COMPACT DIRECTIONAL COUPLERS USING COMBINATION OF MICROSTRIP AND SLOT LINES

Context. Transition of modern electronics to higher frequencies is directly related with an extremely important problem of miniaturization of microwave integrated circuits. Conventional planar structures such as microstrip directional couplers have the feature – their linear dimensions are defined by the wavelength in the transmission lines, so the use of such structures for miniaturization of microwave integrated circuits becomes problematic. Objective.  Using 3D-structures on combinations of transmission lines to study frequency properties of two possible implementations of quarter-wave directional couplers based on a combination of microstrip and slot transmission lines. Obtaining simple analytical expressions for calculating the electrophysical parameters of these directional couplers and confirm their properties by rigorous electrodynamic calculation. Methods. An even-odd mode decomposition technique and the scattering matrix theory were used to derive simple analytical formulas for calculating impedances of transmission line segments that define the topology of couplers considered. Results. Electrodynamic modeling of proposed couplers with dispersion and losses in the lines showed that the proposed constructions have better frequency characteristics in comparison with traditional three-branch microstrip directional couplers. It is also shown that the considered designs of couplers have great potential in the selection of the desired electrical characteristics of devices. Conclusions. The presented compact couplers can find a broad range of applications in mobile communication systems for decoupling of channels, division of power and frequency conversion. The method of transition from planar to three-dimensional structures used in the development of directional couplers on combinations of transmission lines permits not only to create compact devices with desired characteristics but also paves the way for significant decrease in the size and costs of the broad range of electronic equipment utilizing such couplers.


INTRODUCTION
Microwaves and millimeter-waves are rapidly finding new applications. These include modern mobile communication systems where the problem of miniaturization is of crucial importance. An important part of many microwave circuits are directional couplers on the base of microstrip lines which are used not only as decoupling devices with the function of bridges but also as circuit elements for directional diversion of a certain part of the power from the main line. For consistent mathematical description of such couplers, it is convenient to apply an even-odd mode decomposition technique using symmetry properties of the circuit [1].
It is well known that increasing the number of branches in the coupler leads to better coupler parameters in the frequency band. Moreover, if the condition of equal power division is set which corresponds to the hybrid coupler it is necessary to increase the impedance of end branches to ensure the matching requirements. This fact imposes technological limitations in the implementation of strip structures on substrates with 10 ≈ ε r and therefore in practice two-branch couplers are the most widely used. However if an unequal power division is used instead one can avoid most of the above-mentioned technological limitations as shown in [2]. For the codirectional coupler the power division ratio between operating ports 3 and 4 is defined as Then for a two-branch coupler ( Fig. 1) the ratios for determining the impedances of branches will have the form 1 ; Here Z 0 is the input impedance. For a three-branch coupler (Fig. 2) one can implement different relations between the impedances.
-option 2: It should be noted that relations (3) or (4) are not unique. In these formulas, only Z 1 parameter is uniquely determined, and one of the other two parameters of Z 2 or Z 3 (which are related to each other by a certain ratio) can be selected in accordance with technological or other limitations. This means that, for example, the formula for Z 3 in (3) is obtained by choosing Z 2 =Z 0 /√2, and in (4), the expression for Z 3 is obtained by choosing Z 2 = Z 0 . With a different choice of Z 2 expressions for Z 3 will be different.
In the case of a four-branch coupler several different relations between the characteristic impedances may also be realized [2]. Fig. 3 shows the frequency dependence of the scattering parameters of two-and four-branch 3 dB lossless directional couplers (quadrature hybrids) in the frequency range  It can be seen from Fig. 3, when the number of branches is increased the operating bandwidth of the coupler is expanded but the longitudinal dimensions of the device are increased significantly in this case.

PROBLEM STATEMENT
As mentioned above, the main disadvantages of traditional microstrip couplers are large size and technological limitations when using substrates with 10 ≈ ε r . Table 1 shows the parameters of traditional 3and 4-branch microstrip couplers, which is nontechnological (Z 1 for 3-branch and Z 1 and Z 2 for 4branch) and at the same time, the longitudinal dimensions of these couplers are large enough (λ 2 /2 for 3-branch and 3λ 2 /4 for 4-branch couplers). In this regard the task of the primary importance is the development of a new structures of small directional couplers with sufficiently wide bandwidth and without technological restrictions in the manufacturing process on dielectric substrates with a large value of r ε . This problem can be successfully solved by using the idea of combining different types of transmission lines.

REVIEW OF THE LITERATURE
In the literature at the miniaturization of microwave devices focus is on the development of new element base based on the traditional planar structures. So in [3] for the reduction in the size of microwave devices is proposed to use buried microstrip lines, which have better electrodynamic parameters as compared to conventional microstrip lines. The works [4,5,6] are dedicated to the use of air-gap transmission lines for millimeter-wave applications. Various variants of microstrip lines with inclusions of SRR-structures (split-ring resonators) to reduce the size and improve the electrical characteristics of microwave devices are discussed in [7,8,9]. Several examples of using combinations of different planar type transmission lines to create directional couplers are given in [10]. A wide review of the use of known types of planar structures for miniaturization of microwave and millimeter-wave integrated circuits is presented in [11,12] where it is noted that further progress in this area should be associated with the transition to the threedimensional structures.

MATERIALS AND METHODS
The first conceptual design of a compact coupler on a combination of microstrip and slot line is shown in Fig. 4 a where the top plane is the topology of stripline structure and the lower plane is the topology of slotline structure. Numbers 1, 2, 3, 4 correspond to the numbers of ports of the device and Z 1 , Z 2 , Z 3 are the impedances of corresponding lines. The equivalent scheme of the coupler is shown in Fig. 4 b). The scattering matrix of such coupler using even-odd mode decomposition technique and a symmetry of the scheme can be written in the general case as It can be seen from Fig. 4 b) that this scheme of coupler is anti-directional; in this design working ports are 2 and 3 and port 4 is isolated. Accordingly the power division ratio will be determined by the expression from which using (6) it is easy to obtain unambiguous relations for calculating the impedances Z 2 and Z 3 from Z 1 and k: Another design of a compact coupler on the combination of microstrip and slot line is shown in Fig.5. The notation here is same as in Fig. 4. Analogously to the structure shown in Fig. 4, the general form of the scattering matrix of this coupler is of the form: Under conditions of full matching and decoupling matrix (9) can be simplified: from which simple formulae to calculate the impedances Z 2 and Z 3 are obtained: . , 1 1 Calculated frequency dependences of scattering parameters for both of the proposed combined microstrip/slot line coupler designs are shown in Fig. 6 (red and green lines). The calculation assumes no dispersion, no losses in the lines, and equal division of power between the output ports. For comparison, the isolation of a classic variant of the three-branch microstrip line hybrid bridge is shown in the same figure (blue curve). Fig. 6 shows that in the operating band both schemes of couplers have nearly identical characteristics. Importantly, it is apparent from comparison of the curves, both of the proposed designs have better isolation (comparison of red, green and blue line in Fig. 6) as compared to the conventional three-branch hybrid bridge built on a microstrip lines.  Fig. 7 where Fig. 7 a) shows the topology of microstrip structure and Fig. 7 b) the topology of slotline structure. It should be noted, that the characteristics of proposed structure is rather sensitive to varying the topology. For example, small modification of coupler slotline structure (with the same stripline structure) as shown in Fig. 8 can significantly change the frequency characteristics of the circuit.

RESULTS
Electrodynamic simulation was performed in the frequency range 12-16 GHz using a dielectric GaAs substrate of thickness h = 1 mm and parameters 8 . 9 = ε r and 0005 . 0 tg = δ . Simulation results of the coupler with the power division ratio in working arms k=5 are shown in Fig. 9. Under these conditions, the geometric dimensions of the structure were as follows: microstrips (Z 1 =50 Ω) W 1 =1.037 mm, (Z 2 =77.133 Ω) W 2 =0.354 mm, slot line (Z 3 =111.803 Ω) W 3 =0.637 mm.  As one can see such simple modification of slotline structure leads to a significantly (about 20 dB) improved isolation (S41) at the operating frequency as compared with the previous version of structure. It also expands the working frequency band of the circuit and improves matching across it that is shown on Fig. 11 where it is seen VSWR < 2 over the entire frequency range with the minimum value of VSWR = 1.04 at the operating frequency, which demonstrates excellent matching of scheme with the line having characteristic impedance of 50 Ohms. It should be noted that in work [10] several variants of structures of directional couplers on combinations of transmission lines are considered, however, there are no results of theoretical analysis, numerical simulation or experiment. In other literary sources, the authors did not find analogues of similar structures. Thus, the directional couplers considered in this paper are proposed for the first time and their characteristics are described in detail analytically and verified by numerical simulation.
The proposed method of designing multilayer structures on combinations of transmission lines has a very great potential in the selection of the required electrical performance of the devices.

CONCLUSIONS
The proposed directional couplers are small in size but have better frequency characteristics than a classic threebranch coupler on microstrip lines. Detailed electrodynamic modeling with the dispersion and losses in the lines confirms the characteristics of proposed directional couplers. The presented compact coupler designs can find a broad range of applications in mobile communication systems for decoupling of channels, division of power and frequency conversion provided that output ports are not required to be adjacent.
The method of transition from planar to threedimensional structures used in the paper and in particular the development of directional couplers on combinations of transmission lines permits not only to create compact devices with desired characteristics but also paves the way for significant decrease in the size and costs of the broad range of electronic equipment utilizing such couplers.