Lipparini* anazysis which compare favourabzy with experimentaz results. The same modez. described. It is shown that the discrepancies between computed

Transcription

1 ACCURATE ANALYSIS AND DESIGN OF MICROSTRIP INTERDIGITATED COUPLERS Vittorio Rizzoli*- Alessandro Lipparini* Abstract. The ezectricaz behaviour of interdigitated directionaz coupzers in an inhomogeneous diezectric medium is anazyzed. Thanks to the symmetry properties of the device, the concepts of even and odd networks can be appzied, Zeading to simpze, closed-form expressions for coupzer anazysis which compare favourabzy with experimentaz results. The same modez azzows the most important parasitic effects to be understood and quantitativezy described. It is shown that the discrepancies between computed and experimentaz data can be accurately expzained in terms of the parasiticsarising from junction discontinuities. FinaZZy, design data for azumina-microstrip interdigitated couplers are presented in graphic form. INTRODUCTION In the last few years, considerable attention has been devoted in literature to the problem of predicting microstrip interdigitated coupler behaviour on a quantitative basis. Analyses based on the homogeneous-dielectric assumption have been presented first {f1,2}, showing the theoretical equivalence between the interdigitated device and the conventional twowire one {2}. More recently, the same concept has been extended to the microstrip case {3}, leading to the definition of equivalent even and odd modes of propagation. These approximate approaches are usually adequate for computing the coupling coefficient and are generally suitable for obtaining qualitative information of technical interest about coupler performance and feasibility. On the other hand, if a complete and accurate characterization of coupler behaviour is required, a rigorous analysis should be carried out. This is particularly true when coupler directivity is concerned. In fact, the amount of power being coupled to the insulated port arises from the interference of nearly in-phase and nearly equal-amplitude waves, which must be carefully evaluated if directivity is to be accurately found. Such a rigorous analysis is attempted in this paper. COUPLER ANALYSIS AND DESIGN Let us consider a microstrip interdigitated coupler in the "unfolded" configuration as described in ref. {4} and schematically shown in fig. 1. This device basically consists of a length of an axially uniform fourmicrostrip system whose alternate conductors are short-circuited at both ends of the coupled section to yield the interdigitated topology. The reactances of the bonding wires will be assumed to be negligible, as is actually the case at microwave frequencies up to about 12 GHz. The strips will be further assumed to be equal and equally spaced since this is the most commonly encountered configuration. Thus the only two design parameters are strip width (w) and spacing Cs), apart from substrate thickness and permittivity. As a first step of the analysis procedure, the device is modelled as a *Istituto di Elettronica, University of Bologna, Villa Griffone, Pontecchio Marconi, 444 Bologna, ITALY. 642

2 //t// z FIG. I loss-free, inhomogeneous, quasi-tem four-wire line and any parasitic effects are neglected. If this is the case, the normal modes of propagation are defined by the following eigenvector matrix: 1 1 OC 3 c -ai1 a2-1 M al a a3 -a4 where the a's are dependent on coupler geometry. From (1) the network is seen to support two even and two odd modes with respect to the axial plane of symmetry. Thus, despite of the interdigitated topology, one can take advantage of the concepts of even and odd networks {5} and reduce the analysis problem to one of two independent two-port networks. In turn, each one of these simply consists of a couple of independent trasmission lines, since only the even (odd) modes are fed in the case of even (odd) excitation. This allows simple, explicit analysis formulae to be derived in a straightforward way. The latter are not reported here for the sake of brevity. To show the validity of this approach, in fig. 2 the measured and computed performances of an alumina 3-dB coupler having w=7 pm and s=5 pm are compared. Though the agreement is not perfect, it is evident that the coupler operation, including directivity, can be predicted with practically significant accuracy. In the simple schematization considered so far, the scattering matrix of the coupler depends on frequency only through the product f$, where i is the length of the coupled section. Thus a universal (i. e., frequencyindependent) design chart can be drawn for any given substrate characteris tics. Such a chart for.635 mm alumina is given in fig. 3, where constant coupling and directivity curves are plotted in the w-s plane. All coupling and directivity values refer to center band, which is defined as the value of the product fk yielding minimum coupling (in de3). Only the region corresponding to a VSWR less than 1.2 is shown in the figure. The center band value of ft typically ranges from in/sec to 3.1*16 m/sec for e =1 alumina. From fig. 2 it is evidqnt that coupling values between 2 and 6 db with good directivities and technically significant strip widths and spacings can be realised by this technique. In particular, it is in- 643

3 EXPERIMENT THEORY (NO PRRASITICS) THEORY [INCLUOING PRERSITICS) a.,: C3 (1) 'm - I? C:, Q L) oi _ C? S.5 9 FREQUENCY [GHZ) Ct C3? C)i \ I~~~~~~~~~~~~~~~~~~~~~~~~~~~ \ X 11~~~~~~~~~~~~ "I~~~~~~~' 'NN N a TI - - -r- T -r I- I- - I I I I I _ N "I z,.. ns z / :;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i 2 lt 1I - --I FItG 2 644

4 a %*C(DB) - D(DB) z V5WR<1.2 -a ( B a85. 9 S W (M ICRONS) FIG. 3 teresting to observe that coupling essentially depends on strip spacing only (at least, as far as the limitation V/SWR<1.2 is retained) and, for any given coupling value, there exists an optimum strip width, yielding maximum directivity..in order to refine the analytical model of the coupler and t;o improve accuracy between theory and experiment, additional effects such as discontinuity parasitics i conductor losses and dispersion shou ld be taken into account. UJnfortunately,n when these are considered it is no longer possible to draw a frequency-independent design chart such as fig. 3. since the coupler scattering matrix no lonlger contains frequency in the fq combination only. Thus, for a practical design this chart would be best used to find a reasonable starting point for a local optimization to be carried out by a more sophisticated model. As an example, the effects of junction discontinuity parasitics will be briefely discussed here. Let us separately consider the even and odd networks. For each one of these, the electrical situation at both ends of the coupled section is much the same as due to an impedance step in a conventional microstrip. Thus launching parasitics can be modelled as lumped LC low-pass ladder networks which are cascade connected at the input and out- 645

5 put ports of both networks {6,7}. Fig. 2 clearly shows that these effects are mainly responsible for the previously observed discrepancies between theoretical and experimental results. The only fact that this model is still unable to describe is the.4 db 'insertion loss of the coupler. To predict the latter, conductor losses in microstrip should be obviously taken into account. CONCLUSION It has been shown that the quasi-tem analysis is adequate for describing microstrip interdigitated coupler behaviour up to 12 GHz, provided that the TEM mode distribution be accurately taken into account. Making use of the even- and odd-network concepts, analysis bec:omes simple and may be carried out by explicit formulae. The latter can be used to generate design charts yielding good starting points for optimization of practical designs. REFERENCES 11} W. P. Ou, "Design equations for interdigitated directional couplers", IEEE Trans., NTT-23, pp , Febr (2} V. Rizzoli, "Stripline interdigitated couplers: analysis and design considerations", Electron. Lett., vol. /11, pp , Aug {31 S. J. Hewitt and R. S. Pengelly, "Design data for interdigital directional couplers", Electron. Lett., vol. 12, pp , Febr (4} R. Waugh and D. La Combe, "Unfolding the Lange coupler", IEEE Trans., NTT-2, pp , Nov {5} J. Reed and G. J. Wheeler, "A method of analysis of symnetrical fourport networks", IRE Trans., MTT-4, pp , Oct {6} A. F. Thomson and A. Gopinath, "Calculation of microstrip discontinuity inductances", IEEE Trans., MTT-23, pp , Aug {7} P. Benedek and P. Silvester, "Equivalent capacitances for microstrip gaps and steps", IEEE Trans., MTT-2, pp , Nov This work was partially sponsored by the Italian National Research Council (CNR). 646