Design and optimization of multi-band Wilkinson power divider

Abstract

In this paper, a general and easy procedure for designing the symmetrical Wilkinson power divider that achieves equal-power split at N arbitrary frequencies is introduced. Each quarter-wave branch in the conventional Wilkinson divider is replaced by N sections of transmission lines, and the isolation between the output ports is achieved by using N resistors. The design parameters are the characteristic impedances and lengths of the N transmission line sections, and the N isolation resistors. The even-odd modes of analysis are used to derive the design equations. Closed-form expressions, which are suitable for CAD purposes, are derived for the dual-band divider. For N ≥ 3, closed-form expressions are not available, and therefore, the powerful particle swarm optimization method is used to obtain the design parameters. Examples of the dual-, triple-, and quad-band dividers are presented to validate the proposed design procedure, and the results are compared, wherever possible, with published results using other methods.

Design Methodology of Multi-Frequency Unequal Split Wilkinson Power Dividers Using Transmission Line Transformers

“…Referring to Figure 3 with N = 2, the input admittance seen at the output port 2 is given as follows [10]:…”

“…Equation (10), along with Equation (3), can be split into two equations for the real and imaginary parts. Solving these two equations, the following expressions for R 1 , R 2 can be obtained [10]:…”

“…After a rather extensive mathematical derivation, an optimization process was used to find the values of the design parameters. In [8][9][10], equal split multi-frequency WPDs were studied. To our knowledge, the design of tri-frequency and quad-frequency unequal split WPDs has not been presented before in the literature.…”

Analysis of Coupled Microstrip Lines for Quad-Band Equal Power Dividers/Combiners

“…Several dual-band Wilkinson power dividers have been developed based on Monzon's dual-band transformer using two cascaded sections of transmission line transformers [17]. His theory was extended to provide tri-band [18] and quad-band [19] transformers using cascaded transmission lines, which are further more used in the design of multiband power dividers/combiners [20][21][22]. Dual-band power dividers can also be achieved using T-sections [23] and Pi structures [24][25][26] by connecting open or short stubs to the conventional transmission line, but the main drawback of using such techniques is their large physical size.…”

Design and Analysis of Dual-Frequency Modified 3-Way Bagley Power Dividers

“…In [8,9], triple and quad-frequency equal split WPDs were designed and investigated. The general design of multi-frequency equal split WPD was presented in [10]. In [11], the multi-frequency operation was extended to the unequal split WPD.…”