Defected-ground coupled microstrip lines and its application in wideband baluns M.A. Salah-Eddin and A.M.E. Safwat Abstract: Defected-ground coupled lines (DCL) is introduced. It consists of edge coupled microstrip lines with a defected ground. The equivalent circuit model, which is based on separating the two modes of the coupled lines into the common and differential modes, is also developed. The model is validated by comparing the results of ten conventional coupled-line circuits using DCL with EM simulations and excellent agreement was achieved (error is less than or equal to 1.5%). In DCL, the propagation characteristics of the common and differential modes are controlled separately. This permits the design of novel wideband baluns that have a reduced area and a superior perform- ance compared with the multisection quarter wavelength coupled-line baluns. Design guidelines of the proposed baluns are detailed, and single-section and three-section DCL-baluns are implemented. The single-section DCL total length is 0.16l, it provides 10% increase in fractional bandwidth, and it occupies 60% of the area when compared with the five-section quarter wavelength balun bandwidth and area, respectively. The single-section and three-section baluns have a fractional bandwidth of 40 and 70%, a maximum amplitude balance of 0.5 dB (for both) and a maximum phase balance of 108 and 38, respectively. Measurements, circuit and EM simulations of one conventional coupled-line circuit with DCL and the two baluns are in excellent agreement. 1 Introduction Defected ground structure (DGS) emerged from photonic bandgap (PBG) in the early 1990s. The later, which consists of a lattice of a certain unit cell etched in the ground plane of microwave circuits, was originally introduced in the optical fields but during the last decade it was adopted in the micro- wave field. In contrast to PBG, DGS represents a single unit cell. It may have different shapes, which are etched on the ground plane of microstrip lines or coplanar waveguides [1–4]. DGS shows a bandstop behaviour. Therefore it is simply represented by a parallel R, L and C equivalent circuit [1]. This behaviour has opened the door for many applications in microwave/millimetre-wave devices (phase noise reduction in oscillators, suppressing harmonics in bias lines, filtering applications and so on.) [5–7]. In this paper, the dumbbell-shaped defect is introduced beneath the edge coupled microstrip lines, as shown in Fig. 1a, creating a defected-ground coupled lines, DCL. Owing to the field configurations of both the common and differential modes, shown in Fig. 1b, the dumbbell defect affects mainly the common mode while leaving the differ- ential mode almost unperturbed. This allows the separate control of the behaviour of both modes. Based on this argu- ment, the equivalent circuit model of the DCL is developed, as shown in Fig. 2. Benefiting from the advantages of the DCL, two wideband baluns have been implemented. This paper is organised as follows. In Section 2, a trans- mission matrix in terms of the differential/common modes is derived for the coupled lines. Based upon it, the con- ditions of a wideband balun are determined. The DCL balun is introduced in this section as well. Section 3 presents the DCL, its equivalent circuit model and the verification of the model using ten conventional two-port coupled line cir- cuits. The DCL balun is detailed in Section 4, which includes the design criteria, and the implementation of single-section and three-section baluns. All theoretical pre- dictions are verified experimentally. 2 Theory 2.1 Coupled line differential-common modes To construct the z-parameters of the coupled lines, the ABCD matrix, shown in (1), is first derived in terms of the even and odd modes V 1,4 o I 1,4 o V 1,4 e I 1,4 e 2 6 6 6 4 3 7 7 7 5 ¼ cos u o jZ c,o sin u o 0 0 j sin u o Z c,o cos u o 0 0 0 0 cos u e jZ c,e sin u e 0 0 j sin u e Z c,e cos u e 2 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 5  V 2,3 o I 2,3 o V 2,3 e I 2,3 e 2 6 6 6 4 3 7 7 7 5 (1) where V is the voltage, I is the current, Z c is the characteristic impedance, u is the electrical length, the subscripts o, e cor- respond to the odd and even mode, respectively, and the superscript 1, 2, 3, 4 correspond to the physical port number as shown in Fig. 3. Since the relation between the external nodes of the coupled lines and the even/odd # The Institution of Engineering and Technology 2007 doi:10.1049/iet-map:20070018 Paper first received 26th January and in revised form 10th May 2007 M.A. Salah-Eddin is with the SySDSoft, PO Box 38, Giza 12211, Egypt A.M.E. Safwat is with the Electronics and Communication Engineering Department, Faculty of Engineering, Ain Shams University, 1 Elsarayat St, Abbassia 11517, Cairo, Egypt E-mail: matef99@yahoo.com IET Microw. Antennas Propag., 2007, 1, (4), pp. 893–899 893