Unequal Divider with Asymmetric Shunt Open Stub for Reduced Size and Harmonic Suppression

This study presents an unequal divider with asymmetric shunt open stubs to reduce circuit size and achieve harmonic suppression. The design method was derived from Sto admittance parameter conversion of unequal divider. We validated the use of the parameter conversion method to reduce the size and achieve harmonic suppression of the unequal divider by implementing the divider at a power ratio of 3 at a center frequency of 1 GHz. The measured characteristics agreed well with the results of the calculation and the harmonic suppression was improved by more than 14 dB between the 2 nd and 4 th harmonics with 20% reduction in size compared to a conventional divider.


INTRODUCTION
A power divider is a basic component for RF/microwave system and performs functions such as power divide and combine network for amplifier (Jang et al., 2014;Feng et al., 2013) and mixer (Razavi, 1997) modules and feed networks for antenna (Nikfalazaar et al., 2016;Stutzman and Thiele, 2000).Wireless systems require a harmonic rejection filter (Madadi et al., 2016;Guo et al., 2015) for the microwave circuit, because the harmonic signals cause normal operation to malfunction.However, this filter increases the cost and the size of the equipment.
To eliminate influence of the harmonic signal, the wireless systems require to insert a harmonic rejection function at the point which signal split and combine occurs.Recently, many paper for divider and combiner have been reported for harmonic suppression, such as two quarter-wave open stub located at the center of the quarter-wave branches (Yi and Kang, 2003), an asymmetric spiral defected ground structure in quarterwave line (Woo and Lee, 2005), an electromagnetic band-gap structure (Lin et al., 2007;Zhang and Li, 2008), a high-low impedance resonator cell (Wang et al., 2009), a series inductor (Mirzavand et al., 2013) and a general π-type structure for an equal divider (Wang et al., 2015).Most of these papers are concerned with equal dividers for harmonic suppression and unequal dividers have not received much attenuation.
This study describes an unequal divider with harmonic suppression and size reduction based on S-to admittance parameter conversion.Figure 1 shows the equivalent circuit of conventional and the proposed unequal divider.The quarter-wave line of conventional unequal divider in Fig. 1a can be change to a line with asymmetric shunt open stubs in Fig. 1b, which consists of one transmission line and two shunt open stubs and their characteristic impedance and electrical length are different all.In contrast to the even-/odd-mode analysis method, the S-to admittance parameter conversion (Miao et al., 2014(Miao et al., , 2012;;Kim, 2016) constitutes a simple design method for unequal divider to include phase delay information and arbitrary port impedances and asymmetrical configurations.Thus, parameter conversion methods are introduced for unequal dividers, the design equations are derived and synthesis procedures are provided.The reported general π-type structure divider in reference (Wang et al., 2015) is a special case of one proposed in this letter.The performance of an unequal divider with power ratio of k 2 = 3 at operating frequency of 1 GHz is evaluated by measuring its insertion loss, reflection and harmonic suppression characteristics and its ability to reduce circuit size.

MATERIALS AND METHODS
When and where this study was conduct: This research was conducted at Kumoh National Institute of Technology test facility in 2016.
The equivalent circuit of an unequal divider with power ratio k 2 (= P 3 /P 2 ) is depicted in The S-to admittance parameter conversion can be performed using following equations: where Y 01 = 1/Z 01 , Y 02 = 1/Z 02 and Y 03 = 1/Z 03 are the port admittance and U is the unit matrix.Using Eq. ( 2), the admittance matrix of an unequal divider with power ratio k 2 and electrical length θ = 90° is given as: (1 ) (1 ) ( 1) On the other hand, according to the definition of an admittance parameter, the admittance parameters of the proposed unequal divider in Fig. 1b We obtain the simple design equations of the proposed unequal divider by assuming the following conditions: , , Imposing admittance parameter equality of ( 4) and ( 5) and using ( 6) ~ ( 10), the design parameters specified in Fig. 1b can be obtained as follows: (1 ) (1 ) , sin sin

RESULTS AND DISCUSSION
We designed the proposed unequal divider by calculating the impedance values using Eq (13) ~ ( 16).Characteristic impedance values from 10 Ω to 150 Ω were chosen to obtain the possible width of implementation transmission line in microstrip technology.
The impedance values of divider are obtained when the electrical length of θ 2 and power ratio of k 2 using Eq. ( 13) are varied.The impedance values of Z 2a and Z 2b are presented in Fig. 2a in case of Z o = 40 Ω.When the power ratio of k 2 and electrical length of θ 2 are determined, the graph showed the relation between the electrical length θ 3 and impedance values of Z 3a and Z 3b in Fig. 2b.In addition, when the power ratio of k 2 and the electrical length of θ 2 and θ 3 are determined, the relation between electrical length θ 1 and impedance values of Z 1a and Z 1b can be obtained, as shown in Fig. 2b.This relationship graph between impedance values of Z 1a and Z 3a and electrical length θ 1 and θ 3 represents the same data if the impedance ratio satisfied the condition of Z 1a = Z 1b /k 2 .
We validated the proposed unequal divider with asymmetric shunt open stubs by designing and   Figure 3 shows a photograph of the fabricated 3:1 unequal divider with asymmetric shunt open stubs.The main circuit size is 45 mm × 40 mm (0.237 λ g by 0.21 λ g ), only about 80% of conventional divider (0.31 λ g by 0.2 λ g ).The PCB was fabricated Teflon PCB of Taconic, with dielectric constant ε r = 2.5, a height of h = 0.787 mm and conductor thickness of t = 0.035 mm.This unequal divider was designed and optimized with the Microwave Office software, developed by National Instruments.
The measured data for this proposed unequal divider are shown in Fig. 4; the simulated and measured results can be seen to be almost coincident.
In Fig. 4, the insertion losses are |S 21 | = 7.16 dB and |S 31 | = 2.06 dB.These values are slightly different from those obtained from the simulation, because of the PCB substrate and fabricated losses.The isolations are |S 23 | = 27.5 dB and return losses are more than |S ii | = 17 dB, where i = 1, 2 and 3.The harmonic signals are rejected more than 14 dB at port 2 and 7 dB at port 3, respectively, between the 2 nd and 4 th harmonics, as seen in Fig. 4c.There is a frequency range between 0. 98 ~ 1.04 GHz for phase difference of ±5° between output ports.
A comparison of power dividers for reduction size and harmonic suppression is summarized in Table 1.As the results show, this study presents a size reduction unequal divider with harmonic suppression.

CONCLUSION
This study describes the development of an unequal divider with asymmetric shunt open stubs using the simple design method of S-to admittance parameter conversion.The experimental results show that the performance characteristics of the fabricated unequal divider correspond to the simulation results and that harmonic suppression of more than 14 dB at port 2 and 7 dB at port 3 between the 2 nd and 4 th harmonics is achieved.In addition, the size of the newly developed unequal divider is reduced by 20% compared to that of a conventional divider.

FigFig. 1 :
Fig. 1: Equivalent circuit of (a) conventional and (b) proposed unequal divider parameters of this divider with phase delay θ can be expressed as:

Fig. 3 :Fig. 4 :
Fig. 3: Photograph of the fabricated unequal divider with asymmetric shunt open stubs can be written as:

Table 1 :
Summary of published power divider