I. Introduction
In VARIOUS microwave circuits, such as balance amplifiers, image rejection mixers, and phase shifters, quadrature hybrids are used to achieve the desired circuit characteristics. The most commonly used microwave quadrature hybrids are the branch-line Langer couplers, which consist of four or several coupled quarter-wavelength lines [1], [2]. At the lower microwave frequency bands, the quarter-wavelength lines constructed on a conventional microwave integrated circuit (MIC) or a monolithic microwave integrated circuit (MMIC) occupy too much valuable chip area. Thus, various lumped-element quadrature hybrids are proposed for using in MIC or MMIC applications [3]–[7]. The generalized method of synthesizing lumped- and lumped-distributed-element directional couplers in co-directional, contra-directional, and trans-directional configurations was first proposed by Vogel [4]. Recently, we proposed a design method for realizing a two-section co-directional lumped-element hybrid with wide-band characteristics [5]. Other than the capacitive coupling mechanism employed in the above papers, Ali and Podell proposed a contra-directional transformer-coupled hybrid, which shows a very wide-band characteristic [6]. In this paper, we propose a new hybrid design, which consists of two-section transformer-coupled -networks connected by a single inductor in the center, as shown in Fig. 1. This hybrid features fewer components than the previous conventional configurations. A new set of design equations are also proposed to realize the hybrid with good magnitude and phase balances at the output ports and at the same time, an operation bandwidth only slightly less than conventional ones is achieved. Lumped quadrature hybrid realized by two-sectional -network with transformer-coupling feature.