SUBSTRATE integrated waveguide (SIW), also called

Transcription

1 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL Measurement of Frequency-Dependent Equivalent Width of Substrate Integrated Waveguide Chao-Hsiung Tseng, Member, IEEE, and Tah-Hsiung Chu, Member, IEEE Abstract In this paper, a method is developed to measure the frequency-dependent equivalent width (FDEW) of the substrate integrated waveguide (SIW). Based on the deembedding concept, the formulas of the measurement procedures are derived, and then the measured equivalent width corresponding to each frequency is applied to the transmission/reflection method to acquire the substrate dielectric constant. The measurement method is experimentally verified over the frequency range from 26 to 40 GHz. The measured FDEW of the SIW is compared with that calculated by the empirical equation. Furthermore, the results of the measured dielectric constant are shown to be in reasonable agreement with those measured by the ring resonator method. It demonstrates that the developed method is an effective measurement approach to characterizing the SIW. Index Terms Calibration, dielectric measurements, microwave measurement, substrate integrated waveguides (SIWs). I. INTRODUCTION SUBSTRATE integrated waveguide (SIW), also called laminated waveguide [1] or post-wall waveguide [2], is a synthetic rectangular waveguide formed by the top and bottom metal plates of a dielectric slab and two sidewalls of metallic via-holes. Unlike the metallic waveguide components with bulky size and high manufacturing cost, the SIW can be fabricated on the printed circuit boards (PCBs) or the low-temperature co-fired ceramics (LTCCs) to reduce size, weight, and cost. As the SIWs are operated in the modes, they preserve the characteristics of conventional rectangular waveguides [3], and the propagation energy of modes is almost confined in the substrate. Therefore, the SIWs have a higher factor [4] and lower loss than other planar guided-wave structures such as microstrip lines and coplanar waveguides (CPWs). For millimeter-wave range applications, the SIW is an attractive guided-wave structure to realize circuit components and subsystems. Hence, one can find a number of devices implemented using SIWs, such as bent and Tee structures [1], sixport junctions [5], waveguide filters [6] [8], oscillators [9], and waveguide slot array antennas [10], [11]. In addition, since transitions to other guided-wave structures [4], [12] [15] are well developed, using the SIW technique also takes advantage of Manuscript received July 22, 2005; revised December 13, This work was supported by the National Science Council of Taiwan, R.O.C., under Grant NSC E PAE and Grant NSC E C.-H. Tseng is with the Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA USA, on leave from the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C. ( chtseng@ntu.edu.tw). T.-H. Chu is with the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C. ( thc@ew.ee.ntu.edu.tw). Digital Object Identifier /TMTT easily integrating millimeter-wave passive and active components on a single substrate as a compact and high-performance subsystem. In order to investigate the guided-wave properties of the SIW, numerical algorithms of finite difference frequency domain [16] and method of moments [17] have been adopted to simulate its characteristics. In addition, based on the combination of the multimode calibration method and the commercial full-wave simulator, the method in [3] can solve the eigenvalue problems to calculate its propagation constant. Therefore, the SIW can be equivalent to a metallic rectangular waveguide with a constant equivalent width by fitting the curve of the propagation constant. To simplify the SIW related circuit design, the empirical equations [3], [18] are given to calculate a constant equivalent width for the -mode passband. In other words, the equivalent width calculated from empirical equations is frequency independent. It may have limitations in the millimeter-wave range. Since the two sidewalls of the SIW are formed by via-holes, the shorter guided wavelength, operated at the higher frequency, leads to more loss leaked from the space between two adjacent via-holes. Therefore, the equivalent width should be a function of frequency with a wider equivalent waveguide width for a higher frequency. In this paper, a method is developed to measure the frequency-dependent equivalent width (FDEW) of the SIW in the -mode passband. The measurement procedures firstly extract the propagation constant from two SIWs with different lengths using the self-calibration algorithm [19], [20]. Meanwhile, changing the distance of two via-hole sidewalls, two SIWs with different lengths are used to obtain the other set of propagation constants. The FDEW of the SIW can then be calculated from these two sets of propagation constants using the formulation presented in Section II. Furthermore, based on the transmission/reflection (T/R) method [21], [22], the measured FDEW can be exploited to calculate the substrate complex dielectric constant. The measured results are compared with those measured by the ring resonator method [23], [24] and the open resonator method [25]. Measured results of the complex propagation constant, FDEW, and dielectric constant of the SIW using the developed method are shown in Section III. II. MEASUREMENT METHOD A. Propagation Constant of the SIW Based on the multiline calibration method [19], the propagation constant of the SIW can be measured by two SIWs with different lengths shown in Fig. 1. The length difference between these two SIWs is properly chosen to be approximately /$ IEEE

2 1432 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006 Fig. 1. Two SIWs with length difference `. Fig. 2. Two SIWs with sidewall distances of: (a) a and (b) a +, and their equivalent metallic waveguides., where is an integer and is the guided wavelength of the SIW. For the measurement, the bilateral ends of the SIWs are linked with two SIW-to-microstrip transitions [13] to connect to the vector network analyzer (VNA). The measured results of two SIWs can be represented as (1) (2) where and are transmission parameter (or -parameter) matrices converted from the measured -parameters of two SIWs using the formula Matrices and include the characteristics of the SIW, the SIW-to-microstrip transition, and the microstrip feed line. represents the propagation characteristic of the SIW of length, and its -parameter matrix is given as where is the complex propagation constant of the SIW. From (1) and (2), one can obtain an eigenvalue equation as Since is a diagonal matrix, two eigenvalues and of equal the diagonal elements of, namely, and. Therefore, the complex propagation constant becomes (3) (4) (5) Note that, in (6), after performing a natural logarithm of, the imaginary part of the result has to be first unwrapped, then the principal value in the general solution of can be used to calculate the phase constant. The formulation in this section is in the single-mode case, i.e., mode. It can be extended to the multimode case with the multimode calibration technique [26], and then (5) can be rearranged as [3] can be ob- The multimode complex propagation constant tained by solving this eigenvalue problem. (8) B. FDEW of the SIW As with the SIW shown in Fig. 2(a), the two via-hole sidewalls are fabricated on the substrate with the thickness, and are separated by the distance. It can be equivalent to a metallic sidewall and dielectric-filled waveguide with the FDEW and height. The phase constant can be measured using the procedures described in Section II-A and then used to find the guided wavelength of the equivalent metallic sidewall waveguide as where and are the passband and cutoff wavenumbers, respectively. As the substrate is nonmagnetic material, namely, relative permeability, and the waveguide is operated in the mode, one can get (9) (10) where and are the attenuation and phase constant, respectively. is the average of the two eigenvalues as (6) and (11) (7) where is the operating frequency, is the relative dielectric constant of the substrate, and is the velocity of light. Substi-

3 TSENG AND CHU: MEASUREMENT OF FDEW OF SIW 1433 tuting (10) and (11) into (9) and performing proper algebraic manipulation, (9) can be written as (12) For the other metallic sidewall waveguide with FDEW, shown in Fig. 2(b), (12) can be rewritten as (13) where. The corresponding phase constant and guided wavelength are then and, respectively. As the two SIWs shown in Fig. 2 are fabricated on the same substrate and are operated at the same frequency, namely, and in (12) are the same as those in (13), the variables and can be eliminated by dividing (12) to (13) as (14) By replacing and by and, respectively, one can then obtain (15) where and are the phase constants corresponding to the SIWs with the FDEWs and, respectively, and they can be measured by the procedures in Section II-A. Note that although the operating frequency is eliminated in (14), the variables,,, and in (14) imply frequency dependence. As and are substituted into (15), a quartic equation is given as (16) In (16), is calculated from the measured phase constants and, and is the known increment of the distance between two via-hole sidewalls. Note that should be properly chosen to give overlapping -mode passbands of the two SIWs given in Fig. 2. Therefore, the variable in (16) can be solved to give four roots including a real, an imaginary, and a pair of the complex conjugate roots. Since is the FDEW of the SIW, the real root is the reasonable solution. C. Dielectric Constant of the SIW Substrate The FDEW of the SIW determined by the procedures in Section II-B can be exploited to measure the dielectric constant of the SIW substrate. In the T/R method [21], [22], the material sample with length is inserted into an air-filled rectangular waveguide, and then the transmission coefficient of the substrate sample can be measured using the deembedding technique. One can relate the complex dielectric constant to the transmission coefficient by (17) Fig. 3. Two pairs of SIWs with different distances between two via-hole sidewalls: (a) a and (b) a + for the measurement of the propagation constant, FDEW, and dielectric constant of the substrate. where is the free-space wavelength and is the cutoff wavelength of the waveguide. With and, (17) can be rewritten as (18) For measuring the low-loss substrate sample, using the T/R method easily leads to the multiple reflection effects on the interfaces between the air and substrate. In order to reduce the measurement perturbation and uncertainty caused by multireflection, in [20], the two dielectric-filled waveguides with different lengths are used to measure the dielectric constant with the multiline calibration technique. The measured propagation constant is then used to calculate the dielectric constant. The similar measurement procedures are also suitable to determine the complex dielectric constant of the SIW substrate. For the nonmagnetic substrate and replacing by (11), (18) then becomes (19) where and are the FDEW and the corresponding complex propagation constant of the SIW, respectively. They can be measured by the method in Sections II-A and B. The measurement procedures of the FDEW and the dielectric constant of the SIW are summarized as follows. 1) Two pairs of SIWs shown in Fig. 3(a) and (b) with the respective distances between two via-hole sidewalls and are designed and fabricated. As shown in Fig. 3(a) or (b), the length difference between two SIWs in each pair is properly chosen about the corresponding guided wavelength multiplied by the factor. 2) Following the procedures in Section II-A, the two SIWs shown in Fig. 3(a) can be used to obtain one set of the complex propagation constant. The other

4 1434 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006 set is extracted from the two SIWs shown in Fig. 3(b). 3) Calculate from the measured phase constants and and then substitute with the known increment into (16). The quartic equation can be solved to obtain the FDEW of the SIW. 4) Combine and obtained from 2) and 3) with (19) to determine the dielectric constant of the SIW. III. EXPERIMENTAL RESULTS A. Design Parameters The measurement method described in Section II is experimentally validated over the -band (26 40 GHz). To cover this -mode passband, the internal width of the SIW, namely, the distance between two inside edges of two via-hole sidewalls, shown in Fig. 1, is approximately decided from the dimension of the WR-28 standard waveguide divided by the square root of the dielectric constant of the SIW substrate. The SIWs used in the measurement are fabricated on the Rogers RO4003 substrate ( at 10 GHz) with thickness mil and covered with 0.5-oz copper. The internal width is then selected as 160 mil and the guided wavelength is approximately 245 mil at 33 GHz. Two pairs of the SIWs illustrated in Fig. 3(a) and (b) with respective center-to-center distances between two via-hole sidewalls, mil and mil are implemented as shown in Fig. 4(a). According to the schematic shown in Fig. 1, two sidewalls of the SIWs are formed by single-layer metallic via-holes whose diameter is 15 mil and separation is 30 mil. The length difference between two SIWs for each pair is 300 mil (approximately at 33 GHz). In order to measure the -parameters using Cascade Sumit 9000 probe station with two ground signal ground (GSG) probes, the bilateral ends of the SIWs are connected via 50- microstrip lines with width mil, and then microstrip-to-waveguide transitions [13] with CPW pads. The linear tapered microstrip line acts as a broad-band transition to transfer energy from microstrip to the SIW with low transmission loss over the -band. The length of the microstrip taper is 200 mil, and the widths are 72 and 88 mil for the pairs and, respectively. The other set of the SIWs with double-layer metallic viaholes are fabricated as shown in Fig. 4(b). They are used to evaluate the effectiveness of measuring the FDEW of the complex sidewall structures. The detailed schematic is illustrated in Fig. 4(c). Besides 45-mil via-separation, 15-mil layer separation, and 540-mil length difference (approximately at 33 GHz), all other parameters are the same as the SIWs with single-layer via-holes. B. Measured Results of the SIW Characteristics and FDEW The -parameters of the SIWs shown in Fig. 4(a) are measured by an HP 8510C VNA with on-wafer short, open, load, thru (SOLT) calibration over the frequency range from 26 to 40 GHz with 101 frequency points. The measured -parameters are then converted to the -parameters by (3). Applying the formulas in Section II-A, one can extract two sets of the complex propagation constants and corresponding to the pairs Fig. 4. Two pairs of the SIWs with: (a) single-layer via-holes and (b) doublelayer via-holes with (c) the detailed schematic. and of the SIWs, respectively. Fig. 5(a) shows the measured results of the attenuation constants and extracted from two pairs of SIWs of Fig. 4(a). The measured results of the phase constants and are also shown in Fig. 5(b) and then used to calculate the guided wavelength and shown in Fig. 6. Following the formulas in Section II, should be firstly calculated from and, and then substituted into (16) with the known increment. The FDEW of the SIW shown in Fig. 7 is acquired by solving the quartic equation (16). For comparison, the equivalent width calculated using the empirical equation of [3, eq. (9)] is also depicted in Fig. 7. Over the frequency range, the empirical equation gives a constant equivalent width. The FDEW measured in this study is shown to be wider as the operating frequency increases. It is because the SIW operated at higher frequency has more fields leaking from the space between two adjacent via-holes. For broad-band and millimeter-wave applications, the FDEW can then provide more accuracy information in the circuit design. In addition, based on the measurement procedures in Section II, two pairs of the SIW with double-layer via-holes shown in Fig. 4(b) are also used to acquire its FDEW given in Fig. 7. The FDEW of double-layer via-holes is shown to increase more rapidly than that of the SIW with single-layer via-holes. As shown in Fig. 4(c), since the separation of two adjacent via-holes

5 TSENG AND CHU: MEASUREMENT OF FDEW OF SIW 1435 Fig. 7. Measured FDEW of the SIW with single- and double-layer via-holes in comparison with the equivalent width calculated by the empirical equation of [3, eq. (9)]. Fig. 8. Schematic of the microstrip ring resonator for the dielectric-constant measurement. Fig. 5. Measured results of: (a) attenuation constant and (b) phase constant extracted from two pairs of SIWs of Fig. 4(a). Fig. 6. Guided wavelength calculated from the measured phase constants. in the inner layer is larger than that of the single-layer case, in the higher frequency, the FDEW then becomes wider due to more field leaked from the inner-layer via-holes. However, the outer-layer via-holes act as obstacles to prevent the leakage from radiating out of the SIW. Note that the -parameters of the SIWs can be measured without using the SOLT calibration of the VNA because the measurement method in Section II-A carries the ability of removing systematic errors of the VNA. In order to obtain more accurate measurement results as shown in this paper, the SOLT calibration is first performed to remove the systematic errors of the VNA, and then the formulas in Section II-A are used to deembed the effects of feeding microstrip lines, transitions, and a portion of the SIW. C. Measured Results of the Substrate Dielectric Constant Based on the T/R method, the measurement procedures of the complex dielectric constant of the SIW substrate slab are developed in Section II. In order to evaluate the measured results, the conventional ring resonator method [23], [24] is adopted to measure the dielectric constant of the Rogers RO4003 substrate for comparison. Fig. 8 shows the schematic of the microstrip ring resonator with the ring radius (from the center of the ring to the midline of the microstrip line). The width of the microstrip line and the gap between the ring and feed lines are represented as and, respectively. The ends of two feed lines are connected with the CPW pads for on-wafer measurement. To accurately measure the th order of the resonant frequency, the VNA is calibrated with the settings of 801 frequency points and 128 average factors. The measured results of two ring resonators with and mil are given in Table I. Note that only the resonant frequencies in the range from 26 to 40 GHz are listed for the comparison with the results acquired using T/R method.

6 1436 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006 TABLE I MEASURED RESULTS USING RING RESONATOR METHOD also demonstrates the effectiveness of the measurement method in Section II to measure the FDEW of the SIW. Fig. 9(b) shows the loss tangent calculated from the ratio of the imaginary part and real part of the measured complex dielectric constant. For comparison, the measured results of the loss tangent using the open resonator method are also given in Fig. 9(b). Note the results obtained by the method proposed in this paper include the losses contributed from the dielectric, conductor, and radiation. Hence, they are larger than the dielectric losses measured by the open resonator method. In addition, it is observable that the radiation loss can be effectively reduced by adding the outer layer of via-holes. IV. CONCLUSION In this paper, a method has been developed to measure the FDEW of the SIW. Based on the developed deembedding concept, two sets of the complex propagation constants have been extracted by measuring two pairs of the SIWs with different distances between two via-hole sidewalls. Substituting the measured propagation constants into a quartic equation, the FDEW can be calculated and further applied to measure the substrate dielectric constant of the SIW. The measured FDEWs of the SIWs with single- and double-layer via-holes have been presented and compared with the equivalent width calculated by the empirical equation. They are also adopted to acquire the substrate dielectric constant using the T/R method. The measured results using the T/R method with the measured FDEW are shown to be in reasonable agreement with those using the ring resonator method. It then demonstrates that the developed method is an effective approach to acquiring the measured FDEW of the SIW over the operating frequency range. In addition, the developed method can determine the dielectric constant of the substrate of the SIW in the millimeter-wave range. Performing the measurement procedures given in this paper accompanies achieving the complex propagation constant, guided wavelength, FDEW, and substrate dielectric constant. Therefore, the developed method is an effective measurement approach to characterizing the SIW, and can be applied to measure the characteristics of the other guided-wave structures. Fig. 9. Measured results of: (a) the dielectric constant and (b) the loss tangent. In the formulation of Section II, the complex propagation constant and the FDEW are two critical parameters to determine the complex dielectric constant. Substituting the measured and obtained from Section III-B into (19), the real part of are calculated shown in Fig. 9(a). This figure presents both calculated results using the FDEW of the single- and double-layer via-holes. The measured results using the method proposed in this paper are shown in reasonable agreement with those using the ring resonator method and the open resonator method [25]. However, as shown in Fig. 9(a), the equivalent width calculated using the empirical equation of [3 eq. (9)] is not suitable to calculate the substrate dielectric constant. From the measured results of the dielectric constant, it ACKNOWLEDGMENT The authors would like to thank W. Huang, Material Research Laboratory (MRL), Industrial Technology Research Institute (ITRI), Hsinchu, Taiwan, R.O.C., for the substrate measurement using the open resonator method (Project D341AD5110). REFERENCES [1] H. Uchimura, T. Takenoshita, and M. Fujii, Development of a laminated waveguide, IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp , Dec [2] J. Hirokawa and M. Ando, Efficiency of 76-GHz post-wall waveguide-fed parallel-plate slot arrays, IEEE Trans. Antennas Propag., vol. 48, no. 11, pp , Nov [3] F. Xu and K. Wu, Guided-wave and leakage characteristics of substrate integrated waveguide, IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp , Jan [4] D. Deslandes and K. Wu, Integrated transition of coplanar to rectangular waveguides, in IEEE MTT-S Int. Microw. Symp. Dig., 2001, pp

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Matsui, Open resonator for precision dielectric measurements in the 100 GHz band, IEEE Trans. Microw. Theory Tech., vol. 39, no. 10, pp , Oct [26] C. Seguinot, P. Kennis, J. F. Legier, F. Huret, E. Paleczny, and L. Hayden, Multimode TRL A new concept in microwave measurements: Theory and experimental verification, IEEE Trans. Microw. Theory Tech., vol. 46, no. 5, pp , May Chao-Hsiung Tseng (S 03 M 05) was born in Miaoli, Taiwan, R.O.C., in He graduated in electronic engineering from the National Taipei Institute of Technology, Taipei, Taiwan, R.O.C., in 1994, and received the M.S. and Ph.D. degrees in communication engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 1999 and 2004, respectively. From 1999 to 2000, he was an Associate Microwave Researcher with the Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu, R.O.C. From 2001 to 2002, he was a Teaching Assistant with the Department of Electrical Engineering, National Taiwan University, where he became a Post-Doctoral Research Fellow in He is currently a Visiting Scholar with the Department of Electrical Engineering, University of California at Los Angeles (UCLA). His research interests include left-handed metamaterials, microwave measurements and calibration techniques, and microwave-imaging systems and techniques. Tah-Hsiung Chu (M 87) received the B.S. degree from National Taiwan University, Taipei, Taiwan, R.O.C., in 1976 and the M.S. and Ph.D. degrees from the University of Pennsylvania, Philadelphia, in 1980 and 1983, respectively, all in electrical engineering. From 1983 to 1986, he was a Member of Technical Staff with the Microwave Technology Center, RCA David Sarnoff Research Center, Princeton, NJ. Since 1986, he has been on the Faculty of the Department of Electrical Engineering, National Taiwan University, where he is currently a Professor of electrical engineering. His research interests include microwave-imaging systems and techniques, microwave circuits and subsystems, microwave measurements, and calibration techniques.