Modified Ring Power Divider Using Stepped-Impedance Resonator

— In this paper, the design of a modified ring power divider dedicated for wideband communication or measurement systems is presented. The proposed power divider is built by using a conventional ring power divider and an additional Stepped-Impedance Resonator (SIR). The even-odd mode analysis is used to derive the design equations. In order to observe the bandwidth improvement, a comparative study between the designed device and the previously reported ring power divider is conducted. The electromagnetic (EM) simulated results show that the proposed divider has a fractional bandwidth of 90.2 % at the center frequency of 3.17 GHz. The measurement results of the fabricated prototype demonstrate high performance over the considered operational bandwidth from 1.7 GHz to 4.64 GHz with a return loss lower than -10 dB while maintaining a good insertion loss and a good isolation between the output ports. The maximum amplitude imbalance is better than 0.21 dB and the phase imbalance is better than 2.5 degrees between the output signals. The simulation and measurement results are in good agreement over the whole band of interest.

broadband power divider achieving good in-band responses across a 62 % fractional bandwidth was proposed in [9] by arranging two open-circuited stubs and three coupled-line sections around the ring resonator. However, these power dividers require complex design configuration due to the use of different layers or coupled-line sections which makes the fabrication process more complicated.
Recently, a compact ring power divider has been proposed in [10]. It introduces a circular layout with the addition of two half-wave transmission lines to connect the 100 Ω isolation resistor, converting the layout in a ring circuit of 1.5 λ g length. The corresponding electric lengths θ 1 and θ 2 are π/2 and π, respectively, and the normalized ring characteristic impedance z 01 (which is equal to z 02 ) is found to be [10]. The circuit has been rebuilt to operate at the center frequency of 3.12 GHz as shown in Fig. 1. This circuit is offering very good performance over a wide bandwidth compared to the traditional Wilkinson power divider. In addition, this design had shown more stability and larger bandwidth than previous implementations among valid solutions. Furthermore, this circuit has a size reduction of around 20 % compared to classical Wilkinson power divider and improved performances in terms of RF input/output matching and isolation between the output RF ports [11].
In this work, a modified ring power divider operating in the frequency band from 1.7 GHz to 4.64 GHz is introduced and it consists of the same circular structure as in [10] with the addition of a stepped-impedance resonator (SIR) to the old structure. The circuit in Fig. 2 represents the layout of the proposed ring power divider. For this structure, the simulation results show that the fractional bandwidth has a significant increase of 27.2 % compared to the old structure as it will be seen in section II and this without affecting the circuit size since the added element is inside the ring structure.

II. DESIGN AND SIMULATIONS
The circuit diagram of the proposed wideband ring power divider is shown in Fig. 3. It consists of six transmission lines of characteristic impedances (Z 01 , Z 02 , and Z 03 ), a Stepped-Impedance Resonator (SIR), and an isolation resistor R=100 Ω. Microstrip resonators have been widely used in the design of microwave filters with wide stopband characteristics [12]- [14]. In addition, Stepped-impedance resonators (SIRs) have been found advantageous in the design of microstrip bandpass filters with good stopband performance [15]- [17].
A typical SIR is used to modify the structure of the ring power divider and is built by joining three microstrip-line sections of different characteristic impedances Z 04 and Z 05 as shown in Fig. 4. The microstrip line at the center has a characteristic impedance of Z 05 with an electrical length of θ 5 whereas the identical lines at the two sides both have a characteristic impedance of Z 04 with an The structure of the proposed ring power divider is symmetric; thus, we can apply the even-odd mode analysis [18] in order to analyze the divider parameters. In this study, the known parameters as defined in the previous analysis [10] are the normalized characteristic impedances z 01 = z 02 = z 03 = z 04 = 2 ; and θ 1 =π/2 and (θ 2 + θ 3 ) =π. The following analysis is performed in order to find the main characteristics of the added element to the old ring structure.

A. Even -mode analysis
In the even mode, ports 2 and 3 are excited by signals of the same magnitude and phase, which Referring to Fig. 6, the input impedances Z ine1 and Z ine2 can be expressed as follows 5 (9) Let Z X be the parallel combination of these impedances Z ine2 and Z ine3 , then the equivalent admittance Y X can be written as: The equivalent impedance Z eq2e can be expressed as the input impedance of a transmission line terminated by Z X : Since the output is matched, the input admittance for the even-mode Y ine viewed from port 2 should be equal to Y 0 = 1/Z 0 : By replacing Z eq1e and Z eq2e in (12) with their values in (5) and (11) Comparing (10) and (14) (17) Which is the second resonance condition given by (2) for the even-mode resonance of a typical stepped-impedance resonator [16].

B. Odd -mode analysis
In the odd mode, ports 2 and 3 are excited by signals of the same amplitude but of opposite phases.
The introduction of equal and contrary voltages implies a diverging current that can be represented by short circuits at the plane of symmetry which has the effect of introducing a virtual ground along the line of symmetry as shown in Fig. 7. In this analysis, we can choose θ 2 = θ 3 = π/2 in order to have a symmetric design which will reduce the computational complexity. The calculation of the input impedance Z ino viewed from port 2 is simplified and corresponds to Z eq1 and Z eq2 connected in parallel.
From the transmission line theory, we can easily calculate Z eq1 as the input impedance of a shortcircuited line.
The input admittance Y ino seen from port 2 must be matched to Y 0 =1/Z 0 . Since θ 1 = π/2 and Z 0 = R/2; then after simplification, the matching condition in equation (26) becomes: Which is the first resonance condition given by (1) for the odd-mode resonance of a typical steppedimpedance resonator. Since the two conditions for even and odd mode resonance are satisfied, this proves that the added element is an SIR.
The SIR is designed with fixed fundamental frequency, but different first spurious mode (f s1 ) by choosing different combinations of K and α from Fig. 5 and thereby the dimensions of the SIR can be determined. The impedance ratio K and the stepped percentage α are then tuned using electromagnetic (EM) simulation in order to consider step discontinuities [16].
It has been demonstrated that by changing the width ratio w 5 /w 4 of the low-impedance (Z 05 ) line to the high-impedance (Z 04 ) line, which result in the modification of K, the position of the transmission zeros can be adjusted. Furthermore, it is evident that by increasing the width ratio w 5 /w 4 , resonance frequency is varied [17].
A parametric study is conducted to evaluate the effect of SIR's characteristic impedance ratio on the bandwidth of the proposed power divider. Fig. 8 shows the effect of variation of K on the transmission S-parameter magnitude of the proposed power divider. It can be seen from Fig. 8, that when K increases, there is almost no effect on the lower transmission zero; however, the second transmission zero is shifted to a lower frequency. The simulation results are also compared to the case of the conventional ring power divider (without SIR).
It is noticed that for K =2, we get the wider bandwidth with two transmission zeros situated at 1.2 GHz and 5.21 GHz with -52 dB and -44 dB attenuation values respectively.
Following the above guidelines, the optimized parameters of K=2 and α = 0.95 can be used in order to get a wide bandwidth from 1.7 GHz to 4.6 GHz of the proposed divider. As a result, the stepped impedance resonator can be designed to have the characteristic impedances Z 04 =40 Ω and Z 05 =20 Ω, and the electrical lengths θ 4 and θ 5 are set to 84.5˚ and 7.8˚ respectively. This can be used in order to calculate the dimensions of the Stepped Impedance Resonator (SIR) cell. The microstrip widths and lengths corresponding to characteristic impedances Z 0 , Z 01 , Z 04 and Z 05 are shown in Table 1. The radius of the ring is 15 mm.  . 9 and Fig. 10 show the EM simulation results of the conventional and proposed ring power divider respectively obtained by using the Advanced Design System (ADS) software. As can be observed from these figures, the conventional ring structure [10] has a fractional bandwidth of 63 % ranging from 2.14 GHz to 4.11 GHz (S 11 <-10 dB), while simulations of the proposed ring structure show that the fractional bandwidth has increased up to 90.2 % producing therefore a remarkable bandwidth enhancement of 27.2 % as mentioned in section 1. By comparing the results of the two ring power dividers, we can notice that the proposed ring power divider has an insertion loss which is between -3.04 dB and -3.58 dB over the whole band (1.74-4.6 GHz) with quasi-null amplitude imbalance (S 21 =S 31 ) while the conventional power divider has an insertion loss between -3.06 dB and -3.61 dB over a narrower band (2.14-4.11 GHz). In addition, it is obvious that the proposed divider has better return loss and better isolation between the output ports which are lower than -10 dB in the whole band (1.74-4.6 GHz), providing thus a significant wide bandwidth contribution compared to the previous reported ring divider which operates from 2.14 GHz to 4.11 GHz as can be clearly seen from Fig. 9 and Fig. 10.
Compared with other wideband power dividers present in the literature such as in [8]- [9], it is obvious that apart from its simpler structure, the proposed ring power divider has better performance over a wider operational bandwidth. It is to be noted that the power dividers developed in [8]- [9] have a fractional bandwidth of 68.6 % and 62 % respectively.   The S-parameter measurements were accomplished using the Agilent E8362B vector network analyzer over the frequency range from 1 to 6 GHz. The EM simulations and measured S-parameter results of the proposed power divider are shown in Fig. 12 and Fig. 13. The measurement results show that the proposed power divider has an insertion loss of 0.74 ranging from -3.36 dB to -4.1 dB between 1.74 GHz and 4.64 GHz. The measured return loss is less than -10 dB from 1.6 GHz to 4.71 GHz. The output return loss is lower than -10 dB from 1.7 GHz to 4.64 GHz. The isolation between the outputs is better than -10 dB between 1.42 GHz to 5.21 GHz. It can be concluded by comparing the measurement and EM simulation results that there is good agreement over the whole band of interest.  The measured amplitude and phase imbalances between outputs of the proposed divider are shown in Fig. 14. These results show that the proposed power divider has a maximum amplitude imbalance of 0.21 dB in the whole band from 1.7 GHz to 4.64 GHz which implies that the power is divided evenly between the 2 outputs. In addition, the two outputs are in-phase in the whole band with a tolerance of less than 2.5 degrees over the whole bandwidth of interest which proves the good phase performance of the fabricated power divider.

IV. CONCLUSION
In this work, we have designed a modified ring power divider to cover the frequency bandwidth of 1.7 GHz to 4.6 GHz by adding an SIR to the old structure to improve its operational bandwidth. A detailed even-odd mode analysis of the proposed ring power divider has been performed. To validate the theoretical analysis and simulations, a prototype is fabricated on a single layer substrate. The experimental results show that the proposed circuit is broadband with a high factor amplitude balance over the considered bandwidth. The proposed ring power divider has the advantages of compact size and ease of fabrication which makes it very suitable for many wideband microwave applications.