Study of parallel coupled-line microstrip filter in broadband

modifying the VSWR, gain, and radiation pattern. The error ob-tained between mathematical model and measurements is close to 3.3%.

ACKNOWLEDGMENT

This work was supported by SEMAR-CONACyT project 2003-C03-11873, Mexico.

REFERENCES

1. R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip antenna design handbook, Artech House, Norwood, MA, 2000.

2. M. du Piessis and J.H. Cloete, Tuning stubs for microstrip-patch anten-nas, IEEE Antennas Propagat Soc Mag 36 (1994), 52–55.

3. D.H. Schaubert, Microstrip antennas with frequency agility and polar-ization diversity, IEEE Trans Antennas Propagat AP-29 (1981), 118 – 121.

4. Handbook of microstrip antennas, J. James and P.S. Hall (Eds.), Peter Peregrinus, London, 1989.

5. J.A. Tirado-Mendez et al., A proponed defected microstrip structure (DMS) for reducing rectangular patch antenna size, Microwave Opt Technol Lett 43 (2004), 481– 484.

© 2005 Wiley Periodicals, Inc.

STUDY OF PARALLEL COUPLED-LINE

MICROSTRIP FILTER IN BROADBAND

1_{Institute of Electronics}

National Chiao Tung University Hsinchu, Taiwan

2_{Institute of Communication}

National Chiao Tung University Hsinchu, Taiwan

Received 26 August 2005

ABSTRACT: A parallel coupled-line microstrip filter is designed and

implemented on PCB with its maximum bandwidth. In this paper, this filter has presented almost very good characteristics including the simu-lated bandwidth of 67%, the measured bandwidth of 64%, lower inser-tion loss of 1.27 dB, and flat response in the pass-band. The maximum bandwidth fabricated on PCB shows good agreement with the theoreti-cally calculated bandwidth of 70% due to the narrower gap size be-tween the coupled lines. © 2005 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 48: 373–375, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21353

Key words: parallel coupled-line microstrip filter; PCB; narrower gap

1. INTRODUCTION

Microstrip band-pass filters [1– 4] have been widely used in the RF front end of microwave transceivers because of their planar struc-ture, ease of synthesis method, and low cost [5]. Parallel coupled-line microstrip filters (PCMFs) are usual components in micro-wave integrated circuits due to their simple design and versatility [6, 7]. Due to the need of newly proposed ultra-wideband (UWB) specifications, band-pass filters with GHz bandwidth will be re-quired. The parallel coupled-line microstrip filter fabricated on a printed ceramic board (PCB) usually has a relatively small band-width. This is mainly due to the fact that the reductions of w/d and

s/d using conventional fabrication methods were limited.

How-ever, this limitation has been surmounted, since the gap between

two coupled lines can be scaled down to 4␮m [8], which allows PCMFs to be used successfully in broader bandwidth.

Previously, we have shown coplanar planar waveguide (CPW) and microstrip ring resonators, broadband and narrowband filters, and antenna and transmission lines on ion-implanted silicon sub-strates with excellent RF performance up to 100 GHz [9, 11]. This achievement is partially due to a sufficiently small-sized gap fabricated on a low RF loss silicon substrate, which is generated by ion-implantation and lithography technique.

In this paper, the bandwidth calculated using the theory previ-ously proposed in [5] is presented. The lithography technique is applied in order to experimentally realize the broadband parallel coupled-line microstrip filter on PCB. Both the theoretical and experimental bandwidths are found to be in agreement.

2. DESIGN AND FABRICATION

The formulas of the theoretical calculation for the parallel band-pass filter are given by [5]:

J1Z0⫽

冋

册

冑

冋

册

the element value and the characteristic impedance of the parallel band-pass filter, respectively. Based on Eqs. (1)–(3), the charac-teristic impedances for odd and even modes, Z_0oand Z_0e, can be determined by

Z0en⫽ Z0关1 ⫹ JnZ0⫹ 共 JnZ0兲2兴, (4) Z0on⫽ Z0关1 ⫺ JnZ0⫹ 共 JnZ0兲2兴. (5)

Using these two expressions, the characteristic impedances of the multisection parallel coupled-line filter for odd and even modes can be carried out. In our work, we focused on the five-section parallel coupled-line filter. This filter was designed as a Cheby-TABLE 1 Characteristic Impedances of the Parallel Coupled-Line Microstrip Filter for Odd and Even Modes and Values of

w and s Bandwidth 60% 70% 80% Z0o1 ⍀ 136 146 157 Z0e1⍀ 45 49 52 Z0o2 ⍀ 115 132 150 Z0e2⍀ 40 44 50 Z0o3 ⍀ 125 134 143 Z0e3⍀ 43 36 47 Bandwidth [mm] 60% 70% W1mm 0.18 0.12 — S1mm 0.12 0.1 — W2mm 0.34 0.21 — S2mm 0.15 0.13 — W3mm 0.25 0.19 — S3mm 0.14 0.11 —

shev-type filter, with ripple of 0.1 dB. Then the element values for our designed filter can be obtained by g0⫽ 1, g1⫽ 1.146, g2⫽

1.371, and g₃⫽ 1.975 [3]. Substituting these four element values into Eqs. (1)–(5), the characteristic impedances of our filter for odd and even modes were calculated, and the results are listed in Table 1. These calculated characteristic impedances can help us to find the corresponding values of w/d and s/d from the calibration plot shown in Figure 1, where w is the metal width, s is the gap size, and d is the substrate thickness. The obtained values of w and s are also listed in Table 1. We can see that the maximum bandwidth is 70%. By meeting the theoretically determined values of w and s for the maximum bandwidth of 70%, we fabricated a five-section parallel coupled-line microstrip filter, the photograph and structure of which are displayed in Figures 2(a) and 2(b), respectively.

To realize the smaller gap width in this filter, the circuit was fabricated using a conventional low-cost IC process with a⬎1-␮m resolution (nearly two decades older than the current VLSI tech-nology) and standard FeCl etching. This technology has a better pattern transfer and sharper corner edge that can help extend the PCB process for making a narrower metal width and interval gap. In our experiment, for fabrication, we used a Duroid/6010 sub-strate with subsub-strate thickness of 1.27 mm, metal thickness of 1/2 oz., and dielectric constant of 10. The circuit measurements were performed using an Agilent/HP 8720C vector network analyzer.

3. EXPERIMENTAL RESULTS AND DISCUSSION

3.1. Parallel Coupled-Line Microstrip Filter for 70% Bandwidth

As shown in Figure 3, the simulated fractional bandwidth was found to be 67% close to the ideal destination of 70%. In the pass-band, the best simulated insertion return losses were 1.76 and 12.99 dB, respectively. On the other hand, the measured fractional bandwidth result was 64%, which agrees with the simulated result. Some mismatch may be due to the small power reflection of the nonideal situation. The best in-band insertion and return losses are only 1.27 and 16.7 dB, respectively. It can be observed that the smaller coupling-gap size not only achieves small insertion loss, but also exhibits the broadband characteristics of a band-pass filter. Its characteristics can modify the conventional type of this filter in order to obtain more advantages for broadband communications. Figure 1 The general solution of s/d and w/d under the range of 1.27

mm and this special case of the s/d and w/d from 1.27 mm into 4␮m

Figure 2 The pictures of (a) fabricated and (b) enlarged structure of the five-section parallel coupled-line filter

Figure 3 The parallel coupled-line microstrip filter with a central fre-quency fc⫽ 5 GHz: (a) simulated response frequency equal as 67%; (b)

measured responses frequency equal as 64%

4. CONCLUSION

With the rapid development of broadband communications, flatter coupling response and wider bandwidth are very important issues for UWB applications. In this paper, we have used the lithography technique to improve the gap width, and this technique can help us to achieve the wider bandwidth, low insertion loss, and high-performance characteristics of designed parallel coupled-line mi-crostrip filters. The theoretically calculated results show that the maximum bandwidth obtained was up to 70%. The experimental data also show good agreement with the calculated results.

ACKNOWLEDGMENTS

Albert Chin would like to acknowledge the help of Director and Prof. Tsu-Jae King at EECS, UC-Berkeley. This work has been supported by NSC (93-2215-E-009-017).

REFERENCES

1. T. Edwards, Foundations for microstrip circuits design, 2nd_{ed., Wiley,}

New York, 1992, ch. 5.

2. J.-T. Kuo and E. Shih, Wideband band-pass filter design with three-line microstrip structures, Int Microwave Symp Dig Phoenix, AZ, 2001. 3. G.L. Mattaei, L. Young, and E.M.T. Jones, Microwave filters,

imped-ance-matching network, and coupling structures, Artech House, Nor-wood, MA, 1980.

4. K.C. Gupta, R. Garg, and I.J. Bahl, Microstrip lines and slotlines, Artech House, Norwood, MA, 1979, ch. 3.

5. D.M. Pozar, Microwave engineering, 2nd_{ed., Wiley, New York, 1998, ch. 8.}

6. M. Velazquez-Ahumada, J. Martel, and F. Medina, Parallel coupled microstrip filters with ground-plane aperture for spurious band sup-pression and enhanced coupling, IEEE Trans Microwave Theory Tech 52 (2004), 1082–1086.

7. K. Chang, Microwave ring circuits and antennas, Wiley, New York, 1996. 8. A. Chin, K.T. Chan, H.C. Huang, C. Chen, V. Liang, J.K. Chen, S.C.

Chien, S.W. Sun, D.S. Duh, W.J. Lin, C. Zhu, M.-F. Li, S.P. McAli-ster, and D.L. Kwong, RF Passive devices on Si with excellent performance close to ideal devices designed by electromagnetic sim-ulation, Int Electron Devices Mtg (IEDM) Dig (2003), 375. 9. K.T. Chan, A. Chin, J.T. Kuo, C.Y. Chang, D.S. Duh, W.J. Lin, C.X.

Zhu, M.F. Li, and D.L. Kwong, Microwave coplanar filters on Si substrates, IEEE MTT-S Int Microwave Symp Dig Philadelphia, PA (2003), 1909 –1912.

10. Y.H. Wu, A. Chin, K.H. Shih, C.C. Wu, S.C. Pai, C.C. Chi, and C.P. Liao, RF loss and cross talk on extremely high resistivity (10 K–1 M⍀-cm) Si fabricated by ion implantation, IEEE MTT-S Int Micro-wave Symp Dig 1 (2000), 221–224.

11. K.T. Chan, A. Chin, S.P. McAlister, C.Y. Chang, V. Liang, J.K. Chen, S.C. Chien, D.S. Duh, and W.J. Lin, Low RF loss and noise of transmission lines on Si substrates using an improved ion implantation process, IEEE MTT-S Int Microwave Symp Dig 2 (2003), 963–966. © 2005 Wiley Periodicals, Inc.

PRACTICAL IMPEDANCE MATCHING

USING GENETIC PROGRAMMING

Institute of Microelectronics and Department of Electrical Engineering National Cheng Kung University

Tainan 70101, Taiwan

Received 18 August 2005

ABSTRACT: A genetic programming method for impedance matching

is presented. The method is applied to an impedance-matching problem where the element values available are restricted to a set of preferred

values. The experimental results show that this method can effectively generate practical and economical solutions. Since it can additionally deal with other design considerations, this method is useful for practical impedance matching. © 2005 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 48: 375–377, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21354

Key words: genetic programming; impedance matching 1. INTRODUCTION

In order to maximize power transmission, an impedance-matching network is required between the given source and load imped-ances. In conventional design approaches [1–5], the element val-ues are assumed to be continuous (that is, they can be any real number). In reality, however, the element values are discrete. This limitation occurs in the design of discrete-element circuit because the element values available from vendors are restricted to a set of preferred values. It also occurs in integrated circuit design for high-frequency applications, such as RF or microwave integrated circuits (MICs), where capacitors may be implemented using an interdigital structure and inductors using a spiral structure [6]. Because the number of fingers or turns is an integer, the element values that are a function of integers are discrete.

In this paper, we propose a genetic programming (GP) method, based on our previous work [7, 8], to automatically generate impedance-matching networks consisting of elements with re-stricted values. The experimental results show that the proposed method can effectively generate practical and economical solu-tions. In addition, this method has the following advantages [7, 8]. First, the tree structure of GP is dynamic rather than fixed length, which is a desirable property in the design cases where the circuit complexity and topology cannot be predicted. Second, a circuit-analysis algorithm based on the tree structure is fast and suitable for symbolic circuit analysis, which is convenient for calculating circuit characteristics such as element sensitivity, group delay, and step response. Third, the tree structure is capable of representing any series-parallel RLC circuits; therefore, a resonant structure is allowed. Finally, the GP method can deal with other design con-siderations; for example, the element values are frequency depen-dent and restricted to a set of preferred values. The abovemen-tioned advantages make it a practical method for solving impedance-matching problems.

2. GENETIC PROGRAMMING

The GP method is based on previous work [7, 8] in which we proposed a binary tree structure to represent series-parallel RLC circuits. Figure 1 shows the template of impedance-matching prob-lems, where ZS and ZLdenote the source and load impedances,

respectively. The kernel of this method is the GP algorithm de-scribed below. At first, an initial population is created, which is composed of 500 individuals randomly chosen among the building blocks, as shown in Figure 2. The inductor L or capacitor C node is assigned a value randomly selected from a set of element values. The crossover and mutation operations are then applied to the population in order to explore the circuit topology and element values, respectively. The evolutionary process continues itera-tively until a fully compliant solution is found or a maximum number of iterations is reached.

For a specified minimum transducer power gain (GT,min), the

GP algorithm incorporating the following fitness function can be used to find compliant networks with size less than or equal to the maximum allowable circuit size, max:

fitness⫽

再

elsewhere, (1)