Wideband and Compact Wilkinson Power Divider Utilizing Series Delta-Stub and Folded Stepped-Impedance Transmission Line

In this paper, a Wilkinson power divider is modified using four-series delta-stub and folded steppedimpedance transmission line (FSITL) in order to achieve a reduced circuit size of 84% and fractional bandwidth of 116%. Series delta-stubs are used instead of open shunt stubs to obtain an optimum shifting frequency and wider bandwidth. Folded stepped-impedance transmission line (FSITL) is used to achieve reduced circuit size. The proposed power divider is fabricated using RT/duroid 5880 substrate with thickness of 0.38 mm. The dimension of the power divider is 13 mm × 6.5 mm. The proposed power divider has typical power division of –3 dB and insertion loss less than –1 dB, better than –13 dB of isolation, less than –10 dB return loss and phase imbalances less than 2° from 1.5 to 3 GHz. Both simulation and measurement results show a good agreement.


Introduction
Conventional Wilkinson power dividers (WPD) [1] are usually used for power division in microwave communication systems since they have a good isolation between the two separated output ports, a low insertion loss, and a simple fabrication process.However, these power dividers have large circuit size due to the application of long transmission line (λ/4 length) to match the output port to the input port, particularly for lower operating frequencies RF systems.In addition, the conventional circuit has a narrow bandwidth.
Recently, the design of WPD has adopted many techniques [2][3][4][5][6][7][8][9][10][11][12] to miniaturize the circuit size of the power divider, nevertheless, these techniques suffered serious degradation of the return-loss bandwidth compared with the conventional structure.For instance, in [9], the WPD was proposed using two-section asymmetrical T-structures to achieve a significant size reduction.The asymmetrical T-structures were represented by two series of high-impedance lines but the phase delay was not 90°.Due to this reason, the isolation circuit should consist of not only resistance but also capacitance/inductance [23].
Step impedance transmission lines (SITL) was used to reduce the size of microstrip components as in [7], [8], [10].In [7], they proposed a new idea based on SITL to compact the quarter wave length transmission lines in the WPD.According to [11], [12], folding stepped-impedance transmission line (FSITL) can provide a more compact circuit size.Even though, these approaches can provide up to 60-80% circuit size reductions, they have limited bandwidths.
Recent efforts [13], [14] have shown that the Wilkinson's design can be modified to achieve a wider bandwidth.Multilayer PCB technology was used by [13], to enhance the operating bandwidth of the power divider.Some researchers [15] enhanced the bandwidth of the power divider via coupled microstrip lines and shunt open-ended stubs resulting in a good power splitting performance.On the other hand, it increases the size and the complexity of circuit fabrication.De Lima Coimbra [16], [17] was the first to propose the single delta-stub which provides wider bandwidth.In [18], they incorporated delta-stub in both WPD arms to achieve ultra-wide band (UWB) characteristics; however they did not reduce the size although high center frequency of 6.85 GHz was used.All these proposed techniques may increase the circuit size and insertion loss [10].Some of the methods also make the structure complex, costly to manufacture and incompatible with microstrip circuits [20], [21].In this study, a series delta-stubs (SDS) is implemented to shift the high operating frequency to low frequency while maintaining short branch lines.In addition, by adjusting the dimensions of the delta-stub, the operating bandwidth can be widened.The quarter-wave line section was replaced by folded stepped-impedance transmission line (FSITL).The series stub, which is a combination of four-series delta-stub, is applied in each branch to achieve a more compact size and wideband.In this work, wideband and compact Wilkinson power divider of center frequency 2.4 GHz was developed.

Proposed Design
The designed Wilkinson power divider is shown in Fig. 1 for a desired center frequency of 2.4 GHz.Two parts of the modified power divider are going to be discussed separately: series delta-stub (SDS) and folded steppedimpedance transmission line (FSITL).
The SDS is modified based on a single delta openstub shown in Fig. 2. By considering the single delta-stub, it can be divided into n discrete segments of microstrip transmission line of length δ.The length δ should obey the condition δ << λ g , where λ g is the electrical wavelength.The narrow width segment of the stub which has higher characteristic impedance is merged with the microstrip transmission line of the power divider.The last widest segment of the stub with low impedance plays a role as an open ended discontinuity as shown in Fig. 2(b).The analytical design procedures of the delta-stub are demonstrated by several steps: Step 1: First, the desired size of the designed power divider circuit is fixed to be (13 × 6.5) mm 2 .However, the smaller size of the power divider circuit was given 3.2 GHz of the operating center frequency, f c , which is higher than expected center frequency, f c ' = 2.4 GHz.Here, the modification of the pre-designed circuit was done in order to shift f c from 3.2 GHz to 2.4 GHz without increasing the physical transmission length.
The empirical equations (1) to (5) were obtained by polynomial regression fitting based on the CST simulation data.Up to 15 fitting coefficients (a 1 ,...,a 5 ; b 1 ,…,b 5 ; c 1 ,…,c 5 ) are chosen to provide a greater degree of freedom for the regression fitting.
where the shifted frequency, Δf is given as: Symbols α, β and γ in (2) are expressed as: where θ (in degree) is the vertex angle of the delta-stub and n series is the number of delta-stub connected in series form First of all, the required shifting frequency, Δf (in GHz) from high to low needs to be determined.The number of series delta-stub, n series in each branch is chosen and it must be a positive integer ≥ 1.
Then, the angle, θ of the delta-stub is chosen within the range of 10° < θ < 65°, and substituted into (3) to (5).Once the values of α, β, and γ are obtained, they are substituted along with n series into (2) to make sure that Δf is the same as the determined shifting frequency.If Δf is less than the determined shifting frequency, the value of θ or n series should be slightly increased and vice versa.
In this study, the reason behind choosing exactly four-series delta-stubs in each branch with θ = 26° is to meet the required performance parameters at 2.4 GHz, such as:   Step 2: Secondly, the transmission line widths, W nδ of the segment are calculated by [18]     where subscript n is the number of the segments in the delta-stub.It is worth to mention that θ = 26° was chosen based on studying different angles for four-series deltastubs in order to get the desired center frequency of 2.4 GHz as shown in Fig. 3(a).
The input impedance, Z in(n) of each n-segment is obtained by (7) with the exception of the final section (Z in(N) ) since it has the open ended discontinuity.For W nδ /h > 1, the Z in(n) of each n-segment is calculated as [1]: where the characteristic impedance, Z o(n) of each n-segment is expressed as: o( ) e 120 1.393 0.667 ln 1.444 and the effective dielectric constant, ε e in ( 8) is given as: The input impedance of the delta-stub can be found from the computation of the input impedance, Z in(n) of each cascaded transmission line with incremental distance δ.According to (6) to (9), n was chosen to be 42 to enable calculating the impedance of the delta-stub, Z in(1) = 57.94Ω and Z in(N) = 83 Ω.The electrical parameters for the deltastub were computed as: W g = 0.5 mm, L = 1.88 mm, r i = 1.14 mm, θ = 26°, W nδ = 0.95 mm, δ = 0.048 mm, ε r = 2.2 and thickness, h = 0.38 mm.When adding the four-series delta-stubs, the center frequency was successfully shifted to 2.4 GHz.This resulted in a size reduction of 44% compared to the conventional Wilkinson power divider at the same center frequency; however, fractional bandwidth (FBW) is reduced by 8%.Therefore, in order to improve the reduction of bandwidth and get more size reduction, stepped-impedance transmission line is used [7], [8], [24], [28].

Step 3:
Figure 4 shows the second step in the design process which is to replace the uniform branch line with non-uniform SITLs while maintaining the impedances of input and output ports at 50 Ω.The stepped-impedance-stub lines design equations provide two degrees of freedom for circuit dimensions determination.These degrees of freedom can be used to reduce the circuit size [7].
The SITL possesses two different characteristic impedance lines and both appeared to be symmetrical.A stepped-impedance transmission line consisting of a low impedance line section and two identical high impedance line sections is depicted in Fig. 4. The low impedance line section (Z 1 line) is in the middle with electrical length θ 1 and the two identical high impedance line sections with characteristic impedance Z 2, and electrical length, θ 2 /2 are on both sides.The desired total electrical length, θ t = θ 1 + θ 2 is less than 45° at center frequency of 2.4 GHz [7].The impedance ratio, Z 2 /Z 1 = K of SITL can reduce the length when K > 1 [7], [24].The equations from (1) to (6) in  [7] are used to determine the optimum values of Z 2 , Z 1 and Selecting a very high impedance ratio, K is necessary to achieve compactness in the lines length; however, the limitations for achieving very high impedance lines (W/h << 1) and very low impedance lines (W/h >> 1) should be taken into account.Furthermore, high impedance ratio, K leads to high discontinuity effects.This means that high value of Z 2 is required, but this will result in a very narrow bandwidth.In addition, if Z 1 is extremely low, this will result in a wider microstrip line.Due to this reason, it will be difficult to fabricate.In this work, the desired total electrical length of the structure is θ t = θ 1 + θ 2 and θ t should be less than 40° at center frequency of 2.4 GHz.By folding the stepped-impedance line [7], the total physical size was reduced by 84% as shown in Fig. 5.The dimensions and parameters of FSITL are tabulated in Tab. 1.

Results
The proposed Wilkinson power divider is designed to operate for equal power division across the band 1 GHz to 3.5 GHz. Figure 6 shows the actual circuit of the proposed power divider using four-SDS and FSITL structures.This modified power divider has 84% reduction size compared to the conventional power divider at the same center frequency of 2.4 GHz.The simulated and measured S-parameters results of the modified power divider are presented in Figs.7 and 8(a), respectively.In spite of the fact that the simulation and measurement results show significant agreement, there is a minor difference due to the tolerance in fabrications.The measurements were taken by using an Agilent E5071C network analyzer.interval from 1.65 GHz to 3.3 GHz.This is equivalent to 69% fractional bandwidth and the isolation, |S 23 | between two output ports is better than -13 dB from 1.5 GHz to 3.1 GHz.It is obvious from Tab. 2 that the results achieved by this study are superior compared to the previous studies.

Conclusion
A compact Wilkinson power divider has been successfully designed and fabricated using four-series delta stubs with a stepped-impedance transmission line (FSITL) on each branch in order to obtain a compact size and a wider bandwidth.The modified power divider achieves a significant size reduction of 84% compared to a conventional power divider at 2.4 GHz.The measured results of the modified power divider showed a 116% fractional bandwidth.It also achieved good impedance matching, equal power splitting, and high isolation performance over the range shown by simulation and measurement results.

Ref.
Center

Figure 3 (
Figure3(a) depicts the relationship between the number of delta-stubs, center frequency, f c and angle, θ.From Fig.3(a), it can be noticed that the center frequency, f c is shifted to a lower frequency, f c ʹ by increasing the number of delta-stubs, n series and the angle, θ.It should be taken into account that adding more series of delta-stub improves

Fig. 3 .
Fig. 3. (a) 2D plot, the relationship between number of series delta-stubs, angle and the resonant frequency, (b) 2D plot.the return loss, |S 11 |, on the other hand, that will influence the bandwidth as shown in Fig. 3(b).
Nor Hisham KHAMIS is an Associate Professor in the Communication Engineering Department (CED), Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Skudai, Johor, Malaysia.He received his B.Sc.E.E.from the University of Evansville, Indiana, USA in 1988, M.E.Sc.E.E.from the University of New South Wales, Australia in 1992, and PhD from UTM in 2005.He joined UTM in 1989 and currently is the Head of Radar Laboratory.He is also the subject coordinator for radar courses at the faculty.His research interest includes antenna design, especially microstrip antenna, planar microwave components, wireless transmission, and propagation studies; and now is the Head of Sonar Technology and Marine Instrumentation (STAR) Research Group.He is a member of Eta Kappa Nu (Electrical Engineering Honor Society, USA).Mohamad Ngasri DIMON was born in 1961.He obtained his B.Sc. degree in Electrical Engineering (Telecommunication Engineering Option) from University of Southwestern Louisiana, Lafayette, Louisiana, USA in 1987.He completed his Master of Electrical Engineering in Acoustics Engineering in 1992 and PhD in Acoustics Engineering from UTM in 2002.Recently, he is an Assoc.Prof. at Communication Engineering Department, Faculty of Electrical Engineering, Universiti Teknologi Malaysia (UTM), Malaysia.His main research interest is in acoustics engineering with emphasis on room acoustics modelling, building acoustics local standard adaptation and development of electromagnetic wave application at microwave frequencies.