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Coupled Transmission Lines As Impedance Transformer Downloaded from orbit.dtu.dk on: Sep 25, 2021 Coupled Transmission Lines as Impedance Transformer Jensen, Thomas; Zhurbenko, Vitaliy; Krozer, Viktor; Meincke, Peter Published in: IEEE Transactions on Microwave Theory and Techniques Link to article, DOI: 10.1109/TMTT.2007.909617 Publication date: 2007 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA): Jensen, T., Zhurbenko, V., Krozer, V., & Meincke, P. (2007). Coupled Transmission Lines as Impedance Transformer. IEEE Transactions on Microwave Theory and Techniques, 55(12), 2957-2965. https://doi.org/10.1109/TMTT.2007.909617 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 1 Coupled Transmission Lines as Impedance Transformer Thomas Jensen, Vitaliy Zhurbenko, Viktor Krozer, Peter Meincke Technical University of Denmark, Ørsted•DTU, ElectroScience, Ørsteds Plads, Building 348, 2800 Kgs. Lyngby, Denmark, Phone:+45-45253861, Fax: +45-45931634, E-mail: [email protected] Abstract— A theoretical investigation of the use of a coupled line transformer. line section as an impedance transformer is presented. It is shown This paper focuses on developing the necessary formulas for how to properly select the terminations of the coupled line applying coupled line sections in matching applications, as structures for effective matching of real and complex loads in well as the appropriate basic analysis of the coupled line both a narrow and a wide frequency range. The corresponding circuit configurations and the design procedures are proposed. section. Establishing a design framework will enable a Synthesis relations are derived and provided for efficient widespread use of coupled line structures as novel impedance matching circuit construction. Design examples are given to matching elements, in addition to the standard lines and demonstrate the flexibility and limitations of the design methods lumped elements. and to show their validity for practical applications. Wideband In the lower GHz range the loading of the through and matching performance with relative bandwidth beyond 100% and coupled ports can be done with lumped elements which allows return loss RL > 20 dB is demonstrated both theoretically and experimentally. Good agreement is achieved between the for easy matching of both real and imaginary impedance measured and predicted performance of the coupled line values. At higher frequencies it is not possible to use lumped transformer section. elements, but the difference between the even and odd mode Index Terms—Coupled transmission lines, directional coupler, impedances is a parameter which makes it possible to turn a impedance matching, impedance matrix, microstrip lines, strip mixed real and imaginary control load at the through port into lines. a purely imaginary one, which can be implemented with a transmission line stub. I. INTRODUCTION Equations for matching purposes, which are based on n recent years, coupled transmission lines have been controllable parameters of coupled transmission line sections, suggested as a matching element due to greater flexibility I are presented for backward-wave couplers including and compactness in comparison to quarter wavelength microstrip and stripline transmission line couplers. transmission lines [1-3]. It has been demonstrated that The coupling required for a given application often becomes matching real and complex loads with coupled lines leads to too tight for a practical implementation. Therefore an more compact realizations and could therefore become investigation into the range of load values that can realistically important at millimeter-wave frequencies for on-chip or Low be matched with the coupled line section has been carried out. Temperature Cofired Ceramics (LTCC) matching solutions. Finally loading of the through and coupled port with an Another area where coupled line structures are useful is interconnecting transmission line is considered with the matching of antenna array structures, as successfully purpose to achieve a wide operating frequency range. In [5] a demonstrated in [2]. broadband impedance transformer based on coupled The quarter-wave transformer is simple and easy to use, but transmission lines is presented. The synthesis procedure for it has no flexibility beyond the ability to provide a perfect this circuit is explained. By using this procedure it is possible match at the center frequency for a real-valued load, although to shape the frequency response by placing transmission a complex load of course can be matched by increasing the minima in the spectrum. length of the quarter-wave transformer. The coupled line section provides a number of variables which can be utilized II. THE USE OF A COUPLED LINE SECTION AS AN IMPEDANCE for matching purposes. These variables are the even and odd TRANSFORMER mode impedances and loading of the through and coupled Fig. 1 shows the general coupled lines configuration. There ports. This loading can be done in form of a feedback is no established terminology for use of the coupled line connection which provides additional zeros for broadband section as an impedance transformer, in this paper it is found matching. useful to use the port names from directional coupler These variables can be chosen to provide a perfect match or terminology in the discussion of the circuit, but the numeration any desired value of the reflection coefficient at the operating used corresponds to filter design with coupled line sections frequency. The bandwidth of the coupled line transformer can because the theory is developed from that point of view. be further increased in case of mismatch. In addition, as will be shown, it is also possible to match a complex load. This is a generalization of matching with a quarter-wave transmission 2 Coupled Lines operating frequency in terms of the difference between the even and odd mode impedance. This condition is similar to the well-known relation Z = Z Z , for a quarter-wave Z0e, Z0o, θ 0 g L coupled isolated 2 3 transmission line transformer, when the characteristic impedance is exchanged with the difference between the even input through and odd mode impedances of the coupled lines. 1 4 It is also possible to retain the reflection coefficient in the formula and use it as a parameter, yielding Fig. 1. Coupled transmission lines. The port names are in agreement with directional coupler terminology for a backward-wave coupler, while the 1+ ΓIN numeration is the same as used in filter design with coupled line sections. Z − Z = 2 Z Z . (7) 0e 0o g L 1− Γ IN The impedance matrix for the 4-port open-circuited coupled The parameter Z- can be chosen within reasonable limits. A line section in Fig. 1, where transverse electromagnetic (TEM) large value of Z- implies a tight coupling, where the coupling wave propagation and symmetric transmission lines are Z − Z coefficient is given by C = 0e 0o . Tight coupling implies assumed, can be expressed in terms of the even and odd mode Z0e + Z0o impedances, Z0e and Z0o, and the electrical length, θ [4]: a large value of C and requires a large difference between the Z = Z = Z = Z = − j 2(Z + Z )cotθ , (1a) 11 22 33 44 0e 0o even and odd mode impedances. A large value of Z- necessitates a very narrow gap between edge-coupled Z = Z = Z = Z = − j 2(Z − Z )cotθ , (1b) 12 21 34 43 0e 0o transmission lines or a large ground plane spacing, e.g. in Z13 = Z31 = Z24 = Z42 = − j 2(Z0e − Z0o )cscθ , (1c) stripline technology. From (7) it can be seen that transforming a large-valued = = = = − ( + ) θ , (1d) Z14 Z41 Z23 Z32 j 2 Z0e Z0o csc load requires a tighter coupling than a small-valued load, and even though a non-zero reflection coefficient can increase the j = −1 . bandwidth it also requires tighter coupling. The input impedance of the coupled line section with the The quarter-wave transformer has the same length as the coupled and through port open-circuited and the isolated port coupled line impedance transformer for a given application terminated in the load impedance ZL, can be calculated from and requires only one transmission line, so the only obvious the current and voltage at the input port advantage of the latter is that it constitutes a perfect DC block. V Z Z + Z However, a load attached to the through port opens for Z = 1 = 11 L , (2) IN improvement of the transformer characteristics for the coupled I1 ZL + Z22 line section as will be shown in the next sections. where Z = Z11Z22 − Z21Z12 . In the following derivations only the center frequency is A. Loading of the through port for extended matching capabilities. considered and hence, θ = π 2 , cotθ = 0 , and cscθ = 1. Using the input port as input and with the load to be Furthermore the notation Z = Z + Z and Z = Z − Z is + 0e 0o − 0e 0o transformed attached to the isolated port leaves two available used. Then (2) simplifies to ports (the through and coupled port) that can be exploited to 2 2 2 − Z21Z12 − (− j 2) Z− Z− improve the matching capabilities. The loading of the through Z IN = = = . (3) Z L Z L 4Z L port will be considered in this section.
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