Wilkinson power divider is one of the most widely used passive components, which allows microwave signals to split equally or unevenly. The simplest Wilkinson power divider is shown in Figure 1(a). It is a single-stage component with 50 Ω input and output ports, two 70.7 Ω quarter wavelength transformers, and a 100 Ω resistor bridged between the two output ports to provide isolation and matching. Its disadvantage is the limited bandwidth. Due to the rapid growth of wireless communications, there is a great demand for broadband components, including broadband Wilkinson power dividers. Therefore, the study of broadband Wilkinson power dividers is of great significance at this time. For this purpose, manly wideband power dividers [1]-[6] have been developed so far. But few of them introduce the millimeter-wave wideband Wilkinson power divider. Typically, multi-stage Wilkinson power dividers have improved operating bandwidth compared to standard single-stage Wilkinson power dividers. According to the characteristics of millimeter wave Wilkinson power dividers, as the operating frequency increases, the influence of parasitic parameters on chip resistors will become significant. If the number of chip resistors increases, the performance of the millimeter wave Wilkinson power divider will deteriorate. In order to overcome the influence of multiple resistors and effectively improve the bandwidth of a single-stage Wilkinson power divider, this paper proposes a millimeter wave broadband Wilkinson power divider using micro-strip branch lines.

The general circuit of a multi-stage Wilkinson power divider is shown in Figure 1(b). It contains N pairs of equally transmission lines and N bridge resistors, distributed from the input port to the two output ports. It is easiest to analyze through even mode and odd mode excitation methods [7].

As is well known, with the increase of transmission line segments and resistors, the bandwidth of the Wilkinson power divider has been effectively improved. In order to achieve broadband isolation, the resistors of the multi-stage Wilkinson power divider provide multiple transmission paths for electromagnetic waves, such as path 1, path 2, path N, etc., as shown in Figure 1(b).

The transmission line modeling (TLM) of the 2 way equal split Wilkinson power divider (WPD) is shown in Figure 2. This power divider contains one input port, two quarterwave transmission line, two output ports and one isolation resistor across the output ports.

The expressions of input return loss (S₁₁) and transmission coefficient (S₂₁) of WPD from the above TLM circuit are

S 11 ( f ) = − 1 ( 3 + j 2 2 tan ( β l ) ) S 21 ( f ) = ( 1 − S 11 2 ( f ) ) 2

The even and odd mode analysis computes the output responses (S₂₂ and S₂₃) of WPD very easily and a voltage excitation of Vs is applied at port 2 for the analysis of even and odd mode. The voltage excitation at port 2 and 3 for even and odd mode are Vs/2, Vs/2 and Vs/2, −Vs/2 respectively. The even and odd mode diagrams of WPD are shown in Figure 3. From these even and odd mode analysis the derived expressions of output response (S₂₂ and S₂₃) are

S 22 ( f ) = 1 ( 8 tan 2 ( β l ) − j 8 2 tan ( β l ) − 3 ) S 23 ( f ) = − 2 − j 2 2 tan ( β l ) ( − 8 tan 2 ( β l ) + j 8 2 tan ( β l ) + 3 )

In order to increase the bandwidth of the input and output responses of the power divider, we used micro-strip branch lines in our research.

In [8], an improved Wilkinson power divider for suppressing nth harmonic output is proposed by adding a short cut transmission line between the resistor and each output port. We can imagine that multiple resistors in Figure 1(b) can be replaced with branch lines to increase the bandwidth of a single-stage Wilkinson power divider. Then, a new broadband Wilkinson power divider was proposed. To demonstrate its improved performance, a broadband Wilkinson power divider with four branches was designed using only one resistor in Figure 2. It was modeled using Ansoft HFSS and designed on an Al₂O₃ ceramic substrate with a relative dielectric constant of 9.8 and a thickness of 0.254 mm. We use thin film resistor in our design. The original size of the power distributor is determined using the same method used in the design of multi-stage Wilkinson power distributors. In addition, multiple resistors are replaced by branch lines with the same characteristic impedance. In order to minimize the complexity of the simulation model, the width of its two main output lines is the same, 0.25 mm, and the length of all branch lines is the same. After optimization by HFSS, its simulation model is shown in Figure 4.

The final simulation results and dimensions of the new broadband power divider are shown in Figure 5 and Figure 6. The results are in good agreement with the ideal values. According to simulation results, the output return loss and isolation are better than 15 dB in the frequency range of 18 to 40 GHz (76%), and the input return loss is better than 15 dB in the 90% bandwidth of 15 to 40 GHz.

From Figure 5(b), it can be seen that the two output ports have good phase consistency between 15 GHz and 40 GHz. And, the increase in branch lines significantly improves the performance of the single-stage Wilkinson power divider.

Its simulated results are compared with the simulated S-parameters of the conventional single-stage Wilkinson divider [9] in Figure 7, which is fabricated on the Rogers RT/duroid 5880 dielectric substrate and consists of a 0402 chip resistor. As seen, the operation bandwidth of the modified Wilkinson divider is almost as wide as four times of the bandwidth of the traditional single-stage Wilkinson divider. Thereby, the addition of branch lines significantly improves the performance of a single-stage Wilkinson divider.

In order to increase the bandwidth of a single-stage Wilkinson power divider, a Miniaturized Wilkinson power divider using micro-strip branches instead of multiple resistors is proposed. So, it overcomes the influence of multiple resistances. An improved four branch single stage Wilkinson power divider has been designed. Its bandwidth is almost four times that of a traditional single-stage Wilkinson power divider. Therefore, the increased branch lines effectively increase the bandwidth of traditional single-stage Wilkinson power dividers. These clearly indicate that the proposed Wilkinson power divider can be well applied to microwave and millimeter wave systems.

The author declares no conflicts of interest regarding the publication of this paper.

Zhou, T.F. (2023) A Miniaturized Broadband Wilkinson Power Divider Using Micro-Strip Branch Lines. Journal of Computer and Communications, 11, 102-108. https://doi.org/10.4236/jcc.2023.1112007