WIDE-BAND circuits are now in demand as wide-band

704 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Compact Wide-Band Branch-Line Hybrids Young-Hoon Chun, Member, IEEE, and Jia-Sheng Hong, Senior Member, IEEE Abstract Wide-band branch-line couplers are designed and tested. The proposed couplers feature compact size on a single circuit layer structure without via-holes. For the broad-band property and cost effectiveness, we have designed a four-branch hybrid with mixed distributed and lumped distributed elements. Analysis on the equivalent circuits was performed carefully in order to obtain a sufficient bandwidth with reduced design area. The fabricated hybrids have the fractional bandwidth larger than 56% at the center frequency of 2 GHz. They also show size reduction up to 55.2% compared with the conventional design method. Index Terms Branch-line, broad-band, couplers, hybrids, lumped distributed elements, microstrip line, planar circuits. I. INTRODUCTION WIDE-BAND circuits are now in demand as wide-band systems such as ultra-wideband (UWB) become practical. In general, a wide-band circuit requires a large design area or complicated structure such as a three-dimensional coupling structure or wire-bonding connections. Modern communication systems also need various hybrids to enable digital data transmit via microwave bands. Thus, several types of microwave quadrature hybrids have been reported for the realization of balanced circuits and matched attenuators and phase shifters [1] [4]. The branch-line coupler is one of the most popular hybrids for the convenience of design and implementation. It, however, has narrow-band characteristics and requires a large circuit area. In order to reduce the size of branch-line hybrids, many authors have suggested several solutions [3] [7]. While lumped or lumped distributed elements give us a chance to have a small design area, they cannot enhance the bandwidth. Only the cascaded branch line can enlarge the bandwidth when we choose it as a quadrature hybrid circuit. In fact, there are other circuits for a broad-band hybrid, such as a Lange coupler, tandem coupler, and so on. Although they show wide-band performances with small sizes, most of them need multilayered or air-bridged structures for tight coupling and signal routing (crossover) over a wide frequency range. The requirement for air-bridges results in more masks and fabrication processes, leading to more costs. Moreover, these air-bridges would represent a bottleneck for power handling and, hence, limit the applications of Lange and tandem couplers. To this end, it would be desirable to develop an alternative hybrid that can achieve a better tradeoff between bandwidth, size, and power handling. This study stemmed from Manuscript received July 10, 2005; revised September 12, 2005. This work was supported in part by the U.K. Engineering and Physical Science Research Council under Grant GR/S68910/01. The work of Y.-H Chun was supported by the Korea Research Foundation under a Postdoctoral Fellowship Program. The authors are with the Department of Electrical, Electronic, and Computer Engineering, Heriot-Watt University, Edinburgh EH14 4AS, U.K. (e-mail: younghoon@ieee.org; j.hong@hw.ac.uk). Digital Object Identifier 10.1109/TMTT.2005.862657 Fig. 1. Size reduction scheme using lumped distributed elements. (a) Conventional transmission line. (b) Equivalent transmission line with a series transmission line and two open stubs. (c) Equivalent lumped-element model for calculating the cutoff frequency. our recent development of high-power RF microelectromechanical systems (MEMS) switches for which 90 -hybrids with high power-handling capability are needed for designing high power single-pole double-throw (SPDT) switches. The loaded line is a popular method to reduce the size of transmission-line circuits such as branch-line and ring hybrids, which is important for planar integrated circuits [5] [7]. The results using a loaded line show good efficiency with regard to size reduction. Nevertheless, more consideration of analysis and design for wide-band applications is required. In [8], we have shown a highly miniaturized branch-line hybrid, as well as its simple analysis. In this paper, we further propose a novel design of a cascaded branch-line coupler, which has four branch lines using lumped distributed elements. The desired 90 hybrid should have a good performance such as return loss and isolation better than 20 db over 55% or wider bandwidth, and a small size on a single-layer circuit without using any air-bridges. The investigation has led to the design of the proposed hybrids. For our design, we use an approach based on circuit models. Since an equivalent circuit may make the bandwidth shrink in general, and it can be critical when it is used for broad-band designs, we take into account the frequency responses of the equivalent circuit used and decide a proper configuration for broad-band circuits. Furthermore, the simulated and measured results of the proposed hybrids are also presented. II. ANALYSIS Fig. 1 shows a conventional transmission line and its equivalent circuit using lumped distributed elements. By applying a matrix formulation, the -parameters of the equivalent circuit shown in Fig. 1(b) can be deduced. Equating the 0018-9480/$20.00 2006 IEEE

CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 705 -matrices for both the circuits shown in Fig. 1(a) and (b) results in (1), shown at the bottom of this page, where is the input admittance of the open stubs in Fig. 1(b). From (1), two design equations can be derived as follows: Note that we assume for our applications and discussions, which makes in (3) always positive for a capacitive loading. We can also estimate the cutoff frequency for the low-pass filter-like structure in Fig. 1(b) and its equivalent circuit in Fig. 1(c). Each parameter in Fig. 1(c) is defined as follows [9]. Define a 3-dB cutoff frequency as follows: We then obtain where is the cutoff frequency of the equivalent circuit in Fig. 1(b) and is, in general, a nominated operation frequency at which the equivalent lumped elements and are determined. In our case, can be taken as the center frequency of a coupler. Equation (6) sets out the higher frequency or bandwidth limit for the equivalent circuit, which depends on several design parameters. For wide-band operations, a larger ratio of is desirable, which, however, will be a tradeoff with size reduction. Using (4) and (6), Fig. 2 plots the cutoff frequency and the required characteristic impedance of series transmission line against the ratio of the electrical length and for given values of and. The ratio of and represents the size reduction of the transmission line. Its lower value ensures the compact design area. Fig. 2 indicates a guideline to choose a unit section. For a demonstration, we select a transmission line of Fig. 1(a) with the characteristic impedance and the electrical length as a unit line section. It can be replaced by an equivalent distributed lumped element circuit in Fig. 1(b) with the characteristic impedance of a series transmission line (2) (3) (4) (5) (6) and the cutoff frequency varying with the value of the electrical length of a series transmission line. This is shown in Fig. 2(a). Fig. 2(b) shows the ranges for and the cutoff frequency when the electrical length of the unit line section is 45. For a broad-band circuit, we should choose a unit section with the higher cutoff frequency. As shown in Fig. 2, a transmission line of Fig. 1(a) can hardly be converted into a single unit section of Fig. 1(b) for wide-band operation. In order to have more than 50% higher cutoff frequency, the maximum size reduction is approximately 10% when we look at Fig. 2(a). Compared with this result, a equivalent transmission line, which consists of two 45 unit sections, as shown in Fig. 2(b), has a higher cutoff frequency than the case of using a single unit section in Fig. 2(a). If the desirable size reduction is 50%, the ratio of and should be approximately 0.5. For this condition, the cutoff frequency can be improved from 0.8 to 1.5 when the unit length is shortened from 90 to 45, which is found in Fig. 2(a) and (b). The cutoff frequency is, however, defined as a 3-dB degrade frequency for a unit section such as (5). Therefore, cascading unit sections shrink the bandwidth. For example, while a unit section has the cutoff frequency of 7.7 GHz, the cascade circuit with four unit sections has the cutoff frequency of 7.2 GHz. Moreover, the line impedance varies as the frequency goes near the cutoff frequency. Furthermore, the dimension of an open stub, as well as the unit length of a series line, influences the cutoff frequency. It arises from the frequency-dependent characteristic of a distributed element that has not only capacitive, but also inductive characteristics while the analysis is performed for a capacitive loaded line. The amplitude and phase responses of the reduced lines with the same series line and different open stubs are plotted in Fig. 3. As the impedance of an open stub decreases, the cutoff frequency increased. This is because the length of the open stub shrinks for a lower line impedance in order to have a desired admittance given by (3) and, thus, a shorter open-circuited stub with lower characteristic impedance leads to a better approximation to a lumped-element capacitor over a wide frequency range. For the case of using a 50- open stub, the cutoff frequency can go down up to 80% of the calculated cutoff frequency, and it can be enhanced by the use of a short open stub (low-impedance line stub). The higher limit for this value is close to the calculated value in (6), which is also shown in Fig. 4. From this condition, even if a 45 unit section could enhance the performance rather than a 90 unit section, we need higher cutoff frequency for wide-band applications, which require more than 50% fractional bandwidth. As you can find in Fig. 2(c), when we adopt a 30 line section for the unit section, (1)

706 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Fig. 3. Block diagram of: (a) a miniaturized transmission line and its characteristics with different open stubs. (b) Amplitude responses. (c) Phase responses. Fig. 2. Z and the normalized cutoff frequency variations as a function of =. (a) Z =50and =90. (b) Z =50and =45. (c) Z = 50 and =30. we can get a cutoff frequency ratio of 2.2, which guarantees a wide-band operation in spite of degradation due to cascading unit sections and adopting open stubs. From the results in this section, we can assume that unit element with the length of 12.5 (for a size reduction factor of and the impedance of an open stub of less than 50 make the fractional bandwidth more than 50%. III. DESIGN OF WIDE-BAND HYBRIDS With the results in Section II, we can start to design hybrids with wide bandwidth more than 50%. Initially, we followed a design method described in [10], and designed a cascaded branch-line coupler, which has four branch lines to achieve a fractional bandwidth of 60%, as shown in Fig. 5(a). The design parameters can be found as follows: This design, however, occupies a large circuit area. In order to reduce the area, we adopted lumped distributed elements, as

CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 707 TABLE I CHOICE OF OPEN STUB Fig. 4. Comparison of frequency responses between distributed model in Fig. 1(b) (solid lines) and lumped-element model in Fig. 1(c) (symbolized lines) when the line impedance of the open stub is 15. Fig. 6. Simulation result of a prototype branch-line hybrid, which adopts ideal transmission-line elements with the calculation results from the Section III. the parameters as follows because its cutoff frequency will be high enough and its dimension is practical to implement: Fig. 5. Conventional branch-line hybrid with four branch lines. (a) Schematic diagram. (b) Designed prototype hybrid. At the same time, we can design the 58- line as well by the identical method. Its design parameters are as follows: shown in Fig. 1. We should consider frequency responses for the equivalent circuit over a wide frequency range because it would be used in a broad-band circuit. Thus we chose to be 30 for the broad-band property, and to be 12.5 for the size reduction and implementation of the high characteristic impedance of. Once is determined, and can be calculated by (3) and (4). The dimensions for an open stub can also be determined by (2) and the layout conditions. We designed the initial values for a unit section, which operates as a transmission line with as follows: We can choose one of the parameters of open stubs in Table I with the susceptance of S. In this case, we decide S Other four high impedance lines with and will maintain their parameters because the impedance of a series line for an equivalent circuit is too high to implement for a meaningful size reduction. Fig. 6 shows the simulation result for the parameters that are calculated here. All the elements in this simulation are ideal transmission lines. IV. SIMULATED AND MEASURED RESULTS For experimental demonstration, two hybrids were constructed using a dielectric substrate with a relative dielectric S

708 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Fig. 7. Fabricated hybrids. (a) Type A: each open-stub is rearranged for size reduction. (b) Type B: high-impedance lines are meandered for further reduction. Fig. 9. Measured phase difference between two quadrature outputs for hybrids of types A and B. TABLE II SUMMARY OF PERFORMANCES FOR HYBRIDS Fig. 8. Simulated and measured S-parameters of the hybrids: (a) type A and (b) type B. (Solid lines simulated results, symbols measured results.) constant of 3.05 and a thickness of 1.54 mm. The two quadrature hybrids operated at the center frequency of 2 GHz were designed using the design parameters that were determined in Section III. We have performed both circuit modeled simulation and electromagnetic (EM) simulation using Agilent ADS. The lumped distributed elements make the frequency responses different from the prototype hybrid, which consists of conventional transmission lines. In order to achieve a good frequency response, optimization was performed using Agilent ADS. The fabricated hybrids are shown in Fig. 7. Type A in Fig. 7(a) has open stubs, which are arranged to reduce the circuit area. The further size reduction can be achieved by meandering the highimpedance lines. The resultant coupler is shown in Fig. 7(b) as type B design. Scattering parameter measurements were performed using an Agilent 8753 D network analyzer over the frequency range from 1 to 3 GHz. Fig. 8 gives the simulated and measured responses of the hybrids in which the fractional band width were found to be over 55%. Furthermore, the phase unbalance between two quadrature outputs of less than 3 over the operating bandwidth was observed in Fig. 9. Comparing modeled and measured results reveals a very good agreement. It was believed that the little discrepancy between simulated and measured results is mainly caused by the junction discontinuities and the tolerance in fabrications. Table II shows a comparison of the bandwidth and the circuit areas occupied by the conventional hybrid design and those proposed in this paper. The size of the proposed branch-line coupler is from 44.8% to 54.0% of a conventional design, while the fractional bandwidth was similar to conventional hybrids. This level of size reduction is expected to be achievable for other frequencies and substrates.

CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 709 V. CONCLUSION This paper has proposed a compact broad-band branch-line hybrid and has analyzed it. Following a design process through this analysis, we have designed and tested two types of wideband hybrids. It is promising for high-power and wide-band applications with a single-layered structure. The measurement of experimental demonstrators has demonstrated that the proposed quadrature hybrid does have a broad bandwidth and small size. This hybrid can be easily constructed by applying conventional monolithic-microwave integrated-circuit (MMIC) techniques. It could be an especially good choice for the application in which the operating bandwidth increases and the handling power goes higher. Furthermore, we hope that it helps to decrease the fabrication costs and increase the yields because it consists of no element that needs a multilayered or air-bridged structure. The application of this type of hybrid to the development of high-power RF MEMS SPDT switches is under consideration. REFERENCES [1] J. Lange, Interdigitated strip-line quadrature coupler, IEEE Trans. Microw. Theory Tech., vol. MTT-17, no. 12, pp. 1150 1151, Dec. 1969. [2] G. Carchon, W. De Raedt, and B. Nauwelaers, Integration of CPW quadrature couplers in multilayer thin-film MCM-D, IEEE Trans. Microw. Theory Tech., vol. 49, no. 10, pp. 1770 17 776, Oct. 2001. [3] D. P. Andrews and C. S. Aitchison, Wide-band lumped-element quadrature 3-dB coupler in microstrip, IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2424 2431, Dec. 2000. [4] Y.-C. Chiang and C.-Y. Chen, Design of a wide-band lumped-element 3-dB quadrature coupler, IEEE Trans. Microw. Theory Tech., vol. 49, no. 3, pp. 476 479, Mar. 2001. [5] R. W. Vogel, Analysis and design of lumped- and lumped-distributedelement directional couplers for MIC and MMIC applications, IEEE Trans. Microw. Theory Tech., vol. 40, no. 2, pp. 253 262, Feb. 1992. [6] K. W. Eccleston and S. H. Ong, Compact planar microstripline branchline and rat-race couplers, IEEE Trans. Microw. Theory Tech., vol. 51, no. 10, pp. 2119 2125, Oct. 2003. [7] H. Ghali and T. A. Moselhy, Miniaturized fractal rat-race, branch-line, and coupled-line hybrids, IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2513 2520, Nov. 2004. [8] Y.-H. Chun and J.-S. Hong, Design of a compact broad-band branchline hybrid, presented at the IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005. [9] J.-S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications. New York: Wiley, 2001, ch. 4, pp. 93 102. [10] M. Muracuchi, T. Yukitake, and Y. Naito, Optimum design of 3-dB branch-line couplers using microstrip lines, IEEE Trans. Microw. Theory Tech., vol. MTT-31, no. 8, pp. 674 678, Aug. 1983. Young-Hoon Chun (M 00) received the M.S. and Ph.D. degrees in electronic engineering from Sogang University, Seoul, Korea, in 1995 and 2000, respectively. From 2000 to 2005, he was with the research staff of the Millimeter-Wave Innovation Technology (MINT) Research Center, Dongguk University, Seoul, Korea. In June 2004, he visited Heriot-Watt University, Edinburgh, U.K. Since July 2005, he has been a Research Associate with the Department of Electrical, Electronic, and Computer Engineering, Heriot-Watt University, Edinburgh, U.K. His research area includes microwave active filters, RF MEMS, passive and active millimeter-wave devices, and multifunctional integrated devices for RF front-ends. Jia-Sheng Hong (M 94 SM 05) received the D.Phil. degree in engineering science from the University of Oxford, Oxford, U.K., in 1994. His doctoral dissertation concerned EM theory and applications. In 1994, he joined the University of Birmingham, where he was involved with microwave applications of high-temperature superconductors, EM modeling, and circuit optimization. In 2001, he joined the Department of Electrical, Electronic, and Computer Engineering, Heriot-Watt University, Edinburgh, U.K., as a faculty member leading a team concerned with research into advanced RF/microwave device technologies. He has authored and coauthored over 100 journal and conference papers. He also authored Microstrip Filters for RF/Microwave Applications (Wiley, 2001). His current interests involve RF/microwave devices, such as antennas and filters, for wireless communications and radar systems, as well as novel material and device technologies including RF MEMS, ferroelectric, and high-temperature superconducting devices.