106 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 2, FEBRUARY 2007 A Stub Tapped Branch-Line Coupler for Dual-Band Operations Hualiang Zhang and Kevin J. Chen, Senior Member, IEEE Abstract—This letter presents a stub tapped branch-line coupler for dual-band applications. In the new design, a tapped stub is used to realize 90 phase change at two frequencies. Both the character- istic impedance and the length of the proposed branch lines are adjusted accordingly compared with the conventional structure. Explicit design equations are derived using the ABCD-matrix. To verify the design concept, a microstrip coupler operating at 0.9 and 2 GHz is fabricated and measured on a Rogers’ RO4003 board. Index Terms—ABCD-matrix, Branch-line coupler, dual-band, monolithic microwave integrated circuit (MMIC), quarter-wave- length. I. INTRODUCTION T HE advances in modern communication systems are im- posing new requirements, such as compact size, broad- band, and multiple-band operations, to the design of the passive circuits. To meet these different requirements, the branch-line coupler [1] as an important passive component needs to be re- designed. In the past, much effort has been made to size reduc- tion [2] and bandwidth enhancement [3], which leads to great improvement in these two aspects. However, for the dual-band operations, only several designs [4]–[6] have been reported up to now. Dual-band circuits provide the benefits of reducing the overall size and the fabrication cost of radio frequency (RF) modules. In this letter, we present a new structure of the dual-band branch-line coupler. The desired dual-band operations are realized by virtue of stubs tapped to the center of each branch line. To provide a design guideline for the coupler, closed form formulas are derived by analyzing the ABCD-matrix of the proposed branch line structure. The final layout of the coupler is designed based on these formulas using a circuit simulator. To verify the design concept, a microstrip coupler featuring the tapped stubs and exhibiting dual-band operation is demonstrated on Rogers’ RO4003 board. It is designed to work at 0.9 and 2 GHz. The measured results confirm the dual-band operations of the proposed structure. II. THEORETICAL ANALYSIS OF THE NEW BRANCH-LINE STRUCTURE The key in the dual-band coupler design is to substitute the conventional quarter-wavelength branch line with a section that exhibits the desirable characteristics at two different frequen- cies. In our new branch-line coupler, the structure of the mod- Manuscript received August 17, 2006; revised September 12, 2006. The authors are with the Department of Electronic and Computer Engi- neering, Hong Kong University of Science and Technology, Kowloon, Hong Kong (e-mail: brucezh@ust.hk; eekjchen@ust.hk). Digital Object Identifier 10.1109/LMWC.2006.890330 Fig. 1. Structure of the proposed T-shaped line which is equivalent to a quarter- wavelength transmission line at two prescribed frequencies. ified branch line is shown in Fig. 1. A shunt stub is tapped to the center of a conventional line as shown in Fig. 1, where and represent the characteristic impedances and the electrical lengths of the series and shunt sections. To ob- tain the design equations, the ABCD-matrix formulation is used. By cascading the matrices of the three different sections, the ABCD-matrix of the T-shaped pattern can be written as (1) with each element of the ABCD-matrix given by (1a) (1b) (1c) Since the proposed structure is intended to be equivalent to a quarter-wavelength transmission line, the ABCD matrix of the structure should be equal to that of a conventional 4 line, yielding (2) where is the characteristic impedance of a conventional 4 line. By setting 0, we obtain (3) 1531-1309/$25.00 © 2007 IEEE