I. INTRODUCTION
Most of diplexers are composed of two bandpass filters, which separate two desired frequency bands for using in the modern wireless communication systems. With the growing of wireless applications, many different structures have been introduced for the planer diplexers. Although low passband insertion loss is an important advantage, some of the earlier works have proposed diplexers with high insertion loss [Reference Chinig1–Reference Hsu, Tung, Hsu, Lin and Yang4]. In order to achieve high-performance diplexers, the interdigital capacitors [Reference Nath3], interdigital hairpin resonators [Reference Hsu, Tung, Hsu, Lin and Yang4], spiral-based resonators [Reference LU, WANG, XU and YIN5], and the closed loops with interdigital structures [Reference L-Morales, Sun, C-Chavez, Itoh and Cervantes6] have been used. Since the use of a complex interdigital and spiral resonators leads to hard fabrication as well as low accuracy of measurement data, a simpler diplexer has been realized in [Reference Li, Huang, Zhao and Wen7]. In [Reference Liu, Xu, Zhang and Guan8], a microstrip diplexer has been implemented using a step-impedance resonator, which provides a degree of freedom to improve the rejection band. In [Reference Cheng, Lin, Song, Jiang and Fan9], a high isolation diplexer has been introduced using a dual-mode resonator. By using this structure, the insertion losses at both passbands have been decreased clearly. In [Reference Kuan, Yang, Weng and Chen10], a diplexer has been presented using slot-line resonators to generate the filtering response. In [Reference Brinda and Anisha Parveen11], a microstrip diplexer has been designed, which has low insertion losses at lower and higher passbands, but takes up a lot of space. Furthermore, the frequency response of this diplexer confirms the poor frequency selectivity so that S 31 is not well attenuated below its passband. In [Reference Shi, Chen and Bao12], three demonstrative diplexers have been presented. To reduce the overall size of them, resistors, open stubs, and shorted stubs have been imbedded inside the open-ended loop resonators. However, the insertion losses at lower and upper passbands are large as well as most of the earlier works. In [Reference Yang, Guan, Zhu and Liu13], a microstrip diplexer based on a symmetric structure has been introduced to operate at two quite close channels (2.35/2.59 GHz). In [Reference Cabral, Bezerra and Melo14], H-type resonators have been utilized to miniaturize a microstrip diplexer, which operates at the UMTS upload and download bands. In this paper, first, two bandpass filters are realized using four microstrip cells and a coupled lines structure. Then, an equivalent LC circuit of the coupled lines is studied to determine the geometrical structure of the cells. After determining the cells a microstrip diplexer is designed to operate at 2.36 and 4 GHz for the wireless applications. The passband about 2.36 GHz (UHF band) can be used in the wireless local area networks, microwave links, radars, satellites, and navigation aid systems. Furthermore, a passband, which covers near the frequency range of 4 GHz is a subset of SHF band that can be used in radars, microwave links, terrestrial mobile communications, and satellite communications. Another achievement of this paper is the improved insertion losses at both passbands by employing a simpler structure than the interdigital and spiral resonators.
II. DIPLEXER DESIGN
As shown in Fig. 1(a), the coupled lines, which are connected to the extra microstrip cells are applied to create a resonance frequency. In Fig. 1(a), the parameters (V 1, I 1) and (V 2, I 2) are the voltages and currents of port1 and port2, respectively and Z 1, Z 2, Z 3, and Z 4 are the characteristic impedances of the microstrip cells. According to Williams and Kim [Reference Hong and Lancaster15], an optional equivalent LC circuit of the symmetric coupled lines can be replaced as shown in Fig. 1(b). The inductors L C are used to model the coupling between the lines. The equivalent circuit of the each half of the distributed line includes an inductor L e and a capacitor C e . Due to the symmetric structure of the coupled lines, the magnetic/electric walls are established between the coupled lines [Reference Williams and Kim16] that make L C an open/short circuit. By considering the predetermined resonance frequency, the challenge is to characterize the geometrical structure of the microstrip cells, while the inductors L C are open/short circuited because of the magnetic/electric walls. Under three conditions a simplified equivalent model of the proposed resonator (see Fig. 2(a)) can be obtained as follows:
-
1. Magnetic wall between the coupled lines;
-
2. Microstrip Cell4 becomes a step with an LC model, which is composed of capacitors and inductors. Also the effect of C e , which is connected to the microstrip Cell4 is ignored;
-
3. The LC equivalent circuit of the microstrip Cell3 becomes an inductor equal to
$L = (C_e \omega _o^2 )^{ - 1} $
(where ω
o
= 2πF
o
and F
o
is the resonance frequency). We assume that this inductor removes the effect of the capacitor C
e
, which is connected to microstrip Cell3.
Fig. 1. (a) Proposed resonator, (b) replacing the equivalent LC model of the coupled lines in the proposed resonator.
Fig. 2. (a) Simplified circuit of the proposed resonator under three circumstances: magnetic wall, elimination of the effect of the capacitor C e connected to the microstrip Cell3 and microstrip Cell4 by Z 3 and Z 4. (b) Simplified circuit of Fig. 1(b) under three circumstances: electric wall, elimination of the effect of the capacitor C e connected to the microstrip Cell3, and microstrip Cell4 by Z 3 and Z 4.
The transmission matrix of the proposed resonator at the resonance frequency F o , is calculated as follows:
$$T = \left[ {\matrix{ A & B \cr C & D \cr}} \right] = \left[ {\matrix{ 1 & {Z_1} \cr 0 & 1 \cr}} \right]\,\left[ {\matrix{ {A_{LC} \,\,\,} & {B_{LC}} \cr {C_{LC} \,\,\,\,} & {D_{LC}} \cr}} \right]\,\left[ {\matrix{ 1 & {Z_2} \cr 0 & 1 \cr}} \right],$$
where
$$\eqalign{& \left[ {\matrix{ {A_{LC}} & {B_{LC}} \cr {C_{LC}} & {D_{LC}} \cr}} \right] = \left[ {\matrix{ 1 & {\displaystyle{1 \over {j\omega _o C_e}}} \cr 0 & 1 \cr}} \right] \times \left[ {\matrix{ 1 & 0 \cr {\displaystyle{{j\omega _o C_c} \over 2}} & 1 \cr}} \right] \cr & \quad \times \left[ {\matrix{ 1 & {j2\omega _o L_e} \cr 0 & 1 \cr}} \right] \times \left[ {\matrix{ 1 & 0 \cr {\displaystyle{{j\omega _o C_c} \over 2}} & 1 \cr}} \right] \times \left[ {\matrix{ 1 & {\displaystyle{1 \over {j\omega _o C_e}}} \cr 0 & 1 \cr}} \right].} $$
In Equation (1), ω o = 2πF o . From ABCD matrix the input admittance Y in viewed from port1 is:
$$Y_{in} = \displaystyle{{I_1} \over {V_1}} \left \vert {_{V_2 = 0} =} \right.\displaystyle{{D_1} \over {B_1}} = \displaystyle{{Z_2 C_{LC} + D_{LC}} \over {B_1}}. $$
In order to excite the resonator, the numerator in Equation (2) should be zero. Therefore, the resonance condition is obtained as follows:
$$Z_2 = - \displaystyle{{D_{LC}} \over {C_{LC}}} = \displaystyle{{\displaystyle{{C_c} \over {2C_e}} + (1 - \omega _o^2 C_c L_e )} \over { - 1 + j(0.5\omega _o^3 C_c^2 L_e - \omega _o C_c )}}.$$
According to Equation (3), the geometrical structure and dimensions of the microstrip Cell2 are dependent on the coupled lines structure and a requested resonance frequency.
By replacing the electric wall, the proposed resonator is changed as shown in Fig. 2(b). Hence, the input impedance of the equivalent circuit seen from port1 (Z in ) can be written as follows:
$$Z_{in} = Z_1 + \displaystyle{1 \over {j\omega _o C_e}} + \displaystyle{{2L_e} \over {j\omega _o L_e C_c + 1/j\omega _o}}. $$
Due to the electric wall, the resonance condition is obtained for Z in = 0. Under this condition Z 1 should be calculated by the following equation:
$$Z_1 = \left( {\displaystyle{1 \over {\omega _o C_e}} - \displaystyle{{2L_e \omega _o} \over {1 - \omega _o^2 L_e C_c}}} \right)j.$$
Equation (5) shows that Z
1 is the sum of an inductor L (in H) and a capacitor C (in F), which are given by
$L = (C_e \omega _o^2 )^{ - 1} $
and
$C = (1 - \omega _o^2 L_e C_c )/2L_e \omega _o^2 $
. Therefore, the microstrip cell1 can be replaced by a step-impedance cell. Based on the above analysis, two similar microstrip bandpass filters are designed to operate at 2.3 and 4 GHz. The layouts and frequency responses of the 2.3 and 4 GHz filters are shown in Figs 3(a) and 3(b), respectively. By integrating the proposed filters at port1, a microstrip diplexer is realized. The layout of the proposed diplexer is shown in Fig. 4(a). The filters dimensions are exactly equal to the dimensions of the proposed diplexer. The measured and simulated frequency responses of the proposed diplexer are presented in Figs 4(b) and 4(c). A photograph of the fabricated diplexer is shown in Fig. 4(d).
Fig. 3. Layouts and simulated frequency responses of the proposed: (a) 2.36 GHz filter, (b) 4 GHz filter.
Fig. 4. (a) Configuration of the proposed diplexer (all dimensions are in mm), (b) transmissions curves (S 21 and S 31), (c) return loss at port1 (S 11) and isolation (S 23), and (d) fabricated diplexer.
III. RESULTS
First, the designed diplexer is simulated by ADS software using Momentum Simulator, and then it is implemented on a RT Duroid 5880 substrate. The thickness of the dielectric substrate is 31 mil with ε r = 2.22 and the loss tangent 0.0009. The dimensions of the proposed structure are shown in Fig. 4(a) where all dimensions are in mm. The frequency response of the proposed diplexer confirms that the insertion losses (S 21, S 31) at 2.36/4 GHz are 0.2/0.4 dB, while the achieved return losses at the lower/higher resonance frequencies are −15/−16.8 dB. The isolation (S 32) at critical frequencies is measured, so that −49 dB at 2.36 GHz and −19.8 dB at 4 GHz are obtained. The measured S 33 at 2.36 GHz is −14.33 dB and the measured S 22 at 4 GHz is −10.04 dB. The overall size of the proposed diplexer is 27 × 29.9 mm2. In Table 1, the insertion losses, return losses, implementation area, and resonance frequencies of the proposed diplexer are compared with the previous works. In Table 1, S 21 and S 31 are the insertion losses at the lower and upper passbands, respectively. According to Table 1, in comparison with the previous works, the best insertion losses and reasonable return losses are obtained at the both passbands.
Table 1. Insertion losses, return losses, diplexer size, and resonance frequencies of the proposed diplexer in comparison with the previous works.
IV. CONCLUSION
In this paper, the coupled lines, which are connected to the microstrip cells, are presented as a resonator. Using the equivalent LC circuit of the coupled lines, the proposed resonator is analyzed to estimate the structures of the microstrip cells and coupled lines under consideration of the predetermined resonance frequency. Based on the proposed resonator structure, two microstrip bandpass filters are realized. By integrating the proposed filters at a common port a high-performance microstrip diplexer is achieved to operate at 2.36 and 4 GHz. The designed diplexer has the improved insertion losses and high isolations at the both resonance frequencies, so that the obtained isolation (S 32) is −49 dB at 2.36 GHz and −19.7 dB at 4 GHz.
ACKNOWLEDGEMENT
The authors would like to express our sincere thanks to the editors and reviewers of this paper’s manuscript for their constructive comments and suggestions, which greatly improved the quality of this paper.
Leila Noori received B.S. and M.S. in Electrical Engineering from Razi University in 2009 and 2011 and Ph.D. degree in Electrical Engineering from Shiraz University of Technology, Shiraz, Iran, in 2015. His main research interests are design and fabrication of microwave device such as microstrip filter, couplers, low-noise amplifiers, diplexers, etc.
Abbas Rezaei is an Assistance Professor of Electrical Engineering in Kermanshah University of Technology. Abbas Rezaei received the B.Se., M.Se., and Ph.D. in Electronics Engineering from Razi University, Kermanshah, Iran, in 2005, 2009, and 2013, respectively. His current research interests include computational intelligence, microstrip devices, and nanotechnology.
