IEEE TRANSACTIONS
ON MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-30,
NO.
2, FEBRUARY
155
1982
Theory and Design of Low-Insertion
Fin-Line Filters
FRITZ
ARNDT,
JENS BORNEMANN,
DIETRICH
GRAUERHOLZ,
Abstract —A design theory is deseribed for low-insertion loss fin-line
filters that includes both higher order mode propagation and finite thickness of the dielectric substrate and the metallic fins. Design data for
three-resonator type fin-line filters with several substrate thicknesses are
given for midband frequencies of about 15,34, and 66 GHz. The measured
insertion losses in the passband are 0.25, 0.5, and 1.3 dB, respectively, for
these three frequencies.
I.
NTEGRATED
I
for
FIN-LINE
is a very attractive
applications
vantages of these circuits
include
tion
loss designs,
(Fig.
1) are taken into account
three-dimensional
data
and
[1]-[ 11].
the potential
if extremely
design theory for such fin-line
experimental
high
gap widths
1
l---
filters.
structures,
so far,
theories
([2]–[7])
Wall
Metal
Fms
spectral
domain
solution
only
are
technique
A com-
accompanied
are
calculated under the assumption that the thickness of the
substrate is very small in comparison
with the waveguide
width. The influence of the finite thickness of the dielectric
as well as of the copper cladding,
neglected, since it plays a significant
loss, stopband
however, cannot be
role concerning mid-
attenuation,
g.b
J_
1.
Fin-line
grounded
configuration.
(a) General cross section with bilateraf
fins. (b) Low insertion loss fin-line filter structure.
is
a gradual change of
of propagation.
In
cross section
L~=”
Substrate
Fig.
by a
is used in [4], but this theory
modes of the fin-line
Oieleti
Ptetal Fins
,
/
on the low loss
mode coupling is
discontinuities.
only valid as long as there is simply
line discontinuities
in the direction
insertion
Metal
a------+
/
first-order
of the coupled-mode
band
(a)
ad-
a
in the analysis of fin-line
the hybrid
Substrate
of low-inserg/b=
fin-line
bination
[5]-[7],
VAHLDIECK
medium
The
[2]. This paper introduces
available with considerable
restrictions
design. In [2] and [3], the higher order
neglected
AND RUDIGER
INTRODUCTION
millimeter-wave
For
Loss
and midband
finite
thickness
of the substrate
and metallic
fins, and the
sudden changes in the gapwidths.
The theory
is verified
by measurements.
The measured
frequency response of the fin-line
filters that have been
designed and operated at about 15, 34, and 66 GHz shows
good agreement between theory and practical results. The
high-Q design leads to passband insertion losses of typically only 0.25, 0.5, and 1.3 dB, respectively,
frequencies.
at these three
frequency.
Fin-line
width
g/b
filter
cross sections
= 1 (Fig.
l(b))
with
extremely
do not require
like in [8]-[ 11]. For the field theory
fin-line
treatment
high
solutions
given in this
paper, the high-Q fin-line filter (Fig. l(b)) is regarded as
consisting of alternating waveguide structures: a waveguide
with a dielectric
slab and three parallel waveguides, the
middle of which is filled with dielectric
(Fig. 2(a)). The
method of orthogonal
expansion into suitable eigenmodes
[12] is used together with the field matching at the steps
investigated.
mode
This allows consideration
excitation
up to a desired
of the higher
number
A. Scattering
Matrix
Finite
within
Length
the
of Bre-
0018-9480/82/0200-0155
THEORY
of the Three- Waveguide
a Waoeguide
Structure
of
,
For each subregionl v = I, II, III, IV (Fig. 2(b)) the fields
are derived from the x-component
of the vector potential Q
which is assumed to be a sum of suitable eigenmodes
Q;=
order
of modes,
Manuscript
received July 7, 198 I; revised September 3, 1981.
The authors are with the Microwave
Department,
University
men, Kufsteiner
Str., NW 1, D-2800 Bremen, 33, West Germany.
II.
gap
(p’,
f*,
and
kj~
i
~=]
z4jsin
()
!&
are explained
1The analysis is given for the general
metrically
in the E-plane of rectangular
applications
of the dielectric
$00.75 01982
IEEE
.e-Mn~
in
.
the Appendix.)
(1)
The
case of structures placed unsymwave-guides to include possible
slab structure
as phase shifters.
156
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Wawguide
Wifh a
Dielectric
Slab
I
l;,
I
AND
TECHNIQUES,
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MTT-30,
NO.
2, FEBRUARY
1982
etc.
/
/
J,,,..,,.,.,.>,,.
I
I
I
.G
e
I
1
‘a)
Three Parallel
Wavquides
THEORY
XxXx
1
;1
Ire,
W,,,,<
~z.,.,.
A/2
(b)
‘-
~
<+-S=
:;L-l
_(.
three- wa v@desstructure
r
,.?
~124
(c)
(d)
Fig, 2. Configuration
for the field-theory
treatment.
(a) Alternating
waveguide
structures.
(b) Transition
to three parallel waveguides.
(c)
Wave amplitude vectors of the structures of finite length. (d) Transition
to dielectric
slab structure.
coefficients
A%
are
normalized
P:=
The components
lated by
/ F“
to
the
E X H*dF=
related
lW.
of the electromagnetic
and Z=12
power
(2)
field
(x,
y)EFI’
(x, y) EF’ll
are calcu-
(x, y)GF”v
(x,
y)
G F“I’
(x, y) GF1va
(x, y),GF’I
(.x, y)c
(x, y)GF’v
(3)
where
k“==
a2pOcv
Cv=co. cr(u).
By matching
the field components
at the corresponding
interfaces F Pof the adjacent subregions (Fig. 2(b)) at z = O
F1lI
(4)
the coefficients xl; in (1) can be determined after multiDlication with the appropriate
orthogonal
function related to
each subregion. This leads to the coupling integrals elucidated in the Appendix.
If the forward
and backward
waves at the two steps (Fig.
ARNDT
et al.
: LOW-INSERTION
2(c)) of the structure
together,
LOSS FIN-LINE
of finite
then ( l)–(4)
157
FILTERS
length
1 ~ are suitably
can be written
related
dielectric
as the desired scatter-
slab
~jI = ~111
EII=EIV
ing matrix
H,ll = H:v
(%)=(::;
::~l::;)
“)
with
@l=
.=. +;
&m
y
‘d-;” is obtained
‘8)
“’
y a system
With (7(a-d)),
of linear equations
where the determinant
is required to be zero. This leads to
(s,,) =(s22)=(w)-'{[( u)+(E)] -l(v) [(v)+ (E)]-'(v) -[(v) +( E)]-l[(u)-(E)]}
(S,,)
=( S,l)=(W)-l{[(U)
The abbreviations
B. Scattering
Finite
Length
are explained
Matrix
within
(V)-[(U)+(E)]-l
in the Appendix.
of the Dielectric-Slab
Structure
of
2(c), (d)) the waves in regions2 I,
II, 111, and IV are expanded
(V)[(U)+(E)]-l[(
a transcendental
a Waveguide
For this structure.(Figs.
E:=
+( E)]-'
U)-(E)]}.
equation
(6)
for the propagation
factor
k,~
which is solved numerically
~.tan(k&(d
k~~
-c-e))+-&
Xm
into the eigenmodes
– UP ~ k~mA~sin
~=]
TX.
. tan
e–Jkimz
((
k~~
a—d+;
))
+
*ta@”(c+i))
xm
cm
~=1
(7b)
~=1
(7C)
where the relation
E~v=
H~v=
– Up ~ kzmA~vsin(k~~.x).
~=1
– j
~
~=1
kZ~k~~A~vcos
k;;
(k~.
k~:z
x). e-JkZ.’
k:;z
[1[]
HIV=
x
~ (k1v2 – k~~2)A~sin(k~~.x).
~=1
The common
propagation
and IV is determined
2Seefootnote 1.
factor
by the boundary
holds
e-jk,.’
e-Jk’mz.
kzm in regions
conditions
k;. c,
=
k;
k;=
–k;M,
ti2pOc0.
(lo)
k;
(7d)
II, 111,
The scattering matrix
(Fig. 2(c)) is given by
S of the structure
of finite
length 11
along the
([:;)
=(!:!
!2;)(:::)
’11)
158
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TRANSACTIONS
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AND
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VOL.
MTT-30,
NO,
2, FEBRUARY
1982
TABLE I
COMPUTER OPTIMIZED DESIGN DATA FOR LOW-INSERTION Loss
FIN-LINE FILTERS (DIELECTRIC MATERIAL: RT/DUROID
5880
c, =2,22; COPPER
CLADDING
THICKNESS
e = 17.5 pm (INCLUDED
IN THE COMPUTATIONS))
L---
Fin–1ine
a .—--+
Substrate
th,
ck”ess
t
Filter
12=18
11=19
mm
mm
mm
mm
15
. .
f
27.079
2.178
8.390
E. ’lka
8.400
15.19
560
0 .01,,
27.565
2.075
8.400
7.760
8.4D0
15.285
601
D.02’I
20.127
1.976
B.350
7.372
8.350
15. ?52
560
‘1/32$t
13.706
1.860
8.300
6.984
8.300
19.207
557
1/16,!
15.660
1.500
8.000
5.840
8.000
15.190
52b
Ka-bsnd
0 .005,,
19.5575
0.715
3.740
4.115
3.7L5
3b.02
620
a.7. l12mm
b=3.556mm
0 .01,$
19.928
0.660
3.740
3.800
3.745
33.989
698
0 .02,,
20.580
0.550
3.630
3.420
3.640
33.9a2
675
1/32,,
21.260
0.480
3.525
2.970
3.530
33.99
635
U-band
0.0D5,9
14.770
0.347
1.895
2.D38
1.900
66.09
1055
a.3.76mm
b.1.88mm
0.01,,
lb .824
0.353
1.855
2.038
1.860
65.940
1080
3dB
limits
a = 15.799 mm, b =7.899
@(Q2,)
(S,2)=(M=(Q,2)( ~)(W(Q2J.
(12)
The abbreviations
are explained in the Appendix.
The scattering matrix of the total fin-line filter structure
is obtained by suitably combining the transitions, the length
2(b)) being
reduced
tures A and B (or inverse) are joined
to zero if struc-
together
directly.
For
the computer calculation
the expansion into twenty eigenmodes in every region has turned out to be sufficient.
III.
filters
MHz
0 .005,,
(&,)= (&)=(Q,,)+ (Q,,)(@(FV)(Q,,)(
I (Fig.
Af*)
a=15.799mm
b. 7.899mm
with
of waveguide
Bandwidth
o
GHz
Ku-band
“)
Fin-line
14=16
13=17
DESIGN
of the three-resonator
type (that
means
mm),
and WR
15 (V-band,
RT/duroid
5880
(c, = 2.22)
has turned
relatively
electrical
varies
thickness
are WR
62 (Ku-band,
out
mm,
to be a
material with “sufficiently
good
chosen substrate thicknesses t
have also been investigated for substrate materials showing
similar results.
The design process is started with filter dimensions given
in [5], [6] for the narrow slot filter (g< b, Fig. 1), which
exhibits
a relatively
poor measured insertion
loss (e.g.,
about 2 dB for a midband frequency of about 15 GHz.) An
optimizing
computer program is used [13] and [14], which
corresponding
housings
cheap substrate
properties;
the
a =7.112
a =3.76
commercially
available are 0.005 in, 0.01 in, 0.02 in, 1/32
in, 1/16 in Rexolite (c, = 2.54), and Polyguide (c, = 2.32)
with four metal inserts) for midband frequencies of about
15, 34, and 66 GHz are chosen for design examples. The
waveguide
mm), WR 28 (Ku-band,
mm, b =3.556
b = 1.88 mm).
the
parameters
lZ to 15 (Table
of the dielectric
I)
and of the copper
for
the given
cladding,
as
ARNDT et a[. : LOW-INSERTION LOSS FIN-LINE FILTERS
well as for the roughly
bandwidth,
until
yields a minimum
mum.
(11 =/9
the dielectric
evolution
fixed midband
frequency
and 3-dB
the insertion
loss within
the passband
and the stopband attenuation
an opti-
is determined
substrate
strategy
by the chosen total
due to the measuring
[13],
[14] was applied
instance,
the Fletcher–Powell
method,
entiation
step in the optimizing
length
housing.)
instead
of
The
of,
-50-
1-
-LO
F&4
for
because no differ-
-30- –
process is necessary, which
reduces the involved
computing
time. This was further
reduced by including some physical considerations
into the
optimization
process: the dimensions 13= IT and 15 of the
resonator
sections determine
essentially
the midband
frequency &, the widths of the metal fin bridges determine
essentially
the ripple
of the passband
cause the midband
critical,
frequency
insertion
was assumed
loss. Be-
to be not
-20 I
–
-10 —
+ measured
so
S21m,n=-0,25dB
merely coarse steps were foreseen for the resonator
sections.
The
total
computing
time
for
the optimization
01
tations.
Table
16
14
process of one set of filter parameters was about 20-30
min. A SIEMENS-7880
computer was used for the compu-
18
flGHz —
(a)
I shows
low-insertion
the
computed
loss fin-line
data
filters.
of
the
optimized
For the Ku-band
design
all commercially
available
substrate
thicknesses
for
RT/duroid
5880 material were considered.
For the Kaband and the V-band design the thicker substrates
not taken into account. This is because the related
band attenuation
thicker
than
important
is reduced considerably
about
amount
one quarter-wavelength,
of power
were
stop-
if the substrate
allowing
to be propagated
an
the influence
thickness
chosen substrate,
commercially
of etching
should
be as thin
however,
available.
substrates
filters
errors,
the copper
the designed
filter
substrate
lengths
the already low matching
will
insertion
for both examples,
measured
16
v+
include
18
flGHz —
section
begins
and ends with
with the metallized
practical advantage
inserts.
of stan-
this choice, in addition,
reduces
IU3SULTS
Fig. 3 shows the calculated and measured insertion-loss
(scattering
coefficient
S21) in decibels as a function
of
frequency for three-resonator
Ku-band fin-line filters with
substrate thicknesses of 0.01 in and 1/16 in. The calculated
losses for both
+
or
of 17.5 pm was
investigations
loss.
IV.
minimum
S21mln=-0.6dB
For the
with about 5-~m gold cladding.
the dielectric
slab and not
Besides the above mentioned
dardized
+ measwed
-10-
Since its fundamental
mode differs scarcely from the
fundamental
TE ,O-waveguide mode the low-insertion
loss
filter requires no tapered transitions
to the waveguide.
Further,
-20-
the error
as possible.
only a thickness
Further
Y
\
-30
directly
is also included
midband frequency (e.g., for the Ku-band
would be about 400 MHz).
To reduce
I
!g40
is
in the computations.
The neglect of the metallization
influence would mainly lead to incorrect calculations
of the
cladding
-s0
+
across the dielectric slab.
The finite thickness of the metallization
Quartz
k
losses in the passband
which
substrate
values are about
indicates
are about 0.1 dB
the very low matching
thicknesses.
The corresponding
0.25 and 0.6 dB, respectively.
(b)
Fig. 3
Calculated
and measured
insertion
loss of Ka-band
fin-line
filters (Table 1). (a) Thickness of the dielectric
substrate: 0.01 in. (b)
Thickness of the dielectric substrate:
I/16 in
These
insertion
The
results
compare
well
loss of the inductive
comparison
shows tliat
attenuation,3
also higher
the wider
included in
with
the
low
strip bandpass
of the two
filter
experimental
filter
responses
[15].
of Fig.
3
the thicker substrate ~rovides better stopband
but the measured passband insertion loss is
because of the higher amount of energy within
lossy dielectric.
The dielectric
losses are not
the computations.
3This is because the reduction of the space between the metallic inserts
and the waveguide sidewafls increases the cutoff frequency
of the first
higher order filter mode. On the other hand this allows increased power
propagation
directly across the dielectric slab. Therefore,
the upper limit
are substrate thicknesses of about one quarter-wavelength.
160
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,
VOL.MTT-30,NO.2, FEBRUARY
1982
-50”
I
&l
dB
-40-
-30
-20
-J--kI
1
S21m“
o
32
-30
34
36
38
/.,
(a)
Fig.
5.
#
\
I
I
60
70
65
75
Mil-lz —
Calculated and measured insertion-loss
of a V-band fin-line
(Table I). Thickness of the dielectric substrate: 0.005 in.
+
-50-
55
50
40
flGHz —
filter
1
I
I
-40-
-3-
-20Fig. 6.
V-band
fin-line
structure
(66.8 GHz),
stopband behavior is obtained.
Fig. 5 shows the calculated and measured
-10-
o-r
30
Photoetched
/
32
for a designed
V-band
tric
The calculated
substrate).
fin-line
filter
minimum
about 0.1 dB (versus the measured
34
36
38
miz
40
—
The photoetched
fin-line
(0.005-in
insertion
thick
loss
dielec-
insertion
loss is
value of about
1.3 dB).
structure
(V-band)
is shown
in
Fig. 6.
(b)
Fig. 4. Calculated
and measured insertion
loss of Ku-band
fin-line
filters (Table I). (a) Thickness of the dielectric
substrate: 0.01 in. (b)
Thickness of the dielectric substrate:
1/32 in.
The frequency displacement
between the calculated and
measured curves is caused by etching errors and production tolerances of the available material:
copper cladding
thickness about a 2.5 pm, substrate thickness about Y 20
pm. This has been checked by using the measured
try of the etched filters in the theory.
occur
higher
statistically,
the displacements
and lower frequencies.
geome-
Since the latter errors
are
towards
both
For
the thicker
substrate,
again,
better
CONCLUSION
A design theory has been described
fin-line
filters,
consisting
for low-insertion
of alternating
metallic
loss
bridges
and gaps on a dielectric slab mounted between the broad
walls of a rectangular
waveguide.
This theory includes
higher order mode propagation,
as well as the finite thicknesses of the dielectric slab and the metallic fins.
Three-resonator
The low-insertion
insertion
midband
tively.
The corresponding
insertion losses of Ka-band
fin-line
filters with substrate thicknesses of 0.01 in and 1/32 in are
given in Fig. 4. The calculated minimum
insertion
losses
are about 0.3 dB, the measured values about 0.5 and 0.8
dB, respectively.
V.
are chosen for design
examples.
loss design leads to measured
filters
passband
losses of about 0.25, 0.5, and 1.3 dB for the
frequencies of about 15, 34, and 66 GHz, respec-
More
resonators
yield higher
stopband
attenuations
and steeper characteristics
but the insertion loss in passband is also higher (e.g., for a five-resonator
filter by about
1.4 dB in Ku-band).
The low-insertion
loss values result from the considerably higher unloaded Q of this filter resonators in compari-
161
ARNDT et d. : LOW-1NSERTION LOSS FIN-LINE FILTERS
son with
the common
that no tapered
structure
are required.
neutralized
if
small-gap
the g/b
small gap design and from
transitions
from
= 1 structure.
loss of constructed
applications
and therefore
But
however,
may
suitable
long exponential
is
necessitate
transitions
since the additional
20-mm
the fact
to the fin-line
The second advantage,
solid-state
integration
waveguide
ent substrate
of the characteristics
thicknesses
vide better stopband
amount
of energy
passband
shows that thicker
attenuation,
because
of
its
is suitable
lower
Lower losses also result
porting dielectrics.
(u)=
the dielectric,
RT/duroid
matrix
pro-
;
[2( L)”(((E)-(R)”(R)
”)-’((N)”)-’}
~nll
-( L)”((N)”)-’]
(V)=
with differ-
substrates
=unit
(E)) -’(v) ((u)+ (E)) -’(T”)
(R)’
j
[2( L)7(E)-(R)V(R)V)
v=II
=diagonal
matrix
with finite
-’(R)
P((N)V)-’)]
of the three-waveguides
structure
length lZ
the
5880 is
To reduce losses and etching
errors, fused silica (quartz)
tions
within
is also higher.
material.
(E)
but because of the higher
propagated
insertion-loss
used for substrate
of filters
(l’v)=(E)-((u)+
transi-
tions (g/b = 1 to g/b =0.2 and back to g/b=
1) for the
complete Ku-band
was only typically
about 0.5 dB, the
low-loss fin-line filter design may still compare favorable
with the small-gap design also for these applications.
A comparison
in (5)
to
insertion
double
Abbreviations
loss
from
and
for further
investiga-
surface
roughness.
a complete
absence of sup-
(N)”: (N)ll=(DHmn)-’(
DHnn)
APPENDIX
(N)lll=(DHmk)-’(
Abbreviations
DHkk)
in (1)
(N)*V=(DHWZ,)-’(DHH)
f’
f
with the matrix
x
coefficients
D Hnn
H
d–c–e
=
d–;–x
f
f
D Hkk
a—x
IV
=
x
and coupling
P1
a
P1l
d–c–e
integrals
—
—
P
P
111
IV
a—
()
n
e
..
111
k;:zAII
2
d+;
H~[=
1
‘–”2
~=o
~_;
L
sin~xsin~(x)dx,
a
C—E
2
(~)”:(~)ll=(~~mm)-’(
DEmn)
m7r
(–)
2
(L)lll=(DEmm)-’(
DEmk)
(L)lv=(DEmm)-’(
DEm/)
a
mn
2
with the matrix
coefficients
(-)P1l
m7r
2
(-)P 111
m77
(-)P
IV
2
DEmm = ;k:~A:
a– d – 1
2
/@J12#II
IEEE TBANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, vOL. MTT-30, NO. 2> FEBRUARY 1982
162
and coupling
H.n =~~-C~,,
H~~=
Hlm
a
/ x=d+
=
sin ~ _n~_,
(d – ~ – x) sin ~xdx
k~
“
(a–x)sin~xdx
‘lna–&+
[8]
[9]
application,”
Arch. Elek. Ubertragung,
vol. 31, pp. 40–44,
A, Beyer, “Analysis
of the characteristics
of an earthed
[3]
[4]
e/2
‘-’/2
sin
mv
x sin — xdx .
a
1~
~=o
J
P, J. Meier, “Integrated
fin-line
millimeter
components,”
IEEE
Trans. Microwave
Theoiy Tech,, vol. MT1-22,
pp. 1209-1216,
Dec.
1974,
P. J. Meier, “Millimeter
integrated circuits suspended in the E-plane
of rectangular
waveguide,”
IEEE Trans. Microwave
Theory Tech.,
vol. MTT-26,
pp. 726–732, oct. 1978.
D. Mirshekar-Syahkal
and J. B. Davies, “Accurate
analysis of
tapered planar transmission
lines for microwave integrated circuits,”
IEEE Trans. Microwave
Theoiy Tech., vol. MTT-29,
pp. 123-128,
Feb. 1981.
A. M. K. Saad and K. Schtinemann,
“A simple method for analyzing fin-line structures,”
IEEE Trans. Microwave
Theoty Tech., vol.
MTT26,
pp. 1002-1007,
Dec. 1978.
A. M. K. Saad and K. Schiinemann,
“Design and performance
of
fin-line bandpass filters,” in Proc. 10th European Microwave
Conf.,
(Warsaw), Sept. 1980 pp. 397-401.
H. E. Hennawy
and K. Schiinemann,
“Anafysis
of fin-line discontinuities,”
in Proc. 9th European Microwaoe Conf., (Brighton),
Sept.
1979, pp. 448-452,
H. Hofmann,
“Dispersion
of planar wavegtrides for millimeter-wave
[2]
integrals
~—c
[5]
2
[6]
Abbreviations
in (11)
(W)=((E)-(Q22)(
R)(Q22)(R))-1
R mm
Scattering
coefficients
=
[7]
e–Jk~J1,
of the single step
IEEE
(Q,,) =2(%I-’(LJ(J4)-(E)
[10]
(Qn)=2(~)
(Q,2)=Z(%-’(LY)(
M)(DE)-’(%)
(Q22)=Z(Jf)(%-’(
[11]
LE)-(E)
(W=((%-’(%)+(%)
-’(%))-’
[12]
D ~~~ = ;k;~A;
[13]
D ~~~ = :k::A;
.
[14]
The coefficients
of the matrices
(;J
and ( L~)
are given
by
kzk(A~lI:k
+ B;lI~;
+ A;l(–
T1kI~;
+1;[)+
A~vI~v~)
[15]
Trans.
Microwave
Theoy
Tech., vol. MTT-29,
1971.
fin-line,”
pp. 676-680,
July 1981.
A. Beyer and I. Wolff, “A solution of the earthed fin-line with finite
metallization
thickness,”
in 1980 IEEE
MTT-S
Int. Microwave
Sywyr. Dig. (Washington,
DC) pp. 258-260.
L. P. Schmidt,
T. Itoh,
and H. Hofrnann,
“Characteristics
of
unilateral
fin-line
structures with arbitrarily
located slots,” IEEE
Trans. Microwave
Theoty Tech., vol. MTT29,
pp. 352-355,
Apr.
1981.
F. Arndt and U. Paul, “The reflection definition
of the characteristic impedance
of microstrips,”
IEEE
Trans. Microwave
Theory
Tech., vol. MTT-27, pp. 724-731, Aug. 1979.
A. Hock and J. Rinderle, “Zur Anwendung
der Evolutionsstrategie
auf Schaftungen
der Nachrichtentechnik,”
Frequenz,
208-214,
1980.
H. Schmiedel, “Anwendung
der Evolutionsoptimierung
wellenschaltungen,”
Frequenz, vol. 35, 1981.
vol.
34, pp.
bei mikro-
Y. Konishi and K. Uenakada, “The design of a bandpass filter with
inductive strip-planar
circuit mounted in waveguide,”
IEEE Tram
Microwave
Theory Tech., vol. MT1-22,
pp. 869-873, Oct. 1974,
*
= L~~~
with
the abbreviations
T1k=tan(k~~.
Coupling
a).
couplers and microstrip
techniques at the Techticaf University
of Darmstadt.
Since 1972 he has
been a Professor of Microwave
Engineering
at
the University
of Bremen,
Germany.
His research activities are at rxesent in the area of the
solution of field problems of waveguide and fin-~ine structures, of antenna
design, and of microwave holography,
Dr. Amdt
is member of the VDE and NTG
(Germany).
In 1970
received the NTG award,
integrals
I;~k =
d – e/2
J
cos(kj-x)sin(~x)dx
~=c+e/2
w
= J:;::,2sin
I:;
=
~:;[=
“
/ ~Id~e/z
sin ( %X
cos ( k~~x ) sin
a
Jx=d+
I~vk =
(w
sin ( k~~x ) sin
e/2
c – e/z sin ( k:~x ) sin
()
()
) dx
m77
7X
dx
*
dx
~X
a
mv
‘X
J~ =0
()
dx.
REFEREFJCES
[1]
P. J, Meier, “Equivalent
of integrated
fin-line,”
Apr. 1~73.
Fritz Arndt was born in Konstanz,
Germany, on
April
30, 1938, He received the Dipl.-Ing.,
the
Dr.-Ing.,
and the Habilitation
degrees from the
Technical University
of Darmstadt,
Germany, in
1963, 1968, and 1972, respectively.
From 1963 to 1972 he worked on directional
relative permittivity
and unloaded
Electron. Lett,, vol. 9, no. 7, VD.
L.
Q-factor
162– 163.
Jens Bornemann
was born in Hamburg,
West
Germany,
on May 26, 1952. He received the
Dipl.-Ing.
degree in electrical engineering in 1980
from the University
of Bremen, West Germany.
Since 1980 he has been with the Microwave
Department
of the University
of Bremen. His
topics of interest include waveguide
structures,
discontinuity
problems, and numerical techniques
in electromagnet tic theory.
163
IEEETRANSACTIONS
ONMICROWAVE
THEORY
ANDTECHNIQUES,
VOL.MTT-30,NO.2, FEBRUARY
1982
Riidlger
Vahfdieck
was born in Heiligenhafen,
Germany, on July 8, 1951. He received his Dipl.Ing. degree in electrical
engineering
from the
University
of Bremen, West Germany, in 1980.
His present research activities are in the field
Dietrich
Grauerholz
was born
in Krems
II,
Germany,
on September 22, 1945. He received
the Dipl.-Ing.
in 1971.
From 1971 to 1973 he worked in the HighFrequency
Laboratory
of
Elektro-Spezial
(Philips).
In 1973 he joined the Microwave
De-
of microwave
integrated
circuits and in solving
electromagnetic
field problems for severaf waveguide discontinuities.
Since 1980 he has been
with the Microwave
Department
of the University of Bremen.
partment
of the University
of Bremen, where he
has been engaged in the research and development of microstnp
circuits,
fin-line structures,
and microwave measurements.
Radial-Symmetric
N-Way TEM-Line
IMPATT
Diode Power
Combining Arrays
DEAN
A bsfract —Ckcuit
class of IMPA’fT
radial-symmetric
circuit
N-way
ered.
circuits
to perfo~
combiners
and resistively
10-dB
predicts
examples
frequencies
IMPATT
X-band
and provide
properties
Theoretical
X-band
design and stability
diode
an optimaf
stabilized
this
A 1OO-W resistively
a 150-MHz
locking
function.
N-way
combining
Predictions
a l-dB
integration
adding
which make use of reatistic
indicate
are developed
These combiners
the power
of
properties.
combiner
gain.
criteria
diode power combiners.
for
of device and
Both
combiners
a 30-W
stabilized
1O-GHZ
Iossless
are considare given
experimentally
bandwidtb
for a new
make use of
technique
locking
bandwidth,
F. PETERSON,
ten-diode
Iossless
of 300 MHz
ten-diode
also at 10-dB locking
at
determined
and
combiner
gain.
MEMBER, IEEE
cylindrical
T
he purpose
TMO~O cavities
of the nonresonant
Wilkinson
hybrid
of Harp
N-way
et al. [3]–[6].
combiner
include
[7] and the five-way
combiner
of this paper is to present a new approach
to circuit-level
power
combining
of negativeresistance devices in general and IMPATT
diodes in partic-
of Rucker
Each of these power combining circuits has its associated
performance
limitations,
design criteria,
and problems.
Corporate or serial combiners have the advantage of isolation
between
and provide
devices to eliminate
broadband
of often
deleterious
performance,
substantial
circuit
require
stabilization
resistors
among devices and undesired
interactions
but have the disadand combining
[1], often at high power levels. Resonant
INTRODUCTION
Examples
the nonplanar
[8].
vantage
I.,
‘
to
N-way
suppress
oscillation
losses
combiners
interactions
modes in a high-Q
ular. In a recent review article, the present state of microwave
power combining
techniques
was effectively
summarized by Russell [1], to which the reader is referred for
an in-depth discussion of various combiner types and their
cavity, leading to narrow-band
although
high-efficiency
combining.
Nonresonant
N-way stWctures usually provide
larger bandwidths
with a corresponding
increase in the
mode suppression problem. Rucker’s techqique [8] analyzed
by Kurokawa
[9] has been successful, as has apparently
performance.
been a conical line technique
be classified
the outputs
Basically,
roughly
from
into
level, combiners
two categories:
all devices are combined
and corporate (hybrid)
levels
at the circuit
are successively
N-way,
in which
in a single step,
or serial, in which increasing
combined.
N-way
can
power
combiners
are
often additionally
separated into resonant and nonresonant structures. Examples of the former are the waveguide
combiner
of Kurokawa
and Megalhaes
[2] and the circular
spaced TEM
tor power combining
The combining
haps be classified
networks.
July 2, 1981; revised August 31, 1981. This work
Air Force AvioNcs
Laboratory,
Wright-Patterson
Contract F3361 5-77-C-1132.
the Electron
Physics Laboratory,
Department
of
Engineering,
University
of Michigan, Ann Arbor,
arrays of equally
for transis-
[1 1].
circuits treated in this paper could peras N-way nonresonant ‘transmission-line
opposed
however, the “circuit”
intertwined
such that
dently.
Manuscript
received
was supported by the
Air Force Base, under
The author is with
Electncaf and Computer
MI 48109.
As
[ 10]. Radial
lines have been used successfully
to
other
networks
and “device”
each cannot
Hence the combiner
of
this
type,
properties are closely
be specified indepen-
represents,
in some sense, an
optimal
integration
of device and circuit to perform
the
power adding function. Both lossless and resistively stabilized
symmetrical
combining
circuits
are considered
and
each can provide the desired suppression of the unwanted
non-power-producing
modes while affording
design flexi-
0018-9480/82/0200-0163$00.75
,01982 IEEE