Design of Miniaturized Dual-Band Wilkinson Power Divider Using Dual and Cascade π-Shaped Transmission Lines

This paper presents a design of compact dualband Wilkinson power divider (WPD). The cascaded πshape and dual transmission lines are used instead of conventional transmission line sections of the reference WPD in order to miniaturize the circuit area. Therefore, 62% size reduction has been achieved without much affecting the performance of power divider. The insertion-loss of the output ports is within (3.4 ± 0.3) dB, for the reflection coefficient better than –15 dB and isolation better than 18 dB at the lower frequency band of 1.1 GHz. Similarly the insertion-loss is within (3.4 ± 0.3) dB, for the reflection coefficient better than –18 dB and isolation better than 24 dB at the upper frequency band of 2.55 GHz. The proposed WPD is analyzed, fabricated and tested. It is found that the measurement results are in good agreement with the simulated one.


Introduction
Nowadays communication industries motivate the researchers to design the microwave components to be operated at multiple frequency bands.Power dividers are one of the important microwave components used for combining and dividing the microwave signals, as a result of which they are used in many microwave subsystems, such as power amplifiers, modulators, antenna arrays and so on [1], [2].Power divider is a circuit in which input signal is received from one port and outputs are taken from others ports.To achieve equal power division at outputs, Wilkinson power dividers (WPD) are widely used due to their simplest design, impedance matching at all ports and high isolation between output ports.Researchers are giving more attention to design of multi-band WPD.Various methods are available in the literature which offers dualband WPD with improved performance such as, cascading two transmission lines [3], incorporating lumped element (R, L, C), but it offers additional parasitic effect especially at high frequency [4][5], stepped impedance [6], adding shunt stubs [7][8][9], extension of all ports [10], [11], shunt open-stubs with enhanced attenuation characteristics [12], three transmission line sections [13], and simplified approach for three transmission line sections [14] are recommended.However, the circuit size of a power divider becomes large specifically at lower frequencies due to the structural dependence on the quarter wave length (λ/4) line.Many researchers have proposed several techniques to reduce the overall size of the microwave circuits (power divider and couplers) [15][16][17][18][19][20][21][22].In [15] parallel coupled line, composite right-/left-handed (CRLH) transmission line [16], electromagnetic band-gap (EBG) structure [17], [18], defected ground structure (DGS) [19], high-low impedance resonator [20], cascaded π-shape transmission lines [21], and dual transmission line [22], are used for miniaturization as well as harmonic suppression of microwave circuits.Recently dual-band PD was efficiently designed with high selectivity [23], based on port extension [24], combination of T-junction and step impedance line [25], however all the designs are having larger circuit size.The major drawback of using CRLH transmission line based on complementary split ring resonator (CSRR) and the DGS is that they need additional etching technique in fabrication process, and causes back radiation which affects the operation of other microwave components.
In this manuscript, the design and implementation of a miniaturized dual-band WPD is demonstrated.Firstly a dual-band WPD is designed at 1 GHz and 2.6 GHz frequency band using three quarter wavelength transmission line sections.To reduce the circuit size all the transmission lines are replaced by a dual transmission lines, as a result of which significant size reduction of 65% is achieved.To improve the reflection coefficient and isolation performance of the circuit, the second dual transmission line section is replaced by a cascaded π-shape transmission line and the rest of the design remains unchanged.Therefore, the overall circuit area is reduced by 62% compared with reference dual-band WPD.The reflection coefficient and isolation performance are improved by 15 dB and 2 dB, respectively, at lower frequency band.The isolation performance is improved by 10 dB at the upper frequency band.The proposed design is simulated using HFSS full wave EM simulator and fabricated on Arlon substrate with dielectric constant ε r of 2.2, thickness h of 0.787 mm and loss tangent of 0.0009.

Dual-Band Wilkinson Power
Divider and its Miniaturization

Design of Dual-Band Wilkinson Power Divider
Figure 1 shows the layout of the reference (Ref.)dualband WPD composed of three transmission line (TL) sections [13].To satisfy the dual band response, electrical lengths at f 1 and f 2 should follow (1-2), where R is the frequency ratio.Therefore, electrical length θ f1 is 50 calculated from (1) with respect to the lower frequency band of 1 GHz for the frequency ratio (R = f 1 /f 2 ) of 2.6.For the miniaturization point of view, we choose the average electrical length θ f for all the transmission line sections to design dual-band WPD.The values of the characteristic impedances (Z 1 , Z 2 and Z 3 ) and the comparison between physical lengths corresponding to θ f1 and θ f2 of three TL sections are shown in Tab. 1. From the table it is clear that in both the cases physical length is the same.The load impedances at each port are Z 0 = 50 Ω and isolation resistance is100 Ω.
The optimized design parameters are tabulated in Tab. 2. The simulated S-parameters response of the ref.
dual-band WPD is shown in Fig. 2. From Fig. 2 it is found that output at port 2 and port 3 (S 21 and S 31 ) is -3.5 dB with reflection coefficient S 11 < -25 dB and isolation between the output ports > 19 dB at lower frequency 1.03 GHz.Similarly, the output at port 2 and 3 is -3.6 dB with reflection coefficient and isolation < -10 dB and > 18 dB, respectively, at the upper frequency 2.6 GHz.The phase differences between the output ports are 0.5 and 0.8 at the lower and upper frequency band, respectively.

Miniaturization of Dual-Band WPD Using Dual Transmission Line (TL)
Figure 1 shows a dual-band WPD composed of three TL sections resulting in a large circuit size.In order to reduce the overall size, all the λ/4-TLs are replaced by dual TL, namely designed 1.In the dual TL, single λ/4 TL of the initial design is split into a two parallel TL's structure as shown in Fig. 3. Here, Z a , Z b , θ a , and θ b are defined as the characteristic impedances and the electrical lengths of dual TL's, respectively.Here θ (90) is the electrical length of single TL and the transmission matrix (ABCD parameter) is written in (3).Similarly ABCD matrixes are written for both line 'a' and 'b' in (4)(5).The expression for the characteristic impedances and the electrical lengths are obtained from (3), ( 4), (5) and given in (6-8) [22].From ( 6), (7) it is clear that, if the electrical length is to be chosen smaller, the impedance becomes higher which is to some extent difficult to fabricate.Therefore equal impedance is taken for simplicity and the electrical lengths are maintained as θ a < θ= 90 < θ b and θ a + θ b = π in order to have compact size.Therefore, this dual transmission lines are composed of two high impedance lines with different electrical lengths.Out of these two lines, the longer one θ b is meander in shape to reduce the circuit area.Using the design equations of (6-7), the variation of characteristic impedances of dual TL as a function of θ a is shown in Fig. 4, for three TL sections having characteristic impedances (Z) of 36.4Ω, 58.6 Ω, and 50.3 Ω, respectively.
a a a 0 a a a a a a line1 cos j sin j sin cos In design 1 a dual TL is used instead of conventional line.Therefore electrical lengths of dual TL, θ a and θ b are chosen as 45 and 135, respectively for transmission line section 1 and 3.The corresponding characteristic impedances

Performance Improvement of Miniaturized Dual-Band WPD Using Cascade π-shaped Transmission Line (TL)
To improve the reflection coefficient as well as isolation performances of the design '1' at both the frequency bands, dual transmission line of section 2 is replaced by cascade π-shaped TL.Dual transmission line consists of two lines having different electrical lengths with high impedance.Out of the two lines in design 1, the longer line is meandered in shape to reduce the circuit area.The meandered section increases the number of discontinuity by bending and the coupling between the close bended lines increases.Any kinds of microstrip discontinuity (bend, gap and step) in the line generate surface waves that degrade the overall performances of the circuits.In order to minimize the discontinuity as well as coupling between the closed bended lines, the dual transmission line is replaced by cascaded π-shaped transmission line as a second transmission line section, namely design 2. The performances are improved due to minimizing the number of discontinuities caused by dual transmission line.A cascaded π-shape transmission line consists of two series transmission lines  3), (9).By evaluating ( 3) and ( 10), Z c and Z d can be solved as ( 12), ( 13) [21].Equations ( 12), ( 13 where Layout of the proposed power divider (design 2) and its LC equivalent circuit are shown in Fig. 7

Simulation and Experimental Results
The proposed dual-band WPD is designed and fabricated to operate at 1 GHz and 2.6 GHz.The proposed designs are as follows: design 1 consists of a dual transmission line and design 2 consists of a cascaded π-shape TL and dual TL for miniaturization of the ref.dual-band WPD.Therefore, the proposed technique provides a substantial miniaturization of around 65% for design 1 and 62% for design 2 without degrading the other performance factor of the ref.power divider.Figure 8 shows the simulated S-parameters response for both design 1 and 2 and compared with ref. dual-band WPD.From Fig. 8 it is clear that the simulated response of the proposed power divider (design 2) provides the good response as compared to the design 1 and ref. dual band WPD for both the frequency bands.The reflection coefficient and isolation performance are improved by 15 dB and 2 dB compared to design 1 at lower frequency band, respectively.Similarly, the isolation performance is improved by 10 dB at the upper frequency band.Finally, simulated S-parameter responses of design 1 and 2 are shown in Fig. 9. From Fig. 9(a) it is clear the operating frequencies are 1.2 GHz and 2.5 GHz for design 1. Figure 9(b) shows the electromagnetic (EM) simulation and simplified LC equivalent circuit simulation results of the proposed power divider (design 2).From this figure it is clearly seen that the circuit simulation of the proposed WPD has two transmission bands near 1.05 GHz and 2.6 GHz, whereas EM simulation operated at 1.1 GHz and 2.55 GHz.In this way, one can justify the validity of the circuit model.
The photographs of the fabricated unit are shown in Fig. 10 for both design 1 and 2, respectively.An Agilent vector network analyzer is used to test the performance of the fabricated power divider.The measured S-parameter responses are compiled with the simulated response for both design 1 and 2 to ensure that the proposed dual-band WPD exhibits good performance in the real time environment as shown in Fig. 11 and 12, respectively.From Fig. 11 fractional bandwidth (FBW) is found to be 20% for the insertion loss of (3.45 ± 0.3) dB at the output ports with reflection coefficient better than -15 dB and isolation > 15 dB for the lower frequency of 1.25 GHz.Similarly, for the upper frequency of 2.5 GHz, FBW is found to be 17% for the insertion loss of (3.5 ± 0.3) dB with reflection coefficient < -15 dB and isolation > 14 dB.
From Fig. 12 the FBW is found to be 21% for the insertion loss of (3.4 ± 0.3) dB at the output ports with reflection coefficient better than -15 dB and isolation better than 15 dB for the lower frequency of 1.2 GHz.Similarly, for the upper frequency of 2.6 GHz, FBW is found to be 15% for the insertion loss (3.4 ± 0.3) dB with reflection coefficient better than -15 dB and isolation better than 20 dB.The phase difference (PD) between the output ports are 0.6 and 0.2 at the lower and upper frequency band, respectively.

Ref., Year
The dual-band property along with other characteristics of the proposed design is also compared with some other works and the comparison is tabulated in Tab. 5.In comparison, it is found that the design 1 is 3% more compact than design 2, but the isolation and return loss performance is poor compared to design 2. So, in terms of overall performance factors (return loss, isolation, and insertion loss) design 2 is better compared to design 1, despite a little bit miniaturization.

Conclusion
A compact dual-band Wilkinson power divider (WPD) is designed based on cascaded π-shape and dual transmission lines.The proposed design is occupied only 38% circuit area compared to ref [13].It is to be further noted that despite the miniaturization, no other performance factors are degraded.Herein lies the advantage of the proposed design over the existing design, although the dual line is a little bit complicated.Since the proposed structure is very compact thus making it suitable to be used in compact and sophisticated microwave systems.

Fig. 3 .
Fig. 3. Equivalent model of single TL with dual TL.

Fig. 4 .
Fig. 4. Design curve of dual TL as function of  a for the proposed design.

Fig. 5 .
Fig. 5. Layout of design 1. (Z a and Z b ) are calculated from equations (6-7), where Z is taken as 36.4Ω for TL section 1 and 50.3 Ω for TL section 3, therefore Z a = Z b = 103.5 Ω and Z a = Z b = 142.2Ω, respectively.Similarly for TL section 2, the electrical lengths of dual TL, θ a and θ b are chosen as 65 and 115, respectively and the corresponding characteristic impedances Z a = Z b = 129.3Ω for Z = 58.6Ω.The optimized designed parameters are tabulated in Tab. 3 and the layout of design 1 is shown in Fig. 5.

Fig. 6 .
Fig. 6.Conventional line and its equivalent cascaded π-shape TL. of characteristic impedance Z c , electrical length θ c and four shunt open stubs of characteristic impedance Z d , electrical length θ d .The equivalent transmission line model of cascaded π-shape and conventional transmission line are shown in Fig. 6.The transmission matrix (ABCD) of quarter wavelength TL is equated with the ABCD matrix of cascaded π-shape TL in order to find the characteristic impedances and electrical lengths of line.The ABCD-matrix of quarter wavelength section and proposed TL are given by (3),(9).By evaluating (3) and (10), Z c and Z d can be solved as (12), (13)[21].Equations (12), (13) are used to find the characteristics impedances of cascaded π-shape transmission line by properly choosing the electrical length of the series and shunt open stub of the proposed TL.The characteristic impedances (Z c and Z d ) of the lines are evaluated from (12), (13) where Z is taken as 58.6 Ω and the electrical lengths (θ c and θ d ) are selected as 20 and 40 in order to achieve miniaturization, respectively for K = 1.5 and therefore Z c = 123 Ω and Z d = 70 Ω.Once impedance and electrical lengths of series and shunt lines are known, the width and length of the series line and open stubs are easily obtained by using well know microstrip line equation.Finally, the optimized design parameters are tabulated in Tab. 4.
) are used to find the characteristics impedances of cascaded π-shape transmission line by properly choosing the electrical length of the series and shunt open stub of the proposed TL.The characteristic impedances (Z c and Z d ) of the lines are evaluated from (12), (13) where Z is taken as 58.6 Ω and the electrical lengths (θ c and θ d ) are selected as 20 and 40 in order to achieve miniaturization, respectively for K = 1.5 and therefore Z c = 123 Ω and Z d = 70 Ω.Once impedance and electrical lengths of series and shunt lines are known, the width and length of the series line and open stubs are easily obtained by using well know microstrip line equation.Finally, the optimized design parameters are tabulated in Tab. 4.
Authors... Mukesh KUMAR (*1989) received the B.Tech.degree in Electronic and Telecommunication Engineering from the Biju Patnaik University of Technology, Rourkela, Orissa in 2011, and the M.Tech.degree in Electronics and Communication Engineering from the National Institute of Technology, Durgapur in 2015.He is currently pursuing the Ph.D. degree in Microwave Engineering with the Electronics and Tele-Communication Engineering Department, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India.His current research interests include microwave planer circuits, power divider, couplers.Susanta Kumar PARUI (*1965) received the B.Sc. degree in Physics and the B. Tech degree in Radio Physics and Electronics from the University of Calcutta in 1987 and 1990, respectively.He has done the Master degree in Microwave Communication Engineering from the Bengal Engineering College, India in 1993.From 1993 to 2000, he worked as an Instrument Engineer.Since 2000, he is associated with the Department of Electronics and Telecommunication Engineering, Bengal Engineering and Science University, India and presently holds the post of Senior Lecturer.His current research interests include the planar circuits, filters, antenna elements and electromagnetic band gap structures.Santanu DAS (*1968) received the B.E. degree in Electronic and Telecommunication Engineering from the Bengal Engineering College in 1989 and the M.E degree in Microwave Engineering from the Jadavpur University, Calcutta in 1992.He obtained the Ph.D. (Engineering) degree in the year 1998 from the Jadavpur University.As Lecturer in Electronics and Telecommunication Engineering, he joined the department of the Bengal Engineering and Science University in 1998 and presently holds the post of a Professor at the same department.His current research interests include the microstrip circuits, antenna elements and arrays, FSS and defected ground structures.He is a life member of the Institution of Engineers, India.

Tab. 1. Dimension of the reference dual-band WPD. Parameters l 1 l 2 l 3 l 4 l 5 W 1 W 2 W 3
Tab. 2. Design parameters of the reference dual-band WPD.