A Simple Approach for Improving Bandwidth and Isolation of Wilkinson Power Divider

. A simple approach to improve both the bandwidth and isolation of the Wilkinson power divider for using in L-band satellite communications is presented in this paper. To enhance the bandwidth, a multi-section method based on the Chebychev impedance transformation is employed. In order to improve the isolation performance between output ports, the values of isolation resistors are carefully determined by using the iterative approximation method combined with an investigation procedure. In order to validate the proposed design, a two-way and eight-way power divider prototypes were fabricated and tested on a Rogers RO4003C material. Good agreements between simulations and measurements are obtained in a frequency range from 0.8 GHz to 2.2 GHz. The two-way power divider had a fractional bandwidth of 106% with an isolation of better than 30 dB. The eight-way power divider achieved the bandwidth and isolation of 109% and better than 24 dB, respectively. Both the power dividers exhibit the phase imbalance of less than 3 degrees, and amplitude imbalance of less than 0.02 dB. Compared with the other works, the proposed power dividers deliver broader bandwidth and improved isolation while still retaining good insertion loss, low phase and amplitude imbalance in the operation frequency range.


Introduction
Wilkinson power divider (PD) is commonly used in a variety of important applications such as frequency mixing circuits, power amplifiers, phased array antenna, and satellite communication because of its promising advantages including low insertion loss and high isolation [1], [2]. However, conventional Wilkinson PD exhibits a narrow bandwidth, making it difficult to be used in broadband communication systems. Different modified PD structures have been proposed to expand the bandwidth.
In [3], a wideband PD is designed employing defected ground structures [3]. In [4], a PD of high selectivity using four pairs of coupled lines loaded with a T-shaped stub has been proposed. A power divider with ultra-broadband based on tapered lines is designed in [5]. In these works, although the bandwidth can be improved, the isolation is not improved simultaneously. In addition, the isolation performance presented in [3], [4] is only 20 dB while this level in [5] is 15 dB. In [6], an ultra-wideband Wilkinson power divider is fabricated using a hermetic multi-wafer level packaging technology. It allows to expand the bandwidth and reduce the size of the circuit. However, the disadvantage of this circuit is that it has a high insertion loss of more than 1 dB and high amplitude imbalance of 0.4 dB as well as a high phase imbalance of higher than 3°.
Numerous techniques have been introduced in an attempt to improve the isolation of PDs, such as using distributed isolation to replace the conventional resistor isolation network [7], using an 'RLCT' isolation network [8], employing multistage isolation [9], and by introducing a highly symmetric coupling structure of the divider [10]. However, these methods are not capable of improving the bandwidth simultaneously. The isolation level achieved in [7] is better than 23 dB, but the bandwidth is only 56.6%. In [8], the PD has wider bandwidth at a level of 61% with a minimum isolation of 20 dB. However, the insertion loss of 1 dB is relatively high. The PD presented in [9] achieves a wide bandwidth and an insertion loss of 0.3 dB, but the isolation level is just 20 dB. The PD in [10] gives an isolation of better than 30 dB, but it exhibits a narrow bandwidth of 3.5% with a high insertion loss of 1.4 dB and a high amplitude imbalance from 0.22 to 0.65 dB.
In this paper, we propose a simple approach to simultaneously improve the bandwidth and isolation of the Wilkinson PD while still retaining the remaining performance such as insertion loss, phase and amplitude imbalances. Two-way and eight-way PDs were designed, fabricated, and tested to verify the proposed approach.

Proposed Approach
The traditional Wilkinson PD is composed of quarterwavelength microstrip lines to match impedances between input and output ports as shown in Fig. 1.
To improve the isolation performance, an isolation resistor R S is added between two branches of the circuit, the values of Z C and R S are determined by the expressions: ( The traditional Wilkinson PD exhibits an inherent narrow bandwidth. In order to extend the bandwidth of this circuit, multi-section impedance transformation technique is applied in this work. According to this technique, multiple segments are used instead of using one microstrip line to match load and transmission line impedances. According to the small reflection theory (TSR) [11], the reflection coefficient of the circuit including N segments with the same electrical length θ can be defined by the reflection coefficients of each segment. Therefore, by selecting appropriate number of segments N and reflection coefficients of each segment, we can obtain the desired reflection coefficient of the entire circuit Γ(θ). In order to approximate response function of the circuit, the Chebyshev function is employed. According to [11], fractional bandwidth (FBW) of the transmission line can be calculated using (3): where f 0 is the central frequency and θ m is the corner electrical length at the maximum allowed magnitude of Γ(θ) in the passband and is given as: where Z L and Z 0 are load and source impedances, respectively, Γ m is the maximum value of reflection coefficient that can be tolerated over the passband.
From (3) and (4), it can be seen that the number of sections N can be calculated for given FBW and Γ m . In this work, Γ m and FBW are chosen to be 0.015 and 93.3%, respectively. Hence, N is calculated to be 4. The structure of the PD is then constructed as shown in Fig. 2. It consists of four quarter-wavelength transmission line sections having corresponding characteristic impedances Z 1 , Z 2 , Z 3 and Z 4 . Here R 1 , R 2 , R 3 , and R 4 are the isolation resistors. The impedances are calculated using the corresponding reflection coefficient at each section based on the TSR by the following equations: . (11) The calculated results are shown in Tab. 1.
It is well known that the isolation performance of the PD depends mainly on the isolation resistors R 1 -R 4 . These resistors can be calculated by the iterative approximation method [12]. Although this method can improve the isolation, the best isolation is usually limited at a level of 20 dB. In order to further improve the isolation performance, the method needs being modified. The proposed modified method for calculating isolation resistors consists of two steps: the first step is preliminary calculation of the isolation resistors by the iterative approximation method. The second one is optimizing the isolation resistor values by using an investigation method. In the first step, the initially calculated values of the isolation resistors are: R 1 = 106 Ω, R 2 = 155 Ω, R 3 = 281 Ω, R 4 = 708 Ω. In the first step, the value of R 4 is first calculated, and the remaining resistors are then determined depending on the value of R 4 . Therefore, the variation of the isolation between the output ports on the change of R 4 can be investigated. By this way, the values of isolation resistors can be optimized to achieve high isolation performance. This investigation is carried out in the second step. Figure 3 shows the dependence of the isolation between two output ports of the PD on the variation of R 4 . R4=680 Ω R4=866 Ω R4=800 Ω R4=910 Ω R4=708 Ω

Simulation and Measurement of the Proposed Two-way Power Divider
Based on the proposed design procedure, a two-way PD was designed, fabricated and tested. Figure 4 shows the fabricated prototype of PD. The material used is Rogers RO4003C with a substrate thickness of 22-mil and 1-oz copper thickness. The total area of PD is 5.0 cm  5.0 cm. The dimensions of the four sections of the PD circuit are tabulated in Tab. 2.
The ADS 2019 simulator is employed to make simulations and a Vector Network Analyzer PNA-X N5242A from Keysight is used to measure performance of the fabricated PD. The experimental setup is described in Fig. 5. The simulated and measured results of isolation between two output ports of the PD are shown in Fig. 6    As can be seen in Fig. 6, simulated results agree well with the measured ones. Particularly, in the operation frequency range from 0.7 to 2.4 GHz, the measured isolation is better than 30 dB. Figure 7 shows the simulated and measured insertion loss of the proposed power divider. It is clearly seen that the measured results are highly consistent with the simulated one. The measured insertion loss varies from 0.2 to 0.5 dB over the frequency range from 0.7 to 2.4 GHz with a fractional bandwidth of 106%.
After isolation and insertion loss have been both improved, the amplitude and phase imbalance will be validated. The difference between two outputs, namely amplitude imbalance (AI), is calculated by the formula: where S(2,1) and S(3,1) are S-parameters of the PD. The measured amplitude imbalance of the proposed PD is shown in Fig. 8. As can be seen from Fig. 8, within the passband, the measured amplitude imbalance of PD is less than 0.12 dB.
Simulated and measured phase imbalance between two output ports of the designed PD is presented in Fig. 9. The measured results demonstrated that the difference in phase between two output ports does not exceed 1.2 degrees. The slight difference between simulation and measurement is caused by the SMA connector which was not de-embedded in the measurement.
The measured performances of the proposed two-way PD compared with other reported works are summarized in Tab. 3. Meas. Fig. 9. Simulated and measured phase imbalance between output ports of the designed PD. It is clear that the proposed two-way PD exhibits the highest bandwidth and isolation performance, while still retaining good insertion loss when comparing with the other PDs.

Simulation and Measurement of the Eight-way Power Divider
An eight-way PD was then designed to further validate the proposed method after the two-way PD had been successfully designed. The eight-way PD is realized by interconnecting the designed two-way PDs. Figure 10 shows the block diagram of the eight-way PD. It is simply implemented by interconnecting the designed multi-section equal two-way PDs.   The layout of the PD is given in Fig. 11 and Fig. 12 shows the fabricated circuit of the prototype. The material used is Rogers RO4003C with a substrate thickness of 22-mil and 1-oz copper thickness. The two-way PD and eight-way PD occupies an area of 5.0 cm  5.0 cm and 9.0 cm  16.0 cm, respectively. Figure 13 shows the simulated and measured results of the insertion loss of the eight-way PD.

Insertion Loss and Bandwidth
It can be seen from Fig. 13 and Fig. 14 that the simulations agree well with the measurements in the entire frequency range from 0.8 GHz to 2.2 GHz as expected. In this frequency range, the measured insertion loss of the eight-way PD ranges from -10.8 dB to -9.5 dB. This measured low insertion loss in the frequency band of interest well validates the accuracy of the proposed design. Frequency (GHz) S12 S13 S14 S15 S16 S17 S18 S19 Frequency (GHz) S12 S13 S14 S15 S16 S17 S18 S19

Isolation
The eight-way PD has 8 output ports, so it has a total of 28 port pairs. Therefore, the isolation between adjacent ports which have the lowest isolation will be dominated. The simulation and measurement results of the isolation of these port pairs are indicated in Fig. 15 and Fig. 16. As can be seen from Fig. 15 and Fig. 16, the simulated and measured isolation between adjacent output ports are better than 24 dB over the frequency range from 0.7 to 2.4 GHz.

Amplitude and Phase Imbalance
The simulated and measured amplitude imbalance between output ports of the eight-way PD are plotted in Fig. 17 and Fig. 18. Good agreements between the simulation and measurement are observed. It is clear that the amplitude imbalances are less than 0.018 dB in the frequency range from 0.8 GHz to 2.2 GHz.
The simulated and measured phase imbalance between the two adjacent output ports is shown in Fig. 19 and Fig. 20.
As can be seen from Fig. 18 and Fig. 19, good agreements between the simulated and measured results are achieved. It can be seen in Fig. 19 that the differences in phase between the output ports are less than 3 degrees. Finally, a comparison between the proposed eight-way PD and the other works are tabulated in Tab other reported PDs. This superior performance of the proposed PD validates the accuracy of the proposed design method.

Conclusions
In this paper, a simple design approach for improving both the bandwidth and isolation of a Wilkinson PD is proposed. The bandwidth was improved by the multi-section impedance transformation based on the TSR method. The isolation was then improved by a separate process via determining the values of the isolation resistors thanks to the investigation process. To validate the proposed approach, a two-and an eight-way PD prototypes were fabricated and tested. The measurement results well matched with those obtained in simulations. In the experiments, the two-way PD delivered a bandwidth of 106%, with an isolation of better than 30 dB. The eight-way PD achieved a FBW of 109%, with an isolation of better than 24 dB, a phase imbalance of less than 3 degrees, and an amplitude imbalance of less than 0.02 dB. Compared with the other works, the proposed PDs exhibited a broader bandwidth and improved isolation, while still retaining good insertion loss and low phase and amplitude imbalance in the operation frequency range.