Analysis and design of microstrip to balanced stripline transitions

Transcription

1 Analysis and design of microstrip to balanced stripline transitions RUZHDI SEFA 1, ARIANIT MARAJ 1 Faculty of Electrical and Computer Engineering, University of Prishtina - Prishtina Faculty of Software Design, Public University of Prizren - Prizren 1& REPUBLIC OF KOSOVA ruzhdi.sefa@uni-pr.edu, arianitmaraj@yahoo.com Abstract - A design method for microstrip to balanced stripline transition is presented. The transition is suitable for application in feeding arrays of double-side printed antennas. The transition is a Chebyshev taper impedance transformer and the conversion from unbalanced to balanced line relied on a gradual change of the cross-section of the line. The transmission parameters of an asymmetric line are derived with a method based on the quasi-tem wave approximation. Also, in this paper are presented calculated results for 50 microstrip to 100 balanced stripline and 100 microstrip to 50 balanced stripline transitions. Keywords- Microstrip, Balanced stripline, Transformer, TEM mode 1 Introduction Printed dipole radiators have been popular candidates for phased-array antennas that contain many elements because of their suitability for integration with microwave integrated circuit modules [1] [3]. Arrays of double-sided printed strip dipoles fed with corporate networks of parallel striplines and backed by conductor planes were developed for radar and various military applications [4]. Various antenna structures of double-sided printed strip dipoles connected through balanced striplines having dual-band and broadband properties have been reported [5]. These structures are suitable for low-cost base station antennas, because they have simple configuration and can be easily manufactured. To feed a double-sided printed strip antenna from a conventional coaxial connector, however, a transition from unbalanced line to a balanced line must be used to keep the antenna in a balanced state. The transition performs conversion of electromagnetic fields and can be used as impedance transformer. Moreover, the transition must be capable of operating over a large frequency range to be compatible with the antenna performance. Impedance transformation and matching are required in general microwave networks and antenna arrays to obtain maximum power transfer between the source and load. In addition, power often has to be divided between different network elements. At high frequencies, these common functions are usually performed with distributed elements consisting of sections of transmission lines. The most commonly used quarter-wave impedance transformer is shown in Fig. 1. A resistive load of impedance Z L can to be matched to a network with input impedance Z in by using a quarterwave section of transmission line with impedance Z Z Z. The impedance is c in L perfectly matched only at the frequency at which the electrical length of the matching section is L / 4. Figure 1. Quarter wave transformer The bandwidth provided by a quarter-wave transformer may be adequate in many applications, but there are also situations in which a much greater bandwidth must be provided. The bandwidth can be increased by using cascaded quarter wave transformers [6] as shown in Fig.. Each quarter wave section has the same electrical length, and by a proper choice of their characteristic impedances a variety of pass-band characteristics can be obtained [7]. The most commonly used multi- ISBN:

2 section transformers are those with maximally flat (binominal transformer) and equal-ripple (Chebyshev transformer) reflection coefficient characteristics. A typical plot of reflection coefficient of a two-section quarter-wave Chebyshev transformer as a function of is shown in Fig. (b). length. So that the input reflection coefficient follows a Chebyshev response in the pass band. The taper has equal-ripple minor lobes and is an optimum design as it has the shortest length for a given minor lobe amplitude. (a) (b) Figure (a) Multi-section quarter wave transformer and (b) Input reflection coefficient of a two-section quarter wave Chebyshev transformer Cascaded quarter-wave impedance transformers of more than two sections are not practical due to length constrains. Instead, a transmission line which has the characteristic impedance that varies continuously along its length can be used as a broadband impedance transformer. The broadband impedance matching properties of the transformer are obtained by utilizing a continuous transmission line taper as shown in Fig. 3(a) with its characteristic impedance changing smoothly from Z L to Z in. If the variation of characteristic impedance along the taper Z (x) is known, the reflection coefficient can be easily calculated by considering the taper to be made of a number of short transmission line sections. Exponential taper and taper with triangular distribution are two examples of practical designs [7]. A more important problem is to determine Z (x) to give an input reflection coefficient with desired frequency characteristics. An example of practical importance is a taper that has its characteristic impedance tapered along its Figure 3 Tapered transmission line This paper presents a methodology to design microstrip to balanced stripline (printed twinline) tapered transitions, and use them to construct feed networks for arrays of doublesided strip dipoles. The transition is accomplished by narrowing the width of the ground plane of microstrip line in tapered fashion. The cross-section of the microstrip conductor is then varied to obtain the required impedance across the taper length. A quasi-tem method is used to calculate the transmission characteristics of an asymmetric and inhomogenous line. Conductor widths of various printed microstrip to balanced stripline transition are calculated and their characteristic impedance and effective dielectric constant across the length are presented. Microstrip to balanced stripline transition A microstrip to balanced stripline transition is shown in Fig. 4. The transition is performed by gradually changing the cross-section of the line from microstrip (unbalance) at the input to the strips of equal width (balanced) at the output. A smooth change in cross-section of the line, such as tapered line, is required so that the net reflection at the input is arbitrary small [8]. The transition itself together with the conversion of electromagnetic field may be used to perform the transformation of impedance. We use this important advantage to design practically convenient double-sided feed networks. These networks consist of tapered line transitions and cooperate feed network of balanced striplines. ISBN:

3 Figure 4. Configuration of a microstrip to balanced stripline transition. We design tapered lines such that the input reflection coefficient follows a Chebyshev response in the pass band. To synthesize the impedance taper, the parameters of an asymmetric transmission line are derived by using the rectangular boundary division method [9]. The appropriate dimensions of cross-section at each position along the taper are found by assuming that the required taper impedance is equal to the balanced mode characteristic impedance of a uniform asymmetric line of that particular cross-section. 3 Characterization Method A microstrip to balanced stripline transition is designed as an impedance matching section, which requires a synthesis procedure to determine the line profile from the given impedance profile. The tapered impedance profile is selected so that the input reflection coefficient follows a Chebyshev response in the pass band. However, the tapered line shown in Fig. 4 is an in-homogeneous line which supports a non-tem mode with the propagation constant varying along its length. This makes the design procedure very involved. As an approximation, we start with the impedance profile of a TEM Chebyshev taper, which can be obtained by using the standard procedure [6], for given Z m, Z, and desired ripple level. Such an impedance b profile will produce the same reflection coefficient expressed in terms of electrical length for any line structures. After the taper profile is determined, the propagation constant along the taper profile can be found and be included in the calculation of the reflection coefficient. The reflection coefficient obtained in this way will be an approximation but close to the starting reflection coefficient. The length of the taper is determined by the lowest operating frequency and the maximum reflection coefficient which is to occur in the pass band. The shape ratio, w 1 / h and, at any position x along the taper is determined by assuming that the characteristic impedance of the taper at that cross-section is equal to the characteristic impedance of a uniform asymmetric line shown in Fig. 5. The transmission characteristics of the asymmetrical line are determined under the quasi-tem wave approximation, where the problem is attributed to the calculation of the line capacitance. The line capacitance for a given structure is calculated by utilizing the rectangular boundary division method [9]. The structure to be analyzed is placed in a metallic enclosure for the convenience of analysis, but the dimensions of the enclosure are chosen large enough such as the propagation characteristics of the line are not significantly affected. The presence of the metallic enclosure enables the propagation of two fundamental modes (out-ofphase and in-phase modes). The computation of a taper performance based on the mode analysis, however, showed that that spikes on the reflection coefficient due to the excitation of inphase mode appear. In the case of an open structure, the in-phase mode cannot be defined. So, a different definition for the propagating mode based on the balanced condition is used in calculation. For a two conductor system of fig. 5, a linear system of equations can be written as: Q Q 1 C11V 1 C1V C1V 1 CV (1a) (1b) where Q 1, Q denote the line charge per unit length and V 1, V the line potential of each strip conductor. The balanced condition is defined as ISBN:

4 Q Q 1 Q and V V 1 V () Figure 5. Cross-section view of an asymmetrical transmission line Substituting Eq. () into Eq. (1) and rearranging, the balanced mode capacitance is obtained as Q C11C C1 C b (3) V C11 C C1 The capacitance values C 11, C, and C 1 are obtained from three stationary values of electrostatic energy corresponding to three combinations of potentials on conductors and the energy-capacitance relation give by 1 U C ijviv j i 1 j 1 (4) The balanced characteristic impedance and effective permittivity are given as 1 Z c (5) v C C 0 b C b0 b eff (6) Cb0 Where C b0 denotes the balanced mode capacitance in y=the case where the dielectric substrate in the structure is replaced by vacuum and v 0 denotes the phase velocity in vacuum. Two parameters have to be determined from the knowledge of the characteristic impedance at a particular cross-section. This leads to a nonunique solution. However, a profile that changes smoothly along the taper must be selected as to gradually perform the conversion of the electromagnetic field. This is essentially achieved by a tapered bottom conductor, the parameters of which may be calculated knowing the desired impedances of the microstrip and balanced ends, namely w m and w b. Here, we adopt a profile for the bottom conductor, w ( x / ), which can be expressed as L u x w m w ( x / L) wm exp ln (7) L wb The profile of the top conductor is then chosen to achieve the Chebyshev impedance taper between two impedances. The parameter u in Eq. (7) is selected such that the obtained top conductor profile changes smoothly along the taper. Calculation experience showed that a value between and 3 will give satisfactory results. 4 Calculated results The described characterization method was used to find conductor width profiles of microstrip to balanced stripline tapered transitions printed on a substrate of height h 0. 8mm, relative dielectric constant r., and conductor thickness t mm. The goal was to design 50 to 100 tapered transitions with reflection coefficients lower than 40dB over the UMTS frequency band of 1.71GHz ~.17GHz. Assuming that the transition would have an average effective dielectric constant of along the taper and the lowest operation frequency is1.6ghz, the length of transition was found to be L 90mm. For calculation purposes, the transition was considered as a number of short transmission lines with uniform cross-sections. First, the conductor profiles along a 50 microstrip to 100 tapered transition were determined. For the given substrate, the conductor widths on the microstrip and balanced stripline ends were found as w1. 4mm, w 4. 0mm and w 1 w 1. mm, respectively. The lower conductor tapered profile was determined by using equation (7). The width of upper conductor was then determined such as the characteristic impedance along transition is similar to that of Chebyshev impedance taper. The calculated conductor widths along this ISBN:

5 transition are shown in Fig. 6(a). Variations of characteristic impedance and effective dielectric constant along the transition are shown in Fig. 6(b). Although this is an in-homogenous transition with variable effective dielectric constant, the response of input reflection coefficient is similar to that of a typical Chebyshev filter as shown in Fig 6(c). transition were calculated following the same procedure and are shown in Fig. 7(a). Variations of characteristic impedance and effective dielectric constant along the transition are shown in Fig. 7(b), and the input reflection coefficient in Fig. 7(c). Again, the calculated input reflection coefficient resembles that of a Chebyshev taper. (a) (a) (b) (b) (c) Figure 6 (a) Profile of a 50 microstrip to 100 balanced stripline transition, (b) Calculated characteristic impedance and effective permittivity along the taper, (c) Calculated input reflection coefficient Next, the conductor profiles along a 100 microstrip to 50 tapered transition were determined. For the given substrate, the conductor widths on the microstrip and balanced stripline ends were found as w mm w 0. 0mm and w 1 w mm, respectively. The conductor widths of this (c) Figure 7 (a) Profile of 100 microstrip to 50 balanced stripline transition. (b) Calculated characteristic impedance and effective permittivity along the taper. (c) Calculated input reflection coefficient. 5 Conclusion A method to design microstrip to balanced stripline tapered transitions was presented. Such transitions are required when feeding balanced antennas from unbalanced coaxial cables. The ISBN:

6 transitions were also used as impedance transformers to design feed networks that can be used in arrays of double-sided printed strip dipoles. The geometry of transition was selected to provide a Chebyshev taper response as this taper is characterized with smooth variations of characteristic impedance along the taper that is suitable for electromagnetic field conversion and nearly perfect impedance matching over wide frequency bandwidths. The transition was accomplished by narrowing the width of the ground plane of microstrip line in tapered fashion. A quasi-tem method was used to characterize asymmetric and in-homogenous transmission lines encountered in design of microstrip to balanced stripline transitions. Calculated results for 50 microstrip to 100 balanced stripline and 100 microstrip to 50 balanced stripline tapered transition were presented and their input reflection coefficients shown to be similar to that of a TEM Chebyshev taper. [7] R. E. Collin, Foundation for Microwave Engineering. New York: Mc-Graw-Hill, [8] J. W. Duncan and V. P. Minerva, 100:1 bandwidth balun transformer, Proc. IRE, Sep. 1960, vol. 48. Pp [9] E Yamashita, M. Nakajima, and K. Atsuki, Analysis method for generalized suspended striplines, IEEE Trans. Microwave Theory and tech., vol. 34, pp , Dec References: [1] A. J. Parfitt, D.W. Griffin, and P. H. Cole, Analysis of infinite arrays of substratesupported metal strip antennas, IEEE Trans. Antennas Propagat., vol. 41, pp , Feb [] J. R. Bayard, M. E. Cooley, and D. H. Schaubert, Analysis of infinite arrays of printed dipoles on dielectric sheet perpendicular to a ground plane, IEEE Trans. Antennas Propagat., vol. 39, pp , Dec [3] B. Edward and D. Rees, A broad-band printed dipole with integrated balun, Microwave J., pp , May [4] W. C. Wilkinson, A class of printed circuit antennas, in IEEE AP-S [5] F. Tefiku and C. Grimes, Design of broadband and dual-band antennas comprised of series-fed printed-strip dipole pairs, IEEE Trans. Antennas Propagat., vol. 48, pp , Jun [6] Ruzhdi Sefa, Alida Shatri Maraj, Arianit Maraj, Analysis of transmission lines matching using quarter-wave transformer, WSEAS conference, ID: , 011 ISBN: