transversal interaction have been studied and analyzed [11-. 17]. A filter has been ... of a double-sided parallel strip line has been reported for the design of wide.
A Miniaturized Wideband Bandpass Filter Based on 3λ/4 Resonator Loaded With Stepped Impedance Idury Satya Krishna, Rusan Kumar Barik and S. S. Karthikeyan Department of Electronics Engineering Indian Institute of Information Technology Design and Manufacturing Kancheepuram Email: {cds15m002, edm15d003, ssk}@iiitdm.ac.in
Abstract—This article presents the design of a highly miniaturized wideband bandpass filter. The proposed filter unit consists of 3λ/4 resonator loaded with stepped impedance section of short-ended stub. The required scattering parameters are derived using even-odd mode analysis. For validation, a prototype of the proposed filter is fabricated and tested. The overall area of the prototype is 0.25λg × 0.14λg , equivalently 1.95 cm2 . The bandpass filter exhibits a 3 dB fractional bandwidth of 121.6% for 1 dB insertion loss. Stopband response of better than 15 dB is achieved up to 2.8f0 by placing two transmission zeros. The measured results indicate good agreement with the simulated results.
I. I NTRODUCTION Bandpass filters (BPFs) greatly impact the overall performance of a RF/Microwave communication system. Due to its significance in a transmitter/receiver, it is important for a filter to exhibit features such as compactness, minimal insertion loss and good out of the band rejection performance [1]. Filters especially designed in microstrip technology are inexpensive and can be integrated with other components in a system effortlessly. Several design techniques have been explored in the past to design wideband BPF [2-20]. BPF designed using CSRR-based resonator has shown wide passband response along with high selectivity characteristics [2], [3]. The application of electromagnetic bandgap structures for design of BPF has been shown to demonstrate a stopband response up to 4.1f0 [4]. In [5], a BPF is designed by etching slots in the ground plane to achieve increased coupling between microstrip lines in order to improve the bandwidth. The technique of multi-mode resonators (MMR) has been applied widely in the past to design wideband BPF for communication systems [6-10]. To achieve broad-bandpass filters different types of MMR models like, triple-mode resonator [6], quasi-spiral loaded MMR [7], folded MMR [8], short circuited coplanar waveguide MMR [9], and stub loaded MMR [10] have been reported. Design of filters with wide passband using signal transversal interaction have been studied and analyzed [1117]. A filter has been designed for ultra-wide band (UWB) communication by utilizing broadside coupling between two patches via a slot in ground plane separating them [11]. In [12], an UWB filter has been realized by creating two transmission paths with different phase shifts. A marchand balun and a couple of transmission lines are cascaded together c 2017 IEEE 978-1-5090-5356-8/17/$31.00
Fig. 1. Schematic of the proposed miniaturized bandpass filter
to design a a filter for UWB application with good selectivity and harmonic suppression [13]. The use of a double-sided parallel strip line has been reported for the design of wide passband response in filter [14]. In [15], a broad passband response has been achieved by the use of a T -shaped structure on one path and one-end connected coupled lines on the the second path. A BPF with a 3 dB fractional bandwidth (FBW) of 123.4% has been designed based on ring-resonator with different arm electrical length [16]. A filter with two transmission paths consisting of two open-ended coupled lines and a short-ended stub has been proposed to a design fifthorder BPF with stopband response up to 2.7f0 [17]. Modified two-stage cascaded coupled-line section has been made to design a wideband BPF with compact size and deep stopband response [18]. The design of a notched UWB BPF using complementary split ring resonator has been explored in [19]. In this work, a miniaturized with wide bandpass response is presented.The proposed filter reports a 3 dB FBW of 121.6% with circuit a size of 0.25λg × 0.14λg . The proposed topology consists of a series transmission line and stepped impedance section with short-ended stub. The stepped impedance section provides overall size miniaturization. The stop-band response of the filter extends up to 2.8f0 due to the two transmission zeros placed right after the passband. Furthermore, the proposed wideband BPF is fabricated on an inexpensive FR4 substrate.
II. T HEORETICAL ANALYSIS OF THE PROPOSED MINIATURIZED WIDEBAND BANDPASS FILTER
The schematic of the proposed BPF unit is presented in Fig. 1. The proposed topology is composed of a series transmission line (Z1 , θ1 ) in parallel with a stepped impedance section. The T-shaped stepped impedance section has two series transmission line (Z2 , θ2 ), which is centre tapped by a transmission line (Z3 , θ3 ) cascaded with a short-ended line (Z4 , θ4 ). The series transmission line of the topology will act as a 3λ/4 resonator. The S-parameters are determined by giving even and odd mode excitation to the proposed configuration. Fig. 2 shows the simplified even and odd mode circuits. The evenmode admittance (Yine ) and odd mode admittance (Yino ) are given by (2) and (3). Yine1 = j
tan (θa /2) Z1
1 W − [X + Y tan(θa )] + Yine1 Z2 W tan(θa ) − [X tan(θa ) − Y ] cot(θa ) cot(θa /2) Yino = −j + Z2 Z1
Yine = −j
(a)
(1) (2) (b)
(3)
Fig. 2. Simplified circuit after first-order Even-Odd mode analysis (a) Evenmode (b) Odd-mode
where, W = Z2 Z3 cot(θb ) X = Z2 Z4 tan(θb ) Y = 2Z3 (Z3 + Z4 ) The reflection coefficients for odd and even mode circuit (Γe,o ) can be computed in terms of even and odd mode admittances as given in equation (4). Γe,o =
Yo − Yine,ino Yo + Yine,ino
(4)
The S-parameters of a two-port device [1] are computed in terms of the Γe,o as given in equations (5) and (6). Γe + Γ o (5) 2 Γe − Γo S21 = (6) 2 By substituting equation (4) into (5) and (6), S-parameters are calculated as: S11 =
Yo2 − Yine Yino (Yo + Yine ) (Yo + Yino )
(7)
Yo (Yine − Yino ) = (Yo + Yine ) (Yo + Yino )
(8)
S11 = S21
By solving |S21 | = 0, the location of the transmission zeros are obtained as: −2P (1 + Q)tanθb + tanθa tanθb2 − Q tan θa U R= (9) 2P (1 + Q)tanθb (tanθa + cotθb ) where, θ1 = θ2 = θa , θ3 = θ4 = θb
Fig. 3. Theoretically computed S-parameters of the proposed wideband BPF
P = Z3 /Z2 Q = Z3 /Z4 R = Z1 /Z2 U = tan(θa /2) + cot(θa /2) The freedom of setting a value to the impedance ratios P, Q and R is defined by the fabrication limit of the microstrip technology. The design parameters of the proposed BPF are calculated as: Z1 = 87 Ω, Z2 = 55 Ω, Z3 = 50 Ω and Z4 = 35.1Ω for P = 0.9, Q = 1.42 and R = 1.58. The electrical lengths are θa = 90◦ and θb = 22.5◦ for design frequency centering at fo = 2.4 GHz. Since the stepped impedance transmission line has an electrical length of 2θb = 45◦ , it can be conveniently placed inside the unused circuit area without any overlap to achieve a compact size. By substituting equations (2) and (3) in (7) and (8), the theoretical scattering parameters of the proposed BPF are obtained and depicted in Fig. 3. From the plot, low insertion
Fig. 4. Circuit simulated phase response of the proposed wideband BPF
(a)
TABLE I C ALCULATED CIRCUIT PARAMETERS AND DIMENSIONS Parameter
Value
Length (mm)
Width (mm)
Z1 , θ1
87 Ω ,
90◦
17.91
0.48
Z2 , θ2
55 Ω, 90◦
17.26
1.28
Z3 , θ3
50 Ω, 22.5◦
4.28
1.50
Z4 , θ4
35.1 Ω, 22.5◦
4.17
2.61
loss and deep return loss are observed with wide-bandwidth for the proposed third-order BPF. Assuming the proposed BPF is divided into two transmission paths, the generation of transmission zeros can be explained using signal interference technique. The first path consists of a series transmission line (Z1 , θ1 ) and the second path comprises of a T-shaped stepped-impedance section. The bandpass/bandstop response is the result of constructive/destructive interference between the signals emerging from both the paths. Therefore, the exact location of transmission zeros can be obtained from the phase response. Fig. 4 shows the phase responses of the Path 1, Path 2 and combination of both. The transmission zeros are produced at 0, 2fo and 4.068 GHz due to signal cancellation from both the paths. The dependence of bandwidth on the series arms of the BPF is illustrated by the quality factor (QL ) as shown in Fig. 5. The loaded quality factor is defined as
(b) Fig. 5. Variation of quality factor for passband as a function of (a) Z1 , θb and Z2 = 55 Ω (b) Z2 , θb and Z1 = 87 Ω
Fig. 6. Final Layout of the proposed wideband BPF
QL =
fo ∆f3dB
(10)
where fo is the design frequency and ∆f3dB is the 3 dB FBW of the passband. In Fig. 5a, the quality factor is computed by varying Z1 and θb for fixed Z2 and θa . It is observed that the QL of passband increases for Z1 till θb = 10◦ , thereafter QL decreases for increasing θb and Z1 . Similarly the quality factor of passband is plotted for varying Z2 and θb as shown in Fig. 5b. The QL decreases as Z2 increases till θb = 15◦ and thereafter it increases for increasing Z2 and θb . As QL is inversely proportional to ∆f3dB , for a particular value of θb , the values of Z1 and Z2 can be varied to achieve required fractional bandwidth.
III. FABRICATION AND T ESTING To validate the proposed theoretical analysis, a wideband BPF centring at 2.4 GHz is devised on 0.8 mm thick FR4 substrate of εr = 4.4. The derived circuit parameters and dimensions are listed in Table I. Fig. 6 shows the final layout of the fabricated BPF with dimensions: L1 = 19.18 mm, L2 = 8.26 mm, L3 = 4.1 mm, L4 = 4.3 mm, W1 = 0.48 mm, W2 = 1.28 mm, W3 = 1.5 mm, W4 = 2.61 mm. The overall area occupied by the BPF is 1.02 x 1.91 cm2 (excluding ports) or equivalently 0.25λg x 0.14λg , here λg is the guided wavelength at fo . The photograph of the fabricated prototype is depicted in Fig. 7. The fabricated device
TABLE II C OMPARISON OF PROPOSED FILTER WITH THE CURRENT STATE OF THE ART BPF S Ref
Technique
No. of Poles
3-dB Bandwidth %
Effective Circuit Size (λg 2 )
Upper Stopband
[3]
CSRR-based resonator
3
75
0.375
