Transactions Template JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 2, ISSUE 2, JUNE 2015 131 Coupled Resonator Diplexer for LTE-Advanced System H. Abukaresh 1 , T. Skaik 2 UNRWA, Gaza, bh2003azem@hotmail.com Islamic University of Gaza , Gaza, tskaik@iugaza.edu.ps Abstract— This paper presents the design of a microstrip hairpin diplexer. The design is based on coupled- resonator structure using U-Shaped resonators. It is designed to meet The Long Term Evolution-Advanced (LTE- A) system Band 7, operating at uplink (UL): 2.50–2.57 GHz and downlink (DL): 2.62–2.69 GHz for base transceiver station antenna. The structure has three ports with 10-coupled resonators with direct coupling to produce diplexer with chebyshev filtering response. The diplexer does not involve any external junctions for distribution of energy, so it can be miniaturized in comparison to conventional diplexers. Index Terms— Component; Coupled-Resonator, Coupling Matrix, Diplexer, Optimization. I INTRODUCTION The diplexer is a device that isolates the receiver from the transmitter while permitting them to share a common anten- na. It is often the microwave key component that allows two way radios to operate in a full duplex manner. An ideal di- plexer provides perfect isolation with no insertion loss, to and from the antenna. Conventional diplexers consist of two channel filters connected to an energy distribution network. The channel filters pass frequencies within a specified range, and reject frequencies outside the specified boundaries, and the distribution network divides the signal going into the filters, or combines the signals coming from the filters [1]. The most commonly used distribution configurations are E- or H-plane n-furcated power dividers [2,3], circulators [4], manifold structures [5-8], Y-junction [9] and T-Junction [10]. In [11] a coupled resonator diplexer has been implemented at X-band with waveguide cavity resonators. The difference in this paper from the work in [11] is that the diplexer presented here is designed to work on a different frequency band that is used for the full duplex LTE-A system and it is implemented using microstrip technology. The synthesis procedure of the proposed diplexer in this paper is based on elimination of the additional common junction. This approach to diplexer design can achieve re- ductions in the size and volume of the circuit. The coupled-resonator based diplexer, without additional common junction is presented in [11-12]. This method for synthesizing coupled resonator diplexers is based on optimi- zation of coupling matrix of multiple coupled resonators representing a three-port network, and it is performed in the normalized frequency domain. II DIPLEXER SYNTHESIS There are many possible topologies for coupled resona- tors that can achieve a Chebyshev response. One example is illustrated in Figure 1; it is a schematic of a diplexer with resonators. Each circle represents a resonator, and the lines between resonators are internal couplings. The arrowed lines between resonators and ports represent external cou- plings. Figure 1 n -resonator based diplexer. The coupling matrix of a multiport circuit with multiple coupled resonators has been used in the synthesis. A unified solution for the coupling matrix ][ A has been utilized and it is generalized for both types of magnetic and electric cou- plings [13,14]. Transmission (S21, S31) and reflection (S11) scattering parameters of a three-port coupled resonator cir- cuit that have been found in terms of the general coupling matrix may be generalized as [13]: (1) 1 11][ 1 2 1 11   A e q S 1 1][ 1 2 21   xA ex q e q S 1 1][ 1 2 31   yA ey q e q S H. Abukaresh and T. Skaik / Coupled Resonator Diplexer for LTE -Advanced System (2015) 132 It is assumed that port 1 is connected to resonator 1, ports 2 and 3 are connected to resonators x and y respectively. A general normalized coupling matrix ][ A in terms of cou- pling coefficients and external quality factors is as follows [13]: [A] = [q]+ p[U]− j[m] (2)                                      nn m nn m n m nn m nn m n m n m n mm j p ey q ex q e q A )1(1 )1()1)(1(1)1( 1)1(111 100 010 001 1 00 0 1 0 00 1 1 ][              (3) where ei q is the scaled external quality factor ).( FBW ei Q ei q  of resonator i, FBW is the fractional bandwidth given by 0 /) 12 (  FBW , ][U is the ][ nn  identity matrix, n is the number of the resonators, p is the complex lowpass frequen- cy variable, ][m is the coupling matrix and entry ij m is the normalized coupling coefficient between resonators i and j , )/( FBW ij M ij m  , and the diagonal entries ij m account for asynchronous tuning, so that resonators can have different self-resonant frequencies [13]. The optimization of the coupling matrix ][m is based on minimization of a cost function that is evaluated at the fre- quency locations of the reflection and transmission zeros. The cost function used here is given as [13,15], 2 2 1 2010 )(. 1 )])(([ 11 .2 1 2 1 ) 1 )])(([ 11 .2 )( 2 2 1 1 )])(([ 1 .2 2 1 1 1 )])(([ 1 .2                R v R L pv s Ae q pv sAcof R j e q rj sAcof rj s A T k eb q e q tk sA b cof T i ea q e q ti sA a cof (4) where 1e q , ea q , and eb q are the external quality factors at ports 1, 2 and 3 respectively, )( xsA  is the determinant of the matrix ][ A evaluated at the frequency variable x , and )])(([ ysA mn cof  is the cofactor of matrix ][ A evaluated by re- moving the thm row and the th n column of ][ A and finding the determinant of the resulting matrix at the frequency vari- able ys . ti S , tk S are the frequency locations of transmission zeros of 21 S , 31 S respectively, 1 T , 2 T are the numbers of the transmission zeros of 21 S , 31 S respectively, R is the total number of reflection zeros , R L is the specified return loss in dB )0( RL , rjS and pvS are the frequency locations of the reflection zeros and the peaks frequency values of 11 S in the passband. The last term in the cost function is used to set the peaks of 11 S to the required return loss level. It is assumed here that both channels of the diplexer have the same return loss level. III DIPLEXER DESIGN An LTE-Advanced band 7 diplexer operating at uplink (UL): 2.50–2.57 GHz and downlink (DL): 2.62–2.69 GHz with symmetrical channels has been designed using mi- crostrip hairpin resonators. The diplexer has a Chebyshev response with passband centre frequency of 2.535 GHz for channel 1 and 2.655 GHz for channel 2, minimum isolation of 60 dB, and a desired return loss at the passband of each channel is 20 dB. The diplexer topology is shown in Figure 2. Figure 2 Topology of Diplexer with 10 resonators. The total number of resonators is n=10, the fractional bandwidth is FBW = 0.073267. A formula in [13] has been used to calculate the normalized external quality factors of diplexers with symmetrical channels and their values are found as 6e q = 10e q =2.636 and 1eq =1.318. The normalized coupling coefficients between any adja- cent resonators are initially set to 0.5 in the initial coupling matrix, and the same for self-coupling coefficients 3,3 m , 4,4 m , 5,5 m , 6,6 m , 7,7 m , 8,8 m , 9,9 m and 10,10 m . The coeffi- cients 11 m , 22 m and the couplings that do not exist between resonators are set to zero. A gradient based optimization technique has been utilized to synthesize the coupling coefficients, and the cost function in equation (4) has been used. The optimization has been H. Abukaresh and T. Skaik / Coupled Resonator Diplexer for LTE -Advanced System (2015) 133 carried out using MATLAB. The optimized normalized coupling matrix is shown in Table 1, and the response of the diplexer is shown in Figure 3. Figure 3 Diplexer prototype response with 10 resonators from opti- mization process. LTE-Advanced 10-resonator diplexer has been designed using hairpin microstrip coupled resonators. Electromagnet- ic Computer Simulation TechElectromagnetic Computer Simulation technology (EM CST) simulator has been used to extract the desired design dimensions according to a pre- scribed general coupling matrix and external quality factors. The EM simulated performance of the diplexer is shown in Figure 4. It can be shown from the simulation results that the return loss is better than 12 dB in the transmit and re- ceive band, the insertion loss is only about 0.3 dB in trans- mit and receive band and isolation greater than 60 dB in the uplink channel and greater than 35 dB in the downlink channel. Figure 4 The EM simulated performance of the diplexer. The top view of diplexer structure is shown in Figure 5. IV CONCLUSIONS An LTE-Advanced band 7 coupled resonator diplexer has been presented, and its synthesis is based on coupling matrix optimization. The diplexer structure consists of reso- nators coupled together, and it does not involve any external junctions for distribution of energy. This enables miniaturi- zation in comparison to the conventional diplexers. The di- plexer has been designed with microstrip hairpin resonators, and the simulation results showed acceptable return loss and isolation. TABLE 1 Normalized Coupling matrix of diplexer with 10 resonators from optimization process. 1 2 3 4 5 6 7 8 9 10 1 0 0.794 0 0 0 0 0 0 0 0 2 0.794 0 0.379 0 0 0 0.379 0 0 0 3 0 0.379 0.543 0.258 0 0 0 0 0 0 4 0 0 0.258 0.606 0.242 0 0 0 0 0 5 0 0 0 0.242 0.626 0.331 0 0 0 0 6 0 0 0 0 0.331 0.613 0 0 0 0 7 0 0.379 0 0 0 0 -0.543 0.258 0 0 8 0 0 0 0 0 0 0.258 -0.606 0.242 0 9 0 0 0 0 0 0 0 0.242 -0.626 0.331 10 0 0 0 0 0 0 0 0 0.331 -0.613 H. Abukaresh and T. Skaik / Coupled Resonator Diplexer for LTE -Advanced System (2015) 134 REFERENCES [1] I. Carpintero, M. Padilla-Cruz, A. Garcia- Lamperez, and M. 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Lancaster, ―A gradient- based optimization technique employing determinants for the synthesis of micro- wave coupled filters,‖ IEEE MTT-S Inter- national Microwave Symposium, USA, 2004, pp. 1369-1372. H. Abukaresh received the B.Sc. degree in 2007 from the Islamic University of Gaza and M.Sc. degree in Communications Engi- neering in 2013 from the Islamic University of Gaza. He is current- ly IT & Information assistant at United Nations Relief & Works Agency for Palestine Refugees in the Near East, Gaza Field office. T. Skaik received the B.Sc. degree in 2004 from the Islamic Uni- versity of Gaza, where he worked as a teaching assistant until 2006. He was awarded Hani Qaddumi scholarship and received M.Sc. degree in Communications Engineering with distinction in 2007 from the University of Birmingham, UK. He was awarded the ORSAS scholarship for doctoral study at the University of Bir- mingham, UK and received PhD degree in Microwave Engineering in 2011. Throughout his PhD study, he worked as a teaching assis- tant, and also as a research associate on micromachined microwave circuits. He is currently an assistant professor at the Islamic Uni- versity of Gaza.