# A Dual-band Branch-line Coupler Using Quasi-composite Right/Left-handed Transmission Lines

#### A quasi-RH/LH dual-band 3 dB branch-line coupler (BLC) constructed in microstrip form is proposed. The designed BLC circuit replaces the conventional chip inductors in the coupler arms with microstrip stubs for easier circuit integration and lower fabr...

Branch-line couplers (BLC) are widely used as 90° signal dividers in microwave and millimeter-wave circuits. A BLC can provide two quadrature-phased signals from a single local oscillator for use in image rejection mixers.1 It can be used as part of the feeding network for antennas to produce circularly polarized waves.2 In addition, BLCs are often implemented in balanced amplifiers3 and mixers to achieve good return loss. Conventional BLCs are usually constructed using quarter-wavelength (λ/4) right-handed transmission lines (RH TL). They only operate at a fundamental frequency and its odd harmonics. Such BLCs are usually large in size, and their applications to wideband and multiband systems are thus limited. Techniques for improving BLC performance and circuit compactness were developed and reported in the literature during the past few years. C.T. Lin, et al. described a CPW BLC4 designed using bent structures to reduce the size of the normal quarter-wavelength arms. In addition, compensated networks are added at each of the four ports to achieve a wider bandwidth. Cheng and Wang5 have shown a novel approach where each arm of the BLC is replaced with an equivalent circuit, consisting of a shorter high impedance TL section and two shunt elements, to reduce the circuit size and increase the bandwidth. Park and Lee proposed a new BLC geometry6 with an additional pair of cross coupling branches to provide dual-band operation and more design freedom.

In recent years, dual-band BLCs implemented using composite right/left-handed transmission lines (CRLH TL) have been gaining favor. L.H. Lin, et al. described a dual-band BLC7 that employs the phase-lead property of the LH TL to compensate for the phase lag of the RH TL in the circuit design. In this way, the two operating bands of the BLC can be designed with their center frequencies having a ratio other than 1:3; the second operating band needs not be the third harmonic. This feature is shown to be useful in modern communication systems with dual-band operation, since the two operating frequencies are separated by a factor less than three in current wireless standards.

In this article, a newly designed quasi-CRLH TL is used to implement the dual-band BLC. The chip inductors in the LH TL, consisting of lumped elements, are replaced with shorted transmission-line (STL) stubs for easier circuit integration and lower fabrication cost. The STL stubs can be made equivalent to the inductances needed in the construction of the LH TL in the first operating band. This will ensure that each arm of the BLC behaves as a CRLH TL only in the first band, but not in the second band (thus the name quasi-CRLH TL). This is because in the second band the STL stubs may not correspond to the same required inductances. Nevertheless, through circuit analysis and numerical optimization, it is found that if the inductances in the CRLH TL are replaced with capacitances of appropriate values, the entire BLC can still preserve a 3 dB coupling operation in the second band. Careful design of the STLs will make them exhibit the desired inductances in the first band and capacitances in the second band, thus achieving a 3 dB dual-band operation. The BLC arms are meandered to reduce the circuit size. The designed BLC possesses two operating bands with the first one centered at 946 MHz and the second one at 1796 MHz. With a less than 1 dB amplitude-difference requirement and a phase-difference constraint between 80° and 100°, this BLC exhibits dual operating bands having fractional bandwidths of 17.3 and 8.4 percent, respectively, which are wider than those of many dual-band 3 dB BLCs that have been reported in the literature. Compared with the BLC mentioned previously,7 the proposed BLC not only provides a better performance dual-band operation but also features easy fabrication and a relatively compact circuit size.

Dual-band Branch-line Coupler Design

Figure 1 shows the circuit topology for the dual-band 3 dB BLC considered. For convenience, the circuit elements connecting ports 1 and 2 (and also ports 3 and 4) are referred to as being located in the series arms; those connecting ports 1 and 4 (and also ports 2 and 3) in the parallel arms. All four microstripline sections labeled with characteristic impedances Z1 (Z2) are of the same lengths 1 (2) and widths w1 (w2). Similarly, those labeled with Za (Zb) have the same lengths a (b) and widths wa (wb). The capacitances C1 to C4 can be implemented using chip capacitors. If the shunt, shorted transmission-line (STL) stubs on the series arms (parallel arms) are replaced by inductances La (Lb), then this structure becomes the RH/LH dual-band BLC mentioned previously7. It is known that a conventional 3 dB BLC consisting of λ/4 RH TLs operates at a fundamental center frequency and its odd multiple harmonics, provided that the effective dielectric constant and the characteristic impedance of the TL sections therein are insensitive to frequency variations. Nevertheless, the CRLH BLC can be designed for dual-band operation with its first and second operating frequencies (denoted by f1 and f2, respectively) having a ratio other than 1:3. For the circuit design of the CRLH BLC, the procedure outlined by Lin, et al.7 can be employed to find the appropriate values of La, Lb and C1 to C4. In this article, to ease the circuit fabrication process, La and Lb are replaced with STL stubs, such that the input impedances of these two stubs are equal to those of La and Lb at f1. Hence, the circuit elements (including the two STL stubs and the three chip capacitors) between the two microstripline sections in the same arm behave as an LH transmission line at f1.7 However, the CRLH 3 dB coupling operation is not guaranteed at f2, since these STL stubs may not exhibit input impedances corresponding to those of La and Lb at that operating frequency. The proposed BLC is thus only a quasi-CRLH one. Nevertheless, through extensive numerical simulation, it was found that the 3 dB coupling operation at f2 can be achieved if La and Lb are replaced with some appropriate capacitances Ca and Cb, respectively. These capacitance values can be found by performing circuit analysis and numerical optimization. The scattering parameters S21 and S31 of the quasi-CRLH BLC with Ca (Cb) in shunt with the series (parallel) arms are shown in Appendix A. Minimization routines, available in MATLAB,™ can be used to find appropriate Ca and Cb by minimizing the errors ||S21| – |S31|| and ||–S21 – –S31| – π/2|.

The described analysis shows that the BLC circuit with La and Lb provides a 3 dB coupling operation at f1, whereas the one with Ca and Cb has a similar behavior at f2. Thus, the STL stubs can be designed for the proposed BLC, such that they are equivalent to La and Lb at f1 and to Ca and Cb at f2 as

In Equations 1 and 2, the characteristic impedance (Zp) of a microstripline as a function of h, wp and εrp(eff) can be found,8 where h is the thickness of the substrate and wp and εrp(eff) are the width and effective dielectric constant of the microstripline, respectively. Here, the effective dielectric constant (εrp(eff)) is a function of h, wp and εr (the dielectric constant of the substrate).8 Furthermore, the electric length (θp) of the microstrip line can be expressed as

Optimization routines in MATLAB can also be used to determine p and wp, p = a,b. The outlined approach was employed to design the proposed quasi-CRLH dual-band 3 dB BLC. The dual-band operation was demonstrated by replacing the chip inductors with appropriate STLs to ease the circuit fabrication process.

Circuit Implementation and Results

The circuit pattern was printed on a grounded RT/Duroid 6010 substrate 0.635 mm thick and with a dielectric constant of 10.2. The operating bands are designed to be centered at the frequencies of 925 and 1795 MHz. The 0805 chip capacitors are 21.2 mm. Following the described design procedure, the following circuit parameters were obtained: 1 = 24 mm, 2 = 25 mm, Z1 = 35 Ω, Z2 = 50 Ω, wa = wb = 0.2 mm, a = 20.5 mm, b = 21.0 mm, C1 = 36 pF, C2 = 18 pF, C3 = 28 pF and C4 = 14 pF. The four capacitances, C1, C2, C3 and C4, are implemented by combining in parallel three 12 pF capacitors, two 6 pF with two 3 pF capacitors, four 7pF capacitors and two 5 pF with two 2 pF capacitors, respectively. Combining the chip capacitors in parallel provides a better chance of reducing the total deviation of the capacitances from their target values. All the microstripline sections, including the ones with length 1 in the series arms, the ones with length 2 in the parallel arms, and the shunted STL stubs with lengths a and b, are meandered to reduce the circuit size. Figure 2 shows a photograph of the designed dual-band 3 dB BLC, whose circuit board measures only 44 × 24 mm and is less than one fifth of the size of the BLC reported previously.7 Figures 3 and 4 show the simulated and measured magnitudes of the S-parameters, respectively. The simulated results were obtained using the commercial software Ansoft High Frequency Structure Simulator (HFSS). Figure 5 demonstrates the simulated and measured phase-difference between S21 and S31. Table 1 summarizes all the important data for the first operating band and Table 2 for the second operating band. The simulated and measured center frequencies are 945, 1790, 946 and 1796 MHz, respectively, which slightly deviates from the designed ones (925 and 1795 MHz). Three different types of bandwidths have been extracted from the simulated and measured data. The type A bandwidth is defined by the frequency range around the center frequency with ||S21| (dB) – |S31| (dB)| ≤ 1 dB; the type B bandwidth, ||S21| (dB) – |S31| (dB)| ≤ 1 dB and |∠S21–∠S31| ≤ 10°; the type C bandwidth, |S11| ≤ –15 dB and |S41| ≤ –15 dB, in addition to the criteria set in the type B bandwidth. Among these three bandwidth definitions, type C is the most stringent one, while type A is the loosest one. Hence, BW(type A) > BW(type B) > BW(type C) for both operating bands. Note that for the first band, the BW(type C) measured is less than the bandwidth published,7 whereas BW(type A) and BW(type B) are larger. Also, for the second band, all three bandwidths (types A, B and C) measured are larger than the one published.7 A first look at the measured S-parameters may suggest that the parameter ||S21| (dB) – |S31| (dB)| is larger than 1 dB. However, a careful scrutiny into the measured data reveals that near f1 the largest value for ||S21| (dB) – |S31| (dB)| is 0.917 dB (at 972 MHz), a magnitude difference that still meets the type-A bandwidth criterion.

Conclusion

A new dual-band 3 dB BLC has been proposed. The shunt STL stubs in the four arms of the BLC have been designed to replace the chip inductors, thus ensuring easier circuit integration and a lower fabrication cost. Although this circuit behaves as a RH/LH BLC only in the first operating band, its equal power-splitting and quadrature-phased properties at the two output ports can still be maintained in the second operating band. With all microstripline sections in the coupler arms meandered, the circuit size has been greatly reduced. The measured circuit performance has been found to compare favorably with that of many dual-band 3 dB BLCs seen in the literature.

References

1. B. Mayer, “Planar Broadband Image Rejection Mixer,” *Electronics. Letters*, Vol. 27, No. 23, November 1991, pp. 2128–2130.

2. N.C. Karmakar and M.E. Bialkowski, “Circularly Polarized Aperture-coupled Circular Microstrip Patch Antennas for L-band Applications,” *IEEE Transactions on Antennas and Propagation*, Vol. 47, No. 5, May 1999, pp. 933–940.

3. D.M. Pozar, *Microwave Engineering*, Second Edition, John Wiley & Sons Inc., New York, NY, 1998.

4. C.T. Lin, C.L. Liao and C.H. Chen, “Finite-ground Coplanar-waveguide Branch-line Couplers,” *IEEE Microwave and Wireless Components Letters*, Vol. 11, No. 3, March 2001, pp. 127–129.

5. K.K.M. Cheng and F.L. Wong, “A Novel Approach to the Design and Implementation of Dual-band Compact Planar 90° Branch-line Coupler, *IEEE Transactions on Microwave Theory and Techniques*, Vol. 52, No. 11, November 2004, pp. 2458–2463.

6. M.J. Park and B. Lee, “Dual-band, Cross-coupled Branch-line Coupler,” *IEEE Microwave and Wireless Components Letters*, Vol. 15, No. 10, October 2005, pp. 655–657.

7. I.H. Lin, M. DeVincentis, C. Caloz and T. Itoh, “Arbitrary Dual-band Components Using Composite Right/Left-handed Transmission Lines,”* IEEE Transactions on Microwave Theory and Techniques*, Vol. 52, No. 4, April 2004, pp. 1142–1149.

8. J.S. Hong and M.J. Lancaster, *Microstrip Filters for RF/Microwave Application*, John Wiley & Sons Inc., New York, NY, 2001, pp. 78–79.

**He-Kai Jhuang** *received his BS degree in industrial education from the National Changhua University of Education, Changhua, Taiwan, in 2004. He is currently working toward his MS degree in electronic engineering at the same school. His current research interests include microstrip filter design and passive components for wireless communications.*

**Ching-Her Lee** *received his BS degree in electronic engineering and his MS degree in automatic control engineering from Feng-Chia University, Taichung, Taiwan, in 1977 and 1981, respectively. He received his PhD degree in electrical engineering from the University of Texas at Arlington in 1989. From 1981 to 1985, he was on the faculty of the Chin-Yih Institute of Technology, Taichung, Taiwan. In 1990, he joined the National Changhua University of Education, Changhua, Taiwan, where he is presently dean of the college of engineering. His research interests include planar microwave circuits and microstrip antennas.*

**Po-Min Hu** *received his BS degree in electrical engineering from Da-yeh University, Changhua county, Taiwan, in 2004. He is currently working toward his MS degree in telecommunications engineering at the same school. His research interests include the analysis and design of planar/microwave passive components.*

**Chung-I G. Hsu** *graduated from the National Taipei Institute of Technology, Taiwan, in 1980. He received his MS degree from the University of Mississippi and his PhD degree from Syracuse University in 1986 and 1991, respectively, both in electrical engineering. He spent the spring 1992 semester at the microwave and electromagnetics laboratory of Texas A&M University, doing research on the modeling of microstrip antennas. Since August 1992, he has been on the faculty of Da-Yeh University, where he is presently an associate professor of electrical engineering.*