Mikrotalasna revija Decembar 2008. 16 Synthesis and Analysis of Reduced-Size Branch-Line Hybrids Marin V. Nedelchev, Ilia G.Iliev Abstract: This paper proposes a method for synthesis and analysis of reduced size branch-line hybrids with arbitrary power division ratio. Based on dispersion equation of the capacitively loaded transmission line, closed form synthesis formulae are derived. Using the fourfold symmetry of the reduced size branch-line hybrid, analysis formulae are derived. The output ports’ phase difference is analyzed for different synthesis configurations. The fractional bandwidth of the reduced size hybrid is about 10% narrower than the conventional branch-line hybrid. The results presented in the paper are applicable to uniplanar structure designs. Keywords: Reduced size, branch line hybrid, capacitively loaded transmission line. I. INTRODUCTION Quadrature branch-line hybrids play important role as power divider, or power combiner, image rejection mixers, and balanced amplifiers. The classic form of the quadrature branch-line hybrid is shown on Fig.1. 1 4 2 3 1 Z 1 Z 2 Z 4  Fig.1 Conventional branch-line coupler For a given input power at port 1, there will be 90  phase difference between the waves at ports 2 and 3 for the centre frequency. This phase difference varies over 5   for a 10% fractional bandwidth. The usable bandwidth of the branch-line hybrid is constrained by the change in the isolation. Such branchline couplers can be designed for 3-10dB coupling. Main arms of the coupler are of quarterwave length. This size is unacceptable large especially for the lower microwave bands and MMIC applications. The branch-line hybrid occupies large area on the printing circuit board or on the chip. The use of lumped-element hybrid, which uses spiral inductors and lumped capacitors, is one possible solution to this problem [1-3]. However, the design of spiral inductors is requires precise empirical models based on measurement of test elements including parasitics. Marin Nedelchev – Assist. Prof., PhD in Dept. of Radiocommunication and Videotechnologies in Faculty of Communications and Communication Technologies in TU –Sofia E-mail mnedelchev@tu-sofia.bg Ilia G. Iliev – Assoc. Prof., PhD in Dept. of Radiocommunication and Videotechnologies in Faculty of Communications and Communication Technologies in TU –Sofia E-mail igiliev@tu-sofia.bg This design approach becomes difficult for frequencies above 20GHz [4,5]. Another method for the hybrid coupler size reduction is proposed in [2-5]. The branch line is realized as lumped element Π or T equivalent networks. Each lumped element value is determined by equating the ABCD matrices of both structures – transmission line and lumped element. The coupler involves shunt inductors, which are inconvenient for fabrication. However, this method eliminates the uncertainty caused by the lumped inductors. The method presented in [1-5], the branchline hybrid utilizes high impedance lines loaded by shunt lumped capacitors. The authors present a special case for the theory of this coupler. In this paper, we present a general theory of reduced size branch-line hybrid with arbitrary power division ratio, composed of capacitively loaded transmission lined. With the proposed method, a branch-line coupler can be designed for various impedance and capacitor values for a given power division ration. The reduction of the size is connected with increase of the characteristic impedance of the transmission line. The phase difference between the output ports for various characteristic impedances and capacitors is studied. Because of the slow-wave effect of the capacitive loaded line, the phase difference is not symmetrical along the 90 0 value. II. REDUCED SIZE HYBRID The main element in the conventional hybrid coupler is the quarter-wavelength transmission line. In order to obtain reduced-size coupler, shown on Fig.2, in [1-4,7] is proposed to use capacitive loaded transmission line instead of quarter- wavelength line. To assure equivalent electrical parameters, it is examined both circuits shown on Fig.3a and Fig.3b. The circuit on Fig.3b may be considered as a unit element of periodic slow wave structure [4-7]. C C C C 2 2 , Z  2 2 , Z  1 1 , Z  1 1 , Z  1 2 3 4 A A B B Fig.2 Reduced size branch-line coupler The slow-wave line consists of a transmission line loaded on both sides by lumped capacitors C . The main parameters