Design of New Three-Line Balun and Its Implementation ... - IEEE Xplore

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006

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Design of New Three-Line Balun and Its Implementation Using Multilayer Configuration Byoung Hwa Lee, Dong Seok Park, Sang Soo Park, and Min Cheol Park

Abstract—This paper proposes a new balun that is composed of three coupled quarter-wavelength lines. The proposed balun is optimized by using design of experiments to achieve a maximum bandwidth. After the optimization, it is transformed into the balun consisting of a pair of coupled quarter-wavelength lines in connection with an uncoupled quarter-wavelength line. The design method and its implemented results using a multilayer configuration are presented. It is shown that this new balun can be made more compact, providing good performances over the wide frequency range. Therefore, the balun developed here is applicable to many wireless and mobile communication systems. The design equation for a given set of balun impedances at unbalanced and balanced ports is derived from an equivalent circuit of the proposed balun. To demonstrate the feasibility and validity of the design equation, the size 2012 multilayer ceramic chip baluns with three different balun impedances, which operated in the 2.4-GHz industrial–scientific–medical band frequency, are designed and fabricated by the use of low-temperature co-fired ceramic technology. According to the measured results, the maximum insertion loss is 0.81 dB, the maximum in-band phase imbalance is within 7 , and the maximum in-band amplitude imbalance is less than 0.7 dB. Index Terms—Baluns, design of experiments (DOE), low-temperature co-fired ceramic (LTCC), multilayer ceramic (MLC).

I. INTRODUCTION

M

ANY WIRELESS and mobile communication systems often require a balun, which transforms a balanced transmission signal to an unbalanced transmission signal, and vice versa. As these systems advance toward more compact system architectures, it is required to develop smaller and smaller size baluns with better and better performance over the wide frequency range. To meet these requirements, a large number of balun configurations have been reported in literature for applications in a low-temperature co-fired ceramic (LTCC)-multilayer ceramic (MLC) chip [1]–[7] and microwave integrated circuit (MIC) [8]–[20]. Among them, a planar version of a Marchand balun has been adopted for a long time due to its planar structure and good amplitude and phase balance characteristics over the wide frequency band. The planar Marchand balun consists of two sections, and each section is composed of two coupled quarter-wavelength lines. It may be realized using planar transmission lines such as microstrip lines or striplines. Each microstrip line or stripline may

Manuscript received July 11, 2005; revised October 27, 2005 and December 29, 2005. The authors are with the Computer-Aided Engineering Group, Research and Development Center, Samsung Electro-Mechanics Company Ltd., Suwon 443743, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.871242

be implemented as meander-shaped line [16], [19] or spiralshaped line [1], [4], [5], [17], [20] for the size reduction of balun structure. In order to save more space on the substrate, the resonance method [4]–[6] and the stepped impedance method [3] are proposed. Using these methods, it is possible to shrink the physical length of a quarter-wavelength coupled line in the planar Marchand balun. Though various Marchand-type baluns have been intensively studied for their size reduction, three-line baluns [8]–[10] may have the advantage of using a lesser number of quarter-wavelength lines over Marchand-type baluns composed of four quarter-wavelength lines. However, as in the case of Marchand-type baluns, one or both of the balanced signal lines of these balun, which are the lines connected directly to the balanced ports in the balun, must be shorted to GND at the operating frequency. This may be the disadvantage because such a balun circuit topology demands an extra capacitor to make the balanced signal lines RF shorted to GND when used for applications in an LTCC-MLC chip. Many of the RF integrated circuits (RFICs) for modern wireless and mobile communication systems such as wireless local area network (LAN) and Bluetooth modules require a dc voltage to be applied to a chip balun to drive a power amplifier inside an RFIC through the balanced signal lines. The dc voltage source for such cases cannot be directly applied to the RF shorted port of the balun because it is commonly connected together to the RFIC power pin to drive other devices inside RFIC, and the leakage RF signals from the balun may disrupt the system performance through the power network. Therefore, an RF choke to block the RF signals should be placed adjacent to the balun. Consequently, these three-line baluns generally require the additional capacitor to make the balanced signal lines RF shorted to GND for the balun performance. In this paper, we propose a new three-line balun that may be more compact than Marchand-type baluns and more suitable for applications in an LTCC-MLC chip than conventional three-line baluns. The proposed balun is composed of three coupled quarter-wavelength lines, as in the case of [8]–[10], and each line can be easily implemented as a spiral line or meander line for further size reduction. In addition, any of the balanced signal lines is not shorted to GND. Therefore, the balun presented in this paper may be attractive for modern wireless LAN and Bluetooth modules. The design equations are presented for a given set of balun impedances at unbalanced and balanced ports and verified by the high-frequency circuit simulation results, which also shows this three coupled line balun may be used for compact size applications despite its relatively narrow bandwidth. This paper presents the first application of a design of experiments (DOE) using the high-frequency circuit simulations for the proposed balun to have a maximum bandwidth.

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Fig. 1. General configuration of the equivalent circuit of the proposed threeline balun.

By using a DOE, it is easily identified which design factors are more significant for a bandwidth and how they interact with each other [17]. In other words, the proposed balun can be optimized by a DOE for a maximum bandwidth. As a result of the DOE, the proposed balun is finally optimized into the balun consisting of a pair of coupled quarter-wavelength lines in connection with an uncoupled quarter-wavelength line. To demonstrate the validity of the proposed balun and the feasibility of the optimized design equations, MLC baluns with three different impedances at balanced ports, which operated in the 2.4-GHz industrial–scientific–medical (ISM) band frequency, are designed and fabricated using LTCC technology. Each balun’s unbalanced port impedance versus balanced port impedance is chosen to be 50 : 25 , 50 : 50 , and 50 : 100 , respectively. Spiral-shaped lines are used to shorten the physical length of the quarter-wavelength line. Measured results for the designed MLC baluns show that the proposed balun provides good performance over the wide bandwidth despite its relatively simple structure and easy implementation. II. DERIVATION OF DESIGN EQUATION The balun provides balanced outputs to load termination from an unbalanced input with source impedance and and are difvice versa. In general, the impedance ferent. Thus, it also needs to transform impedance between the source and load impedance. Fig. 1 shows the general configuration of the equivalent circuit for the proposed three-line balun. There are a total of six variables (characteristic impedances of lines and couplings between lines) to fix the characteristics of the circuit. The equations for the circuit in Fig. 1 to operate as a balun can be derived, which show the relationships between variables for a given set of port impedances. When all the lines with the voltages and curare a quarter-wavelength rents defined at ports 1, 2, and 3, the impedance matrix of the circuit in Fig. 1 can be expressed as follows:

Fig. 2. Circuit model of the proposed three-line balun for high-frequency circuit simulation.

where denotes the velocity of TEM-mode wave propagation in the medium surrounding the line, while the Maxwellian cadefined in [22] can be given by pacitance matrix

(4) where ( , and ) denotes electrostatic capacitance per unit length between conductor line and ground ( , and ) denotes electrostatic planes, and capacitance per unit length between conductor lines and . and , the relationship between For the impedance and matrix in [23] can be generalized as the following the matrix equation: (5) where

and

are given by (6)

(7) matrix is then transferred to the The follows:

matrix using (5) as

(1) (2) (3)

(8)

LEE et al.: DESIGN OF NEW THREE-LINE BALUN AND ITS IMPLEMENTATION USING MULTILAYER CONFIGURATION

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Fig. 3. Circuit simulation results of the proposed balun. (a) S -parameters. (b) Phase imbalance characteristics.

where

TABLE I FULL FACTORIAL DOE TABLE

(9) 10) (11) (12) (13) (14) The characteristics of baluns can be expressed in terms of the and the sum of and reflection coefficient [9]. Therefore, using (9)–(14), the equivalent circuit in Fig. 1 can behave like a balun when (15) (16) Therefore, when both (15) and (16) are satisfied, the design equation for optimal balun performance can be represented as follows: (17) or

(18) where is expressed in terms of the TEM-mode wave propdefined in (4) as follows: agation velocity and

(19) Consequently, the equivalent circuit in Fig. 1, which is composed of three coupled quarter-wavelength lines, can have ideal balun properties under conditions satisfying (17) or (18). This can be easily verified using the high-frequency circuit simulation. The circuit model for the simulation is shown in Fig. 2. As

an example, when each unbalanced and balanced port impedand are chosen to be 50 : 50 , , , ances , , , and can be selected to be 100, 100, 26.12, 26.12, 100, and 100 , respectively. These impedance values satisfy (17). The calculated impedances ( , , , , , and ), the electrical length , GHz are used as input and the operating frequency variables of a transmission-line model. As shown in the simulation results in Fig. 3, the proposed balun can behave as a balun when (17) or (18) is satisfied and it may be used for compact size applications despite its relatively narrow bandwidth. It is easily noted that, for a given set of balun impedances at and , the solution to unbalanced and balanced ports, and (17) or (18) is not unique. For example, when are 50 , there exist many combinations of and to satisfy (17) or (18). The high-frequency circuit simulation results using the circuit model in Fig. 2 inform us that a different and or and results in a different choice of and also determines a bandbandwidth. In addition, width, though they are not included in (17) or (18).

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Fig. 4. Full factorial DOE results. (a) Main effect plots. (b) Interaction plots.

III. BALUN OPTIMIZATION FOR A MAXIMUM BANDWIDTH To achieve a wide-band balun performance, it is required to investigate the condition for the proposed balun to have a maximum , , , bandwidth by the choice of the values of , , and within the given ranges of these values. bandwidth dB may be a good indicator of the balun bandwidth [9]. Therefore, needs to be represented defined in (19) and electrical length . as a function of Using the equivalent circuit of Fig. 1 and conditions of (15) and can be given by (16) for optimal balun performance,

Fig. 5. Equivalent circuit of the optimized balun to have a maximum bandwidth.

(20) where

(21)

(22) To calculate to 0.1

bandwidth

Fig. 6. Circuit model of the optimized balun for high-frequency circuit simulation.

dB , equating Equation (23) can then be solved for and ( , ) to give (24) and (25) shown at the bottom of this bandwidth can be represented as follows: page. Therefore,

(23)

bandwidth

(26)

(24) (25)

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Fig. 7. Circuit simulation results of the designed balun. (a) S -parameters. (b) Phase imbalance characteristics.

where is the center frequency of the designed balun. As shown in (23)–(26), it may be very hard to find a maximum bandwidth condition analytically. In this case, the DOE using bandwidth or the high-frequency circuit simulation can be the efficient way. Here, the DOE technique is applied to find out this maximum bandwidth condition with minimal computational overhead. It can provide a thorough understanding of all of the design factors involved in the bandwidth of the proposed balun, and identify which are more significant, which are not significant at all, and how they interact with each other. The DOE is carried out using the high-frequency circuit simulations of the circuit model shown in Fig. 2 with the tool for the DOE, i.e., MINITAB (MINITAB Inc., State College, PA). It and are 50 . As shown in the is assumed that both DOE in Table I, the total number of factors are four, which are , , , and , and they are set to be chosen to be two levels, which are 10 and 100 , respectively. Therefore, a total of 16 circuit simulations are performed for the full factorial and are automatically calcuDOE. The impedances and , lated using (17) for the given impedances of bandwidth dB is used as an respectively. output variable. The main effect plots and interaction plots provided by the full factorial DOE are shown in Fig. 4. The main effect plots , , , and increases, the bandshow that as width increases. Comparing the steepness of slope for each plot, is also the most significant factor to determine the bandis the least. According to width of the proposed balun, and the interaction plots, the best choices for a maximum bandwidth and or and at the same is to maximize time. To maximize and may be the easier choice because it can be easily achieved by shielding lines 1 and 2 from line 3. The equivalent circuit for this case is shown in Fig. 5, and its design equation can then be given by

(27) As a result of the DOE, the proposed balun is finally optimized into the balun consisting of a half-wavelength line, which

Fig. 8. Final 3-D layout of the 50- : 50- balun. The dielectric constant of the ceramic sheet is 5.6 and the dielectric loss tangent is 0.003. All conductors embedded in ceramic are silver. (The dashed line represents the vertical connection between lines 2 and 3 via an external electrode.)

Fig. 9. Fabricated MLC chip balun.

consists of lines 2 and 3, and the quarter-wavelength line (line 1) coupled with line 2. In particular, line 3 acts as a phase inverter and, thus, it makes the phase balance between balanced outputs 180 . In addition, it is discovered that the optimized balun becomes the planar version of the type 4C balun in the inverted

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Fig. 10. Measured and simulated results of the fabricated MLC 50- : 50- balun. (a) S -parameters. (b) Phase imbalance characteristics. (c) Magnitude imbalance characteristics.

baluns [21] when line 2 in the balun is perfectly isolated from GND. and are selected to be input facSimilarly, when and are tors and set to be 10 and 100 in the DOE, and then calculated using (18) for the given impedances of . The full factorial DOE for this case shows the exact main effect plots and interaction plots in Fig. 4 with the exception of and by and . As described to replacing obtain the design equation(27) of the equivalent circuit in Fig. 5, maximum bandwidth can be easily achieved by isolating lines 1 and 3 from line 2. The design equation for this case can be expressed by

(28) IV. DESIGN EXAMPLE To demonstrate the feasibility of design equations, MLC chip baluns operated in the 2.4–2.5-GHz ISM band frequency are designed and fabricated by the use of LTCC technology. The size of tthe designed and fabricated balun

1.25 mm 0.95 mm. Each unbalanced port is 2.0 mm versus balanced port impedance is impedance chosen to be 50 : 25 , 50 : 50 , and 50 : 100 , respectively. Baluns are fabricated by using an MLC with a relative dielectric constant and loss tangent of 5.6 and 0.003, respectively. All conductors embedded in ceramic are silver. For compactness, each line is spiral shaped and implemented on each individual ceramic layer. Also, top and bottom GND layers are incorporated for internal shielding. For a maximum bandwidth, the equivalent circuit in Fig. 5 is used. Consequently, another GND layer is used for isolating lines 1 and 2 from line 3. It is inserted between lines 1 and 3 in this paper. The required impedance values for the design of the MLC balun can be obtained by utilizing the following steps. Firstly, is uniquely determined from (27) at a given unbalanced and . Secondly, the and balanced port impedances may be chosen. It is realizable minimum impedance of generally required that a balun is implemented using the predetermined process capability in the very limited space. Accordis minimized to obtain possibly ingly, the impedance of and because it is the least signiflarge impedances of icant factor to determine the bandwidth of the proposed balun.

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Fig. 11. Measured and simulated results of the fabricated MLC 50- : 25- balun. (a) S -parameters. (b) Phase imbalance characteristics. (c) Magnitude imbalance characteristics.

Finally, a pair of and is chosen among many realand to satisfy (27). By izable pairs of impedances choosing the possibly maximum impedance of , gets and a larger bandwidth can be achieved. toward To check the validity of the calculated impedances, the highfrequency circuit simulation is carried out using the equivalent circuit in Fig. 5. Fig. 6 shows the circuit model for the simula, , , and ), tion. The calculated impedances ( and the operating frequency the electrical length GHz are used as input variables of a transmission-line model. The calculated impedance values can be translated into fabricable physical dimensions by utilizing following steps. Firstly, linewidth, spacing and physical length are basically determined by the area and effective dielectric constant of the LTCC substrate. For simplicity, each quarter-wavelength line is implemented on each individual ceramic layer, as previously stated. Using ADS Momentum (Agilent Technologies, Palo Alto, CA), each line can be efficiently simulated and designed for its electrical length to be 90 . Secondly, the distance between the line in (19). Since has 1 and ground is calculated from already been chosen to have a realizable minimum value, this

distance is the minimum ceramic layer thickness that the fabrication processes allow. Thirdly, the distance between lines 1 and in (19) in the same way. Finally, the distances 2 is given by of lines 2 and 3 from the ground are also determined from and using (19). Once all initial physical dimensions are determined, the electrical characteristics of the complete layout should be examined using the full three-dimensional (3-D) electromagnetic simulation because parasitic couplings may have an effect on the electrical performance of the balun. In general, manual tuning is applied to obtain a balun with some reasonable electrical characteristics. As an example, when each unbalanced and balanced and are chosen to be 50 : 50 , port impedances is 35.4 . , , and are also selected to be 300, 31.6, and 50 , respectively. The circuit simulation results using the calculated values are shown in Fig. 7. As expected, and is 3 dB over the ISM band freeach magnitude of quency and the phase imbalance between balanced outputs is 0 . bandwidth dB is also as wide as 1.82 GHz. Fig. 8 shows the final 3-D layout of the 50- : 50- balun designed by using the full 3-D electromagnetic simulation. The designed linewidth and line spacing of each spiral line are both

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Fig. 12. Measured and simulated results of the fabricated MLC 50- : 100- balun. (a) S -parameters. (b) Phase imbalance characteristics. (c) Magnitude imbalance characteristics.

80 m. Minimum 25- m-thick ceramic sheets and 10- m-thick conductor patterns are used. Fig. 9 presents a photograph of a fabricated MLC chip balun. , , , and are The impedance values of also calculated for 50 : 25 and 50 : 100 baluns. For , the 50- : 25- balun, the designed impedance values of , , and are 25, 600, 24, and 50 , respectively. , For the 50- : 100- balun, the impedance values of , , and are chosen to be 50, 450, 45, and 50 , respectively. V. MEASUREMENT METHODS AND RESULTS Network analyzers with two ports can be used for the characterization of a balun. A measurement technique using them has been explained in detail [20]. However, this measurement usually requires some complicated processes such as repeated two-port measurements until all port measurements are finished, measuring reflection coefficients for loads to terminate idle ports, and calculations for obtaining the final -parameters. After finishing these processes, all balun characteristics are calculated from the final -parameters using the equations of insertion loss, return loss, amplitude imbalance, and phase

imbalance in [20]. As many modern components tend to have more than two ports and differential ports, there has been a strong demand for measuring these devices efficiently. Therefore, many network analyzers have been introduced for the efficient measurements. One of them is Agilent ENA(E5071A) [24]. This has three or four test port measurement capability. It also has the built-in functions to provide differential -parameters without needing to make any external calculations and to mathematically convert measured results from 50- test port impedance to user-defined port impedance. Consequently, it is very suitable for the characterization of baluns. In this paper, all fabricated baluns are measured using this instrument. Both the measured and full-wave electromagnetic simulation results are compared in Fig. 10. Although the overall measured results show good agreement with the simulated ones, minor discrepancy is observed due to the fabrication error. The measured insertion loss is also higher than the simulated result because the conductor surface roughness is not considered in the simulation. In spite of the gap between the measured and simulated results, the proposed balun shows the great performances. According to the measured results, the insertion loss is 0.8 dB, the amplitude imbalance at the balanced output ports is

LEE et al.: DESIGN OF NEW THREE-LINE BALUN AND ITS IMPLEMENTATION USING MULTILAYER CONFIGURATION

within 0.1 dB, and the phase imbalance is less than 5 over the 2.4–2.5-GHz ISM band frequency. Figs. 11 and 12 also show the measured and simulated results for 50- : 25- and 50- : 100- baluns, respectively. For a 50- : 25- balun, the insertion loss is 0.81 dB, the amplitude imbalance at the balanced output ports is within 0.7 dB, and the phase imbalance is less than 7 over the 2.4–2.5-GHz ISM band frequency. For a 50- : 100- balun, the insertion loss is 0.75 dB, the amplitude imbalance at the balanced output ports is within 0.1 dB, and the phase imbalance is less than 4 over the 2.4–2.5-GHz ISM band frequency. VI. CONCLUSION This paper has proposed a new balun that is composed of three coupled quarter-wavelength lines. An equivalent circuit and the design equation of the proposed balun have been presented. The proposed balun is easily optimized for a maximum bandwidth by using the DOE technique. After the optimization, it is transformed into the balun consisting of a pair of coupled quarter-wavelength lines in connection with an uncoupled quarter-wavelength line. Using the design equation of the optimized balun, a design procedure for implementing this threeline balun as a multilayer configuration has been suggested. This design procedure has been verified by fabricating MLC baluns operated in the 2.4–2.5-GHz ISM band frequency. The experimental results have shown that the new balun can be made more compact, providing good performances over the wide frequency range. This balun is highly applicable to many wireless and mobile communication systems. ACKNOWLEDGMENT The authors would like to thank S. J. Park and B. S. Lim, both of the Chip Device Division, Samsung Electro-Mechanics Company, Suwon, Korea, for their technical support in the fabrication of the MLC chip baluns. REFERENCES [1] Y. Fujiki, H. Mandai, and T. Morikawa, “Chip type spiral broadside coupled directional couplers and baluns using low temperature co-fired ceramic,” in Electron. Compon. Technol. Conf., 1999, pp. 105–110. [2] D. W. Lew, J. S. Park, D. Ahn, N. K. Kang, C. S. Yoo, and J. B. Lim, “A design of the ceramic chip balun using the multilayer configuration,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 1, pp. 220–224, Jan. 2001. [3] C. W. Tang, J. W. Sheen, and C. Y. Chang, “Chip-type LTCC-MLC baluns using the stepped impedance method,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2342–2349, Dec. 2001. [4] C. W. Tang and C. Y. Chang, “A semi-lumped balun fabricated by low temperature co-fired ceramic,” in IEEE MTT-S Int. Microw. Symp. Dig., 2002, pp. 2201–2204. [5] ——, “LTCC-MLC chip-type balun realized by LC resonance method,” Electron. Lett., vol. 38, pp. 519–520, 2002. [6] ——, “Using buried capacitor in LTCC-MLC balun,” Electron. Lett., vol. 38, pp. 801–803, 2002. [7] I. Gavela, M. A. Falagan, and H. Fluhr, “A small size LTCC balun for wireless applications,” in 34th Eur. Microw. Conf., 2004, pp. 373–376. [8] C. M. Tsai and K. C. Gupta, “CAD procedures for planar re-entrant type couplers and three-line baluns,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, pp. 1013–1016. [9] C. S. Cho and K. C. Gupta, “A new design procedure for single-layer and two-layer three-line baluns,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2514–2519, Dec. 1998.

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[10] I. Toyoda, M. Hirano, and T. Tokumitsu, “Three-dimensional MMIC and its application: An ultra-wideband miniature balun,” IEICE Trans. Electron., vol. E78-C, pp. 919–924, 1995. [11] K. S. Ang and I. D. Robertson, “Analysis and design of impedancetransforming planar Marchand baluns,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 2, pp. 402–406, Feb. 2001. [12] K. S. Ang, Y. C. Leong, and C. H. Lee, “Multisection impedance-transforming coupled-line baluns,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 2, pp. 536–541, Feb. 2003. [13] B. P. Kumar and G. R. Branner, “Optimized design of unique miniaturized planar baluns for wireless applications,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 3, pp. 134–136, Mar. 2003. [14] K. S. Ang, Y. C. Leong, and C. H. Lee, “Analysis and design of miniaturized lumped-distributed impedance-transforming baluns,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 1009–1017, Mar. 2003. [15] M. Chongcheawchamnan, C. Y. Ng, K. Bandudej, A. Worapishet, and I. D. Robertson, “On miniaturization isolation network of an all-ports matched impedance-transforming Marchand balun,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 7, pp. 281–283, Jul. 2003. [16] Y. J. Ko, J. Y. Park, J. H. Ryu, K. H. Lee, and J. U. Bu, “A miniaturised LTCC multi-layered front-end module for dual band WLAN (802.11a/b/g) applications,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 563–566. [17] D. Staiculescu, N. Bushyager, A. Obatoyinbo, L. J. Martin, and M. M. Tentzeris, “Design and optimization of 3-D compact stripline and microstrip Bluetooth/WLAN balun architectures using the design of experiments technique,” IEEE Trans. Antennas Propag., vol. 53, no. 5, pp. 1805–1812, May 2005. [18] M. C. Tsai, “A new compact wide-band balun,” in IEEE Microw. Millimeter Wave Monolithic Circuits Symp. Dig., 1993, pp. 123–125. [19] K. Nishikawa, I. Toyoda, and T. Tokumitsu, “Compact and broad-band three-dimensional MMIC balun,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 1, pp. 96–98, Jan. 1999. [20] Y. J. Yoon, Y. Lu, R. C. Frye, M. Y. Lau, P. R. Smith, L. Ahlquist, and D. P. Kossives, “Design and characterization of multilayer spiral transmission-line baluns,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 2, pp. 1841–1847, Sep. 1999. [21] R. C. Johnson and H. Jasik, Antenna Engineering Handbook, 2nd ed. New York: McGraw-Hill, 1984, pp. 43.23–43.27. [22] D. W. Kammler, “Calculation of characteristic admittances and coupling coefficients for strip transmission lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-16, no. 11, pp. 925–937, Nov. 1968. [23] D. M. Pozar, Microwave Engineering. New York: Wiley, 1998, pp. 196–199. [24] “Agilent E5070A/E5071A ENA Series RF Network Analyzers User’s Guide,” 2nd ed. Agilent Technol., Palo Alto, CA, 2002.

Byoung Hwa Lee was born in Taejeon, Korea, in 1969. He received the B.Eng. degree from Inha University, Incheon, Korea, in 1993, and the Ph.D. degree from Imperial College, London, U.K., in 1997. In 1997, he joined Samsung Electro-Mechanics Company Ltd., Suwon, Korea, as a Research Engineer involved in microwave passive component design. He is currently a Principal Research Engineer with Samsung Electro-Mechanics Company Ltd. His research interests include design, analysis, and measurement of microwave passive components.

Dong Seok Park was born in Seoul, Korea, in 1967. He received the B.Eng. degree from Yonsei University, Seoul, Korea, in 1993. In 1994, he joined the Samsung Electro-Mechanics Company Ltd., Suwon, Korea, as a Research Engineer involved in magnetic sensor development. Since 2000, he has been involved in microwave passive component development. He is currently a Senior Research Engineer with the Samsung Electro-Mechanics Company Ltd. His research interests include design, analysis, and measurement of microwave passive components.

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Sang Soo Park was born in Seoul, Korea, in 1972. He received the B.S. degree in electrical engineering from the University of Suwon, Suwon, Korea, in 1998, and the M.S. degree in electrical engineering from Chung Ang University, Seoul, Korea, in 2000. Since 2000, he has been with the Samsung ElectroMechanics Company Ltd., Suwon, Korea, as a Research Engineer involved in microwave component design. He is currently an Assistant Research Engineer with the Samsung Electro-Mechanics Company Ltd. His research interests include design, analysis, and measurement of microwave passive components.

Min Cheol Park was born in Kwangju, Korea, in 1973. He received the B.S. and M.S. degrees in electrical engineering from Sungkyunkwan University, Suwon, Korea, in 1998 and 2001, respectively. Since 2001, he has been with the Samsung ElectroMechanics Company Ltd., Suwon, Korea, as a Research Engineer involved in microwave component design. He is currently an Assistant Research Engineer with the Samsung Electro-Mechanics Company Ltd. His research interests include design, analysis, and measurement of microwave passive components.