Compact Two-Way and Four-Way Power Dividers ... - IEEE Xplore

KIM et al.: COMPACT TWO-WAY AND FOUR-WAY POWER DIVIDERS 131Fig. 2. Simulated performance of two-way power divider for various ZZ combinations.andFig. 3.Photograph of the fabricated power divider: (a) two-way (b) four-way.Fig. 1. (a) Structure of the proposed two-way power divider. (b) Cross-sectionalview of the 3-conductor coupled line in a microstrip form. (c) Structureof the proposed four-way power divider.Then, the power is assumed to be injected into port 2 inorder to derive the conditions for impedance matching at port2 and isolation between port 2 and 3. In this excitation, thefollowing relations hold: ,and . Applying Kirchhoff current law at port 3,, these relations can be solvedwith (1)–(6) for to giveSubstitution of (7) and (8) into (1)–(6) leads toand , which implies perfect impedance matching at port2 and perfect isolation between port 2 and 3.The symmetric three-conductor coupled line of Fig. 1(b) approximatelysatisfies [5].This relation simplifies the (7) toThe and can be written as and, where and are the even-mode andodd-mode impedance, respectively, of a two-conductor coupledline with identical conductor width and spacing to a three-conductorone [6]. By applying these relations to (9), the followingequation can be obtained:(8)(9)(10)In summary, (8) and (10) can be used to determine the initialvalues of the isolation resistor , conductor width andspacing .B. Four-Way Power DividerThe proposed topology is extended to design a planarfour-way power divider as depicted in Fig. 1(c). It consists oftwo two-way power dividers with impedance transformationproperty from to . The isolation between two-waypower dividers is achieved by a resistor . The analysis showsthat varies with even and odd mode impedance of coupledlines. It was determined to be in this work, consideringthe manufacturability of the coupled lines. Compared to theconventional microstrip Wilkinson power divider, this four-waypower divider can be smaller in size.III. SIMULATION AND MEASUREMENTAccording to (10), there can exist many combinations ofand to design the proposed two-way power divider. Fig. 2shows the simulated and of the designed two-waypower divider at 2.0 GHz for various combinations of andusing 30 mil-thick substrate with the dielectric constant of4.5. The simulation was performed using a three-conductor coupledline model in Agilent ADS [7]. This figure demonstratesthat the smaller (or higher ) provides the widerbandwidth. Therefore, the conductor spacing was selectedto be the minimum value available from our photolithographyprocess which was 0.07 mm. Then, the conductor widthwas initially determined to be 0.58 mm by (10) and optimizedto be 0.45 mm by full-wave simulation using Agilent ADS Momentum.The length was determined to be 17.68 mm by the simulation.Fig. 3(a) shows the fabricated two-way power divider.