Variable Z0 Applied to Biogeography Based Optimized Multi-Stub Matching Network Nihad I. Dib and Ashraf H. Sharaqa
Richard A. Formato
Electrical Engineering Department Jordan University of Science and Technology P. O. Box 3030, Irbid 22110, Jordan
[email protected],
[email protected]
Consulting Engineer & Patent Attorney P. O. Box 1714, Harwich, MA 02645, USA
[email protected]
Abstract—Variable Z0 technology is applied to the problem of designing a multi-stub matching network (MSMN) using Biogeography Based Optimization (BBO). BBO is a newlyproposed stochastic global search and optimization evolutionary algorithm. It will be used to determine the lengths and locations of the stubs in a multi-stub matching network for optimum (minimum) reflection coefficient. Two cases are investigated: in the first case, Z0 is a fixed user-specified parameter (the traditional methodology), whereas in the second, it is a true variable quantity whose value is determined by the optimization methodology. BBO’s fixed Z0 results are compared to published data with BBO exhibiting better performance. BBO’s results are improved even more using Variable Z0 technology.
I.
INTRODUCTION
Traditional design and optimization methods begin by assuming a fixed value for the feed system characteristic impedance Z0, but doing so automatically excludes all matching networks and antennas whose performance is better with a different value. Variable Z0 addresses this limitation by making Z0 a true variable quantity whose value is determined by the design or optimization methodology [1-4]. Variable Z0 produces better networks and antennas by introducing another degree of freedom into the design or optimization space, thereby making it easier to meet any set of performance objectives. As an example of Variable Z0’s effectiveness, this paper describes a Multi-Stub Matching Network (MSMN) designed using Biogeography Based Optimization (BBO). Matching networks are important in all communication systems because they maximize power delivered to the load, improve signal to noise ratio (SNR), and reduce the amplitude and phase errors in power distribution networks by minimizing the reflection coefficient [5]. BBO has been demonstrated to be an effective optimization technique compared to other methodologies [6]. It has been successfully applied across a range of engineering problems. BBO’s robustness and effectiveness against complex problems have been further improved by hybridizing BBO with other optimization techniques, thereby taking advantage of the best features of both algorithms [7, 8]. Figure 1 is a schematic representation showing an Nparallel (shunt) MSMN that matches an arbitrary load impedance ZL to a transmission line with characteristic impedance Z0. The optimal match is achieved by minimizing
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the input reflection coefficient within a specific frequency range. In this work, this is accomplished using the Biogeography-Based Optimization (BBO) technique [6], where the optimization parameters are the distances between the stubs and their lengths (dn, lns). II.
EXAMPLE
As an example, the same problem addressed in [9], where Nelder-Mead (NM) optimization method was used, is considered here. Two cases are considered: (a) optimization with fixed characteristic impedance Z0=50 Ω; and (b) optimization with Variable Z0 as described in [1-4]. In Variable Z0 methodology, instead of fixing a value for Z0, the feed system characteristic impedance is considered as a variable quantity whose value is determined by the optimization methodology, which in this case is the BBO. The obtained SWR plots appear in Figure 2. Figure 2(a) shows that the BBO curve is closer to the desired SWR than the NelderMead (NM) optimization curve [9], thus demonstrating BBO’s effectiveness in solving the MSMN problem. From Figure 2(b), it is apparent that Variable Z0 approach markedly outperforms fixed Z0 for all stub configurations. Using Variable Z0 achieves almost exactly the desired response. In addition, only three stubs are required to get very close to the desired response, whereas using seven stubs with fixed Z0 results in an inferior SWR. III.
DISCUSSION AND CONCLUSION
Of course, the tradeoff in using Variable Z0 is that the feed system impedance is not the “standard” value of 50 Ω . But, as a practical matter for the MSMN, any impedance that is appropriate from fabrication perspective is acceptable, and typical values range from 20 to 150 Ω . In this example, Variable Z0’s optimized impedance values ranged from 128 to 143 Ω . Variable Z0 is an attractive new concept that holds out the possibility of considerably better performance played against a non-standard feed system impedance. Whether or not that tradeoff is desirable is case specific, but it always merits consideration because the end result very well may be much better.
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REFERENCES 1.15 Three stubs (BBO) Five stubs (BBO) Seven stubs (BBO) Seven stubs (NM) Desired SWR
1.
R. Formato, ‘‘New Techniques for Increasing Antenna Bandwidth with Impedance Loading,’’ Progress In Electromagnetics Research B, Vol. 29, pp. 269-288, 2011.
2.
R. Formato, ‘‘High-Performance Indoor VHF-UHF Antennas: Technology Update Report,’’ National Assoc. of Broadcasters (NAB), FASTROAD (Flexible Advanced Services for Television and Radio On All Devices), Technology Advocacy Program, 15 May 2010:http://www.nabfastroad.org/NABHighperformanceIndoorTVanten naRpt.pdf
3.
R. Formato, ‘‘UWB Array Design Using Variable Z0 Technology and Central Force Optimization ver. 2,’’ August, 2011: http://arXiv.org/abs/1108.0901.
SW R
1.1
1.05
4.
R. Formato, ‘‘Improving Bandwidth of Yagi-Uda Arrays,’’ Wireless
Eng. and Technology, Vol. 3, 18-24, 2012. 1 1.1
1.12
1.14
1.16
1.18
1.2
1.22
1.24
1.26
1.28
5.
D. Pozar, Microwave Engineering, 3rd ed., New York: John Wiley, 2005.
6.
D. Simon, ‘‘Biogeography-based optimization,’’ IEEE Trans. Evolut. Computat., Vol. 12, 702---713, Dec. 2008.
7.
W. Gong, Z. Cai, and C. Ling, ‘‘DE/BBO: A hybrid differential evolution with biogeography-based optimization for global numerical optimization,’’ Soft Computing, Vol. 15, No. 4, pp. 645-665, 2011.
8.
H. Kundra and M. Sood, ‘‘Cross-country path finding using hybrid approach of PSO and BBO,” International Journal of Computer Applications, Vol. 7, No. 6, pp. 15-19, 2010.
9.
C. Regoli, ‘‘Impedance matching by using a multi-stub system,’’
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Frequency (GHz)
(a) 1.14 Three stubs Five stubs Seven stubs Desired SWR
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1.1
Proceedings of the 7th WSEAS International Conference on Simulation, Modeling and Optimization, Beijing, China, 15-17, 2007.
1.08
1.06
1.04
1.02
1 1.1
1.12
1.14
1.16
1.18
1.2
1.22
1.24
1.26
1.28
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(b) Figure 2. Standing wave ratio versus frequency for (a) fixed Z0 (b) variable Z0.
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