# Highly Unequal Three-Port Power Divider: Theory and Implementation

Authors: Duolong Wu; Adriana Serban; Magnus Karlsson; Shaofang Gong
Journal: International Journal of Antennas and Propagation
 (2018)

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## Abstract

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 the Wilkinson 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 5.8 GHz 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.


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## Body

## 1. 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 high-frequency 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 low-noise 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.Figure 1
Simplified block diagram of the front end of a monostatic Doppler radar.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 b22:b32=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 three-port 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 Figure1, 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.


## 2. 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.


### 2.1. Feedback Model

A schematic of the three-port power divider with a feedback mechanism is shown in Figure2. 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 θ1=2πL1/λg and θ2=2πL2/λg, where L1 is the length of TL1, L2 is the length of TL2, λg 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.Figure 2
Schematic of the three-port divider with a feedback mechanism.To take account of reference phases at all ports of the directional coupler, the scattering matrix of the directional coupler in Figure2 is a reciprocal four-port network and rewritten as SDC [3]
(1)SDC=S1S2S2S1,S1=αejψ10110,S2=βejψ200ejψ3,where α and β are the positive reals and satisfy the condition of α2+β2=1, ψ2+ψ3−2ψ1=2n+1π,n∈N, and N is an integer. The quantities characterized the symmetric coupler are defined as follows: the insertion loss L=−20logS21 dB, the coupling coefficient C=−20logS31 dB, and the isolation I=−20logS41 dB. If ψ1=−π/2 and ψ2=ψ3=−π, it is a symmetric coupler. If α=β=1/2, ψ1=−π/2, and ψ2=ψ3=−π, it is a quadrature hybrid. If ψ1=ψ2=−π/2 and ψ3=−3π/2, it is an antisymmetric coupler.The scattering matrix of the Wilkinson power divider in Figure2 is rewritten as on the same grounds
(2)SWPD=S3S4S4T0,(3)S3=ejϕ11+K20110,(4)S4=Kejϕ21+K210,where K2=b32/b2′2is a power division ratio of the Wilkinson power divider, according to the traditional notation. The transpose of a matrix S4 is denoted by S4T. The shunt resistor is determined by R=Z0K+1/K[3], where Z0 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 asa12=a1a2T, a3′4′=a3′a4′T, b12=b1b2T, and b3′4′=b3′b4′T. Similarly, two wave vectors of the Wilkinson power divider are defined as b1′2′=b1′b2′Tand a1′2′=a1′a2′T. The scattering matrix of the three-port power divider is derived
(5)b1′2′=S3a1′2′+S4a3,b3′4′=S2a12+S1a3′4′,(6)b12=S1a12+S2a3′4′,b3=S4Ta1′2′,(7)a1′2′=S5b3′4,a3′4′=S5b1′2′,(8)S5=e−jθ100e−jθ2.Equations (5) and (7) can be solved simultaneously to give the vectors of a1′2′ and a3′4′
(9)a1′2′=S5−1−S1S5S3−1S2a12+S5S1S5−1−S3−1S4a3,a3′4′=S5S3S5−1−S1−1S2a12+S5−1−S3S5S1−1S4a3.From (6) and (9), the vector of b12 and the variable of b3 are found
(10)b12=S1+S2S5S3S5−1−S1−1S2a12+S2S5−1−S3S5S1−1S4a3,b3=S4TS5−1−S1S5S3−1S2a12+S4TS5S1S5−1−S3−1S4a3=S2S5−1−S3S5S1−1S4Ta12=S2S5−1−S3S5S1−1S4Ta12.Equation (10) can be simplified as the following forms:
(11)b12=0S21S210a12+S310a3,b3=S310a12,(12)S21=α1+K2ejθ1+θ2−ψ1−ϕ1−11+K2ejθ1+θ2−ψ1−ϕ1−αejψ1,(13)S31=βKejθ2+ψ2+ϕ2−ψ1−11+K2ejθ1+θ2−ψ1−ϕ1−α.From (11), the scattering matrix of the three-port power divider is determined with S21 and S31
(14)S=0S21S31S2100S3100.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=ST, Sii=0i=1,2,3, S23=0, and S212+S312=1 are simultaneously satisfied. The power division ratio for the three-port power divider in Figure 2 is defined
(15)1KTWD2=S212S312=α2β2K21+K2+α−2−2α−11+K2cosθ1+θ2−ψ1−ϕ1,(16)max1KTWD2=α2β2K21+K2+α−12,where θ1+θ2−ψ1−ϕ1=2n+1π,n∈Nin (16).


### 2.3. Analysis

In (16), the item of α2/β2=b22/b3′2 is the power division ratio of the directional coupler. When the power division ratio for the directional coupler is b22:b3′2=1.34:1 and that for the Wilkinson power divider is b2′2:b32=1:1, the power division ratio for the three-port power divider will be achieved by b22:b32=10:1. 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 Figure2 is a symmetric coupler. We give a computation on the power division ratios as the following: the symmetric coupler with C=7dB b22/b3′2=4, ψ1=−90°, and ψ2=ψ3=−180°, and the Wilkinson power divider with ϕ1=ϕ2=−115.52°, which is from the simulation result with Advanced Design System (ADS).The computation results with MATLAB are shown in Figure3 with 1/K2=1,2,3,1/2,1/3, respectively. Because of the presence of the minimum length in the physical structure, the value of θ1+θ2 is taken from 180° to 540°, that is, the length of L1+L2should be from 0.5 λgto 1.5 λg. The results reveal that a region of θ1+θ2 exists to ensure that the power division ratio of the three-port power divider is more than 10 in the listed values of 1/K2. The maximum of the power division ratio occurs at the value of θ1+θ2=450°+ϕ1=338.48°, and the region of θ1+θ2 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.Figure 3
Computation on the power division ratio withC=7 dB, ψ1=−90°, ψ2=ψ3=−180°, and ϕ1=ϕ2=115.52°. The power division ratio is 1/KTWD2 and the TL1 and TL2 phase delay is θ1+θ2.


## 2.1. Feedback Model

A schematic of the three-port power divider with a feedback mechanism is shown in Figure2. 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 θ1=2πL1/λg and θ2=2πL2/λg, where L1 is the length of TL1, L2 is the length of TL2, λg 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.Figure 2
Schematic of the three-port divider with a feedback mechanism.To take account of reference phases at all ports of the directional coupler, the scattering matrix of the directional coupler in Figure2 is a reciprocal four-port network and rewritten as SDC [3]
(1)SDC=S1S2S2S1,S1=αejψ10110,S2=βejψ200ejψ3,where α and β are the positive reals and satisfy the condition of α2+β2=1, ψ2+ψ3−2ψ1=2n+1π,n∈N, and N is an integer. The quantities characterized the symmetric coupler are defined as follows: the insertion loss L=−20logS21 dB, the coupling coefficient C=−20logS31 dB, and the isolation I=−20logS41 dB. If ψ1=−π/2 and ψ2=ψ3=−π, it is a symmetric coupler. If α=β=1/2, ψ1=−π/2, and ψ2=ψ3=−π, it is a quadrature hybrid. If ψ1=ψ2=−π/2 and ψ3=−3π/2, it is an antisymmetric coupler.The scattering matrix of the Wilkinson power divider in Figure2 is rewritten as on the same grounds
(2)SWPD=S3S4S4T0,(3)S3=ejϕ11+K20110,(4)S4=Kejϕ21+K210,where K2=b32/b2′2is a power division ratio of the Wilkinson power divider, according to the traditional notation. The transpose of a matrix S4 is denoted by S4T. The shunt resistor is determined by R=Z0K+1/K[3], where Z0 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 asa12=a1a2T, a3′4′=a3′a4′T, b12=b1b2T, and b3′4′=b3′b4′T. Similarly, two wave vectors of the Wilkinson power divider are defined as b1′2′=b1′b2′Tand a1′2′=a1′a2′T. The scattering matrix of the three-port power divider is derived
(5)b1′2′=S3a1′2′+S4a3,b3′4′=S2a12+S1a3′4′,(6)b12=S1a12+S2a3′4′,b3=S4Ta1′2′,(7)a1′2′=S5b3′4,a3′4′=S5b1′2′,(8)S5=e−jθ100e−jθ2.Equations (5) and (7) can be solved simultaneously to give the vectors of a1′2′ and a3′4′
(9)a1′2′=S5−1−S1S5S3−1S2a12+S5S1S5−1−S3−1S4a3,a3′4′=S5S3S5−1−S1−1S2a12+S5−1−S3S5S1−1S4a3.From (6) and (9), the vector of b12 and the variable of b3 are found
(10)b12=S1+S2S5S3S5−1−S1−1S2a12+S2S5−1−S3S5S1−1S4a3,b3=S4TS5−1−S1S5S3−1S2a12+S4TS5S1S5−1−S3−1S4a3=S2S5−1−S3S5S1−1S4Ta12=S2S5−1−S3S5S1−1S4Ta12.Equation (10) can be simplified as the following forms:
(11)b12=0S21S210a12+S310a3,b3=S310a12,(12)S21=α1+K2ejθ1+θ2−ψ1−ϕ1−11+K2ejθ1+θ2−ψ1−ϕ1−αejψ1,(13)S31=βKejθ2+ψ2+ϕ2−ψ1−11+K2ejθ1+θ2−ψ1−ϕ1−α.From (11), the scattering matrix of the three-port power divider is determined with S21 and S31
(14)S=0S21S31S2100S3100.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=ST, Sii=0i=1,2,3, S23=0, and S212+S312=1 are simultaneously satisfied. The power division ratio for the three-port power divider in Figure 2 is defined
(15)1KTWD2=S212S312=α2β2K21+K2+α−2−2α−11+K2cosθ1+θ2−ψ1−ϕ1,(16)max1KTWD2=α2β2K21+K2+α−12,where θ1+θ2−ψ1−ϕ1=2n+1π,n∈Nin (16).


## 2.3. Analysis

In (16), the item of α2/β2=b22/b3′2 is the power division ratio of the directional coupler. When the power division ratio for the directional coupler is b22:b3′2=1.34:1 and that for the Wilkinson power divider is b2′2:b32=1:1, the power division ratio for the three-port power divider will be achieved by b22:b32=10:1. 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 Figure2 is a symmetric coupler. We give a computation on the power division ratios as the following: the symmetric coupler with C=7dB b22/b3′2=4, ψ1=−90°, and ψ2=ψ3=−180°, and the Wilkinson power divider with ϕ1=ϕ2=−115.52°, which is from the simulation result with Advanced Design System (ADS).The computation results with MATLAB are shown in Figure3 with 1/K2=1,2,3,1/2,1/3, respectively. Because of the presence of the minimum length in the physical structure, the value of θ1+θ2 is taken from 180° to 540°, that is, the length of L1+L2should be from 0.5 λgto 1.5 λg. The results reveal that a region of θ1+θ2 exists to ensure that the power division ratio of the three-port power divider is more than 10 in the listed values of 1/K2. The maximum of the power division ratio occurs at the value of θ1+θ2=450°+ϕ1=338.48°, and the region of θ1+θ2 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.Figure 3
Computation on the power division ratio withC=7 dB, ψ1=−90°, ψ2=ψ3=−180°, and ϕ1=ϕ2=115.52°. The power division ratio is 1/KTWD2 and the TL1 and TL2 phase delay is θ1+θ2.


## 3. 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 35μm.Both the schematic of the test sample and the basic principle of the following layout implemented in ADS schematic are provided in Figure4, 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.Figure 4
Schematic of the three-way divider withC=7 dB and K=1 in ADS.The symmetric coupler withC=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.


### 3.2. Layout

The microstrip layout of the test sample was designed in ADS layout at the center frequency of 5.8 GHz, see Figure5. The dot-dash lines indicate the microstrip paths of TL1 and TL2. Reference planes of the symmetric coupler are A1 and A2 and that of the Wilkinson power divider are B1 and B2. The full size is 33 mm × 46 mm fed by 50 Ω microstrip, and the parameters of the three-port power divider are listed in Table 1.Figure 5
Layout of the three-way divider withC=7 dB and K=1. The ADS layout exported a DWG format file, which was inserted and processed in Microsoft Visio.Table 1
Parameters of the three-port power divider.
Objects
Parameters
Dimensions (mm)
TL1
L1
5.90
TL2
L2
27.90
RF input
L3
12.85
W1
3.40
Symmetric coupler
L4
9.40
W2
13.06
L8
4.97
W4
7.70
Wilkinson power divider
L7
13.17
W3
5.12
W5
1.84
RF output 2
L5
10.75
RF output 3
L6
12.81


### 3.3. Circuit Simulation

Simulation results of the symmetric coupler and Wilkinson power divider using ADS in the schematics are shown from Figures6–8.Figure 6
Amplitudes of the scattering parameters of the symmetric coupler simulated in ADS schematic withC=7 dB.Figure 7
Amplitudes of the scattering parameters of the Wilkinson power divider simulated in ADS schematic withK=1 and R=100Ω.Figure 8
Phases of the scattering parameters of the symmetric coupler (SC) and Wilkinson power divider (WPD) simulated in ADS schematic withC=7 dB, K=1, and R=100Ω.The parameters of the symmetric coupler areS21=−0.93 dB, S3′1=−7.01 dB, ψ1=−89.81°, and ψ2=ψ3=−182.34°. We have noticed that there was a phase shift of 5.06°, because of ψ2+ψ3−2ψ1=−185.06°. The reason is that all simulations in both Figures 6 and 8 were conducted with the conductor (Cu) copper conductivity of 5.8×107 S/m. The parameters of the Wilkinson power divider are S2′1′=S31′=3.07 dB and ϕ1=ϕ2=−111.52°. The identical phase shift of TL1 and TL2 is θ1+θ2=403.66°. The scattering matrix of the three-port power divider is S21=−0.35 dB and S31=−12.89 dB. It is found that the power division ratio for the three-port power divider is 1/KTWD2=17.92 at 5.8 GHz in the ADS simulation. The computation results with MATLAB in Figure 3 are 1/KTWD2=18.50 with θ1+θ2=403.66°. Compared with the ADS simulation, the relative error of 1/KTWD2 is equal to 18.50−17.92/17.92=3.2%, although the above theory is in the ideal conditions without any conductor loss.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.


### 3.4. Experiment

The test sample of the three-port power divider withC=7 dB and K=1 was fabricated as shown in Figure 9. All scattering parameters of the above test sample of the three-port power divider are provided in Figures 10 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.Figure 9
Fabricated sample of the three-way divider withC=7 dB, K=1, and R=100Ω.Figure 10
Comparisons ofS11, S22, S33, and S32 between the electromagnetic simulation in ADS and measurement.Figure 11
Comparisons ofS21 and S31 between the electromagnetic simulation in ADS and measurement.Figure 12
Comparison of power division ratio (PDR) between the electromagnetic simulation in ADS and measurement. The measured PDR is 13.59 at 5.8 GHz.


## 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 35μm.Both the schematic of the test sample and the basic principle of the following layout implemented in ADS schematic are provided in Figure4, 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.Figure 4
Schematic of the three-way divider withC=7 dB and K=1 in ADS.The symmetric coupler withC=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.


## 3.2. Layout

The microstrip layout of the test sample was designed in ADS layout at the center frequency of 5.8 GHz, see Figure5. The dot-dash lines indicate the microstrip paths of TL1 and TL2. Reference planes of the symmetric coupler are A1 and A2 and that of the Wilkinson power divider are B1 and B2. The full size is 33 mm × 46 mm fed by 50 Ω microstrip, and the parameters of the three-port power divider are listed in Table 1.Figure 5
Layout of the three-way divider withC=7 dB and K=1. The ADS layout exported a DWG format file, which was inserted and processed in Microsoft Visio.Table 1
Parameters of the three-port power divider.
Objects
Parameters
Dimensions (mm)
TL1
L1
5.90
TL2
L2
27.90
RF input
L3
12.85
W1
3.40
Symmetric coupler
L4
9.40
W2
13.06
L8
4.97
W4
7.70
Wilkinson power divider
L7
13.17
W3
5.12
W5
1.84
RF output 2
L5
10.75
RF output 3
L6
12.81


## 3.3. Circuit Simulation

Simulation results of the symmetric coupler and Wilkinson power divider using ADS in the schematics are shown from Figures6–8.Figure 6
Amplitudes of the scattering parameters of the symmetric coupler simulated in ADS schematic withC=7 dB.Figure 7
Amplitudes of the scattering parameters of the Wilkinson power divider simulated in ADS schematic withK=1 and R=100Ω.Figure 8
Phases of the scattering parameters of the symmetric coupler (SC) and Wilkinson power divider (WPD) simulated in ADS schematic withC=7 dB, K=1, and R=100Ω.The parameters of the symmetric coupler areS21=−0.93 dB, S3′1=−7.01 dB, ψ1=−89.81°, and ψ2=ψ3=−182.34°. We have noticed that there was a phase shift of 5.06°, because of ψ2+ψ3−2ψ1=−185.06°. The reason is that all simulations in both Figures 6 and 8 were conducted with the conductor (Cu) copper conductivity of 5.8×107 S/m. The parameters of the Wilkinson power divider are S2′1′=S31′=3.07 dB and ϕ1=ϕ2=−111.52°. The identical phase shift of TL1 and TL2 is θ1+θ2=403.66°. The scattering matrix of the three-port power divider is S21=−0.35 dB and S31=−12.89 dB. It is found that the power division ratio for the three-port power divider is 1/KTWD2=17.92 at 5.8 GHz in the ADS simulation. The computation results with MATLAB in Figure 3 are 1/KTWD2=18.50 with θ1+θ2=403.66°. Compared with the ADS simulation, the relative error of 1/KTWD2 is equal to 18.50−17.92/17.92=3.2%, although the above theory is in the ideal conditions without any conductor loss.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.


## 3.4. Experiment

The test sample of the three-port power divider withC=7 dB and K=1 was fabricated as shown in Figure 9. All scattering parameters of the above test sample of the three-port power divider are provided in Figures 10 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.Figure 9
Fabricated sample of the three-way divider withC=7 dB, K=1, and R=100Ω.Figure 10
Comparisons ofS11, S22, S33, and S32 between the electromagnetic simulation in ADS and measurement.Figure 11
Comparisons ofS21 and S31 between the electromagnetic simulation in ADS and measurement.Figure 12
Comparison of power division ratio (PDR) between the electromagnetic simulation in ADS and measurement. The measured PDR is 13.59 at 5.8 GHz.


## 4. 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.



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*Source: 9141964-2018-07-19.xml*