An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines

Transcription

1 An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines 123 An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines Ravee Phromloungsri 1 and Mitchai Chongcheawchamnan 2, Non-members ABSTRACT A method using lumped inductors to compensate unequal even and odd mode phase velocities in microstrip parallel- coupled lines is presented. The optimum inductor value and the electrical length of the compensated coupled lines are given in closed-form expressions. Improvement of 7 db on the directivity of microstrip coupled lines over the uncompensated coupled lines at operating frequency f0 is obtained. To demonstrate the technique s applicability, the compensated coupled lines are used to improve the amplitude/phase balance in a Marchand balun as well as to suppress the spurious response in parallelcoupled filter. The experimental results of a compensated microstrip Marchand balun operating at 900 MHz and parallel-coupled microstrip filter operating at 1.8 GHz are presented. Keywords: Parallel-coupled lines, microstrip, coupled line resonator, Marchand balun, parallel-coupled filter 1. INTRODUCTION Parallel-coupled lines are extensively used in microwave and millimeter-wave circuits for filters, impedance matching networks, directional couplers, baluns and combiners [1],[2], since they are easily incorporated in hybrid and monolithic microwave integrated circuits [3] which are commonly designed with microstrip technology. However poor directivity [4] resulting from the inequality of even- and oddmode wave phase velocities [5],[6] can be obtained from parallel-coupled microstrip lines. The unequal phase velocities in parallel-coupled microstrip lines not only cause poor directivity in couplers but also significantly deteriorate the performance of other component based circuits. For example, it is well known that parallel-coupled microstripline filters does have asymmetrical passband response and spurious responses at harmonics of the filter passband [7]. Recently [8], it was reported that degra- Manuscript received on July 23, 2006 ; revised on November 1, The author is with Department of Telecommunication Engineering, ravee@mut.ac.th 1,2 The authors are with Research Center of Electromagnetic- Wave Applications (RCEWs), Mahanakorn University of Technology (MUT), Thailand, mitchai@ieee.org dation in amplitude/phase balance of the microstrip Marchand balun partly stems from the unequal phase velocities. In the past decades, the notorious problem of unequal phase velocities in parallel-coupled microstrip lines has been tackled by several previously proposed techniques. The techniques can be classified into two main categories,which are distributed and lumped compensation approaches. The methodology based on the distributed approach is to modify either the parallel-coupled line structure [9], [10], dielectric layer or ground plane, such that the phase velocities of both modes are equalized. The main disadvantage of this approach is lack of closed-form design equations, meaning the design task relies heavily on the electromagnetic simulation stage which in turn consumes much effort and computing time. The lumped compensation approach [1],[11] involves connecting external reactive components between or shunted with the parallel-coupled lines ports. Based on the reactive types, this approach can be categorized into two techniques, which are capacitive [1],[9] and inductive compensation techniques [9],[11]. The size of the lumped-compensated parallel-coupled lines is about the same as the uncompensated coupled lines. Another distinct advantage of the lumped compensation technique is its simple design procedure because the closed-form design equations can be derived. The disadvantages of the technique are the lumped components parasitics and difficulty in layout [1],[9]. In this paper, we present a simple effective inductive compensation technique to improve the directivity of the parallel-coupled microstrip lines by connecting small inductors in series with the coupled lines ports. The paper is organized as follows: Section 2 presents the proposed singly-inductive compensated parallelcoupled lines. Applications of the inductively compensated coupled-line circuit to the microstrip Marchand balun and parallel-coupled microstrip filter will be illustrated in Section 3. The paper is finally concluded in Section THEORY Due to the different phase velocities associated with the even- and odd-mode wave propagation, parallelcoupled microstrip lines cannot easily achieve directivity values better than 12 db [3]. Here, we propose an inductive compensation technique to equal-

2 124 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007 ize phase velocities in coupled microstrip lines, which in turn leads to a high-isolation and hence highdirectivity coupled microstrip lines Singly-Inductive Compensated Parallel- Coupled Lines Fig. 1 shows the schematic of parallel-coupled lines using a single inductor for compensation. These coupled-lines has characteristic impedance of Z 0 and Fig.1: Schematic of the singly-compensated parallelcoupled lines. coupling coefficient of k which are related to the evenand odd-mode characteristic impedances (Z oe and Z oo ) [3]. After some mathematical manipulation, we obtain the optimum value of L s as shown [12],[13]:- L s = 1 { } Zoe sinh θ e Z oo sinh θ o Z o Im (1) 4πf 0 Z oe sinh θ o Z oo sinh θ e Z o where = cosh θ o cosh θ e, the validity of the singly inductive compensation technique for parallelcoupled line design is proven by comparing their directivity and isolation performances of the compensated coupled lines with those of the uncompensated one [11, 12, 13, 14] Marchand Balun The planar Marchand balun is basically formed by two parallel-coupled line sections connected in backto-back configuration. Each coupled-line section has coupling coefficient of k, characteristic impedance of Z 0, and electrical length of π/2. This conventional (uncompensated) Marchand balun can transform unbalanced port impedance (Z u ) to balanced port impedance (Z b ) if k is selected as follows [8]:- 1 k = 2Z b Z u + 1 (2) It has been reported that the Marchand balun exhibits poor amplitude/phase balance when the circuit is realized in inhomogeneous media such as microstrip. The imbalance partly comes from the poor directivity of the parallel-coupled microstrip lines [8], hence an approach to improve the directivity of the coupled lines can enhance the amplitude/phase balance of the Marchand balun. For simplicity s sake, the singly-compensated technique is applied to the Marchand balun. Fig. 3 shows the efficiency of proposed technique based on the singly-compensated technique compare with the uncompensated technique. The optimum value of L s can be calculated from (1). From Fig. 2, the Fig.2: Schematic of the singly-compensated coupled line based Marchand balun. driving-point impedance at unbalanced port (port 1) at f 0, denoted by Z mb (f 0 ), is calculated from the Z- parameters of the singly-compensated coupled line. For our analysis, the electrical length of each compensated coupled-line section (θ f ) is obtained by applying the following condition:- Hence, Re[Z mb (f 0 )] Z u (3) θ f (L s ) = cot 1 { 4πf0 L s + Z oo cot(π/2)θ Z oe + Z oo } (4) Designing the proposed balun with L s and θ f calculated from (1) and (4), the real part of Z mb (f 0 ) is nearly equal to Z u while the imaginary part of Z mb (f 0 ) is inductive. This inductive part must be cancelled out to make the compensated Marchand balun well matched at the unbalanced port by a series capacitor :- C s (f 0 ) = 1/ω 0 IM{Z mb (f 0 )} (5) Fig.3: Analysis results of amplitude and phase imbalance of the Ω compensated Marchand balun with various values of the compensating inductors.

3 An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines 125 The design procedure of the balun based on the singly-compensated coupled lines starts by determining k from (2). With the known substrate and uncompensated coupled-line parameters, all electrical parameters (Z oo, Z oe, θ o, θ e, ε effe, ε effo ) can be calculated. Subsequently, L s, θ f and C s are calculated from (1), (4) and (5). With this design procedure, a balun design with good amplitude/phase balance and good return loss at unbalanced port across a large bandwidth can be obtained. The sensitivity to L s of the amplitude/phase imbalance is investigated for the Ω Marchand balun. Based on the analysis results, variations of amplitude and phase balance resulting from different compensated inductors are shown in Fig. 3 and, respectively. The amplitude and phase balance of the singly-compensated Marchand balun is excellent across the operation bandwidth. The proposed technique is rather practical for the balun since the balance performance is not very sensitive to the optimum value of the compensating inductor Parallel-Coupled Filter In an inhomogeneous media such as microstrip, each coupled-line resonator in the parallel-coupled filter cooperatively contributes a spurious response at twice the center frequency (2f 0 ) and beyond. Since the poor directivity is an outcome of phase-velocity inequality, so the inductively compensated coupledline resonator with high directivity can suppress the spurious response of the filter effectively [1],[7]. The resonators based on uncompensated and singlycompensated coupled lines are depicted in Fig. 4, and. The optimum values of compensating inductors L s in Fig. 4 can be determined from (1). To preserve the original filter response, the transmission response (S 21 ) of the compensated resonator would be preserved or minimal change from that of the uncompensated resonator. Hence this condition will be applied for extracting the electrical lengths of each compensated coupler. For tight coupling (k > -13 db), the electrical length of singly inductive-compensated coupled-line resonator (θ s ) can be determined by:- θ f (L s ) = cot 1 { 4πf 0 L s Z oo cot( π 2 Θ)/2Z oe and for loose coupling (-23 db > k < -13 db) } (6) { θ f (L s ) = cot 1 4πf 0 L s Z oe + Z oo cot( π 2 Θ)/2Z oo (7) To explicitly show the spurious-suppression performances of singly-compensated coupled-line resonators, a resonator based on the proposed technique was designed and its frequency response is compared with the result of the uncompensated parallelcoupled resonator. We start with the uncompensated coupled-line resonator, which is designed from 8.6 db } parallel-coupled lines operating at 1.0 GHz on RF microwave substrate from Taconic. Fig.4: Schematics of the uncompensated, and the singly-compensated coupled-line resonators. Fig.5: Frequency responses of the singly- ( ) compensated coupled lines resonator and the uncompensated case ( The required values of Z oe, Z oo are Ω and Ω. Then, the values of L s and θ s for singlycompensated coupled-line resonators were calculated from (1) and (6) and found to be 2.13 nh and 0.46π respectively. The magnitude of S 21 of the uncompensated coupled-line resonator is around -7 db at the first harmonic of the desired passband response (2f 0 ) as shown in Fig.5. Comparing the responses obtained from the singly-compensated resonators with that obtained from the uncompensated resonator, the magnitudes of S 21 around f 0 are nearly equal while the responses around 2f 0 and beyond are distinctly different. The suppression performances obtained from the compensated coupled-line resonators at odd and even harmonics of f0 are considerably better than the uncompensated coupled-line resonator. For the singly-compensated case, the degree of suppression at 2f 0, 3f 0, and 4f 0 are approximately 14, 7, and 7 db, respectively. To apply the compensated coupledline resonators to bandpass filter design, the uncompensated coupled-line resonators are initially synthesized. Then each coupled-line resonator is replaced with the singly-compensated coupled-line resonator. All electrical parameters of the compensated coupledline resonators are calculated from (1), (6) and (7).

4 126 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February DESIGN AND EXPERIMENTAL RE- SULT S 21 S 3. 1 Marchand Balun To prove the validity of the technique for the Marchand balun, 900 MHz microstrip Ω impedance transformation Marchand baluns based on the uncompensated and the singly-compensated coupled lines were designed on FR4 substrate (ε r = 4.55, h = 1.6 mm, tan δ = 0.02). The Z oo and Z oe of the coupled lines are Ω and Ω. Calculated from (1) and (4), L s, and θ f are 1.95 nh, 0.42π, and C s is 11.5 pf, respectively. With these parameters, the physical dimensions of two baluns were synthesized and shown in Table I. Fig. 6 shows the measured results of the uncompensated and proposed Marchand balun. The conventional Marchand balun achieved 3.5 db transmission coefficient and less than 13 db return loss at unbalanced port. The amplitude balance is good only at 900 MHz, while at other frequencies, especially in high- frequency band edge, it is very poor. Fig. 6 shows the measured results of the singly-compensated Marchand balun transmission coefficient at 900 MHz is around 3.7 db and the return loss of the unbalanced port is better than 25 db. The amplitude balance of the proposed technique is excellent, with ±0.1dB tracking from 700 MHz to 1.1 GHz as shown in Fig. 7. Comparing the measured 10 db return loss bandwidth, the bandwidth of the proposed technique is 170 MHz larger than the uncompensated balun. The comparison of the measured output ports phase balance Frequency (GHz) Fig.7: Measured amplitude and imbalance of the uncompensated( )and the phase singlycompensated ( ) Marchand balun. Fig.8: PCB photographs of the fabricated uncompensated and singly- compensated Marchand balun. obtained from the uncompensated balun and the singly-compensated balun, the uncompensated Marchand balun s phase balance (dotted line) is within ±10 over 10% operating bandwidth, while the singly-compensated Marchand balun s phase imbalance (solid line) is less than ±1 o degrees over 40% bandwidth from 720 MHz-1.08 GHz. PCB photographs of the uncompensated and the proposed singly-compensated Marchand balun are shown in Fig. 8. Table 1: Parameters of The Baluns at 0.9 GHz Balun Z oe Z oo C s L s θ f (Ω) (Ω) (pf) (nh) (rad) Uncompensated π Singly inductive π Fig.6: Measured insertion and return losses of the uncompensated ( ) and singlycompensated ( ) Marchand balun Parallel-Coupled Filter The effectiveness of the singly-inductive compensated parallel-coupled filter is proven with two filter designs. These two filters are an uncompensated and singly-compensated design as shown in Fig. 9. The filter prototype is a third-order Chebyshev bandpass filter designed at center frequency (f 0 ) of 1.8 GHz, fractional

5 An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines 127 Fig.9: Schematics of the uncompensated and the singly- compensated parallel-coupled filters. Fig.11: PCB Photographs of the conventional, the singly-compensated parallel-coupled filters. Fig.10: Comparisons of EM simulated and measured results of the singly- ( ) compensated compared with the uncompensated case ( ) parallel coupled filters. bandwidth ( ) of 10%, and passband ripple of 0.1 db. The circuits were designed and fabricated on the RF substrate from Taconic. With the design procedure mentioned in Section III, the parameters of two filters were derived and are shown in Table II. The physical dimensions of all two filters are synthesized from the parameters in Section 2. In our design, the compensation inductor was implemented by shorted stub. The measurement was performed with an HP8720C Vector Network Analyzer test system calibrated from 0.1 to 10 GHz with an SOLT technique. HPVEE6.0 T M software was used to collect the experimental data via GPIB card. Sonnet-Lite T M and MatlabR were used for simulation, data processing, and display. The EM simulated results of the microstrip filter designed with the uncompensated and compensated coupled-line resonators are shown in Fig. 10, while the measured results are shown in Fig. 10. The measured spurious response obtained from the uncompensated parallel-coupled filter (dash line) is around -13 db at 2f 0. More than 39 and 42 db suppression of spurious response at 2f 0 and 3f 0 are obtained from the singlycompensated parallel-coupled filter. Over the operating bandwidth, insertion losses of singly-compensated parallel-coupled filters are less than 2.0 db, while input and output return losses are better than 12 db. Fig. 11, and show the PCB photographs of two filters designed with the uncompensated, and singly-compensated coupled-line section. The total size of the singly-compensated parallel-coupled filters is mm2, which is about 85.4% of the uncompensated parallel-coupled filter s size. 4. CONCLUSIONS We have presented a new method to achieve high directivity parallel-coupled lines in inhomogeneous media and demonstrated the technique applicability to microwave applications. The compensation inductor connected in series with coupled port of the coupled-line structure to equalize phase velocity, leading to a high directivity coupled-line design. The inductive compensation technique is demonstrated in two microwave coupled-line based circuits, which are the planar Marchand balun and parallel-coupled filter. Design procedures for these circuits with the proposed compensation technique have been provided. More important, the closed-form expressions for determining the compensation inductor values and coupled-line parameters are given to facilitate the design task considerably. The authors believed that the technique is highly applicable and suitable for modern wireless communication systems.

6 128 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February ACKNOWLEDGEMENT The authors are grateful to TACONIC Inc. for supplying Taconic RF microwave substrate for this research. The authors also thank to unanimous reviewers for their valuable comments and suggestions. References [1] M. Dydyk, Accurate design of microstrip directional couplers with capacitive compensation, in 1990 IEEE MTT-S Int. Microwave Symp. Dig., May 1990, pp [2] G. L. Matthaei, L. Yoling, and E.M.T. Jones, Microwave Impedance-Matching Network and Coupling Structures, New York: McGraw-Hill, pp , [3] T. Edward, Foundation for Microstrip Circuit Design, West Sussex, England: John Wiley Son, pp , [4] S. L. March, Phase velocity compensation in parallel-coupled microstrip, in 1982 IEEE MTT-S Int. Microwave Symp. Dig., June, 1982, pp [5] A. Riddle, High performance parallel coupled microstrip filter, in 1988 IEEE MTT-S Int. Microwave Symp. Dig., May 1988, pp [6] A. Podell, A high directivity microstrip coupled lines technique, in 1970 IEEE MTT-S Int. Microwave Symp. Dig., May 1970, pp [7] I. J. Bahl, Capacitively compensated performance parallel coupled microstrip filter, in 1989 IEEE MTT-S Int. Microwave Symp. Dig., June 1989, pp [8] C. Y. Ng, M. Chongcheawchamnan, and I. D. Robertson, Analysis and design of a highperformanceplanar marchand balun, in 2002 IEEE MTT-S Int. Microwave Symp. Dig., June 2002, pp [9] M. Dydyk, Microstrip directional couplers with ideal performance via single-element compensation, IEEE Trans. Microwave Theory Tech., vol. 47, no.6,pp , June [10] S. Uysal and H. Aghvami, Synthesis, design, and construction of ultra- wide-band nonuniform quadrature directional couplers in inhomogeneous media, IEEE Trans. Microwave Theory Tech., vol. 37, no.6, pp , June [11] R. Phromloungsri, S. Patisang, K. Srisathit, and M. Chongcheawchamnan, A harmonicsuppression microwave bandpass filter based on an inductively compensated microstrip coupler, in 2005 Asia Pacific Microwave Con., Dec. 2005, pp [12] R. Phromloungsri, K. Srisathit, M. Chongchaewchamnan, and I. D. Robertson, Novel Technique for Performance Improvement in Impedance Transforming Planar Marchand Baluns, in 2005 European Microwave Conf., the 35th EuMC2005, Paris, France, Oct [13] R. Phromloungsri, and M. Chongcheawchamnan, A high directivity design using an inductive compensation technique, in 2005 Asia Pacific Microwave Con., Dec. 2005, pp [14] R. Phromloungsri, Chongcheawchamnan, and I. D. Robertson, Inductively compensated parallel-coupled microstrip lines and their applications, in 2006 IEEE Trans. Microwave Theory Tech., vol. 54, no.9, pp , Sept Table 2: Parameters of The Filter 1.8 GHz BPF Section Z oe Z oo L s θ f (Ω) (Ω) (pf) (nh) (rad) Uncompensated 1, π 2, π Singly- 1, π compensated 2, π Ravee Phromloungsri was born in Khon Kaen, Thailand. He received the B.Sc (Applied Physics in Solid State Electronics) from King Mongkut Institute of Technology, Ladkrabang (KMITL) in 1992, M.Eng. and D.Eng in Electrical Engineering (Telecommunication) from Mahanakorn University of Technology (MUT) in 2000 and 2006, respectively. Since 1992 he joined MUT as a lecturer in department of telecommunication engineering. His research and teaching interests include microwave passive/active and radio frequency circuits design. He is a member of Research Center of Electromagnetic Waves Applications (RCEWs). and power distribution systems. Mitchai Chongcheawchamnan (M 96) was born in Trang, Thailand. He received the B. Eng. (Telecommunication Engineering) from KMITL in 1992, the M.Sc degree in Communication and Signal Processing from Imperial College, University of London, UK in 1995 and the Ph.D. degree in Electrical Engineering from University of Surrey, Surrey, UK in He is currently a Director of Research Center of Electromagnetic- Wave Applications and Assistant Professor with the Department of Telecommunication Engineering, Mahankorn University of Technology. His research and teaching interests include RF and microwave passive and active circuits. He is a member of IEEE and IET.