Highly Unequal Three-Port Power Divider : Theory and Implementation

A three-port power divider consisting of a directional coupler, a Wilkinson power divider, and two transmission lines connected to them is proposed. Theoretical analysis reveals that highly unequal power division can be achieved by a feedback mechanism of two transmission lines along with the coupling coefficient of the directional coupler and the power division ratio of theWilkinson power divider. The three-port power divider inherits the performance characteristics of high isolation, low reflection coefficients at all ports, and the minimum number of components. The proposed power divider is designed at 5.8GHz and fabricated and evaluated through measurements. It demonstrates that electromagnetic simulation results are in good agreement with theoretical prediction and measurement results. The three-port power divider is compact in the planar form, so it can be easily integrated into radio frequency front ends.


Introduction
Two commonly used power dividers are the Wilkinson and Gysel power dividers, invented in 1960 and 1975, respectively [1,2].The Wilkinson and Gysel power dividers have the similar performance for their scattering matrices, but there is a difference in their structures and the later permits higher power loads than the former.The Wilkinson power divider with a power division ratio such as 9 : 1 is difficult to be physically realized in microstrip form because the characteristic impedance of one branch line is 273.86 Ω.A symmetric coupler with 3 dB coupling coefficient is known as a quadrature hybrid or a branch line hybrid [3].We are also facing the same difficulty as to the Wilkinson power divider that a symmetric coupler with the coupling coefficient for more than 8 dB is impractical to be physically constructed utilizing the microstrip technology.
The Wilkinson power divider and the symmetric coupler are mostly applied with equal or low power division ratios.Wilkinson power dividers with parallel RLC components [4], complex isolation component [5], and two-section two-resistor [6] were designed and miniaturized for highfrequency applications.A typical application for highly unequal power division is the Doppler radar [7], as illustrated in Figure 1.The RF input signal is divided into two-way outputs, RF output 2 and RF output 3. RF output 2 is further transmitted through a circulator to the antenna and radiated.Assuming a target moving with a relative velocity ± ν and with a radar cross section σ, the RF signal will be scattered by the target and then received by the antenna.After passing through the circulator, it will enter the radar receiver front end where it is firstly amplified by a lownoise amplifier (LNA) module.The two signals, RF output 3 and RF output 4, are then further fed to a mixer.RF output 3 is used as a reference signal for comparison and frequency downconversion.
One major challenge of accurately processing the information carried by the scattered signal at RF output 4 is the requirement of a good balance between the power levels of the reference signal and scattered signal [8].In fact, it is found out with a computation that the signal level of RF output 3 might be 30 dB higher than that of RF output 4, even if the power division ratio of the power divider is b 2 2 b 3 2 = 10 1 and the gain of the LNA module is 30 dB.A three-port power divider with a power division ratio of 9 : 1 was reported, including about nine LC elements in its fabricated sample [9].A three-port power divider with a power division ratio of 10 : 1 has been presented with a Gysel power divider and two coupling structures of filtering responses [10].A single-section coupled line coupler can be designed with the performance of 20 dB coupling factor and 50 dB isolation, but it is best suited for weak coupling and is a four-port network [3].
There have been some other works reported in the literature concerning highly unequal power dividers, which would not be cited here one by one.We may conclude that a threeport power divider with power division ratios for more than 10 : 1 would be hard to realize in a physical structure, and their research work would be difficult to implement in engineering designs.
Since the RF amplitude balance of the signals to the mixer, that is, RF output 3 and RF output 4 in Figure 1, must be considered in a system design, a highly unequal three-port power divider is proposed in this paper along with its design methodology.Moreover, assuming that a good isolation can be achieved, the proposed power divider could be used without the circulator in Figure 1, which can be used in the microstrip form [11].The paper focuses on theoretical analysis and design of a highly unequal three-port power divider.To verify the developed theory and design, the power divider was fabricated and evaluated through measurements finally.The resulting demonstrator is very compact when implemented in the microstrip planar technology and can be integrated into the entire RF front end including the antenna.

Theory
A model of three-port divider with a feedback mechanism is proposed, which consists of a directional coupler, a Wilkinson power divider, and two transmission lines.The scattering matrix and the maximum power division ratio for the three-port power divider are then formulated.

Feedback Model.
A schematic of the three-port power divider with a feedback mechanism is shown in Figure 2. The power divider consists of four parts, that is, a directional coupler, a Wilkinson power divider, and two transmission lines of TL1 and TL2.The numbers 1, 2, 3 ′ , and 4 ′ are the input port, the through port, the coupling port, and the isolated port of the directional coupler, respectively.The numbers 1′ and both 2′ and 3 are the input port and the output port of the Wilkinson power divider.The phase delays of TL1 and TL2 are θ 1 = 2πL 1 /λ g and θ 2 = 2πL 2 /λ g , where L 1 is the length of TL1, L 2 is the length of TL2, λ g is the guide wavelength, and their characteristic impedances are 50 Ω.Power supplied to the port 1 is coupled to the port 3 ′ and then transferred to the port 1 ′ through TL1.The output power at the port 2′ is fed to the port 4′ through TL2.The functions of TL1 and TL2 are to provide a feedback path, and a power division ratio for the three-port power divider is reallocated.In the meanwhile, the output ports of 2 and 3 are the isolated ports.
To take account of reference phases at all ports of the directional coupler, the scattering matrix of the directional coupler in Figure 2 is a reciprocal four-port network and rewritten as S DC [3] where α and β are the positive reals and satisfy the condition of The scattering matrix of the Wilkinson power divider in Figure 2 is rewritten as on the same grounds where 2 is a power division ratio of the Wilkinson power divider, according to the traditional notation.The transpose of a matrix S 4 is denoted by S T 4 .The shunt resistor is determined by R = Z 0 K + 1/K [3], where Z 0 is the characteristic impedance of transmission lines connected to the three ports, generally taken as 50 Ω.If K = 1, the Wilkinson power divider will be the equal-split (3 dB) case.
2.2.Formulation.Vectors of the incident and reflected waves at the ports of the directional coupler are defined as The scattering matrix of the three-port power divider is derived Equations ( 5) and ( 7) can be solved simultaneously to give the vectors of a 1 ′ 2 ′ and a From ( 6) and ( 9), the vector of b 12 and the variable of b 3 are found Equation ( 10) can be simplified as the following forms: From (11), the scattering matrix of the three-port power divider is determined with S 21 and S 31 S = 0 S 21 S 31 S 21 0 0 S 31 0 0 14 It shows that the scattering matrix (14) of the three-port power divider is similar to (2) of the Wilkinson power divider, where the conditions of S = S T , S ii = 0 i = 1, 2, 3 , S 23 = 0, and S 21 2 + S 31 2 = 1 are simultaneously satisfied.The power division ratio for the three-port power divider in Figure 2 is defined where It is concluded that a feedback mechanism for two transmission lines of TL1 and TL2 is very important to improve the power division ratio for the three-port power divider.
A special case is considered that the directional coupler in Figure 2 is a symmetric coupler.We give a computation on the power division ratios as the following: the symmetric coupler with C = 7 dB b 2 2 / b 3 ′ 2 = 4 , ψ 1 = −90 °, and ψ 2 = ψ 3 = −180 °, and the Wilkinson power divider with ϕ 1 = ϕ 2 = −115 52 °, which is from the simulation result with Advanced Design System (ADS).
The computation results with MATLAB are shown in Figure 3 with 1/K 2 = 1, 2, 3, 1/2, 1/3, respectively.Because of the presence of the minimum length in the physical structure, the value of θ 1 + θ 2 is taken from 180 °to 540 °, that is, the length of L 1 + L 2 should be from 0.5 λ g to 1.5 λ g .The results reveal that a region of θ 1 + θ 2 exists to ensure that the power division ratio of the three-port power divider is more than 10 in the listed values of 1/K 2 .The maximum of the power division ratio occurs at the value of θ 1 + θ 2 = 450 °+ ϕ 1 = 338 48 °, and the region of θ 1 + θ 2 for the power division ratio more than 10 is in a wide range to be used.If the Wilkinson power divider is K = 1, the maximum of the power division ratio for the three-port power divider is 25.65.

Implementation
Based on the above theory developed for the highly unequal three-port power divider, the schematic and layout of a 5.8 GHz power divider were captured using ADS 2015.01, from Keysight Technologies.A comparison between (7a) and the circuit simulation with ADS is first given.To verify the above design, a test sample is fabricated, measured, and compared with the electromagnetic simulation.
3.1.Schematic.Rogers RO4350B substrate has the dielectric constant of 3.66, the dissipation factor of 0.0034 at 5.8 GHz (0.0037 at 10 GHz), the thickness of 1.524 mm, and the copper cladding of 35 μm.
Both the schematic of the test sample and the basic principle of the following layout implemented in ADS schematic are provided in Figure 4, where Term, TL, and Bend are the stardard components in ADS pallete.The transmission line of TL1 (see Figure 2) consists of TL16, Bend4, and TL17.The transmission line of TL2 (see Figure 2) is realized with TL11, Bend1, TL12, Bend2, TL13, Bend3, and TL14.TWD and the TL1 and TL2 phase delay is 4 International Journal of Antennas and Propagation The symmetric coupler with C = 7 dB and the Wilkinson power divider with K = 1 were automatically generated and optimized by the tool of passive circuit of Design Guide in ADS schematic, respectively.The generated circuit components of the symmetric coupler and Wilkinson power divider were integrated into a three-port power divider in a new schematic by the model in Figure 2, a new layout was done by generate/update layout in the ADS schematic, and three test ports of RF input/output were added to it by three SMA connectors, Johnson part number 142-0701-801 of End Launch Jack Receptacle.  5 International Journal of Antennas and Propagation microstrip, and the parameters of the three-port power divider are listed in Table 1.

Circuit Simulation.
Simulation results of the symmetric coupler and Wilkinson power divider using ADS in the schematics are shown from Figures 6-8.
In fact, the lengths of two transmission lines of TL1 and TL2 in the test sample are arbitrarily chosen in the range of power division ratios being more than 10, only for connection with both the symmetric coupler and Wilkinson power divider and can be adjustable to specific applications.and 11, where the prefix of "Sim" represents the electromagnetic simulation with ADS Momentum Microwave and that of "Mea" means the measurement by a Rohde & Schwarz vector network analyzer.Power division ratios for the above test sample are also obtained for both the electromagnetic simulation with ADS and measurement results in Figure 12.A fairly good agreement between the simulation and measurement is seen.It is also shown in Figure 12 that the −10 dB bandwidth of the three-port divider is more than 1 GHz.

Conclusions
Theory of the highly unequal three-port power divider with a feedback mechanism is presented.The three-port power divider can provide with a power division ratio of more than 10.A high isolation and impedance match are achieved at all ports.Moreover, it is compact in the planar form.The presented theory agrees well with the simulated results using ADS and the measurement results.The three-port power divider can be realized in the microstrip form without difficulty and easily integrated into radio frequency front ends.This work has completely solved the problem of limited power division ratios associated with three-port power dividers.

Figure 1 :
Figure 1: Simplified block diagram of the front end of a monostatic Doppler radar.
and b 3 ′ 4 ′ = b 3 ′ b 4 ′ T .Similarly, two wave vectors of the Wilkinson power divider are defined as b 1

Figure 2 :b 3 =
Figure 2: Schematic of the three-port divider with a feedback mechanism.

2. 3 . 2 2 b 3 ′ 2 = 1 34 1 and that for the Wilkinson power divider is b 2 ′ 2 b 3 2 = 1 1 ,
Analysis.In (16), the item of α 2 /β 2 = b 2 2 / b 3′ 2 is the power division ratio of the directional coupler.When the power division ratio for the directional coupler is b the power division ratio for the threeport power divider will be achieved by b

Figure 5 :
Figure 5: Layout of the three-way divider with C = 7 dB and K = 1.The ADS layout exported a DWG format file, which was inserted and processed in Microsoft Visio.

Figure 6 :
Figure 6: Amplitudes of the scattering parameters of the symmetric coupler simulated in ADS schematic with C = 7 dB.

Figure 7 :
Figure 7: Amplitudes of the scattering parameters of the Wilkinson power divider simulated in ADS schematic with K = 1 and R = 100 Ω.

Figure 8 :
Figure 8: Phases of the scattering parameters of the symmetric coupler (SC) and Wilkinson power divider (WPD) simulated in ADS schematic with C = 7 dB, K = 1, and R = 100 Ω.

Figure 11 :Figure 12 :
Figure 11: Comparisons of S21 and S31 between the electromagnetic simulation in ADS and measurement.

Table 1 :
Parameters of the three-port power divider.