BPF analysis and design

The basic BPF structure consists of SCCPW and microstrips on either side of the substrate. We start the analysis by first modeling the SCCPW, followed by its optimized coupling with the top plane. Figure 2(a) depicts the simplified topology of the SCCPW, whereas its transmission line equivalent is represented in Fig. 2(b). The central and end sections of the SCCPW have impedances and electrical lengths of Z ₁, 2θ ₁ and Z ₂, θ ₂. The input resistance Z _input at the left end looking into the right, for a general transmission line of electrical length θ, characteristic resistance Z ₀ and terminated with load resistance Z _L, is given by [Reference Zhu, Sun and Li19]

(1)\begin{equation}{Z_{{\rm{input}}}} = {Z_0}\left( {{{{Z_L} + {Z_0}j\tan \theta } \over {{Z_0} + {Z_{\rm{L}}}\,j\tan \theta }}} \right)\end{equation}

Figure 1. Geometrical representation of the proposed triple notched band BPF. Dark color is the conductor, whereas white shades are the slots. The optimized values are as follows: w ₀ = 0.76 mm, w ₁ = 0.64 mm, g ₀ = 0.4 mm, p = 2.18 mm, q = 2.35 mm, v ₁ = 5.25 mm, v ₂ = 3.5 mm, t ₁ = 0.15 mm, l ₁ = 1.78 mm, l ₂ = 1.28 mm, k ₁ = 5.62 mm, k ₂ = 3.12 mm, k ₃ = mm, a = 2.4 mm, b = 2.4 mm, G ₀ = 2.49 mm, L = 14 mm, W = 11.4 mm.

Figure 2. (a) Topology of the MMR for the proposed BPF. Wide arm of characteristic impedance and electrical length Z ₁, θ ₁ respectively, while the narrow arm has characteristic impedance and electrical length Z ₂, θ ₂ respectively. (b) Equivalent transmission line model of the MMR.

From Fig. 2, the input impedance Z _a, with characteristic resistance Z ₂ and short-circuited load (Z _L = 0), can hence be written as

(2)\begin{equation}{Z_{\rm{a}}} = {Z_2}j\tan {\theta _2}\end{equation}

Eventually, Z _in can be evaluated as

(3)\begin{equation}{Z_{{\textrm{in}}}} = {Z_2}\left( {{{{Z_{\textrm{b}}} + j{Z_2}\tan {\theta _2}} \over {{Z_2} + j{Z_b}\tan {\theta _2}}}} \right)\end{equation}

Placing the values of Z _b and Z _a in terms of Z ₁, Z ₂, (R = Z ₁/Z ₂) and including them in equation (3), we get

(4)\begin{equation}{Z_{in}} = j{Z_{2 }}\left( {{2{\left( {R\tan {\theta _{1 }} + \tan {\theta _{2 }}} \right)}{\left( {R - \tan {\theta _{1 }}\tan {\theta _{2 }}} \right)}} \over {\begin{array}{c}R\left( {1 - ta{n^2}{\theta _1}} \right)\left( {1 - ta{n^2}{\theta _2}} \right)\\ - 2\left( {1 + {R^2}} \right)\tan {\theta _{1 }}\tan {\theta _{2 }}\end{array}}} \right)\end{equation}

At resonance (${Z_{{\textrm{in}}}} = 0),$ equation (4) simplifies to

(5)\begin{equation} R\tan {\theta _1} + \tan {\theta _2} = 0\end{equation}

and

(6)\begin{equation}R - \tan {\theta _1}\tan {\theta _2} = 0\end{equation}

For the above structure, θ ₁ ≈ θ ₂ ≈ θ, hence, equations (6) and (7) reduce to

(7)\begin{equation} R{\textrm{tan }}\theta + {\textrm{tan }}\theta = 0\end{equation}

and

(8)\begin{equation}R - {\tan ^2}\theta = 0\end{equation}

Solving the above equations using the analytical method gives three resonant frequencies:

(9)\begin{equation}\theta \left( {{\,f_\alpha }} \right) = {\textrm{ta}}{{\textrm{n}}^{ - 1}}\left( {\sqrt R } \right)\end{equation}

(10)\begin{equation}\theta \left( {{f_\beta }} \right) = {\pi \over 2}\end{equation}

(11)\begin{equation}\theta \left( {{f_\gamma }} \right) = \pi - {\textrm{ta}}{{\textrm{n}}^{ - 1}}\left( {\sqrt R } \right)\end{equation}

The central section of SCCPW has, x ₁ = 5.25 mm, y ₁ = 5.55 mm, s ₀ = 0.4 mm, for which Z ₁ = Z _0(CPW1) = 38.9 Ω and θ ₁ = 39.3^º. Similarly, the wider end sections have x ₂ = 2.48 mm, y ₂ = 6.86 mm and s ₀ = 0.4 mm corresponding to Z ₂ = Z _0(CPW2) = 37.83 Ω and θ ₂ = 36.31^º. Therefore, R = Z ₁/Z ₂ ≈ 1.

Post the design of SCCPW, its optimized coupling with the microstrip lines on the top plane is considered using the knowledge that maximum coupling of broadside transition of CPW/microstrip occurs for [Reference Baik, Lee and Kim18],

(12)\begin{equation}{Z_{{\textrm{0}}\left( {{\textrm{microstrip}}} \right)}} = 2{Z_{\textrm{0(CPW1)}}}\end{equation}

For our filter under consideration, with t ₀ = 0.15 mm, Z _{0(microstrip)} = 81.4 Ω is obtained, and as calculated above, Z _0(CPW1) = Z ₁ = 38.9 Ω, i.e., equation (12) is balanced. Later, in CPW2, the slot ends are modified to square-shaped DGS to adjust the 3-dB cutoff bandwidth of the filter. Figure 3(a) provides us with the weak coupling response for various values of R and the optimized simulated response of the basic broadside coupled BPF is provided in Fig. 3(b). It can be observed that the passband of BPF extends from 2.35 to 10.78 GHz with return/insertion loss better than 17/0.38 dB. The BPF depicts steep selectivity of >47 and >128 dB/GHz respectively, at lower and upper passband edges due to TZs at 0.95 and 11.2 GHz. The third TZ at 13 GHz extends the stopband till 14 GHz.

Figure 3. (a) Frequency response of the basic BPF for weak coupling. (b) Optimized frequency response of the broadside coupled UWB-BPF.

Notched band implementation and upper stopband extension

Due to the emission mask (−75 mW/MHz) imposed by FCC on UWB systems, they seldom become the source of interference. However, other wireless services like WLAN, C band, X band, etc., present within the UWB passband, are high-power radio-frequency emitters, cause interference [1]. UWB-BPFs are often embedded with bandstop filters (BSFs) to eliminate such interfering threats. These BSFs could be in the form of resonators [Reference Shi, Xi, Zhao and Yang2–Reference Chakraborty, Shome, Panda and Deb5, Reference Wei, Li, Shi and Huang9–Reference Gholipoor, Honarvar and Virdee13], DGS [Reference Ghazali and Pal6–Reference Sazid and Raghava8], DMS [Reference Wang, Zhao and Li14], appended to or coupled with the basic BPF geometry. Here, we inculcate the bandstop filtering characteristics using only resonators, a few of which are embedded in the ground and two independent ones coupled to the top (Fig. 1). These resonators are varied in length to tune their notch frequency and placed at our point of interest within the passband. The resonator lengths are related to their corresponding notch frequency positions through the following equations:

(13)\begin{equation}f\left( {@5.2\;{\textrm{GHz}}} \right) \approx c/\left\{ {2{l_{k1}}\sqrt {{\varepsilon _{{\textrm{reff}}}}} } \right\}\end{equation}

(14)\begin{equation}f\left( {@6.5\;{\textrm{GHz}}} \right) \approx c/\left\{ {2{l_{{\textrm{FSRR}}}}\sqrt {{\varepsilon _{{\textrm{reff}}}}} } \right\}\end{equation}

(15)\begin{equation}f\left( {@7.9\;{\textrm{GHz}}} \right) \approx c/\left\{ {2{l_{k2}}\sqrt {{\varepsilon _{{\textrm{reff}}}}} } \right\}\end{equation}

where c is the velocity of light and ε _reff = 6.08. It is observed that at their frequency of operation, the resonators are approximately a quarter of their guided wavelength. Figure 4 below depicts the depth of tuning of the single/multiple notches within the UWB passband for variable length of each resonator, respectively. This above property helps eradicate unwanted interferences at any operating frequency within the UWB spectrum.

Figure 4. Dynamic positions of (a) single notches for variable values of k ₁, (b) dual notches for variable values of k ₁ and k ₂, (c) triple notches for variable values of k ₁, k ₂, and k _3.

The basic BPF (Fig. 3) depicts good frequency characteristics in terms of its passband and lower stopband. However, the upper stopband needs some attending to. In that respect, LPF, in the form of multiple stubs, is appended to the output feeding line [Reference Zhu, Sun and Li19, Reference Li and Zhu20]. These stubs develop TZ at 14.7 GHz in the stopband to reduce the attenuation below −17 dB and extend the stopband to 18 GHz. Figure 5 below depicts the comparative frequency response of single/multiple notched BPFs with and without embedded LPF. It can be observed that these BPFs have upper stopband attenuated below −17 dB and extended till 18 GHz.

Figure 5. Comparative frequency responses of the single, double, and triple band-notched UWB filter with and without LPF.

The current distribution across the BPF structure is portrayed in Fig. 6, which depicts that at their respective frequencies of operation (5.2, 6.5, and 7.9 GHz), the resonators have the highest current concentration, whereas at 14.7 GHz, the current density is maximum in the LPF. The current density concentration on a particular component of the BPF at that frequency depicts its activeness compared to other components. An approximate equivalent lumped element circuit model of the proposed BPF is constructed (Fig. 7a), and its response is observed against the full-wave EM simulation data in Fig. 7(b). The input feeding line is represented by L ₆, whereas the parallel combination of L ₇ and C ₁₁ represents the output feeding line embedded with the LPF. The parallel combination of L ₁ and C ₁ represents the stubs attached to input/output feeding lines, whereas their separation is depicted by the gap capacitance C ₀. The tank circuit consisting of L ₄, C ₄, and C ₈ portrays the SCCPW-based ground plane in which variable length resonators (described by parallel circuits L ₂, C ₂ and L ₃, C ₃) are coupled through capacitances C ₆ and C ₇. The FSRRs are depicted by the combination of L ₅, C ₅, and C ₉ coupled to the BPF structure through C ₁₀.

Figure 6. Current distribution in the proposed triple-notched BPF at their respective frequencies of (a) 5.2, (b) 6.5, (c) 7.9, and (d) 14.7 GHz.

Figure 7. (a) Approximate equivalent circuit model of the proposed triple notched band BPF. (b) Comparative frequency characteristics for full-wave EM and circuit simulation.

The equivalent circuit model of the proposed UWB filter is based on paper [Reference Lin, Li, Chen, Lin and Houng21]. The location of the notches is evaluated from paper [Reference Lin, Li, Chen, Lin and Houng21], as

(16)\begin{equation}{f_{{{\rm lower }}}}\;\;{\rm{TZ}}\;{{\rm = }}\;1/\{ 2\pi \surd \left( {{L_1}{C_1} + {L_1}{C_0}} \right)\end{equation}

for L ₁ = 4.3 nH, C ₁ = 5.46 pF, and C ₀ = 0.022 pF, we get f = 0.95 GHz.

(17)\begin{equation}{f_{\left( {@{\ }5.2{\textrm{ GHz}}} \right)}} = {\ }1/\{ 2\pi \surd \left( {{L_2}{C_2} + {L_2}{C_6}} \right)\end{equation}

for L ₂ = 1.36 nH, C ₂ = 0.3275 pF, and C ₆ = 0.355 pF, we get f = 5.22 GHz.

(18)\begin{equation}{f_{\left( {@{\ }6.5{\textrm{ GHz}}} \right)}} = {\ }1/\{ 2\pi \surd \left( {{L_5}{C_5} + {L_5}{C_9}} \right)\end{equation}

for L ₅ = 0.721 nH, C ₅ = 0.21 pF, and C ₉ = 0.6145 pF, we get f = 6.55 GHz.

(19)\begin{equation}{f_{\left( {@{\ }7.9{\textrm{ GHz}}} \right)}} = {\ }1/\{ 2\pi \surd \left( {{L_3}{C_3} + {L_3}{C_7}} \right)\end{equation}

for L ₃ = 1.312 nH, C ₃ = 0.1875 pF, and C ₇ = 0.1224 pF, we get f = 7.86 GHz.

It can be observed from above that the values obtained analytically are quite close to that obtained from full-wave EM simulation and circuit simulation. The values of the remaining parameters are fine-tuned using the software. The optimized parametric values of the components are as follows:

C ₀ = 0.022 pF, C ₁ = 5.46 pF, C ₂ = 0.3275 pF, C ₃ = 0.1875 pF, C ₄ = 0.63 pF, C ₅ = 0.21 pF, C ₆ = 0.355 pF, C ₇ = 0.1224 pF, C ₈ = 0.508 pF, C ₉ = 0.6145 pF, C ₁₀ = 0.25 pF, C ₁₁ = 0.01 pF, L ₁ = 4.3 nH, L ₂ = 1.36 nH, L ₃ = 1.312 nH, L ₄ = 1.496 nH, L ₅ = 0.721 nH, L ₆ = 0.274 nH. L ₇ = 0.614 nH.

Fabrication, measurement, and results

The proposed structure is fabricated using the photolithographic effect (chemical etching) and put up for testing using Agilent Vector Network Analyzer N5230A. The data derived from the test is observed and analyzed against simulation results in Fig. 8. It is observed from the measured result that the 3-dB passband is from 2.4 to 10.62 GHz, with three notches at 5.11, 6.4, and 8 GHz having 3-dB fractional bandwidth (FBW) of 3.2%, 2.6%, and 4.4% respectively and attenuation of at least −20 dB. The insertion/return loss within the passband is better than 0.76/12.8 dB before the first notch, 0.63/24 dB between the first and second notch, 0.68/11 dB between the second and third notch, and 0.83/13 dB after the third notch. The passband group delay variation is between 0.22 and 0.62 ns, except at the triple notches. The upper stopband is 18 GHz wide with attenuation greater than 19 dB. The misalignment between measured and simulated data be attributed human error in fabrication/measurement, finite active circuit area of the BPF, and reflections off connectors. An exhaustive comparative study of our proposed triple notched-BPF with other similar BPFs available in the literature is presented in Table 1. The table portrays that papers [Reference Shi, Xi, Zhao and Yang2, Reference Sazid and Raghava8, Reference Peng, Zhao and Wang10, Reference Kamma, Das, Bhatt and Mukherjee12–Reference Chiang, Xu and Liu15] do not possess the necessary UWB passband bandwidth. Papers [Reference Ghazali and Pal6, Reference Ghazali and Pal7, Reference Wei, Li, Shi and Huang9–Reference Basit, Khattak and Hasan11, Reference Liu, Song and Fan17] lack the presence of TZs at both passband edges, whereas papers [Reference Shi, Xi, Zhao and Yang2, Reference Taibi, Trabelsi and Saadi4, Reference Chakraborty, Shome, Panda and Deb5, Reference Borazjani, Nosrati and Daneshmand16] possess TZ only at one passband edge. Our proposed structure is physically smaller than all except paper [Reference Sazid and Raghava8], whereas it is electrically smaller (at the central UWB frequency) than papers [Reference Kumar, Gupta and Parihar3, Reference Taibi, Trabelsi and Saadi4, Reference Ghazali and Pal6, Reference Ghazali and Pal7, Reference Basit, Khattak and Hasan11, Reference Wang, Zhao and Li14–Reference Borazjani, Nosrati and Daneshmand16] and comparable to the rest. Also, our BPF has simple geometrical construction, unlike papers [Reference Wei, Li, Shi and Huang9–Reference Gholipoor, Honarvar and Virdee13], which possess vias, and papers [Reference Shi, Xi, Zhao and Yang2, Reference Kumar, Gupta and Parihar3, Reference Peng, Zhao and Wang10, Reference Kamma, Das, Bhatt and Mukherjee12, Reference Liu, Song and Fan17], whose design are limited by fabrication due to minimal dimension constrains. The implementation of vias in such delicate microstrips needs expertise in drilling and soldering, for any unnecessary soldering may bring about impedance mismatch, thereby affecting the frequency characteristics. Also, improper drilling could lead to the destruction of the BPF. With all the information provided above, it can be concluded that the proposed triple-notched UWB-BPF is simple to design and implement, meets all necessary frequency requirements, hence, better than its contemporaries.

Figure 8. (a) Comparative measured and simulated frequency characteristics. (b) Fabricated prototype.

Table 1. Comparison of present triple notched-BPF with recently known other triple-notched structures in literature