IEEE MTT-V044-I02 (1996-02)

192 Pages·1996·97.406 MB·English

by  FANTOMASPING

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IEEE TRANSACTIONS ON MICROWAVE THEORY ANO TECHNIQUES, VOL. 44. NO. 2, FEBRUARY 1996 169
Methods of Suppression or Avoidance of
Parallel-Plate Power Leakage
from Conductor-Backed
Transmission Lines
Nirod K. Das, Member, IEEE
Abstract- Four useful methods are presented to suppress substrate layers (with different dielectric constants and/or
and/or avoid parallel-plate leakage from conductor-backed thicknesses) on two sides of the central strip is attractive for
printed transmission lines. These include: 1) the use of shorting
a multilayer feed architecture of integrated phased arrays [8],
pins; 2) the use of a dielectric-guide-coupled configuration; 3)
but can be potentially leaky due to the possibility of excitation
using a two-layered conductor-backing configuration; and 4)
dielectric loading on top. New analyses to model the leakage of the parallel-plate mode [3]. It is, therefore, important to
suppression due to the shorting-strips and the dielectric-guide investigate possible methods of suppression and/or avoidance
coupled geometries are presented, with selected demonstrative of the unwanted leakage from useful printed transmission lines.
results and critical discussions. It is concluded that the unwanted
In this paper, we propose four possible methods of suppres
leakage in many printed transmission lines, that are otherwise
sion and/or avoidance of leakage from a conductor-backed
attractive for integrated circuits and phased array applications,
can be successfully avoided and/or significantly suppressed using slotline or coplanar waveguide. Similar techniques will also
the proposed techniques. be applicable for other strip- or slot-type transmission lines
geometries. The proposed methods include: l) the use of
conducting shorting pins to suppress excitation of the parallel
1. INTRODUCTION
plate mode; 2) the use of a "hybrid configuration" (as dis
T HE POSSIBILITY of power leakage from the dominant cussed later), where a small dielectric-guide" structure with
mode of certain geometries of single or multilayered a significantly high dielectric constant compared to that of
transmission lines is now quite well known [I ]-[7]. Power the surrounding substrate, is coupled underneath the slotline
leaks from such printed transmission lines in transverse di or coplanar waveguide; 3) using a two-layered conductor
rections, due to coupling to the characteristic surface-wave backing configuration, instead of the standard configurations
mode(s) of the substrate structure. The leakage can some of [I], [3] with only a single uniform substrate between the
times be severe for specific substrate configurations of the parallel plates; or 4) loading the conductor-backed geome
printed transmission lines, under certain conditions of fre try on top using a thin, high dielectric-constant substrate.
quency and/or physical parameters. Unfortunately, several New analyses are presented to accurately model the leak
novel geometries of printed transmission lines, which are age suppression/avoidance due to the shorting strips and the
otherwise attractive for integrated circuits and phased array dielectric-guide-coupled configurations. Important results are
applications from various practical considerations, potentially presented to demonstrate the success of the proposed methods.
suffer from the unwanted leakage problems. For example, The details of the analyses of the new conductor-backed
a conductor backing behind a standard slotline or coplanar geometries are presented in Section II. Selected results for
waveguide can be attractive to achieve enhanced mechanical different suppression methods are presented in Section III, with
strength. The conductor backing would also allow additional discussion on the general characteristics.
circuit integration on its other side, providing the necessary
electrical isolation in between. However, such a conductor
backed configuration, unlike a standard slotline or coplanar II. ANALYSIS OF THE NEW GEOMETRIES
waveguide, can leak significant power to the parallel-plate
In this section, we will separately discuss the detailed
mode, even at low frequencies [I]. This leakage can be
analyses of the first two geometries we have proposed. The
particularly prohibitive for thin substrates and/or higher fre
analyses of the other two new geometries, with a dielectric
quencies, making the conductor-backed geometries potentially
cover or with a multilayer conductor backing, have been
dangerous to use. Similarly, a stripline with two different
performed using the spectral-domain moment method of [9],
[ 10], [ 11 ], and [3], and have not been duplicated in this
Manuscript received December 22, 1993; revised November 12, 1995. This
work was supported in part by the US Army Research Office, Research paper. Only the results illustrating the leakage suppression are
Triangle Park, NC. discussed in Section III.
The author is with the Weber Research Institute/Department of Electrical
The first geometry uses shorting pins in both sides of the
Engineering, Polytechnic University, Farmingdale, NY 11735 USA.
Publisher Item Identifier S 0018-9480(96)01437-8. central-guide region of a conductor-backed slotline or coplanar
0018-9480/96$05.00 © 1996 IEEE
170 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44, NO. 2, FEBRUARY 1996
y y
I I
I I
I I
I l_i
I I o
•'"
I
I I
w
I I
1---1
I
w b
I •--i
Top View
I
Shorting Conductor Coplanar
Waveguide Dielectric Coplanar Conductor
Boundary
·):::~:::::::::: :::::::::: I ~~ve~g~u~id~e~~~~
f
Cross-Sectional
View D
Er' E'r
a-------<
Conductor
Backing .1
Dielectric Block of Conductor
Fig. 1. Geometry of a conductor-backed coplanar waveguide with short Finite Width Backing
ing-pins used to supress leakage to the parallel-plate mode. A conduc
tor-backed slotline can be obtained by replacing the dual-slots of this coplanar Fig. 2. Geometry of a modified conductor-backed coplanar waveguide with
waveguide by a single slot of width, HI, centered at y = 0. a finite-width dielectric guide coupled to the coplanar waveguide. A similar
modified conductor-backed slotline geometry can be obtained by replacing the
dual-slots of the coplanar waveguide by a single slot of width W centered
at y = 0.
waveguide, placed periodically spaced along the propagation
direction. Fig. 1 shows the geometry of a conductor-backed
coplanar waveguide with "shorting strips." The shorting strips by a nonuniform dielectric structure, as shown in Fig. 2. A
in Fig. 1 have been used for the simplicity of analytical dielectric block of finite width, a is fabricated under the
modeling. The shorting strips would always exhibit similar central slotline or coplanar waveguide. The dielectric constant
characteristic trends as the shorting pins and are henceforth of this dielectric block, Er, should be much larger than the
interchangeably referred to by one name or the other. Such surrounding dielectric medium, E~. The leakage power from
shorting pins or shorting strips electrically connect the two the central transmission line, propagating in transverse (y)
groundplanes of the parallel-plate structure, and have been directions, gets totally reflected from the dielectric boundaries
commonly used in the past by stripline designers to suppress on the two sides. As a result, the leakage is eliminated allow
the possible excitations of the parallel-plate mode. However, ing unattenuated propagation along the longitudinal direction
due to the nonzero gaps between the shorting strips, (b-6) in (x). Such a condition of total reflection from the dielectric
Fig. I, the excitation of the parallel-plate mode will not be boundary between the central guide (Er) and the external
totally eliminated. The shorting strips will only suppress the substrate (E~) is possible, only when the effective dielectric
transversal leakage to the parallel-plate mode, always allowing constant, Eeff, of propagation of the dielectric-guide-coupled
a fraction of the power to escape through the nonzero gaps transmission line is greater than E~
between the strips (see Fig. I). Therefore, it is important to Eeff = /32/k6 > E~ (l)
investigate the effects of the separation between consecutive
shorting strips, b, for different strip widths, 6, and different where ke is the propagation constant of the dielectric-guide
distances, a/2, between the shorting strips and the center of coupled transmission line and ko is the free space propagation
the transmission line, on the leakage level. This would help constant. It is desirable that the width of the central di
design optimal positioning of the shorting pins, in order to electric guide is designed such that the dielectric-waveguide
suppress the power leakage to a practically acceptable low modes are not strongly coupled to. This is important in
level. order to avoid/minimize unwanted excitation of the dielectric
The second geometry we will analyze in this section is a waveguide mode(s) at any circuit discontinuity. It is also
modified conductor-backed slotline or coplanar waveguide. desirable that the relative values of Er and E~ are chosen such
Here the uniform dielectric substrate between the parallel that the wave is highly evanescent in the external substrate
plates of a standard conductor-based configuration is replaced region. This would be useful to avoid unwanted coupling
DAS: METHODS OF SUPPRESSION OR AVOIDANCE OF PARALLEL-PLATE POWER LEAKAGE 171
to an adjacent transmission line, and will require E~ to be 0:::; z:::; D, y = - a/2,
significantly smaller than Eeff and Er· L+oo
For wave-guidance purposes, the desirable mode of exci = ±Zfz p(x - ib)e-jk.ib;
tation for the geometry of Fig. 2 is the printed transmission i=-oo
line-type of mode. However, by increasing the width of the 0 :::; z ~ D, y = a/2, (4)
dielectric guide, a, such that the propagation constant of the
dielectric-waveguide mode is close to that of the printed g:s,
transmission line, a propagating dielectric-guide mode can = lxl :::; 8/ 2;
where, p(x) (5)
also be strongly coupled to. Such a possibility is promising, elsewhere.
permitting design of novel transitions between the conductor
As a standard rule, used above in (4) as well as followed
backed transmission line and the low-loss dielectric guide,
elsewhere in this paper, the top sign of a double-sign notation
for millimeter-wave applications. This will allow convenient
refers to a coplanar waveguide case, whereas the bottom sign
integration of dielectric waveguide and printed circuits.
refers to a slotline case.
The analyses of the two new geometries, with the short
Further assumptions are required in order that the e-ik.x
ing strips or a dielectric guide, that we will present in the variation of slot fields, Es ( x, y), used in (2) is valid. The
following subsections share a common basis of formulation.
fields produced by the slotline or coplanar waveguide can
The additional contributions due to reflections of the leakage
be decomposed into a "bound" part tightly confined around
fields from the shorting strips or the dielectric boundaries of
the central guiding region, and an exponentially "growing"
the dielectric guide are separately derived and then added
part propagating away from the central transmission line in
to a common solution to the central transmission line. The transverse (y) directions [3]. Similarly, the fields produced by
reflections from the shorting strips are modeled by a periodic
the strip arrays can be decomposed into a "bound" part tightly
moment method, whereas the reflections from the dielectric
confined around the strip (at y = ±a/2), and an exponentially
boundaries are obtained by matching the boundary conditions
"growing" part propagating away from the strips. We assume
between different field components at the dielectric interfaces.
that the strips and the transmission lines are sufficiently far
apart, such that only the propagating field components of
A. Analysis of a Conductor-Backed Slotline or a the strips and the central transmission line directly interact
Coplanar Waveguide with Shorting Strips with each other, whereas the bound fields do not. For most
With reference to Fig. 1, we will model the central coplanar practical transmission lines, the "bound" part of the field
waveguide or the slotline by replacing the electric fields, is so tightly confined around the central transmission line,
E.(x, y), in the slot areas by equivalent magnetic currents. that the placement of the strips with a reasonable physical
Equivalent magnetic currents, +Ms and -M are, respec distance from the transmission line would validate the above
8,
tively, placed just below and above the top conductor, and the assumption with good accuracy. Without such an assumption,
slot areas are closed by continuation of the conducting plane the close coupling of the bound fields of the strip array (which
do not have a continuous e-ik.x variation along x) to the
±M.(x, y) = ±z x E8(x, y) = ±J(y)e-ik.x; transmission line would distort the dominant propagating fields
ke = /3 - ja, (2) of the central transmission line. This would invalidate the
assumption of an e-ik.x variation of slot fields in (2).
In addition, the center-to-center separation between the
"NL
J(y) = a3i(y). (3) strips, b, in Fig. I is assumed electrically small, such that only
one propagating Floquet mode is produced due to the excited
i=l
currents on the strip arrays. This would require
For a coplanar waveguide the x-directed basis functions are
>.a
chosen with an odd symmetry, whereas the y-directed basis b < 27r · or, b < - 7-r = --. (6)
functions are chosen with an even symmetry, about the center - koft; + ke' - koft; 2-fi;
line (y = 0). In the case where the above condition is not satisfied, coupling
Now, assume the total surface currents excited on the strip from the strips to the central transmission line is established
arrays, h(x, z), to be along the ±z directions. Also assume through more than one propagating modes with different
that these ±z-directed currents excited on the shorting strips propagation constants, even when the strips are far away from
have an uniform variation along z as well as x. These should the transmission line. Under such conditions, therefore, the
be good approximations for narrow strips and electrically thin assumption of an e-ik.x variation of the slot fields of the
parallel-plate spacings. In addition, the currents on the strip transmission line will not be valid.
array at y = a/2 satisfies an even or an odd symmetry with The spectral-domain analysis of a conductor-backed trans
=
respect to that on the strip array at y -a/2, respectively mission line, without the shorting strips, has been presented in
for a coplanar waveguide or a slotline. With these above [3]. Without the shorting strips, a Galerkin testing procedure
considerations we can write will result in a set of N linear equations
h(x, z) = .zh(x) = Ziz "+Loo p(x - ib)e-jk.ib; LN aiZi1(ke) = O; for all j = 1, · · ·, N. (7)
i=-oo i=l
172 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44. NO. 2, FEBRUARY 1996
Im{K y) H s (y) is the y-variation of the magnetic field (x-variation is
assumed to be e-ikex) produced by the strip arrays just below
=
the conductor at z D.
Using a Floquet mode decomposition of the currents on the
strip array at y = - a/2 (and, similarly for the strip array at
y = +a/2 with a ± sign due to symmetry), we get
h(x, z) = /; .~ P(-ke + 2:i)e+j(-ke+(27ri/b))x;
c Re( Ky) i=-oo
0:::; z :::'.: D, y = - a/2 (12)
where P( kx) is the Fourier transform of the x-variation of the
strip currents, p( x). Considering only the zeroth Floquet mode
-<P,o for coupling to the central transmission line, the magnetic field,
H.(x, y), at the transmission line produced by the two strip
arrays can be expressed as
Fig. 3. The contour of integration, C, on the complex ky plane, in order to
correctly account for leakage to the parallel-plate mode. H (x, y) = ~~P(-ke)e-ikex [ (-x + ::o y) e-i'Pyo(y+a/2)
5
y)
The unknown complex propagation constant, ke, could be ± ( :i; + ::o ei'Pyo (y-a/2)]
obtained by solving the eigenvalue matrix
= H.(y)e-jkex. (13)
(8)
Im(cpyi) > 0, Re(cpxi) < ko,,JE;.;
Im(cpyi) < 0, Re(cpxi) > kojE;,
(14)
(15)
Using (13) in (11), and simplifying using proper symmetry of
(9) Fj(ky) for a slotline or a coplanar waveguide, we can write
where Hii (y) and Hi2 (y) are the y-variations of the magneti=c ZN+1,j= e-j<pby 0a/2 P(-ke) ( - :i:+ ckp : y) ·_F j('Pyo).
fields, respectively, below and above the groundplane at z
0
D, produced due to the ith basis mode of (3). Fi(ky)"' is the ( 16)
Fourier transform of the ith basis function, f;(y), and G's are An additional equation can be obtained via a Galerkin
the suitable spectral-domain dyadic Green's functions [12,"' 11] testing procedure, in order to account for the zero tangential
(see Appendix for the expressions of the components of G). boundary condition on the strips at y = - a/2. Due to the
symmetry of the geometry, the tangential electric field on the
It should be noted, as presented in [3], the contour of
strips at y = a/2 will be automatically satisfied
spectral integration, C, in (9) must be properly deformed
around the pole due to the parallel-plate mode. The required
N
path of integration is shown in Fig. 3. Power leaks from the L a;Z;N+I +IzZN+l,N+l = 0, (17)
transmission line in transverse directions due to coupling to
·i=l
this parallel-plate mode.
With inclusion of the shorting strips, the eigenvalue equa
tions (7), (8) must be modified in order to account for the j·D ; ·6/2
ziN+l = Ezi(x, y = -a/2, z)p(x) d.x dz, (18)
additional fields produced by the strip arrays
0 -6/2
N
L a;Zij(ke) + IzZN+l, j(ke) = O; for all j = 1,. .. 'N f 12
i=l IzZtv+i, N+I = {d 6 Ezs(x, y = -a/2, z)p(x) dx dz
Jo
(IO) -6/2
where the additional term, IzZN+I,j(ke), is the reaction of (19)
the strip currents on the jth basis mode where Ezi(x, y, z) is the z-component of electric field pro
duced due to the ith basis mode on the transmission line, and
Ezs(x, y, z) is the z-component of the electric field produced
by the two strip arrays.
OAS: METHODS OF SUPPRESSION OR AVOIDANCE OF PARALLEL-PLATE POWER LEAKAGE 173
Using the Green's function of Appendix, Ez;(x, y, z < D)
can be expressed as
Central ltansmission Line
+1 1 = j cos (cp1z) (Coplanar Waveguide or Slotline)
Ezi(x, y, z) = - · ( D)
27r . -oo, C, k,=-ke 'PI Sill 'Pl
· (-kyx - key)· F;(ky)e-jk.xejkyy dky. (20) ~ ~
d l'd
E'' £, £''
The contour of integration, C, is as shown in Fig. 3, of which ~r "'~
the residue around the pole at ky = 'Pyo only contributes to y
the propagating field far off the central transmission line for
a
y < 0, whereas the residue around the other pole at ky = -cpyo
only contributes to the propagating field far off the central Fig. 4. Propagating x-component of magnetic field, H.c, at the dielectric
transmission line for y > 0. These propagating fields couple interfaces at y = +a/2 a+n d y = -a/2, far away from the central
transmission line. The - or sign is chosen for a coplanar waveguide or a
to the strips at y = -a/2 and y = a/2, respectively. Applying
slotline geometry, respectively, due to appropriate symmetry considerations.
residue theorem to (20), we get
1
Ez;(x, y = -a/2, z) = - D (-cpyo·i - key) (22), (25). The complex propagation constant, ke, is the root
2 'Pyo of the eigen-matrix equation
. F;(cpyo)e-jk.xe-J'Pyoa/2. (21)
(26)
that can be searched using a Newton-Raphson algorithm.
Equation (21) can be used in ( 18) to get
B. Analysis of Conductor-Backed Slotline or Coplanar
Z;N+I = --1- P(ke )( - cpyoXA - k eYA ) · -F i ( 'Pyo ) e -j<pyoa/2 · Waveguide Coupled to a Dielectric Guide
2cp 0
y (22) We assume that the dielectric interfaces at y = a/2 and
Ezs(x, y, z) in (19) can be decomposed into a part, EzsI, y = -a/2 (see Fig. 2) to be sufficiently far away from the
produced due to the strip array at y = -a/2, and a second part, central transmission line. This is a valid assumption for most
Ez52, due to the strip array at y = a/2, that can be derived practical cases, where a reasonable width of the dielectric
from the Floquet mode decomposition of the source currents guide, a, will be usually larger than the extent of the tightly
on the strip arrays. All FJoquet modes due to the strip array at confined fields of the central transmission line. Under such
y = -a/2, whereas only the propagating Floquet mode due assumption, only the propagation field components excited
to the strip array at y = +a/2, contribute to the total coupling from the central transmission line couple to the dielectric
with the strip array at y = -a/2 interfaces. The propagating x-component of the magnetic field,
Hx, can be written as (see Fig. 4)
+oo
Ezs1(x, y = - a/2, z ) -_ --bIz- ~L ~wµo P( 'Pxi ) e j<p,;x., Hx(x, y, z) = be-jk,x(e+J'Pyv(y+a/2l + re-J'Pyv(y+a/2l);
i=-oo 'Pyi
o::; z::;D. (23) - a/2 < y < 0,
= =t=be-jk.x(e-J'Pyp(y-a/2) + re+J'Pyp(y-a/2));
0 < y < a/2,
= =t=bejk,x(l + r)e-j'P~p(y-a/2); y > a/2,
= be-jk,x(l + r)eJ'P~v(y+a/2); y < -a/2.
(27)
Now, using (23), (24), and (19) (28)
Z N+I, N+I = =Dt=w-µ-oP( - k· e )P(~'·; e ) e -j<p,"0 a
2bcpyo
'PyI p -- VkO2 EI r - k2e>· Im(cp~P) < 0,(3 > koR.;
~ -Dwµo
+. L 2btpy; P(cpx;)P(-cpxi) Im(cp~p) > 0,(3 < koR.,
i=-oo (29)
L+oo
= ±Coe-J'Pyoa + Ci (25)
r = -cpyp + 'P~p
i=-oo (30)
'Pyp + 'P~p
The ( N + 1 )-set of eigen equations ( 10), ( 17) can be solved where r is the reflection coefficient of H. at the dielectric
for the propagation constant, ke, with the expressions for zi.i 's, interfaces, and 'Pyp is the same as 'Pyo in ( 14 ), equal to the
i = 1, · · · ,N + 1, j = 1, · · · ,N + 1, obtained from (9), (16), pole due to the parallel-plate mode in the complex ky plane.
174 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44, NO. 2, FEBRUARY 1996
Without the dielectric interface, the conductor backed slot Using the spectral Green's functions of Appendix, the x
line or coplanar waveguide with a uniform dielectric, Er, component of magnetic field, Hx;(x, y, z), excited by the ith
between the parallel plates, can be analyzed using a method basis mode, f;(y), can be expressed as
1=
presented in [3]. This results in the eigenvalue equations (7),
(8), that can be solved for the complex propagation constant, Hx;(.7:, y, z) = +7!l" .7A : · G::. H1M(-ke, ky, z)
2
ke. With the inclusion of the dielectric interfaces at y = ±a/2, . -oo,C
the above eigenvalue equations (7), (8) must be modified in ·+ F1\ (1k y)a;ejk.xejkyy dky
order to include the additional reflections from the interfaces cos(cp1z)
LN = 27r c,k,=-k. <p1wµo sin (cp1D)
+
a;Z;1(ke) bZN+l,j(ke) = O; for all j = 1, · · ·, N +
· (jkekyil j(k6Er - k;)x)
i=l
(31) · F;(ky)a;e-jk,xe]kyy dky (39)
where the new term, bZN+l,j(ke), is the reaction of the
magnetic fields, Hr ( x, y, z), reflected from the dielectric where the contour of integration, C, is as defined in Fig. 3.
interfaces at y = ±a/2, on the jth basis mode of the The residue part of integration around the pole at 'Pyp (<pyo in
Fig. 3) only contribute to the propagating component of Hx
transmission line 1
for y < 0. Using residue theory
bZN+1,1(ke) = Hr(Y) · f1(Y) dy. (32)
slot
Hr (y) is the y-variation of Hr ( x, y, z) just below the top (40)
conductor at z = D. From the reflected parts of Hx in (27),
and using simple field relationships in a parallel plate structure,
the reflected magnetic field, Hr(x, y, z), can be expressed as Using (40) in (38), we get
::Pii)
Hr(.7:, y, z) = bfe-ikex [ ( x - e-j<pyp(y+a/2) ZiN+l = -Fw'µ(cp f5 ) · ('PypX + keil) ( l ±e- fi'ePv-pJa'P/y2p a ) . (41)
2
0
ii
=F ( X + 'P~p ) e+J'Pyp(y-a/2)] Now, the (N + 1) set of eigen equations (31), (37) can be
= H,.(y)ejk.x; -a/2 < y < a/2. (33) solved for the propagation constant, ke, with the expressions
+ +
for Z;/s, i = 1, · · ·, N 1; j = 1, · · ·, N 1, obtained from
Using (33) in (32), and simplifying using the symmetry (9), (34), and (41). ke is the root of the eigen-matrix equation
conditions for the basis transforms, F 1 ( ky ), we get (42)
2 'P~p ii) ·
ZN+i,j = 2re-i'Pypa/ [ ( x - F1('Pyp)]. (34)
III. RESULTS
An additional linear equation involving the N-unknown
basis coefficients, a;'s, and the unknown coefficient, b, can A. Leakage Suppression Using Shorting Strips/Pins
be obtained. If the propagating part of Hx excited by the Using a minimal number of shorting pins, optimally placed
transmission line in the y < 0 direction is de+i'PypYe-ikex,
around a transmission line circuit, is a feasible approach for
then with reference to the Fig. 4
leakage suppression in MMIC's, hybrid circuits, as well as
interconnect packages. Our analysis evaluates the effects of
(35)
the positioning parameters on the leakage suppression level.
which can be simplified as Figs. 5 and 6 show the results of leakage suppression in a
e-J'Pypa/2 ) conductor-backed coplanar waveguide, as a function of the
( 1 ± re-J'Pypa d-b width, 8, of the shorting strips, center-to-center separation, b,
between the strips, and the distance, a/2, between the strips
e-i'Pvpa/2 ) ( 8N ) and the center of the transmission line. Clearly, the power
d - b- 0 (36)
( 1 ± re-J'Pypa i - ' leakage has been significantly suppressed. As Fig. 5 shows, in
order to reduce the attenuation, a:, it is desirable to place the
shorting strips as close to the center of the coplanar waveguide
N
L
a;Z;N+1 - b = 0, (37) as possible. however, the shorting strips should not be too close
to the slot edges, which may result in undesirable interference
i=l
with the central bound fields of the transmission line.
A sharp increase in attenuation can be observed in Fig. 5
(38) when the distance, a, between the shorting strips and the center
of the transmission line approaches a critical value ac
where d; is coefficient of the propagating part of Hx, excited in
y < 0 direction by the ith basis mode, Ms = ±a;f;(y)e-ik.x (43)
(see (2)).
DAS: METHODS OF SUPPRESSION OR AVOIDANCE OF PARALLEL-PLATE POWER LEAKAGE 175
transmission line with the multiple reflections from the short
ing strips. For the transverse propagation of the parallel-plate
wave, the value of a = ac corresponds to a quarter wavelength
between the shorting strips and the center of the transmission
line (see Fig. I). Hence, the leakage field that is transversally
4 2-78 excited by the coplanar waveguide to one side (say, in +y
direction), partly (significantly) reflects back from the shorting
~ ~ strips at y = a/2 with about the same phase. Further, as can
'-.. '-..
el ~ be seen from the field symmetry, the parallel-plate leakage
fields excited from the coplanar waveguide directly in the -y
2 2.75 direction is in phase with that in the +y direction. (Note, in
contrast, for a conductor-backed slotline these leakage fields
excited to the two sides are 180 degrees out of phase with
each other.) Therefore, the above in-phase reflected field from
the strips at y = a/2 will constructively interfere with the
direct leakage field excited in the -y direction. Together they
a(mm) partly escape through the strips at y = -a/2, and the rest
reflects back in the +y direction, which in turn experiences
Fig. 5. Propagation, (3, and attenuation, a:, constants normalized to
free-space wave number, ko, of a conductor-backed coplanar waveguide multiple reflections and transmissions through the strip arrays.
geometry (see Fig. 1) as a function of the separation, a, between the two The round-trip multiple reflections from the strip arrays also
= = =
symmetric rows of strips. W 0.1 mm, S 0. 2 mm, frequency 10 GHz,
= = o = = constructively interfere with each other when a approaches ac.
€r 13, D 0.2 mm, 0.1 mm, b 1 mm. Notice the leakage increases
as a approaches ac :::::: 6.5 mm. The results beyond a = 5 mm, with much Accordingly, the constructive interference together of all the
higher a: are not shown. direct as well as the multiply reflected leakage fields result in
the increased loss in Fig. 5, as a approaches ac.
______ \ _____ _ Fig. 6 shows the variation of leakage with strip width, 8, and
the center-to-center separation, b. As expected, leakage loss
increases as the center-to-center separation between shorting
No Shorting Strips strips is increased, because it leaves more open area between
6 the strips for the leakage power to escape through. Also
due to the same reason, the leakage loss is seen to increase
for reduced strip widths. It maybe reminded, however, that
the center-to-center separation between the shorting strips, b,
should not be larger than a limiting value given by (6), in order
2 to avoid moding problems due to the excitation of higher order
Floquet modes from the strip arrays.
Figs. 7 and 8 show the results of leakage suppression in
0
conductor-backed slotlines, that can be compared and con
b(mm) trasted with the corresponding results from Figs. 5 and 6
for a conductor-backed coplanar waveguide. The dependence
Fig. 6. Attenuation constant, a:, normalized to the free space wave number,
ko, of the conductor-backed coplanar waveguide geometry of Fig. 5 with of leakage in Fig. 8 on strip width, 8, and center-to-center
a = 1 mm, as a function of center-to-center separation, b, between shorting separation between the shorting strips, b, show similar trends
strips, for different values of strip widths, o.
as in Fig. 6. However, the results of leakage loss, a, in Fig. 7
for a conductor-backed slotline can be seen in distinct contrast
where IPyo is given by (14), and j3 is obtained from Fig. 5. with the results of Fig. 5 for a conductor-backed coplanar
It may be noted that the leakage level close to a = ac is waveguide. Unlike in Fig. 5, in Fig. 7 a decreases as the
significantly large compared to that for smaller values of a, shorting strips are placed farther away from the center of the
=
making the use of the shorting pins/strips ineffective in this slotline and goes to a minimum at the critical value of a ac,
region. The leakage loss close to a = ac can increase to levels given approximately by (43). With the similar arguments
comparable to, sometimes significantly larger than that without made earlier for a conductor-backed coplanar waveguide, the
any shorting pins. Besides, close to and beyond a = ac, minimum value of a for the conductor-backed slotline at
complex mode-coupling with the rectangular waveguide-like a ~ ac can be explained due to a destructive interference
modes (confined between the top and bottom conductors of the of the leakage fields. This is because the two leakage fields
parallel-plate structure, and the two conductor-like strip walls excited by the conductor-backed slotline to the two sides are
at y = ±a/2) would occur, making it undesirable to use such now out of phase with each other, unlike being in phase for a
larger a for practical designs. conductor-backed coplanar waveguide.
The resonance effect in Fig. 5 close to a = ac, showing To comprehend, the placement of the shorting strips/pins
sharp increase in the attenuation, a, can be explained by critically determine the level of leakage suppression that can
interference of the direct leakage fields excited by the central be achieved. For a conductor-backed coplanar waveguide
176 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44, NO. 2, FEBRUARY 1996
similar to Figs. 8 and 6 should be used to determine the
10-4X120 1.38
required spacing, b, that provides an acceptable leakage level.
100 1.36 B. Leakage Avoidance Using
/ Dielectric-Guide-Coupled Geometries
PIKo/
90 / 1.34 By fabricating a small dielectric groove under a conductor
/ backed slotline or coplanar waveguide, one can avoid the
/
parallel-plate leakage problem. As discussed, such transmis
BO / 1.32 0
i. / c~a . sion line geometries would be attractive for mixed integration
<l / of printed circuits with dielectric-guide devices. Figs. 9 and 10
/
70 1.30 show the results of leakage constant, a, in a conductor-backed
coplanar waveguide and a slotline, respectively, coupled to
60 1.28 a dielectric guide. Consistent with the condition (1), in both
cases the attenuation, a, is zero when E;. < (/3/ko)2 (see
Fig. 2). It is seen from computation, that the phase constant,
500 5 10 15 20 1.26 (3, in both example cases is not strongly affected by the outer
E;.,
a(mm) dielectric constant, or the width, a, of the dielectric guide
(except in the regions of strong coupling to the dielectric
Fig. 7. Propagation, /3, and attenuation, a, constants normalized to
free-space wave number, ko, of a conductor-backed slotline geometry (see waveguide mode). Therefore, as per (I), in Figs. 9 and 10
Fig. I) as a fu=nc tion of the separat=io n, a, between =th e two sym=m etric rows the threshold value of E~ between the leaky and the nonleaky
of= st rips. W = 1 mm, frequency 10 GHz, Er 2.55, =D 8.01 mm, regions is practically independent of E~ and a. It is interesting
8 1 mm, b 7 mm. Notice the minimum leakage at a ac :::: 15 mm.
The value of a for the geometry without the shorting strips is about 0.1 ko. to see that the leakage attenuation can also be reduced to
an arbitrary low value by having the dielectric constant of
the outer medium significantly higher than that of the central
10-3x30..-----------------------,
dielectric guide region. Further, as expected, in both cases of
Figs. 9 and l 0 the values of a are the same for all values
of a, when E;. = E,., because the geometry now turns into a
regular conductor-backed geometry with a uniform dielectric
20 medium between the parallel plates. When Er > E;. > (/3/ko)2
the conductor-backed coplanar waveguide in Fig. 9 exhibits
less leakage for wider guides (larger a), but when E;. > Er
it exhibits more leakage for wider guides. The above trends
are seen to have reversed for a conductor-backed slotline
10
in Fig. I 0. As in conductor-backed geometries with shorting
---6 = lmm /
.,,. / strips, such trends of a for different values of a can be
/
explained by interference of the reflected leakage fields from
..,... .,,.,,.
- _ __ -·-6=2mm the dielectric boundaries at y = ±a/2 (see Fig. 2).
.-- . .--· Notice in Figs. 9 and 10 that at the onset of leakage when
4 6 B E~ is slightly greater than (/3/k0)2, there is a sharp increase of
b{mm) a for the conductor-backed slotline as well as the conductor
Fig. 8. Attenuation constant, a, normalized to the free-space wave number, backed coplanar waveguide. At this value of E~ the transverse
ko, of the conductor-backed slotline geometry of Fig. 7 with a = 15 mm, propagation constant in outer dielectric is zero, resulting
as a function of center-to-center separation, b, between shorting strips, for
in a unity reflection coefficient for the parallel-plate mode.
different values of strip widths, 8.
Therefore, the dielectric interface at this critical value of E~
acts like a perfect open circuit, which is a dual condition to the
the shorting pins should be placed as close to the central short-circuiting effects of the shorting strips discussed in the
transmission line as possible, without interfering with the last section. Using dual arguments to that in last Section III-A,
central bound fields of the transmission line. Typically, the one can explain the relative trends of a in Figs. 9 and Fig. 10
bound fields of the coplanar waveguide transversely extend with "a," at the onset of leakage (E~ = (/3/k0)2). Accordingly,
over a distance of the order of one slot width beyond the side these trends can be seen in contrast to the respective trends
edges. Therefore, for best results, the shorting pins should be of Figs. 5 and 7, with shorting strips. For a conductor-backed
placed about one slot-width distance away from the transverse coplanar waveguide, the leakage loss in Fig. 9 at the critical
edges. For a conductor-backed slotline, on the other hand, the value of E~. reduces with increasing a, whereas in Fig. 5 the
shorting pins should be placed at a distance a/2 = ac/2, leakage loss with shorting strips increases with increasing a.
as given by (43), for optimum performance. Besides, the Similarly, for a conductor-backed slotline, the leakage loss in
distance between the consecutive pins along the longitudinal Fig. l 0 at the critical value of E~ increases with increasing a,
(x) direction should be less than >.0/(2Vf;.) in order to avoid whereas for the corresponding range of a the leakage loss in
multiple moding problems, as discussed before. Computations Fig. 7 with shorting strips reduces with increasing a.