[24] [26] [27] [28] [29] [30] [31] CSS Filter SCSS Filter
6 4 2.98 1 0.33 4 1.76 6 7
66 31 52 30 20.5 40 56.7 66 66
0.64 0.46 0.50 0.50 1.48 0.65 0.50 0.31 0.12 0.13 0.25 0.25 52 5 (mm mm) 0.4 0.07 0.32 0.10
15.3 10 18.3 19 20 15 >10 >17 >20
>1 2 >2.5 0.8 0.65 1 <0.85 <0.7 <0.5
Yes Yes Yes Yes Yes Yes No Yes Yes
2.3f0 (15 dB) — 2.51f0 (22.28 dB) — 4.5f0 (32 dB) — – 2.6f0 (21.4 dB) 2.23f0 (20.5 dB)
No No No No No Yes Yes Yes Yes
f0: Central frequency (GHz), RL: Return Loss (dB), IL: Insertion Loss (dB), TZ: Transmission Zero, HS: Harmonics Suppression.
model. According to Fig. 16, it is obvious that there is a good agreement between the simulation and measurement results. However, some tolerances in the fabrication process are observed that make the difference between the simulation and measurement results but it is natural. From Fig. 16(a), it can be seen that the CSS filter exhibits the return loss ðjS11 jÞ of greater than 17 dB in comparison to previous papers [24,25]. The average insertion loss ðjS21 jÞ of this wideband filter is less than 0.7 dB. Furthermore, the out-of-band rejection level of the proposed structure is greater than 20 dB from 8 to 16 GHz. These excellent features of the filter verify that it is appropriate for modern wideband wireless communication systems. As shown in Fig. 16(b), the return loss of the SCSS filter is higher than 20 dB and the insertion loss is less than 0.5 dB from 5 to 9 GHz, respectively. The out-of-band rejection level is better than 21 dB from 9.2 to 15.6 GHz. The group delay (Td) is the derivative of phase with respect to angular frequency that is described as [22]:
Td ¼
d/12 dx
ð10Þ
Fig. 16 also demonstrates the simulation and measurement results of the group delay of the proposed filters. As shown in Fig. 16(c) for the CSS filter, the measured group delay within the 4–8 GHz passband changes between 0.3 and 0.6 ns. In addition, in Fig. 16(d) for the SCSS filter, it varies between 0.2 and 0.52 ns in the range of 5–9 GHz. Large variation of group delay proves that the sharp transition caused in the rejection level can be observed near the filters passband edges. Therefore, the proposed filters have flat group delay in a wide frequency range in the passband. The current density distributions across the proposed wideband filters are depicted in Fig. 17. The current distributions of Figs. 17(a) and (b) for the CSS filter indicate that through the coupling stubs, the input signal at 3.85 and 8.1 GHz, is coupled from L2 to L3, L4 and interdigital capacitor. Moreover, as shown in Figs. 17(c) and (d) for the SCSS filter, the input signal at 4.9 and 9.1 GHz is coupled to L3 and L4.
6. The comparison of the current paper and the previous papers The proposed WB BPFs based on CRLH-TL are compared to the previous structures as depicted in Table 2. Our proposed structures not only have high passband selectivity but also have high out-ofband rejection and low return loss. Furthermore, the proposed filters have the priority of the compact size. Also, one of the most important specifications of the suggested filters is utilizing the CRLH-TL section that reduces the loss compared to the reported wideband filters.
7. Conclusion In this paper, we have represented two tuneable compact wideband bandpass filters based on the CRLH-TL structure. The coupled-shorted stub (CSS) has been utilized for easy control of the filters transmission zeros and the bandwidth by manipulating the dimension of one of the coupled lines or stepped-impedance resonator (SIR). SIR section generates controllable multiple resonance modes. The proposed methods have been enhanced and provided high passband selectivity, high out-of-band rejection and sharp passband skirt. Moreover, two suggested filters exhibit excellent characteristics and features. The CSS and SCSS filters have low insertion loss 0.5 dB and 0.7 dB, return loss >17 dB and >20 dB and a constant group delay from 0.3 to 0.6 ns within 4–8 GHz passband and from 0.2 to 0.52 ns in the range of 5–9 GHz, respectively. The fabrication procedure of the introduced filters is simple and easy. Meanwhile, a good agreement is observed between the simulated and measured results of the proposed filters. The dimensions of the designed filters are 21.6 3.06 mm2 and 14.6 4.2 mm2. Finally, the equivalent circuit and ABCD-matrix have been used to analyse the dispersion properties of the suggested filters and show the CRLH behaviour of them. These filters are convenient for utilizing in wideband wireless systems.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular paper
Compact and wideband bandpass filters with analysis of the CRLH-TL characteristics based on stepped impedance resonator Seyyed Mohammad Mehdi Moshiri, Maryam Khodadadi, Najmeh Nozhat ⇑ Department of Electrical Engineering, Shiraz University of Technology, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 6 March 2019 Accepted 12 June 2019
Keywords: Bandpass filter Composite right/left handed (CRLH) structure Coupled-shorted stub (CSS) Wideband (WB) Stepped impedance resonator (SIR)
a b s t r a c t In this paper, we have investigated two unique wideband (WB) bandpass filters (BPFs) based on composite right/left-handed (CRLH) structure that have high performance in C-band. The proposed filters have been implemented with stepped-impedance resonator (SIR) section and interdigital capacitors on it with a parallel coupled-shorted stub (CSS). High selectivity, high out-of-band rejection, low loss and two transmission zeroes at the lower and upper passband/stopband edges have been observed. The out-of-band rejection levels in two filters are better than 17 dB and 20 dB at the lower and upper band edges, respectively. In addition, the return loss and insertion loss of the proposed CSS filter are greater than 17 dB and less than 0.7 dB, respectively. Also, the return loss and insertion loss of the proposed spiral CSS (SCSS) filter are greater than 20 dB and less than of 0.5 dB, respectively. The presented structures have been investigated analytically and experimentally in order to verify balance between the results of the full-wave simulation and the equivalent circuit model with the experimental ones. The dimensions of the suggested filters are 21.6 3.06 mm2 and 14.6 4.2 mm2. The specifications and compact size of the filters make them suitable for wideband wireless communication systems. Ó 2019 Elsevier GmbH. All rights reserved.
1. Introduction Nowadays there is a necessity of a wide transmission bandwidth for wireless communication systems, which the frequency band is from 3.1 to 10.6 GHz. Therefore, wideband (WB) devices like filters in C-band (4–8 GHz) play a significant role in modern wireless local area networks (WLANs) and Bluetooth transceivers [1]. Since the federal communication commission (FCC) authorized the unlicensed use of ultra-WB (UWB) in 2002 [2], several surveys have been performed to develop wideband BPFs with different methods and structures [3–20]. Researches have proposed many different topologies for designing UWB filters such as stubloaded resonators [3], cascaded ring resonators filters that suffer from physical size but have good frequency response [4–8], UWB BPF with a notched band that suffers from poor skirt selectivity at both passband edges [7], TETRA band filters [11] and steppedimpedance slotline resonators [12]. Some of these structures have poor out-of-band rejection, narrow band transmission and complex design methodology. Recently, electromagnetic metamaterials have been used to design high performance filters [13–20]. The resonant-types of ⇑ Corresponding author. E-mail address: [email protected] (N. Nozhat). https://doi.org/10.1016/j.aeue.2019.06.011 1434-8411/Ó 2019 Elsevier GmbH. All rights reserved.
metamaterial structures that consist of split ring resonators (SRRs) and complementary split ring resonators (CSRRs) have been more used for the design of microwave filters [16,17]. Left-handed transmission lines (LH-TLs) with representing an abrupt transition pole at the lower or upper edge of the passband can improve the sharp attenuations near the passband and increase the bandwidth simultaneously [17–20]. The review of these articles [1,3–20] summarizes and mentions three main advantages in design of a filter. (1) Dimension: the size of the filter should be small enough so that the proposed filter is able to operate as a compact WB filter. (2) Simplicity of the fabrication process: the most microwave-integrated circuits have intricate structures due to the complex construction technology, which results in expensive and difficult fabrication process. However, this novel WB BPF has simple planar geometry and so can be succeeded in facing up to fabrication problems. (3) Improving the performance: a wideband filter must be devised with a high controlled passband selectivity and suitable out-of-band rejection. Hence, it has been suggested to utilize composite right/left handed transmission line (CRLH-TL) and high-low-high stepped-impedance resonator (SIR). It is worth to note that one of the specific features of the CRLH-TL is reduction of the loss [19,20]. In this paper, two unprecedented CRLH-TL wideband BPF topologies have been proposed based on SIR with introducing
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interdigital capacitors on it. In recommended structures the coupled-shorted stub (CSS) has been used to generate the transmission zeroes. The CRLH transmission lines have been applied to enhance the performance of the WB BPF and decrease the loss, effectively. According to these sketching, the prototype filters would have high selectivity with sharp skirt at the upper and lower band edges, high out-of-band rejection and low return loss. To achieve the desired wide band (4–8 GHz for the CSS filter and 5–9 GHz for the SCSS filter) and high out-of-band rejection, we can change the length and width of the SIR section. On one hand, in order to develop the sharp skirt at the upper band edge of the proposed filters, the spiral defected SIR structure has been used. On the other hand, the sharp skirt at the lower band edge and high out-ofband rejection of the bandpass filters can be controlled by the CSS section. Furthermore, in two structures, the left-handed (high-pass nature) section of the filter has been introduced by series interdigital capacitor and shorted shunt inductive line that the length of the section is smaller than kg/4, where kg is the guided wavelength. Also, the right-handed (low-pass nature) characteristic has been rendered by effective inductance of the middle transmission line (TL) section and the effective capacitance nominated by SIR section. As a result, the proposed layouts act as CRLH structures. The structures have been analyzed analytically and numerically by the finite element method (FEM). Moreover, the equivalent circuits of suggested filters are derived to obtain an insight into the working principle and calculate the dispersion diagram to show the CRLH performance of the filters. In addition, the results of the fabricated structures have been compared with the simulated results. The fractional bandwidth of the recommended filters is 66%. The insertion loss of the CSS filter is less than 0.7 dB and the return loss is greater than 17 dB. Furthermore, the insertion loss of the SCSS filter is less than 0.5 dB and the return loss is greater than 20 dB. The most important specifications of our suggested WB BPFs are wide bandwidth, multi-transmission poles, sharp lower and upper edges, compact size, high selectivity, higher outof-band rejection, flat group delay, simple design procedure and low cost. This paper is organized as follows. In Section 2, the fundamental aspects of the proposed filters are studied. In Section 3, design and analysis of two proposed filters are presented. In Section 4, the CRLH-TL characteristics are analyzed. In Section 5, the fabrication and measurement results are shown and compared with the previous works. The paper is concluded in Section 6. 2. Fundamental aspect of the proposed filters 2.1. Multi-mode resonance (MMR) feature The initial bandwidth is determined by high-low-high steppedimpedance resonator section that plays an important role as a multi-mode resonator structure. The schematic view of the SIR is depicted in Fig. 1. The middle TL section in Fig. 1 has the most
Fig. 1. High-low-high stepped-impedance multi-mode section.
important effect to create a wideband filter. The characteristic impedances of the low and high SIR are introduced by Z1 and Z2, respectively, and the electric lengths are defined by h1 and h2 . Two high impedance sections are used to couple with the input and output feed lines [15]. Particularly, one approach to calculate the resonance frequency is to obtain and analyse a circuit model of the coupling. However, for higher multimode microstrip resonator filters, this method is sometimes difficult. The other way to find the resonance frequency is utilizing the transmission line theory. The MMR is considered without the input and output coupling and the input admittance equals to zero. However, because of the reflection symmetry plane in the principle section of the proposed filters (MMR), according to Fig. 1, we should use two benefit strategies: 1. When the symmetry plane M-M0 is short-circuited, it illustrates even mode:
YL þ YR ¼ 0
ð1Þ 0
2. When the symmetry plane M-M is open-circuited, it shows odd mode:
ðY L þ Y R Þ ! 1
ð2Þ
where YL and YR are the input admittances from the middle of the MMRs and given by:
Y L ¼ jY 1
Y 1 tanh1 þ Y 2 tanh2 RZ tanh1 þ tanh2 ¼ jY 1 ¼ YR Y 1 Y 2 tanh1 tanh2 RZ tanh1 tanh2
ð3Þ
where the impedance ratio of the high and low lines is defined as RZ ¼ YY 12 ¼ ZZ21 ¼ k. The odd and even mode analysis is useful for calculating the the resonance frequencies of any multi-mode resonators. Generally, the resonance frequencies can be calculated by considering an appropriate proportion of the electric lengths of the MMR structure ðh1 and h2 Þ [15]. When h1 ¼ h2 , the resonance frequencies are defined as [15]:
f1 ¼
c pffiffiffi tan1 k 2p l
ð4aÞ
f2 ¼
c 4l
ð4bÞ
f3 ¼
c pffiffiffi p tan1 k 2p l
ð4cÞ
f4 ¼
c 2l
ð4dÞ
According to Eq. (4), it should be noted that these calculated resonance frequencies are dependent on the value of k. This dependency represents a relation between the resonant mode frequencies and the fundamental mode [16]. Consequently, the resonant mode frequencies get closer together for k > 1 [15,16]. In our initial proposed filters the correlation of h1 and h2 is considered as 3h1 ¼ h2 and four resonance frequencies are defined as:
c f1 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3ðk þ 1Þ n 2
c f2 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi kþ3 3k þ 1
c f3 ¼ tan1 2p l
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3ðk þ 1Þ þ n 2
ð5aÞ
ð5bÞ
ð5cÞ
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0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 pffiffiffi c @p tan1 3ðk þ 1Þ þ nA f4 ¼ 2pl 2
ð5dÞ
2
n ¼ 9k þ 14k þ 9 According to the Eq. (3) and considering the conditions of Eqs. (1) and (2), we can obtain Fig. 2(a) that illustrates the electric length ratio versus the resonance frequency ratio with k = 4.62. In addition, the relation between the impedance ratio and resonance frequency ratio with 3h1 ¼ h2 is shown in Fig. 2(b). It is observed that the bandwidth of the proposed WB bandpass filter can be controlled by the electric length and impedance ratio of the stepped-impedance line in the first three resonance frequencies.
the effective dielectric constant and transmission line length, respectively.
2.2. Interdigital capacitor on MMR
2.3. Coupled-shorted stub (CSS) section
In design of wideband filters, despite the importance of the bandwidth, the sharpness of the upper and lower edges is also important. Therefore, in order to obtain sharp upper edge, an interdigital capacitor on SIR is used. The schematic view of the interdigital capacitor and its equivalent electrical circuit are depicted in Fig. 3. There are several benefits for using this structure. One of them is the ability to control the location of the transmission zeros by changing the number, length and distance between the digits on the SIR, because of changing the values of capacitance and inductance in its equivalent circuit. The other one is the absence of undesirable parasitic mode in the stopband. In Fig. 3(b), C and L are operated as an interdigital capacitor that we can calculate its resonance frequency as:
Definitely, one of the most significant features in design and construction of a filter is a high out-of-band rejection. As mentioned in pervious section, the SIR creates undesirable modes in stopband and these modes prevent from increasing the out-ofband rejection. Hence, in this paper, in order to achieve an appropriate out-of-band rejection and omit the unfavourable modes, the CSS section is used. This technique generates two transmission zeros, which one of them is used to provide sharp lower band edge and the other one is utilized to increase the bandwidth of the outof-band rejection from 8 GHz to 16 GHz. This advantage is undeniable because of decreasing the effect of deterministic undesirable modes. The schematic view of the CSS section and its equivalent electrical circuit are shown in Fig. 4. The resonance frequency of the CSS can be obtained as:
1 f ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 C ðLP þ LS Þ
ð6aÞ
Fig. 3. The schematic view of (a) the interdigital capacitor and (b) its equivalent electrical circuit.
1 f ¼ 2p
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 LðC P þ C S Þ
ð7Þ
The location of the resonance frequency of sharp upper band edge can be controlled by Eq. (6) as a transmission zero. Moreover, by considering that the transmission line length of the filter is shorter than the wavelength, the desired values of the capacitor and inductor are calculated as [21]:
C¼
l
ð6bÞ
v Z0
Lp;s ¼
lZ 0
ð6cÞ
v
where Z0 and
v ¼ pcffiffiffiffiffi are the characteristic impedance and phase e eff
velocity of the transmission line, respectively. Also,
eeff and l are
Fig. 4. The schematic view of (a) the coupled-shorted stub and (b) its equivalent electrical circuit.
Fig. 2. (a) Normalized resonance frequency versus the electric length ratio with k = 4.62. (b) Normalized resonance frequency as a function of the impedance ratio with 3h1 = h2 .
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The location of the resonance frequency of sharp upper band edge can be controlled by Eq. (7). Combining the MMR, interdigital capacitor and CSS constructs the principle of the introduced filters specifications. In the next sections, the design, performance improvement and selectivity of the suggested filters are described. 3. Filter design and analysis 3.1. Wideband bandpass filter based on CSS (CSS filter) The configuration of the suggested microstrip WB bandpass filter and its physical parameters are illustrated in Fig. 5. For optimizing the dimensions of the recommended filter, the FEM is used. In essence, the main advantage of this structure is its sharp band edges. The upper and lower band edges are sharpened and enhanced by applying interdigital capacitors on SIR and CSS sections, respectively. We have confirmed that in the proposed structure, two resonance frequencies are observed and can be controlled by changing the dimensions of the structural parameters such as L4 and g6. The effect of variation of L4 on jS21 j parameter is plotted in Fig. 6 (a) and it is shown that how this parameter can change the location of the upper zero. Also, by moving the via in an arm of the CSS, the upper transmission zero can be controlled as depicted in Fig. 6(b). Furthermore, as shown in Fig. 6(c), by varying g6, the lower zero is shifted more than the upper zero that illustrates the lower zero can be controlled by g6. In essence, considerable tuning can be achieved by three degrees of freedom for precise location of the transmission zeros. 3.2. Wideband bandpass filter based on spiral CSS (SCSS filter) The configuration of the second suggested microstrip wideband bandpass filter and its physical parameters are illustrated in Fig. 7. For optimizing the dimensions, the FEM method is used. The schematic view of the high coupling CSS and its equivalent electrical circuit are depicted in Fig. 8. The location of the resonance frequency of the band edges have been controlled by Eq. (7). One of the most achievements in this recommended structure is its compactness. The size of the proposed SCSS filter
99
(14.6 4.2 mm2) is smaller than the size of the CSS filter (21.6 3.06 mm2) that is introduced in the previous subsection. Moreover, decreasing the size of the filter is possible with utilizing unexampled spiral coupling method. In the SCSS filter, the function of this new coupling method causes the high coupling between the feed line and the other parts of the filter in comparison to the CSS filter and improves the performance of the suggested filter. In addition, design of the SCSS filter in the range of 5–9 GHz indicates that we can control the passband of the proposed filter by changing the dimensions of the SIR. Furthermore, the tunability of this filter is as an important factor for design and fabrication of a novel and efficient filter in the communications industry. This proposed structure can be affected the sharp skirt at the lower and upper band edges by utilizing the transmissions zeros that introduced in Fig. 7. The simulated frequency responses for different values of L4, L5 and g1 are shown in Fig. 9. It can be seen that there are five main resonance modes, namely, fm1, fm2, fm3, fm4, and fm5 in the range of 4–16 GHz. As shown in Fig. 9(a), by increasing the parameter L4 from 4.1 to 4.7 mm, the odd resonance modes of fm1 and fm5 tend to slowly shift descending and the other modes remain stable and fixed. On the other hand, as Fig. 9(b) depicts, by changing the length of L5 from 2.75 to 3.35 mm, only even resonance mode of fm4 moves towards the lower frequency. In nutshell, by changing the lengths of L4 and L5 we can control the location of the transmission zeros and passband of the proposed filter. It can be seen from Fig. 9(c), as the length of g1 varies from 0.1 to 0.4 mm, just the resonance modes of fm2 and fm3 tend to move towards the lower and higher frequencies, respectively. As a result, the five resonance modes confirm the superiority of the SCSS filter to make a wideband BPF with increased coupling degree. From Figs. 2 and 9, it is obvious that the modes properties of the resonator depend on the stub length and it verifies that we are able to get a significant WB BPF that covers the frequency range of 3.1–10.6 GHz for wideband systems.
3.3. Frequency response of the proposed filters To verify the performance of each part of the introduced filters, the scattering parameters of the MMR, CSS, and interdigital capacitor sections are studied. It is mentioned in Section 2 that the role
Fig. 5. (a) Configuration of the proposed WB filter and (b) physical parameters of the unit cell. L1 = 8.00, L2 = 8.00, L3 = 7.00, L4 = 6.02, 2 L5 = 3.15, g1 = 0.20, g2 = 0.20, g3 = 0.15, g4 = 0.20, g5 = 0.15, g6 = 0.40, g7 = 0.20, g8 = 0.20, g9 = 0.30, g10 = 0.20, g11 = 2.50 (All dimensions are in mm).
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Fig. 6. Simulated jS21 j of the CSS filter for different values of (a) L4, (b) location of via in L3 and L4 and (c) g6.
Fig. 7. (a) Configuration of the proposed WB filter and (b) physical parameters of the unit cell. L1 = 1.55, L2 = 1.25, L3 = 4.3, L4 = 4.20, 2 L5 = 3.55, L6 = 1.65, L7 = 1.10, L8 = 1.55, L9 = 2.05, L10 = 1.80, g1 = 0.20, g2 = 0.15, g3 = 0.15, g4 = 0.50, g5 = 0.20, g6 = 0.30, g7 = 0.20, g8 = 0.10, g9 = 1.00, g10 = 0.10 (All the dimensions are in mm).
of the MMR without utilizing the CSS and interdigital capacitor is creating desired bandwidth, as shown in Fig. 10. In order to enhance the sharpness of the filter, the CSS and interdigital capacitor are used in the microstrip section to add two transmission zeros. As illustrated in Fig. 11(a), the
coupled-shorted stub section is used to add a transmission zero at the lower edge of the CSS filter. Moreover, Fig. 11(b) confirms that by utilizing high coupling CSS in the SCSS filter, not only the lower edge becomes sharpness, but also a transmission zero at the out-of-band rejection near the upper edge creates. Finally,
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the effect of interdigital capacitor on the MMR is investigated. As demonstrated in Fig. 12, utilizing the interdigital capacitor creates transmission zero at the upper edge of the suggested filters. 4. CRLH-TL characteristics
Fig. 8. The schematic view of (a) the coupled-shorted ring stub and (b) its equivalent electrical circuit.
The equivalent circuit of the proposed filters based on the CSS is depicted in Fig. 13 and the parameters values of the suggested filters are given in Table 1. According to Fig. 13, the horizontal section (a) consists of LR1 and series CL1-LR2 resonator and models the effect of the feed line and high impedance of the SIR section. The vertical section (b) includes two identical parallel structures that each one shows a transmission zero created by the CSS. CL3
Fig. 9. Simulated jS21 jof the SCSS filter for different values of (a) L4 (b) L5 and (c) g1.
Fig. 10. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSS filters to show the MMR function without the CSS section and interdigital capacitor.
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Fig. 11. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSS filters to show the CSS function without the interdigital capacitor on the MMR.
Fig. 12. The simulated jS11 j and jS21 j of (a) the CSS and (b) SCSSs filter to show the interdigital capacitor function without the CSS section.
Fig. 13. Equivalent circuit of the proposed filters of Figs. 5 and 7.
and CL4 are used for showing the coupling between the feed line and CSS that are in series with a parallel LL1-CR2 resonator. This parallel resonator models the CSS in the equivalent circuit of Figs. 5 and 7. The horizontal section (c) shows the equivalent circuit of the coupling between the low impedance of SIR and the interdigital capacitor on it. The shunt capacitances of CR1 and CR4 are parasitic and they cannot be omitted. In a nutshell, the proposed structures are composed of series inductance of LR and shunt capacitance of CR, and also series capacitance of CL and shunt inductance of LL that act as right-handed and left-handed topology, respectively. Therefore, the proposed filters are known as a CRLH-TL structure.
To understand the operating principle of the CRLH filters, the ABCD-matrix is used to analyse the circuit properties such as dispersion characteristic. The dispersion relation is calculated by [20–23]:
cosðbpÞ ¼
A þ D A¼D ! cosðbpÞ ¼ A 2
ð8Þ
where p is the unit-cell length. Indeed, as shown in Fig. 13, the equivalent circuit is symmetric. Hence, for analysis of the properties of the proposed filters, the parameter A can be used [20–23]. If the matrix element A sets equal to 1 and the roots are solved, the cutoff frequencies are calculated. These frequencies show the cutoffs of
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S.M.M. Moshiri et al. / Int. J. Electron. Commun. (AEÜ) 108 (2019) 96–106 Table 1 The parameters values of the equivalent circuit of Fig. 13. Parameter
Value (CSS filter)
Value (SCSS filter)
Parameter
Value (CSS filter)
Value (SCSS filter)
LL1 LL2 LR1 LR2 LR3 LR4 CL1
1.11 nH 0.43 nH 0.92 nH 1.83 nH 0.56 nH 0.33 nH 0.78 pF
0.62 nH 0.18 nH 1.00 nH 2.81 nH 0.43 nH 0.31 nH 0.25 pF
CL2 CL3 CL4 CR1 CR2 CR3 CR4
0.39 pF 0.83 pF 0.35 pF 0.40 pF 0.73 pF 0.15 pF 0.56 pF
0.41 pF 0.43 pF 0.86 pF 0.46 pF 0.95 pF 0.23 pF 0.51 pF
the passbands at the left-handed and right-handed edges, respectively [23]. The dispersion is computed with introducing parameter A by S-parameters as [20–23]:
bp ¼ cos1
1 S211 þ S221 2S21
! ð9Þ
The dispersion diagrams of two proposed filters according to the equivalent circuit model and the FEM are illustrated in Fig. 14. The simulation results guarantee the credibility of the proposed equivalent circuit for recommended filters. It is obvious that the left-handed high-pass cutoff frequencies are fCL = 7.69 GHz and fCL = 7.55 GHz for Fig. 14(a) and (b), respectively. The right-handed low-pass cutoff frequencies occurs at fCR = 4.67 GHz and fCR = 5.41 GHz for the CSS and SCSS filters, respectively. Moreover, the phase constant of b is zero when the resonator works at the CRLH region. Therefore, at this resonance mode, the electromagnetic wave can propagate without the phase shift [24].
As shown in Fig. 14 (a) and (b), the frequency changes from RH to LH occurs at 6.20 GHz and 6.31 GHz for the CSS and SCSS filters, respectively. Hence, the proposed filters act as a balance CRLH structures, because in the balance case, the series resonance (xse) is equal to the shunt resonance (xsh) [23]. 5. Fabrication and measurement The photographs of the fabricated proposed filters are shown in Fig. 15 that the CSS and SCSS filters resonate at 6 GHz and 6.5 GHz, respectively. These filters have been fabricated on the RogersRT4003 substrate with 0.5 mm thickness. The dielectric constant of RogersRT4003 at 10 GHz is 3.38 ± 0.05. The sizes of the CSS and SCSS filters are 21.6 mm 3.06 mm (about 0.4kg by 0.07kg ) and 14.6 mm 4.2 mm (about 0.32kg by 0.1kg ), respectively, where kg is the central guided wavelength. The comparison between the frequency response of the simulation and measurement S-parameters of two proposed filters are depicted in Fig. 16. The simulated results come from the fullwave simulation based on FEM method and equivalent circuit
Fig. 14. Dispersion diagram of the proposed (a) CSS and (b) SCSS filters.
Fig. 15. The photographs of the fabricated WB bandpass filters. (a) CSS filter and (b) SCSS filter.
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Fig. 16. The comparison between the simulated, circuit model and measured results of |S11| and |S21| for (a) CSS filter and (b) SCSS filter and the group delay of (c) CSS filter and (d) SCSS with zoomed-in view of the passband.
Fig. 17. Current density distributions for the CSS filter at (a) 3.85 GHz and (b) 8.1 GHz and for the SCSS filter at (c) 4.9 GHz and (d) 9.1 GHz.
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S.M.M. Moshiri et al. / Int. J. Electron. Commun. (AEÜ) 108 (2019) 96–106 Table 2 Comparison of the proposed filters and reported wideband filters. References
f0
FBW (%)
Size kg kg
RL
IL
TZ
HS
CRLH-TL
[24] [26] [27] [28] [29] [30] [31] CSS Filter SCSS Filter
6 4 2.98 1 0.33 4 1.76 6 7
66 31 52 30 20.5 40 56.7 66 66
0.64 0.46 0.50 0.50 1.48 0.65 0.50 0.31 0.12 0.13 0.25 0.25 52 5 (mm mm) 0.4 0.07 0.32 0.10
15.3 10 18.3 19 20 15 >10 >17 >20
>1 2 >2.5 0.8 0.65 1 <0.85 <0.7 <0.5
Yes Yes Yes Yes Yes Yes No Yes Yes
2.3f0 (15 dB) — 2.51f0 (22.28 dB) — 4.5f0 (32 dB) — – 2.6f0 (21.4 dB) 2.23f0 (20.5 dB)
No No No No No Yes Yes Yes Yes
f0: Central frequency (GHz), RL: Return Loss (dB), IL: Insertion Loss (dB), TZ: Transmission Zero, HS: Harmonics Suppression.
model. According to Fig. 16, it is obvious that there is a good agreement between the simulation and measurement results. However, some tolerances in the fabrication process are observed that make the difference between the simulation and measurement results but it is natural. From Fig. 16(a), it can be seen that the CSS filter exhibits the return loss ðjS11 jÞ of greater than 17 dB in comparison to previous papers [24,25]. The average insertion loss ðjS21 jÞ of this wideband filter is less than 0.7 dB. Furthermore, the out-of-band rejection level of the proposed structure is greater than 20 dB from 8 to 16 GHz. These excellent features of the filter verify that it is appropriate for modern wideband wireless communication systems. As shown in Fig. 16(b), the return loss of the SCSS filter is higher than 20 dB and the insertion loss is less than 0.5 dB from 5 to 9 GHz, respectively. The out-of-band rejection level is better than 21 dB from 9.2 to 15.6 GHz. The group delay (Td) is the derivative of phase with respect to angular frequency that is described as [22]:
Td ¼
d/12 dx
ð10Þ
Fig. 16 also demonstrates the simulation and measurement results of the group delay of the proposed filters. As shown in Fig. 16(c) for the CSS filter, the measured group delay within the 4–8 GHz passband changes between 0.3 and 0.6 ns. In addition, in Fig. 16(d) for the SCSS filter, it varies between 0.2 and 0.52 ns in the range of 5–9 GHz. Large variation of group delay proves that the sharp transition caused in the rejection level can be observed near the filters passband edges. Therefore, the proposed filters have flat group delay in a wide frequency range in the passband. The current density distributions across the proposed wideband filters are depicted in Fig. 17. The current distributions of Figs. 17(a) and (b) for the CSS filter indicate that through the coupling stubs, the input signal at 3.85 and 8.1 GHz, is coupled from L2 to L3, L4 and interdigital capacitor. Moreover, as shown in Figs. 17(c) and (d) for the SCSS filter, the input signal at 4.9 and 9.1 GHz is coupled to L3 and L4.
6. The comparison of the current paper and the previous papers The proposed WB BPFs based on CRLH-TL are compared to the previous structures as depicted in Table 2. Our proposed structures not only have high passband selectivity but also have high out-ofband rejection and low return loss. Furthermore, the proposed filters have the priority of the compact size. Also, one of the most important specifications of the suggested filters is utilizing the CRLH-TL section that reduces the loss compared to the reported wideband filters.
7. Conclusion In this paper, we have represented two tuneable compact wideband bandpass filters based on the CRLH-TL structure. The coupled-shorted stub (CSS) has been utilized for easy control of the filters transmission zeros and the bandwidth by manipulating the dimension of one of the coupled lines or stepped-impedance resonator (SIR). SIR section generates controllable multiple resonance modes. The proposed methods have been enhanced and provided high passband selectivity, high out-of-band rejection and sharp passband skirt. Moreover, two suggested filters exhibit excellent characteristics and features. The CSS and SCSS filters have low insertion loss 0.5 dB and 0.7 dB, return loss >17 dB and >20 dB and a constant group delay from 0.3 to 0.6 ns within 4–8 GHz passband and from 0.2 to 0.52 ns in the range of 5–9 GHz, respectively. The fabrication procedure of the introduced filters is simple and easy. Meanwhile, a good agreement is observed between the simulated and measured results of the proposed filters. The dimensions of the designed filters are 21.6 3.06 mm2 and 14.6 4.2 mm2. Finally, the equivalent circuit and ABCD-matrix have been used to analyse the dispersion properties of the suggested filters and show the CRLH behaviour of them. These filters are convenient for utilizing in wideband wireless systems.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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