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IEEETRANSACTIONS ONMICROWAVE THEORYAND TECHNIQUES, VOL. MTT-35, NO. 8,AUGUST 1987
681
Wide-Band Directional Couplers in
Dielectric Waveguide
JOSE RODRiGUEZ AND ANDRES PRIETO
.4/retract —In this work, the H guide is proposed as an alternative in
designing proximity directional couplers using dielectric goides in order to IN
——
obtain coupling factors constant with the frequency, thus increasing the
bandwidth of these devices. The propagation constants of the even and odd Image Isolated Inverted
modes of the coupling zones are determined by means of Schelkunoff’s
Image Strip
method and the effective dielectric constant method (EDCM).
Two directional couplers, 10 dB and 3 dB, made of polystyrene and
Teflon respectively, were designed and measured to work in the millimetric
frequency band (32-40 GHz). The inclusion of metallic walls in the curved
zones avoids additional couplings and results in flat coupling. Furthermore, —EL—
the metallic wafls reduce the radiation losses and allow the coupling factor
to be finely adjusted. The results obtained show a maximum coupling
variation of *0.5 dB for 20-percent bandwidth. T lT
Fig. 1. Cross sections of different dielectric guides.
I. INTRODUCTION
D IELECTRIC GUIDES have received considerable
attention due to their possible application in in- coupler. Three types of directional (couplers exist: the
tegrated microwave circuits within the millimetric and proximity directional coupler (with the two guides placed
submillimetric bands. Although the first studies of dielec- on the same ground plane or on dit’ferent planes), the
tric guides show that these structures propagate only hy- multiholed coupler (with the two guides on each side of a
brid modes [1], the earliest simplified models were based common metallic plane), and the beam splitter coupler.
on the supposition that the’ guided wave modes could be The proximity directional coupler with the two guides on
brought closer by means of two fundamental mode fami- the same ground plane is the one with the simplest struc-
lies, E;q and E~~, where the subscripts p and q refer to ture and a planar circuit, and the present work focuses on
the number of extrema of each field component in the x this configuration. For this type of coupler, the coupling
and y directions, respectively, while the superscripts indi- factor turns out to be a function of the difference between
cate the fundamental component of the electric field [2]. the propagation constants K,e and K,. of the even and
The dielectric guide with the simplest geometry is the odd modes respectively.
image guide; thus, it is the structure which has been Most couplers which have been presented use the image
studied most. However, in order to reduce the losses which guide. A problem common to all these couplers is the
this configuration presents, various modifications of the reduced bandwidth due to the difference between the
image guide have been proposed, such as the isolated propagation constants of the even and odd modes, result-
image guide, the inverted strip guide [3], [4] (Fig. 1), and ing in frequency-dependent coupling. A recent study [9]
modifications like the T and II guides [5], [6] (Fig. 1). suggests modifying the cross section of the image guide to
They can all reduce the conductive losses of the image improve the constancy of the coupling coefficient. Never-
guide by separating it from the maximum concentration of theless, the total coupling factor remains frequency-depen-
electromagnetic energy from the ground plane. Further- dent as a consequence of the additional couplings in the
more, the T and II guides allow a greater concentration of curved areas approaching the parallel zone [10].
the electromagnetic field around the longitudinal propa- Various methods exist to determine the propagation
gation axis. Later, Miao and Itoh [7], [8] placed a dielectric constants of the even and odd modes. Some analyze the
sheet on two image guides, obtaining a structure similar to problem by enclosing the dielectric structure in a conduct-
ing box, which allows the continuous slpectrum of radiated
the II guide, which they called a hollow image guide.
modes to be discretized. However this also increases the
One of the first components to be made with these kinds
of guides (mainly with image guides) was the directional complexity of calculations. Other methods rely on varia-
tional techniques [6], whereby modifications of the original
dielectric structure can be carried out and analyzed without
Manuscript received October 20, 1986; revised April 8, 1987. any additional analytical complexity. Subsequently, ap-
The authors are with the Departamento de Electricidad y Magnetism,
proximate analytical methods such as the EDCM can be
Facultad de Ciencias, Universidad de Santander, 39005 Santander, Spain.
IEEE Log Number 8715416. applied.
0018-9480/87/0800-0681 $01.00 01987 IEEE
682 IEEETRANSACTIONSONMICROWAVE THEORYAND TECHNIQUES, VOL. MTT-35, NO. 8,AUGUST 1987
II. THEORY 1.4-R-.d ..
A. Coupled Dielectric Guides
4
Fig. 2(a) shows a proximity directional coupler consist-
ing of two parallel dielectric guides placed on the same
ground plane. The scattering coefficients for the parallel
coupling region when the power is introduced at arm 1 are
2s
given by [10]
Is,l] = lcos(((Kze - Kzo)/2.) L) [ (1)
, {~ i=image guide (F,=%) ~
[S,ll = lsin(((K=e - K,0)/2).L) I (2) Z=7Tguide (s,=1) 2
t=taper
where K,, and K,O are the propagation constants of the
m=metallic walls
even and odd modes, respectively, and L is the length of
(a)
the coupling zone.
In the curved zones, the distance 2S between the two
guides varies continuously, as do the values of K,, and
K,O. These curved zones introduce additional couplings,
whose description requires (1) and (2) to be replaced by
their corresponding integral forms, both for the nonparal-
lel symmetrical and asymmetrical coupling structures.
If the nonparallel coupling configuration is symmetrical, I I —I ——I _I .—_.I
I I I I I I
the scattering coefficients can be written in the following
I I I I I I
form [10]: Y3 L‘-F~sl l,‘1,l=2,;, I I ~zj-1 I ~z,j II
IS211=ICOS(K.1,)1 (3) Y2 –-i:llh–4_’–k ———tE!_@_ .-l >
lS,ll=lsin(K.l,)l (4) Y,
‘1 ‘2 X3 x j–f x j x j+1 x
in which K is a function of the transversal and longitudi-
(b)
nal propagation constants of each dielectric guide in isola-
tion, as well as its geometry. 1, represents a coupling I
,— R —! T
integral that extends to the nonparallel coupling zone.
When the nonparallel coupling zone is asymmetrical, (3)
and (4) must be adequately corrected due to different
wavefronts [10]:
1111
&ll=lcos(y.K.In)l (5)
ll]lllljl~lv
lS,ll=lsin(y.K.l.)l (6) ‘E ‘E ‘E ‘
I ef21 efll ef21
where K and 1. are functions similar to those used in (3) [Kxl IKXI
{11, ,~21 ,;1
atankdes(4t)h,ewhaisleymmtheetryparaomfettheer coyupislinag correregciotinon intofactaocrcotuhnatt — I 1 1 I 1I l
[xl 1X2 ,X3 ,X4 X5 x
and is determined experimentally [10].
1111
Thus, there are two areas in which the coupling factor (c)
has different expressions: one is the curved section, and
Fig. 2 (a) Top view of aproximity coupler with optional metallic walls.
the other is the zone in which the distance between the (b) Cross :,ection of apartially filled rectangular waveguide with i x ]
guides remains constant. If the ratio between the powers different dielectrics. (c) Cross section of two coupled H gmdes.
that appear in arms 3 and 2, for a parallel coupling zone of
length L, is defined as a coupling factor C, then
cal methods will be used, Schelkunoff’s method [6], [11]
C= tan2(((KZe– K,0)/2). L). (7)
and the EDCM [2]–[5].
From (7), if the length L is fixed, the coupling factor C
B. Schelkunoffs Method
due to this zone will always remain constant as long as the
difference K== – KZOdoes not vary with the frequency. In In dielectric guides with rectangular cross sections, the
the case of the image guide, this difference has a large dielectric interfaces are planes parallel to the yz or xz
frequency dependence. Therefore, other dielectric guides planes, where z is the propagation direction. When the
whose cross sections are different from the image guide structure is enclosed by perfectly conducting metallic walls,
must be sought so that the coupling factor C given by (7) a modified structure is obtained as shown in Fig. 2(b).
will remain relatively constant. To determine the propa- Obviously analytic methods are not suitable, and conse-
gation constants of the even and odd modes, two theoreti- quently variational methods are preferable.
RODRtGUEZ AND PRIETO: DIRECTIONAL COUPLERS IN DIELECTRfC WAVEGUIDE 683
Schelkunoff’s method is variational in nature. The elec- ferred process would be explained as follows: after the
tromagnetic field inside the conducting box can be ex- propagation constant K,n has been clbtained for n modes,
panded into an infinite sum of orthogonal functions be- a new mode will be selected from among those not yet
longing to a complete set which satisfy the boundary chosen in order to produce a new KZ(H+~, so that the
conditions on the walls of the metallic guide. By selecting variation over K;n is maximum in absolute value. It is
the solutions of Helmholtz’s equation for the empty guide, obvious that this latter procedure clemands a very high
the transversal electromagnetic field that corresponds to calculation time.
the guide of Fig. 2(b) can be written in the form However, it is possible to find a solution which practi-
cally coincides with the optimum one by using the follow-
ing procedure: the fundamental even mode for the family
of E~~ modes is E{l, and the two modes in the empty
guide whose electromagnetic configuration resembles the
E{l mode are the TEIO and TMII modes. From these two
modes (TEIO, TMII), we can obtain an approximate phase
1 J
constant K,. Subsequently, we shall form sets of modes
Here, V(z) and l(z) are the ~quivalent vo~ages and made up of TEIO, TMII, and a third mode chosen from
currents of each mode, and 7(,), h~,,, 21,], and k~jl are the among the rest of the empty guide mc}des. After computing
expressions of the electric and magnetic fields of the TM the approximate propagation constant K=, for each set, we
and TE modes respectively of the empty guide; the i‘s shall select those modes whose inclusion as a third mode
and j‘s are therefore double subscripts. produces the greatest absolute difference between K, and
Assuming that the cross section of the guide is uniform K=i, i.e., in IKZ – K=il, and they will thus be those which
in the z direction, one obtains have most influence. As far as the odd mode E.j’l is
concerned, the two preselected modes are TE20and TM 21.
([zl[y]- ~i[i])[V]=O (lOa)
It has been observed that this selection method improves
([yl[zl-Kj[i])[ I]=O (lOb) the convergence of the solution in comparison with the two
methods mentioned above, allowing, the necessary com-
where K, is the propagation constant, [Z] and [Y] are puter calculation time to be reducecl by a factor of 4 to
doubly infinite matrices, [i] is the identity matrix, and [V] obtain a given accuracy.
and [1] are infinite matrices formed by the expansion
C. The Effective Dielectric Constant Method (E.DCM)
coefficients of it and fit, respectively. The terms of the
[Z] and [Y] matrices are given through integrals extended As we shall seelater the results obtained by Schelkunoff’s
to the cross section of the metallic guide. These integrals method make it possible to deduce that the II guide and,
depend on the expressions for- the fields in the empty to a much lesser degree, the isolated image guide can
guide. When the dielectric interfaces are parallel to the x maintain K,, – K,O constant with frequency.
and y axes, as shown in Fig. 2(b), these integrals offer a Since EDCM is much faster with respect to computer
simple analytic solution, thus reducing computer calcula- time than Schelkunoff’s method and provides results with
tion time. sufficient accuracy, the former method has been applied to
The numerical solution of (10) demands the matrix two identical dielectric II guides coupled by proximity
orders to be truncated, indicating the importance of func- according to the well-known procedure [2]–[5].
tions (8) and (9). The first step in the selection process After introducing the first step of the effective dielectric
involves considering the kind of symmetry of the dielectric constant method, which replaces each multidielectric re-
configuration under study and the symmetry of the mode gion in the y direction (regions I, II, III, IV, and V) by
to be resolved. Therefore, if solutions which correspond to homogeneous and infinite regions in the same direction,
an even-type mode are sought, we shall select modes whose with effective dielectric constants 1, c.f2, 6.fl, c.fz, and 1,
electric field is an even type, e.g., TEI(J, TE30, or TM1l. respectively, the dielectric confi@ri~tion of Fig. 2(c) is
Conversely, if the solution corresponds to the odd-type obtained.
modes, we shall take such modes asTM ~1,TM42, or TE20. In the case of two coupled dielectric guides like those of
Within the infinite modes thus selected, a subsequent Fig. 2(c) and restricting our study to the E:~ family of
choice can be made by means of increasing cutoff frequen- modes, we can take the following solutions for the poten-
cies [11] or transfer admittances [6]. However, the pre- tial O(x):
(A.exp(r,(x -xl))
I
j.cos(KX(x –xl))+C. sin(K.(x– xl)) xl<x<x~
O(x) = D.cosh(~2(x –x,))+E”sinh(q, (x–x2)) x2<x<x~ (11)
F.cos(KX(x –x3))+G. sin(Kx(x– x3)) x3<x<x~
H.cosh({l(x –X4))+ l.sinh({l(x –x.)) X4<X
684 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-35, NO, 8, AUGUST 1987
in which {1, KX, and qz are the propagation constants in
the respective media. The application of adequate boundary
conditions leads to the following characteristic equations:
1.15
ll.cosh((l(x ~-xq))+l.sinh({ l(x~-x,)) =0 (12)
for the odd mode and
1.1
H.sinh({1(x5 – x,))+ 1.cosh({l(x5 – x,)) = O (13)
*
for the even mode. 1.05
The propagation constants of the even and odd modes,
K=, and K,O, respectively, are expressed by /
1
KZe, o = Ce~2.K; – K:,, O (14) 8 9 10 11 12
F(GHz)
where KO is the free-space wavenumber, and KXe and KXO
Fig, 3. Normalized propagation constants for two coupled H guides
are the propagation constants in the x direction and are
(cl = <2= 2.56). Dimensions (mm): T= 2, B = 4, R= 20,,4 =14,,s= 2.
solutions of (13) and (12), respectively. — EDCM. --- Schelkunoff’s method. * * * Experimental points.
III. THEORETICAL AND EXPERIMENTAL RESULTS 90
(i)
In this section, we present theoretical results obtained m L
by the former two methods and experimental results. In all
cases, the guides were chosen so that the coupling config-
uration would operate using the lowest even and odd
modes, E/l and E~l, respectively. In Fig. 3, the results
obtained for K,e and K,O normalized to KO are shown.
Good agreement between the theoretical values obtained
by both methods and the experimental results is clearly
demonstrated.
In Fig. 4, the theoretical results obtained for the dif-
ference between the phase constants of three II guide
couplers versus frequency are presented. When this quan-
F(GHz)
tity is represented for other guides, the slopes of the curves
Fig. 4. K=, – K=,, versus frequency for three II guides (c1= 2.6, C2= 1).
are always negative for increasing values of the frequency, Dimensions (mm): (i) T=l, B =1 5,R =4, A =1,,S= 0.5 (ii) T=l.
and this slope is very sharp in most cases. When two II B=l, R=4, A=2, S=0.5(ili) T=l, B=l.5, R=4, A=2, S=0.5,
guides are used with dimensions and the separation dis-
tance properly chosen, the slope of the curves can always be of use to improve the constancy of the coupling factor.
be made positive, negative, or practically zero. This is In this case, the presence of the interior window creates
shown in Fig. 4 for three different II guides. It can be seen this effect.
that graph (ii) presents a K=, – KZO value which is rela- We have also studied how the separation 2S between
tively constant with the frequency. the two guides influences the coupling. Fig. 6(a) shows
In order to check how the dimensions of the II guide K== – K,O as a function of frequency for various values of
window influence the behavior of the coupler, we studied S. As can be seen in this figure, there is an optimum value
the variation of the difference between the propagation
of S which makes the K,, – K=O value very flat for a
constants of the even and odd modes as a function of
broad frequency range, e.g., S = 1 mm. However, due to
frequency for a pair of II coupled guides. In Fig. 5(a), this
the presence of the curved sections at both ends, the
variation is shown when the depth T of the window is
coupling factor will be modified significantly. The cou-
increased. It can be seen that the slope of KZC– KZO pling effect of the curved sections can be minimized by
becomes gradually less negative. There are certain T and B
partially shielding this zone with metallic walls (see Fig.
values which produce an almost flat response for the
2(b)) [12]. Assuming that the curved effect can be
coupler throughout the frequency band. This same behav- eliminated, the length L necessary to obtain a 3-dB cou-
ior is evident when the width of the H guide window, A, is pling in the 30–40-GHz band for an image guide coupler
increased, as shown in Fig. 5(b). Therefore, the II guide and H guide is shown in Fig. 6(b). The necessary length
offers two degrees of freedom when searching for the for a H guide is very constant with the frequency. This
dimensions which lead to a very constant coupling over a explains the flat response of the coupling factor.
given frequency range. Likewise, looking at Fig. 5(a) and
(b), it is obvious that for any II guide there is a frequency
IV. DESIGN, FABRICATION, AND EVALUATION
for which the coupling would be maximum. This can be
used to build a coupler with minimum length for a given Two proximity couplers in the 34–40-GHz band were
coupling factor. In general, any guiding system that re- designed and measured with theoretical coupling factors of
duces the concentration of the electromagnetic field would 10 dB and 3 dB in the parallel zone. The 10-dB coupler
RODRfGUEZ AND PRIETO : DIRECTIONAL COUPLERS IN DIELECTRIC WAVEGUIDE 685
58 80 -
~—
l% -l
S=.5
50 60
1~1 —
s= 1
——
S=l .5
42 40
‘—————___
S=2
. ——————__
34 1 1 t r 1 I 20 1 1 1~~
30 32 34 36 38 4!3 30 32 34 36 38 40
F(GHz) F(GHz)
(a)
(a)
60
60 r
[ A=l.5
40 /
/
t /
“e-–
4g ~
30 32 34 36 30 40
F(GI+z )
F(GHz) (b)
(b) Fig. 6. (a) K=, – K,O versus frequency, using S as parameter, for one
II guide (Cl= 2.55, (z =1). Dimensions (mm): T=l, B = 1, R= 4,A =
(a) K=, – K:,, versus frequency for one Image guide (cl = CZ=
2.1) and for three II guides (cl= 2.1, Cz=1), using T and B as 2,2 (b) Necessary length for a 3-dB coupler using image guide: (---),
((, = c, = 2.7) and II guide: (–) (cl= 2.7, c, =1). Dimensions (mm):
parameters. Dimensions (mm): R =4, A = 2,S= 1. (i) image guide:
T+ B =3. (ii) II guide: T= 0.4, B= 2.6. (iii) II mride: 7’=1.2, B =1.8. T=l, B=l, R=4, A=2.2, S=1.
(iv) H guide:’ T =-2, B =1. (b) K:, – K,O‘versus-frequency, using A as
parameter, for three II guides (cl = 2.1, Cz= 1). Dimensions (mm):
T=l.5, B=1.5, R=4, S=1. R = 4, A = 2.2, L = 10.86,61 = 2.6 (polystyrene), (2 =1;
Rc=17, S=1,9= 30”.
was made entirely of polystyrene (c, = 2.6) and fixed to 3-dB coupler: image guide T+ B = 2.5, R = 4, A = 2.2,
the ground plane by tetrachloroethylene, while the 3-dB c1= c1= 2.1 (Teflon); II guide: T=l.6, B = 0.9, R = 4,
coupler was made of Teflon (c, = 2.1) and was attached to A = 2.2, L = 31.29,(1= 2.1 (Teflon), Cz=1; Rc =19, S =
the metallic plane using adhesive tape. In both cases, the l,e =15°.
parallel coupling zone was carried out in II guide, while
The band center frequency was 35 GHz in the 10-dB
the rest of the device was made in image guide. In the
coupler and 37 GHz in the 3-dB coupler. In both cases, the
curved zones, radiation losses are inversely proportional to
length of the arms of the couplers was 10A ~ (A ~being the
the curved radius and directly proportional to the distance
free-space wavelength at the central frequency), which is
at which the transverse propagation constant, outside the
long enough to make the effects of tine transitions on the
guides, causes the field to decay by a factor l/e of its
coupling zone negligible [14].
maximum value [13]. Since the II guide presents a field
For the 10-dB coupler, the insertion loss in the main
which in the transverse direction is less concentrated than
arm was measured with the transitions in the absence of
the field due to the image guide, the radiation losses in the
the secondary arm. This loss was a~bout 3.5 dB, which
curved zones of the latter will be less than those of the
corresponds quite well to the theoretical loss of 2.9 dB
corresponding II guide. The transition betwen the H
determined by Schelkunoff’s method in the center of the
guide and the image guide took place gradually, both in
band. The losses due to the dielectrics were calculated by
the depth of the II guide window and its width. The return
making the permittivity complex, so that matrices [Z] and
losses of both couplers in the four arms were always less
[Y] of (10) become complex; the losses in the conductors
than 25 dB, and their parameters (see Fig. 2(a)) are as
were determined by means of the perturbation method. To
follows (all dimensions in mm):
determine the radiation loss in the curved regions, we
10-dB coupler: image guide: T+ B = 2, R =4, A = 2.2, compared the insertion loss of a straip~t guide with that of
c1 = Cz = 2.6 (polystyrene); H guide: T = B = 1, an identical curved guide. The loss due to the curves was
686 lJW?1KANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL MTT-35, NO. 8,AUGUST 1987
,.,
/,.
.
>~).- \,
-1
Fig. 8. Experimental coupling factor C versus frequency for three H
0
different directional couplers using IJ gmde. (1) L = 30.15 mm; (ii)
(k) 1
— 2 1.= 3129 mm; (iii) L = 32.22 mm; (. ) theory for L = 31.29 mm.
34 3’6 38 LoF[GHZ)
Flg 7. Coupling factor C’ versus frequency for the 10-dB directional ment between the theoretical and experimental results,
coupler. (e) ( .) coupling straight zone only (theory); (c) (-. -) cou- including slight fluctuation of the coupling factor with the
pling straight and curved zones (theory): (b) (---) coupling straight and
frequency, is very good.
curved zones with losses (theory); (a) (—) measurement (without
metallic walls): (d) (* * *) measurement (with metallic walls).
V. CONCLUSIONS
roughly 1 dB and fairly constant with frequency. When the By using II guides in the construction of directional
complete coupler was set up, the coupling factor, shown in proximity couplers, the coupling factor can be maintained
curve (a) of Fig. 7, was obtained by measuring the relative constant with frequency. However it is necessary to
power level of arm 3 with respect to that of arm 2. Using eliminate additional couplings and radiation loss due to
the previous experimental data, the losses of the dielectric the curved zones. The inclusion of metallic walls makes
guide per unit of length can be calculated. Likewise, by this possible and reduces the total losses of the coupler,
means of (3) and (4), we can find the additional couplings
in the curved zones. Taking these dielectric losses and the
WFERENCES
additional couplings into account along with the radiation
[1] K. Solbach and I. Wolff, “The electromagnetic fields and phase
values in the curved regions, the theoretical coupling was constants of dielectric Image lines,” IEEE Trans. Mzcrowaue Theory
calculated, obtaining curve (b) of Fig. 7, which coincides Tech., vol. MT”l-26, pp. 266-274, Apr. 1978.
[2] P. P. Toulios, “Image line millimeter integrated circuits directional
almost exactly with the previous experimental value. How-
couplers design,” presented at the National Electronics Conference,
ever, if the additional couplings of the curved zones are Chicago, IL, Dec. 7-9, 1970.
taken into account, but neither the dielectric losses nor the [3] T. Itoh. “Inverted strip dielectric waveguide for millimeter-wave
integrated cucnits,” IEEE Trans. Mtcrowaue Theory Tech., vol.
radiation losses in the curved zones are considered, the
MTT-24, pp. 821–827, NOV. 1976.
theoretical coupling which is shown in curve (c) of Fig. 7 is [4] R. Rudokas and T. Itoh, “Passive millimeter-wave IC components
quite far removed from the experimental result. made of inverted strip dielectric waveguides,” IEEE Trans. Micro-
waue Theoty Tech,, vol. MTT-24, pp. 978– 981, Dec. 1976.
In order to eliminate the additional unwanted couplings
[5] E. Rubio, J. L. Garcia, and A. Prieto, “Estudio de las guias T y
and to minimize radiation losses, metallic walls [12] were II,” An. F’zs. B, vol. 78, no. 1, Jan.-Apr. 1982.
introduced, as is shown by the shaded areas in Fig. 2(a). [6] A Prieto and E. Rubio, “Apphcation de la methode de Schelkunoff
aux guides dielectriques,” presented at the S. E. E. Guides et
The shielding had polished lateral walls that were per-
Circuits Dielectriques, Limoges, France, Oct. 1981.
pendicular to the metallic plane to which it was affixed by [7] J. F. Miao and T. Itoh, “Hollow image guide and overlayed image
pressure. The optimum distance from the metallic edges to gmde coupler,” IEEE Trans. Mzcrowat,e Theory Tech., vol. MTT-30,
the edges of the dielectric curves which minimizes the pp. 1826–1831, NOV. 1982
[8] A. Prieto, E. Rubio, J. Rodriquez, and J. L. Garcia, “Comments on
radiation losses turned out to be about 2.2 mm and 2.5 ‘Hollow image guide and overlayed image guide coupler’; IEEE
mm for the 10-dB coupler and 3-dB coupler, respectively. Trans. Microwave Theory Tech ,vol. MTT-31, no. 9, pp. 785-786,
Sept. 1983.
These distances were determined experimentally for the
[9] D. I. Kim, D. Kawabe, K. Arala and Y. Naito, “Directly connected
dielectric guides and curvature radii used in the couplers. image guide 3-dB couplers with very flat couplings,” ZEEE Tram,
In curve (d) of Fig. 7, the new coupling factor obtained Mzcrowaue Theory Tech ,vol. MTT-32, pp. 621–627, June 1984.
[10] T. Tnnh and R. Mittra, “Coupling characteristics of planar dielec-
can be seen to be quite constant throughout the frequency
tric waveguides of rectangular cross section,” IEEE Trans. Micro-
band, with a maximum fluctuation of +-0.5 dB about the wave Theo~ Tech., vol. MTT-29, pp. 875–880, Sept. 1981.
calculated theoretical value, which is shown in graph (e). [11] K. Ogusu, “Numerical analysis of the rectangular dielectric wave-
guide and its modifications,” IEEE Trans. Microwave Theory Tech,,
Both the theoretical and the experimental results for the
VO1. MTT-25, pp. 874–885, Nov. 1977.
3-dB coupler can be seen in Fig. 8. Along with the theoret- [12] M. Desai and R. Mittra, “A method for reducing radiation losses at
ical prediction and measurement of the 3-dB coupler with bends in open dielectric structures,” presented at the MT”FS Int.
Microwave Symp., May 1980
L = 31.29 mm, we present the experimental measurements
[13] K, Solbach, “The measurement of the radiation losses m dielectric
of the coupling factor for two different coupling lengths, image lines bends and the calculation of a minimum acceptable
L = 30.15 mm and L = 32.22 mm. These lengths were curvature radius,” IEEE Trans. Microu,aue Theory Tech., vol.
MT’1-27, pp. 51-53, Jan. 1979.
obtained by slightly modifying the penetration of the
[14] T.A. G. Malherbe, T. Trinh, and R, Mittra, “Transition from metal
metallic shields in the parallel coupling zone. The agree- to dielectric waveguide~’ Microwaue J., pp. 71-74, Nov. 1980.
RODRfGUEZ AND PRIETO : D1RECTIONAL COUPLERS IN DIELECTRIC WAVE GUIDE 687
Jose Rodriguez was born in Lugo, Spain, in Andr6s Prieto was born in Santander, Spain, in
1951. He received the Teaching degree in 1973 1947. He received the L,icenciado en Ciencias
from the Universidad de Oviedo, SpaitIj and the Fisicas degree in 1973 from the Universidad de
Licenciado en Ciencias Fisicas degree in 1981 Vafladolid, Spain, and the Doctors’s degree in
from Universidad de Santander, Spain. 1979 from the Universidad de Santander.
Since 1982 he has been with the Departamento He is Profesor Titular inthe Deparl.amento de
de Electr-&ica of the Universidad de Santander. Electrbnica and is currently working in the area
He has recently presented his thesis on dielectric of analytical and numerical methods of solving
waveguides. His current research interests in- electromagnetic problems in waveguide struc-
clude the electromagnetic field analysis of clielec- tures and microwave circuits.
tric waveguides and integrated optics.
688 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-35, NO. 8, AUGUST 1987
Three-Dimensional Finite-Difference Method for
the Analysis of Microwave-Device Embedding
ANDREAS CHRIST AND HANS L. HARTNAGEL, SENIOR MEMBER, IEEE
,4bstract —The embedding of microwave devices is treated by applying several gigahertz because of the appearance of harmonics
the finite-difference method to three-dimensional shielded structures. A and to avoid pulse widening.
program package was developed to evaluate electromagnetic fields inside
To describe the electrical behavior, most authors have
arbitrary transmission-line connecting structures and to compute the
used lumped-element circuits. Getsinger divided the
scattering matrix. The air bridge, the transition through a wall, and the
lumped-element circuit into two parts, one representing
bond wire are examined asinterconnecting structures. Detailed results are
given and discussed regarding the fundamental behavior of embedding. the package, the other the mount [1]. The parameters of
some diode packages were measured, and the parameters
for mounting into waveguide, strip, and coaxial line were
I. INTRODUCTION
calculated using an approximating theory. Bialkowski and
T HE EMBEDDING PROBLEM is concerned with the Khan calculated the driving-point impedance for diodes in
interconnection of an active semiconductor device, waveguides and similar lines [2]. They verified their results
such as a diode, an FET, or an MIC, with the electrical by measurements. Maeda et al. [3] measured all parame-
surroundings where one considers both electrical and ters for an embedded laser diode. A general measurement
mechanical aspects. Especially at frequencies up to 100 method without the need of reference packages was pre-
GHz, with monolithic integrated millimeter-wave circuits, sented by Greiling and Laton [4], but they could not
the design of embedding structures becomes important. distinguish the packaging and mounting parts. Their
The high permittivity of the semiconductor materials pro- method was applied to diodes but could also handle other
motes field distortions at such structures. From amechani- devices.
cal point of view, the handling, the stability, the protection The parasitic reactance of two microwave transistor
against environmental factors, and the feasibility of fabri- packages (LID and S2) mounted in microstrip were mea-
cating a device and its connecting structure have to be sured by Akello et al. [5] using the resonance method. In
considered. They influence the package geometry and particular, the inductance of the bond wires as a function
therefore also the electrical characteristics of the active of wire spacing and number was examined. Typical values
device. for LID were 0.61 nH to 0.76 nH (one wire). Beneking
Embedding is not only significant inside packages, as presented slightly different values (0.2 nH to 0.5 nH)
often required for protection, but also when these compo- obtained by a time-domain measurement technique for
nents are directly bonded into microstrip or other lines. small reactance and susceptances [6].
Electrically, the embedding can be regarded as the inter- The available values are mostly based on measurements
connection of two or more transmission lines, which may and are restricted to some commonly used but special
be waveguides, coaxial lines, dielectric image guides, mi- packages. Although Akello et al. demonstrated an im-
crostrip lines, or slotlines, using a connecting structure portant influence on the device characteristics, such as
(Fig. 1). gain and stability factor [5], there has until now been no
This is in general a multiport scattering problem and fundamental analysis to find well-matched structures.
can be described by the generalized scattering matrix. Therefore, a numerical method able to examine embedding
The requirements are a small reflection coefficient and a structures is given in this paper and some of the significant
linear phase of the transmission coefficient in the frequency results are presented here. In general, the geometry of such
range of interest. A zero point of the reflection coefficient structures forces a three-dimensional analysis of the elec-
should be looked for in analog applications where the tromagnetic fields, and the expected frequency range for
relative bandwidth is usually small. For the digital case, microwave applications needs the rigorous numerical solu-
the interconnection has to be broad-band from zero up to tion of Maxwell’s equations.
However, the numerical methods tested to handle
scattering problems by finding the scattering matrix, a
Manuscript recemed November 28, 1986; revised April 1, 1987. This frequency-domain problem, often exhibit some lack of
work was supported in part by the Deutsche Forschungsgemeinschaft. generality. The spectral-domain approach [7] can only be
The authors are with the Instltut fttr Hochfrequeuztechnik, Technische
applied to planar structures. The method of moments,
Hochschule Darmstadt, 6100 Darmstadt, West Germany.
IEEE Log Number 8715144. requiring a knowledge of the Green’s function, is practi-
0018-9480/87/0800-0688 $01.00 01987 IEEE
