Idea Transcript
~IEEE
TRAN SACTI 0 NS
ON
MICROWAVE THEORY AND TECHNIQUES JANUARY 1985
VOLUME
MTT-33
NUMBER
1
(ISSN 0018-9480)
A PUBLICATION OF THE IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY
EDITORIAL
... ... .......................... ............ ........... .... .. , ...........................
T. Jtoh
PAPERS
Impedance Transformation and Matching for Lumped Complex Load with Nonuniform Transmission Line ............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . I. Endo, Y. Nemoto, and R. Sato Lossy Inductive-Post Obstacles in Lossy Wa,·eguide .................................. . ..... P. G. Li and A. T. Adams Complex Propagation Constants of Bent Hollow Waveguides with Arbitrary Cross Section .. . .................. M. Miyagi Noise due to Pulse-to-Pulse Incoherence in Injection-Locked.Pulsed-Microwave Oscillators. Part II- Effects of Phase-Locking Dynamics ...... .. ... ........ .... .......... .. .... ... ... ... .... . . .... . D. G. Anderson, M. Lisak, and P. T. Lewin Accurate Analysis Equations and Synthesis Technique for Unilateral Finlines .......... ... ... P. Pramanick and P. Bhartia General Stability Analysis of Peri~ic Steady-State Regimes in Nonlinear Microwave Circuits .... V. Rizzo/i and A. Lipparini Hybrid-Mode Analysis of Coupled Microstrip-Slot Resonators ............................................ K. Kawano A Continuous Comparison Radiometer at 97 GHz .... C. R. Predmore, N . R. Erickson, B. R . Huguenin, and P. F. Goldsmith
2 8 15 20 24 30 38 44
SHORT PAPERS
Active Stabilization of Crystal Oscillator FM Noise at UHF Using a Dielectric Resonator . ....... . .... .. . .... A. G. Mann 140-GHz Finline Components ..... .. .. .......... . ..... ... ..... . ... .... ..... . . . ......... W Menzel and H. Callsen Radial-Line/Coaxial-Line Stepped Junction . ..... . .... .... ... .... ... ........ . ......... .. .. ... .... A. G. Williamson New Analysis of Semiconductor Isolators: The Modified Spectral Domain Analysis .. . . .. . . . ......... S. Tedjini and E. Pie Biological Tissues Characterization at Microwave Frequencies ........... ... ... . . . B. D. Karolkar, J. Behari, and A. Prim Higher Order Mode Cutoff in Polygonal Transmission Lines . .. .... ... .... ... . ... ... ... . H. E. Green and J. D. Cashman An Explicit Six-Port Calibration Method using Five Standards .. . .. . ...... . .. . ..... . ...... J. D. Hunter and P. I. Somlo
51 53 56 59 64 67 69
LETTERS
Comments on "Theory and Measurement of Back Bias Voltage in IMPATT Diodes" ..... .. ... .. .. .... ...... .. . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. C. Tiwari, L. H. Holway, Jr., and S. L. G. Chu Corrections to "Theory and Application of Coupling Between Curved Transmission Lines" .. .... M. Abouzahra and L. Lewin Corrections to "Coupling of Degenerate Modes on Curved Dielectric Slab Sections and Application to Directional Couplers" . .
72 74
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Abouzahra and L. Lewin 75 N. R. Dietrich
76
IEEE COPYRIGHT FORM . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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PATENT ABSTRACTS . .. ..... .. ............ ....... ....... . . . .. ... ... .. .. ............ ... . .. ..... .
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for all frequency
impedance
CO= CL. Step 2) Selecting
k
steps can be
line and the transfor-
for all Frequency Ranges
impedance
ratio three
out when the inequality
ance Z~. Transformation
transformer the above
VWOand the line
mation ratio k of the ideal transformer (IT), the driving point impedance Zin becomes a lumped series RC impedance, which is, in general, different from the load imped-
A. Impedance
The
so that
WO=RL/k2=R0
(12)
K1=l/(k–l).
(13)
set (7)
WO=RL. The driving
point
impedance
observed
at the right-hand
side of the transformer in Fig. 2(b) becomes R ~. Step 3) Selecting the transformation ratio k transformer. We set k={=.
of
the
(8)
The driving point impedance observed at the left-hand side of the transformer becomes the pure resistor R ~ of the
The
line
R ~ = 500.
length
1 versus
CL is shown
In Fig. 3, the parameter
the load impedance.
in
Fig.
3 for
is RL, the real part of
For higher levels of load impedance,
longer line length is needed. Numerical Examples: We show these impedance
a
trans-
formations by numerical examples for loads of CL= 2 pF and R ~ = 300 and 500 Q, respectively, for R ~ = 50 !2. The parameters of the PTL are shown in Table I. The frequency responses of the load impedance and the transformed
driving
point
impedance
are shown in Fig. 4
IEEE
IMPEDRNCE
f
Fig.
4.
D.4
-
The
– 2.5
scheme
ON MICROWAVE
THEORY
AND
COORDINATES
(GHz),
(5E
of afl frequency impedance
Ro
TRANSACTIONS
Ohm
f-
transformation
on the
~
Fig.
6.
B.4
– 2.5
From load
///’///////////// 5.
The circuit
diagram
of achieving one-point lumped inductor.
matching
using
MTT-33,
NO,
1, JANUARY
1985
COORDINATES
(GHz),
(5@ Ohm normalized)
The scheme of one-point impedance matching using the lumped inductor of all frequency transformation designs.
(14), an increase
the load impedance
Fig.
VOL.
IMPEDRNCE
normalized)
impedance chart.
TECHNIQUES,
impedances
of the resistive
component
RL of
Z~ causes a decrease of Q so that the having
broader
band
frequency
resistive
components.
higher
resistive
matching
components
than those having
give lower
the
C. Impedance The
exact
Transformation impedance
for Narrow
Frequency Ranges
transformation
described
in Sec-
for the frequency range ~ = 0.4–2.5 GHz. The impedance loci Z~ of the load impedances are assigned by capital letters A –A’ and B –B’, corresponding to loads A and B,
tion II-A can be carried out under the inequality condition of (9). If the inequality is not satisfied, we may introduce a well-known quarter-wave matching technique for narrow-
respectively,
band impedance
shown in Table I, and the impedance
of the transformed by small letters and
driving
a –a’
B, respectively.
ance loci
point
and b-b’, The load
are located
impedance
are assigned
corresponding impedances
at regions
of very
loci Zi~
to loads A
whose impedhigh
levels
For one-point with
internal
Matching
transformations.
is summarized
Step 1) Cancellation
impedance
of two capacitors
of – C ~ and CL.
CO= CL.
(15)
of line length 1. For a design Step 2) Determination frequency fo, we set the line length 1 of the PTL to a quarter-wavelength,
i.e., ~_lv
(16) 4fo”
matching
between
R ~ and driving
a generator
point
In this step, the driving
point
impedance
Zi~ becomes
impedance
Zi~,
one can use a lumped inductor L in series at the of the PTL by the simple technique as shown in Fig. 5. We show examples of frequency responses of the final driving point impedance ~i~ (one-point matched) in Fig. 6 for frequency ranges of ~ = 0.4–2.5 GHz and the center frequency of& = 1 GHz. When one-point matching is carried out for these cases,
zj.(juo) =*+*
(17)
front-end
L
at the frequency fo. Step 3) Determination of transformer acteristic impedance WO. If we set
ratio
k and char-
the behavior of the network is that of an RLC series resonance circuit, so that the quality factor Q of the
the real part of (17) becomes R o. The unknown
driving
k will
point
Q=
impedance
~i.
1 2~fOkCLR0
transfor-
four steps.
We set
Technique
impedance
This impedance
in the following
are
transformed to the regions of low-impedance levels located on a unit circle of normalized resistance. Evidently, matching techniques for the transformed low-level driving point impedances are easier than those for the original load impedances. B. A One-Point
mation
is given by 1 = 21i’focL{~
(14) “
be uniquely
determined
k=l+
from
1 4focL~~
(2)-(4), >1.
parameter
(15), and (16)
(19)
ENDO
et a[.: LUMPED
Tm
COMFLEX
PARAMETERS
LOAD
ZL
TRANSM1SS1ON
5
LINE
IMPEDRNCE
COORDINATES
DESIGN
=1 GHz)
k
V70[.fl]
1.79
88.3
L[cm]
‘1
= 5oo [n]
‘L
A
NONUNIFORM
TABLE II PTL’s FOR NARROW-BAND
OF
(fO
load
WITH
CL
= 2[pF]
1.26
7.5
c,
Step 4) Determination of network parameters PTL. The line length 1 is given by (16), and
of
the f
K1=(k–1)-1=4&CL~~
(20)
wo=~=y.
(21)
We demonstrate mations
these narrow-band
by numerical
examples
impedance
for loads
CL=
The frequency impedances
point
impedances
described
responses of the transformed
21. and the one-point 21.
in Section
respectively,
(achieved
II-C)
2.5
(GHz),
(Sa
Ohm
normalized)
(a)
IMPEIIRNCE
COORDINATES .
matched
of
~0 = 1 driving driving
the same technique
are shown in Fig. 7(a) and (b),
for the frequency
III.
by
-
transfor-
the PTL are shown in Table II for a design frequency GHz.
a.4
2 pF, and
RL = 10, 300, and 500 Q for R. = 50 Q The parameters
point
-
range j = 0.4–2.5 GHz.
ADMITTANCE TRANSFORMATION AND
MATCHING
FOR LUMPED RL LoADs WITH
.
RECIPROCAL PARABOLIC TAPERED TRANSMISSION LINES The characteristic cal parabolic
impedance
tapered
distribution
transmission
w’(x)
f
!2.4
-
2.5
is given by
(22)
1X2-
[GHz),
(50
Ohm
normalized)
(b)
of the recipro-
line (RPTL)
W.
=
-
Fig. 7. The scheme of (a) narrow-band impedance transformation on the impedance chart. The impedance loci of ZL are assigned by capital letters (A – A’, &B’, and C– C’ correspond to the load shown in Table II). The transformed impedance loci are assigned by smafl letters and (b) one-point impedance matching using the lumped inductor.
()l+~T An RPTL
loaded
by a lumped
YL=++— L
parallel
RL admittance
1
(23)
jtiLL
is shown in Fig. 8(a) and its equivalent Fig. 8(b) [13]. In this equivalent circuit,
Y~
(24)
k=l+~>l 2
admittance
(26)
WO(l+K2)l/(k2v).
transformation
estimations.
length
of LL
frequency
is the dual
of that
de-
scribed in the previous section. Table III gives these formulas and information, the ratio of the imaginary to the real part of the immittance before and after the transfor-
1 as a function
Fig. 9 shows
for the case of all
transformations.
JV.
EXPERIMENTAL RESULTS
Two lumped series RC loads and PTL’s were constructed. These loads consist of a metallized film resistor and a chip capacitor in series. The measured frequency responses
(25)
VWO= Wo/k2
The
for the gain-bandwidth
the line
circuit is shown in the circuit parame-
ters are given as follows:
Lo=
mation,
of these loads (load I and load II) are shown in
Figs. 10 and 11, respectively, for the frequency range of 50–300 MHz, and represent good lumped impedances. In Table IV, typical values of load constants (they are determined from measured responses at ~ =150 MHz) and parameters of the PTL’s designed for all frequency transformations are listed. The line length needed for load II is very short as compared with the wavelength of the measur-
IEEE
TRANSACTIONS
ON MICROWAVE
1
‘&
Ro
w’ (x)
all
TRANSFORMATION
impedance
RC
(RL
Wo
-L o
NO.
1> JANUARY
1985
TLRL
kLO
‘L
with
narrow
WITH
PTL
PTL
AND
parallel
frequency
transformation
onnation
Q = V /
-~L)vcL
/(k-l)
transformation
with
narrow
RPTL
frequency
transformation
(4fo)
=~L
K2=l
admittance
frequency
transformation
i W.
R.
by
RPTL
RL
all
/
k
=
‘~
WO=R
lims Kl=l
MTT-33,
III
FORMULAS
transformation
frequency
transf
VOL.
—
8. (a) The reciprocal parabolic tapered transmission line loaded the lumped parallel RL admittance and (b) its equivalent circuit.
series
WO =
‘!
r
TABLE
transmission
TECHNIQUES,
(b)
IMMITTANCE
=
k:l
Yin
(a)
k
AND
/Llf..Jki
rLRL=EO~
‘L
Fig.
THEORY
/(k-1)
K2=l
‘/&L)vLL
;
‘=vk;’) 0
‘L
K2=l
/(k-1)
o /(k-1)
parameters where
where k
k=~/Ro>l
load
immittance
before
zL(jw)
transformation
part)
(real
+
immittance
(imaginary
(4 foCL~L)
‘L(JoO)
=
Zin(jo)
=
RO
part)
%
+
>
I
k=
RL/Ro
1 LUOCLRL
WkCLRo
part)
‘1
k=l+(~/4foLL)>l
L
LL
transformation
(real
*
1 +
1 KR
Part)
point
after
~
L
(imaginary
driving
=
=
where
where
COORDINFITES
100
~ :
—
t 10
m ~
/
II
,(
I
1X1
1!11
/
u
Fig.
9.
The line length
1
I
I
theoretical
:
m ~
I I Ill
LL[nH]
~
1 versus L= for R. = 50 fl.
[5E!
Fig.
ing frequency. microstrip.
These
PTL’s
are constructed
in
from and
the load
the theoretical
constants
the equivalent
ohm
normal
fzed)
results for the load I shown in Table 11,
theoretical responses. These measurements validity of the impedance transformation the operation
of the PTL notwithstanding
demonstrate technique
the and
the line length.
responses were calculated
and PTL parameters
circuit
Experimental
shielded
The measured frequency responses of the driving point impedance ZiH are shown in Figs. 10 and 11, respectively. In these figures,
10.
shown
in Fig.
in Table
2(b).
IV
Although
there is a slight error apparent in the case of load II, both measured responses seem to be in good agreement with the
V. We have demonstrated
CONCLUSIONS
a simple technique
for designing
a parabolic tapered transmission line and reciprocal parabolic tapered transmission-line impedance transformation
et ai.: LUMPED
ENDo
COMPLEX
LOAD
IMPEDt3NCE
WITH
NONUNIFORM
TRANSMISS1ON
7
LINE
COORDINFITES
[7]
R. Levy and J. Helszajn,
“Specific
equation
for one and two section
quarter-wave matching networks for stub-resistor loads,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 55-63, Jan. 1982. [8]
A. T. Starr,
“The
20, pp. 1052-1063,
_ ?
[13]
[14] Fig.
11.
Experimental
Ohm normalized)
results fortheload
TABLE TYPICAL
VALUES
OF LOAD
DESIGNED
AND
FOR ALL-FREQUENCY
11
networks
for
parabolic
tapered
impedance
both
of
simplet tapered
PTLs
8.59
50
1.060
18.13
90.2
3.29
50
2.913
2.27
RC
and
transmission
K1
RL
degrees in electronics engineering from Ibaraki University, Hitachi, Japan, in 1973 and 1975, respectively.
t [cm]
188.9
parabolic
loads.
Applying
the
lines, we may decrease the
tapered
the admittance
for
Isao Endo was born in Fukushima, Japan, on August 17, 1949. He received the B.E. and M.E.
Wo[nl
lumped
all
frequency
*
parameters
levels of the series RC loads, and applying
reciprocal decrease
OF PTL’s
CLIPI?l
RL[fl]
load
PARAMETERS
transmission
line,
levels of the parallel ranges.
Matching
the
transmission (parallel ordinary
parabolic
line
(reciprocal
can transform
experimental
loads
and have demonstrated
bolic
and reciprocal
and their equivalent
parabolic
parabolic)
tapered
series
results for lumped
the usefulness tapered
of the Institute
of Electronics
and Communica-
are
RC
RL) load into a convenient impedance for impedance matching in narrow frequency ranges.
We have also shown
sign. Mr. Endo is a member tion Engineers of Japan.
loads,
techniques
any lumped
From 1975 to 1980, he was a Research Associate and, from 1980 to 1983, he was a Lecturer in the Department of Electric Engineering, Ibaraki Technicaf College, Katsuta, Japan. He is now an Associate Professor. His research interests include circuit theory and matching network de-
we may RL
with the use of parabolic and reciprocal parabolic transmission lines as proposed in this paper. The
quarter-wavelength
nonuniform transmission lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-29, pp. 81–86, Feb. 1981. K. Kobayashi, Y. Nemoto, and R. Sate, “Equivalent representations of nonuniform transmission lines based on the extended Kuroda’s identity,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 140–146, Feb. 1982.
TRANSFORMATION
constants
I
Table II.
vol.
IV
CONSTANTS
load
load
IIshownin
IRE,
M. N. S. Swamy and B. B. Bhattacharyya, “ Hertnite lines; Proc, NOV. 1966. IEEE, vol. 54, pp. 1577-1578, B. S. Westcott, “Generalized confluent hypergeometric and hypergeometnc transmission lines/’ IEEE Trans. Circuit Thecwy, vol. CT-16, pp. 289-294, Aug. 1~69. M. J. Ahmed, “Impedance transformation equation for exponential, cosine-squarecl, and parabolic tapered transmission lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-29, pp. 67-68, Jan. 1981. K. Kobayashi, Y. Nemoto, and R. Sate, “ Knroda’s identity for mixed lumped and distributed circuits and their application to
[12]
(Se
Proc.
[10]
Flaz
f=50
line;’
H. Kaufman, “Bibliography of nonuniform transmission lines,” IRE Trans. Antennm Propagat., vol. AP-3, pp. 218–220, Oct. 1955.
[11]
:
transmission
June 1932.
[9]
theoretical
? mm
nonuniform
RC
of the para-
transmission
lines
circuits.
Yoshiaki Nemoto (S’72-M73) was born in Sendai City, Miyagiken, Japan, on December 2, 1945. He received the B. E., M.E., and Ph.D. degrees from Tohoku University, Sendai, Japan, in 1968, 1970, and 1973, respectively. Since 1973, he has been a Research Associate with the Faculty of Engineering, Tohoku University. He has been engaged in research works in distributed networks and computer networks using satellites. He is co-recipient of the 1982 Microwave Prize from the IEEE Microwave Theory and Techniques Society. Dr. Nemoto is a member of the Institute of Electronics and Commmtication Engineers of Japan.
REFEmNcEs
[1]
L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures. New York:
G.
McGraw-Hill,
[2] [3]
[4] [5]
[6]
1964.
Foundation for Microwave Engineering. New York: McGraw-Hill, 1966. R. M. Fano, “Theoretical limitations on broadband matching of arbitrary impedances; J, Franklin Inst., vol. 249, nos. 1 and 2, pp. 57-83, 139-154, 1950. “A new theory of broad-band matching: IEEE D. C. Yotda, Trans. Circuit Theory, vol. CT-11, pp. 30-50, Mm. 1964. H. J. Carlirt and W. Kohler, “Direct synthesis of band-pass transmission line structures,” IEEE Trans. Microwave Theory Tech., vol. MTT-13, pp. 283-297, May 1965. H. J. Carlin and J. J. Korniak, “A new method of broad-band equalization applied to microwave amplifiers,” IEEE Trans. Microwaue Theory Tech., vol. MTT-27, pp. 93–99, Feb. 1979.
R.
E.
Collitt,
Rkaburo Sato (SM62–F’77) was born in Furukawa City, Miyagiken, Japan, on September 23, 1921. He received the B.E. and the Ph.D. degree; from Tohoku University, Sendai, Japan, in 1944 and 1952, respectively. From 1949 to 1961, he was an Assistant Professor at Tohoku University, and in 1961 he became a Professor in the Department of Electrical Communications at the same university. Since 1973, he has been a Professor in the Department of Information Science at Tohoku University. From 1969 to 1970, he was an International Research Fellow at Stanfo;d Research Institute, Menlo Park, CA. His research activities include stud-
8
IEEE
TRANSACTIONS
ON MICROWAVE
ies of multiconductor transmission systems, distributed transmission circuits, antennas, communication systems, active transmission lines, magnetic and ferroelectric recording, neuraf information processing, computer networks, and electromagnetic compatibility. He has published a number of technicaf papers and some books in these fields, including Transmission Circuit. He received the Paper Award from the Institute of Electrical Engineers of Japan (IEE of Japan) in 1955, the Kahoku Press Cultural Award in 1963, an award from the Invention Association of Japan in 1966, the Paper Award from the Institute of Electronics and Commtrnication Engineers of Japan (IECE of Japan) ln 1980, a Certificate of
THEORY
AND
TECHNIQUES,
VOL.
MTT-33,
NO.
1, JANUARY
1985
Appreciation of Electromagnetic Compatibility from the IEEE in 1981, and the Microwave Prize of the Microwave Theory and Techniques Society of IEEE in 1982. Dr. Sato was the Vice President of IECE of Japan from 1974 to 1976. He has been a member of the Science Council of Japan from 1978 and a member of the Telecommunication Technology Consultative Committee at NTT from 1976. He is a chairman of EMC-S Tokyo Chapter of IEEE and a member of B.O.D. of EMC-S of IEEE. He is also a member of IECE of Japan, IEE of Japan, the Institute of Television Engineers of Japan,
and the Information
Processing
Society
of Japan.
Lossy Inductive-Post Obstacles in Lossy Waveguide PING
Abstract
— Post
rectangular methods
and wall
transmission
Post
losses
are
losses are obtained
into
account
for
treated
equivalent
line. Post losses may be comparable
NDUCTIVE
inductive rigorously
by perturbational
by a modified
I.
I
LI AND ARLON
and wafl losses are treated
waveguide.
may be taken
GUAN
obstacles by
methods. circuit
TAYLOR
in
moment Losses
and a Iossy
the authors series
post
interactions)
utilized
Z: ~ A ~eJn@ and
necessary
to waft losses.
for lossy filter waveguide
configurations.
The extension in this paper.
by moment
methods
i.n terms terms
of
one to treat
solution.
of a Fourier the
series as
arbitrary
II.
post
extension
of the
methods. Orthogonality is not maintained for wall losses. The waveguide is separated in several regions (with differmethods
applicable
losses. The latter
a lossy
waveguide.
cylindrical
A dominant
inductive
may be treated
in
a
in the z
direction is incident upon the post. A cylindrical coordinate system is centered on the post axis at z = O, y = c. The incident
electric
field may be expressed as E7
=
EOe-Jk(~
(1)
sin%
a where
“=+2-(:12=; and’=: The incident Fourier-series
electric field form [8]
can also be expressed
in the
rza .l~(kr)e~ne )
(2)
where
by a lossy transmis-
~=tan–l
()Z
.
‘b
sion-line model and the former may be treated by further modification of the lumped equivalent circuit. Typical results are presented, It is noted that post losses are significant and may in some cases be comparable to wall losses.
post
mode traveling
to each) and the total
wall losses are calculated. The wall losses may then be separated into two parts: a) the total minus dominant mode (or excess) wall losses, and b) the dominant mode wall
1 shows
POST LOSSES
rigor-
analysis of [8]. The post losses are taken into account by a modification of the equivalent circuit of the obstacle; resistive elements are added and reactive elements are changed in value. The wall losses are obtained by perturbational
ent numerical
Fig.
rectangular
to lossy posts and lossy walls Post losses are treated in a direct
It has been shown in [8] that such
analysis.
have been
moment-method
as many
are used, enabling
is considered ously
a Galerkin
are represented
is desirable.
an assumption is reasonable, even for high-Q filters. The treatment described above permits such a cascaded model
INTRODUCTION
POSTS in rectangular
currents
SENIOR MEMBER, IEEE
For efficient analysis of post filters, the cascading of equivalent circuits (i.e., the neglect of higher order mode
treated by many researchers [1]–[7], starting with the classical treatment by Schwinger. A recent analysis [8] by
The
ADAMS,
The induced be represented
volume
current
density
inside the post may
as
(3) Manuscript receivedMarch 2. 1984; revisedJuly 30, 1984. The authors are with the Department of Electrical and Computer Engineering, SyracuseUniversity, Syracuse,NY 13210
where
0018-9480/85/0100-0008$01
kc is the wavenumber
.0001984
IEEE
of the conductor.
For a good
LI AND
ADAMS:
LOSSY
lNDUCTIVS-POST
OBSTACLES
9
IN LOSSY WAVEGUIDE
The calculation
/
boundary
of scattered fields proceeds as in [8]. The
conditia
canbe
expressed as
E~(r=r
O)+E~(r=r
O)= EX(r=r
O).
x
I
This results in the matrix
equation
[H][a]+[ZL][a]= where matrix
b
[c]
[H], [a], and [c] are given in [8]. The additional [ Zz ] is a diagonal matrix; therefore, its entries are
determined
by
(0, Fig.
1.
A lossy post in a rectangular
.
z nm
waveguide.
_
kC has the form
[9]
As the conductivity
(4) “F-JR where The bution
u is the conductivity free-space
field
due to the current
density
distri-
ficients
proceeds
of (3) is assumed to be m
dE~(r’)
=
~
a.(r’)H~2)(kr)e~
”odr’.
(6)
~=—* Then,
an(r’)
is related
to a: as
in
Integrating
2UC
(6) with
consequent
“
J.(k,r.)”
respect to r’ over the interval
coef-
_i
(15)
(-l)”a”sin(~-na)
(16)
_~ a.sin(~+na). n——cc
equation
[ Z~]
are
of coefficients
(13). In general, determined
by
[a] as determined
the entries of the loss
(14),
where
G.
is de-
is simplified
since
by (9).
good conductors,
the magnitude = m
(o, rO)
and reflection
n-—u
modification
by matrix
For
(7)
all the entries
Note that the only difference between the lossless and lossy cases is the addition of the matrix [Z~] and the
termined Jn(kCr’)
fi; 0
matrix
[8]
k2mr!lH(kr’) an(r’)=–a;
of the transmission
‘0
r= dr’ of
infinity,
as in [8]
(5) and width distribution
(14)
forn=m.
u approaches
T=l+— ~jti
Consider an elementary shell of radius r‘ inside the post. The field due to the current this shell is assumed to be .-.
2a6
of matrix [ Z~] go to zero and (13) reduces to that obtained in the lossless case. The calculations
of the post.
forn+m
TOG. ‘
[ conductor,
(13)
the calculation
of the complex
number
>>1. For large arguments,
approximated
as follows
~ is large, i.e., 1~1
the Bessel function
is
[10]:
yields
‘Orlul>>lo ’17)
JJ~)=&’+-7--a In the integrand
of (9), the ratio
Y.( ~x)/Jn(/3krO)
significant value only as x approaches krO. Applying (17) and formulas sin ( jx) = j sinh x where
cos ( jx)
= cosh x, it is found G.=
has a and
that
krOJn ( krO) ~k’oej~(’0
kr.) dx
and
(18) (lo) where
The
tangential
component
surface can be obtained
of the electric
field
on the
~ = PI – j~l
then e ‘JpkrO
=
and PI=
from (3) G.=
E~(r=r~)=~Jx(r=ro)= Substituting
~
~=—~
~.ejne.
jfl Substituting
–
~ .=_w
eme. n
(12)
‘
(19)
“
(19) into (14) yields
o, 2UE —a TaGn
Because ~lkro >>1,
krOJn ( krO)
(11)
(8) into (11) yields EX(r=rO)=
~~2 (24) and (25) are the Gr~en’s function in rectangular
waveguide.
total
tangential
component
H=
,-Jk,lz-r.
and Hz, stands for the higher
order modes
.e-rml’-’0sineldf3. Hzd When
can
be
evaluated
by
truncation
Izl > rO, (34) can be reduced
(– N < n < N).
to [11]
jTTe-jk’z,
=
(26)
T and
+ re~’”)
for
,
17 are the transmission
Note
and reflection
’27)
a
where a ~ is the coefficient of the equivalent surface current density of the post, {a;} is related to {an} by [11]
that
(36)
represents
a traveling
wave
can be improved
and
(37)
is slow in
by separating
Hzk into
where
%$?=~’”
~ o
~
“:,’”’
~-—~
fields
. sin
m=~’”
. E
~=’”
(30)
cose)
de
(39)
a
E a:.’”’ ~=—~ cc
(29)
(-~)e-m”az-ros’n’ m~(c+r.
(28)
magnetic
~ ~=’
n
by a;= a: /jkc. The incident from (l), let EO = 1
– L cos ~e-’k’z. Up a a
coeffi-
(38)
‘TYe–rm12–ro.m@ld~ . Cos —
H:=
(37)
r.
z rO
represents a standing wave. The convergence of the series in (35), which
2*E
(35)
of the
where
k2z-roJn(kro)
(34)
s’@d~
a
H,d = - &(e-jk”
a
is (y=
(33)
qka
an//__ —
a
mode
~(c + rOcosd)
Using these equa-
slnolde
fields
HZ= HZd+Hzh
H,d stands for the dominant
H,d
‘Tye–rm[z–r.
for
(32)
of the magnetic
, sin
tions, we can obtain the scattered magnetic fields due to the volume current-density distribution inside the post
. sin —
however,
~.
1’1 = jk’,
Equations
by
o, H, = o)
sin~e-rmlz-z’f (24)
where
1985
(31)
r
where
~ sgn(z ~=1
lH’+HS12ds
g.
(Fig.
1) are [4]
HY = –
1, JANUARY
We now consider the numerical calculation of the magnetic fields. First, consider the left-hand side wall. The
WALL LOSSES
losses can be treated
NO.
it is [9]
(22)
III.
//
@ is the intrinsic
good conductor
MTT-33,
on the walls can be calculated
Pal=@
Substituting
VOL.
. sin
rO -[
,–m7r/alz-rosmol
_
m~/a
rm
mr(c+rOcosf3) a
dd
,–rml:–rosin$l
1 (40)
L1 AND
ADAMS:
Equation
LOSSY
INDUCTIVS-POST
OBSTACLES
(39) can be simplified
IN
LOSSY WAVEGUIDE
as
11
where order
subscripts
d, h denote
the
dominant
and
higher
modes, respectively.
Note
that
orthogonality
is maintained
for top wall,
but
not for side wall, losses. where
Substituting
(27) and (30) into (49) yields
27r(c+rocose) ~l(fl)=
exp
fz(d)=
exp
~lz–rOsin81
–
(
)
sin
r’
JaHzdH~
a
dy = — 202p2a ‘Z
0
m(c+rocose) – ~lz–rOsinOl)
(
7r(z-rOsin f3(0)=cosh
sin
a
&
O)
a
Equation
~2”J.(0) Sinqe-’k’zo(’)de
v ‘r. – —————— Re eJk’z [J k’upa2
%’(c+rocose) f4(o)=cos
r:
2
‘mJ,(0) 0
a
(40) is a rapid
be evaluated Similarly, the following
convergent
by truncation. for the right-hand results:
series; therefore,
side wall (y=
it can
a), we have
‘2
J
aH=hH;
(42)
Hz~ + H;;) + H$;)
0
where
-
1
de
(50)
j2T:~Js(6)~2md@Js*(o)
dy = ~
0
Hz=
,–jk’zo(t9)
“O(e) sin —
.
0
~:2(yJ2sin ‘T:(’) m
Hzd –
.
jr up a
~ ~=.~
when
JTrO 2#’ k’a2 Jo
~-jk’z
n(c + rOcos~) ,-jkrp-.Osinq
a~e,aosin
do
(43)
a
Iz 1z rO, (43) reduces, respectively
H,d _
m~co(+)~–rm[,o(e)+,.(+)]
. sin
JTTe-jk’Z,
where J,(O) is the equivalent
surface current
density
distri-
bution on the post; it can be obtained by integrating with respect to r from o to rO. The result is
, to
(3)
(44)
for z > rO
qka
(51)
a
and HZ. = -=$-(e-~k’z
+ I’e~k”),
for z rO. The results are alT12 dy = —
JaHdH; J HdH~
(59)
for z z rO
dy = A [l+lrl’-2Cos2a~ 2?f
0
e
IV. The equivalent two X.
(60)
for the lossless case can be repre-
network
consisting
series reactance and
- rO.
EQUIVALENT CIRCUIT
circuit
sented by a “T”
reflection
of a shunt reactance
X~. The
X~, respectively,
shunt
and
can be related
and transmission coefficients . ,m -
series to the
by
1+1–1
(61)
T and 17 are the transmission
and reflection
coeffi-
cients, respectively. In the lossless case, the right-hand sides of (61) and (62) are purely imaginary. For Iossy posts, we must modify the equivalent circuit by replacing jXd and – jX~ by Z. and Z~, respectively, as shown in Fig. 2. The shunt and series impedances can also be related to the reflection and transmission coefficients by [11]
z=l+r– b l–r+T 1 ‘a=l–r– Section
transmission case. Applying we obtain
II,
we have
and reflection the solutions
the parameters
T
(63)
11 T–?–?zb” shown
of T and r Z:
and
Zj
(1)
waveguides
with
at infrared
as well
[6], [7]. To evaluate method to evaluate
by
n~k~
losses in circular
metallic
as submillimeter
previous
paper
depending
on
mode.
However,
[8], they didn’t R‘2
(R:
l+~msfl
–p’
)
or
noko
H,=
field
out in a
deformations
radius),
in a circular
(3)
– —E. up o
(4)
wavelengths
as pointed
consider
bending
wrong bending loss formulas. To study wave propagation
(
(2)
losses, they used a series expansion field deformations and obtained the
a given
2
R.
power-attenuation constant as the ratio of P1/Pz, where PI is the power lost per unit length and P= is the power carried
noko dEz r3Hz —— r – ‘“P” do ( –)&
1
a uniform
hollow waveguides, a theory presented by and Schmeltzer [5] has been used for the past two
decades
M_I”F33, NO. 1, JANUARY 1985
VOL.
[7]:
E@=–j
bending
dielectric Marcatili
TECHNIQUES,
x 1
Fig.
AND
r ,9
Y
0
THEORY
which
yields
metallic
wave-
where the time and z dependence of the form exp j( at – ~z) are suppressed, and it is assumed that a characteristic length
of the waveguide,
ciently
large,
cannot
be simply
say the core diameter,
~ = n Oko. It should
and
is suffi-
be noted
that
appears, as shown in (10). The axial field and Hz can be determined from
components
only
mentioned
in the book by Lewin that
the coefficient
[9]. However,
On the other in a rather
of the propagation
class of hollow
waveguides,
by substituting Expanding
studying
oversized,
In this paper,
[11], [12] and Linden
arbitrarily
the complex
oversized
waveguides
method.
The
theory
constants
[8] has been
extended
to
6& can be distributions,
and 8~2 can be evaluated from fields depending R-1 but not on R-2, which makes calculations
with
...
(8)
and noticing
[(
n~k~
extremely
waveguide
a bending
radius
with arbitrary R as shown
the denominators
of (1) and (2) can be
terms up to order R-2
by including )2$]-=
1+ ~costl
. rcosd (
ANALYSIS
a hollow
that
approximated
(9)
(;)2{1-2(5$72
on R 0 and
simple.
bent
(7)
P=Bo+&L+j+w 2+”””
of bent
using the wall impedance
~ is approximated by (30+ 8&/R+ 8&/R2, evaluated from only the zeroth-order field
Consider
HI= W+*W*W+
[13] for
waveguides with as-bitrary cross sections and a uniform bending radius R. When the complex propagation constant
II.
...
shaped waveguides. propagation
are studied
previous
fields E (E,, E8, E=), O-U
and magnetic
E=E(0)+ +W+-3(’)+
applicable
to oversized waveguides with finite conductivity, the concept of wall impedance was introduced by Karbowiak [10] and was used by Dragone
(1) and (2) into (5) and (6). electric
(H,, He, H,), and 13as
hand, in order to study wave propagation
general
(6)
he
constant depending on R – 1 is zero, and no expression was presented for the propagation constant depending on R ‘2.
E:
(5)
guide with infinite conductivity, a series expansion method for the field deformations and the propagation constant was also employed
B
replaced by n Ok. when the term 8 – n Ok.
rcosd cross section in Fig.
1. For
convenience, we employ a toroidal coordinate system (r, 0, z) and borrow most of results given in the previous paper [8]. The local rectangular coordinate system (x, y, z) and the coordinate system (v, ~) perpendicular and parallel to the hollow boundary C are also used as shown in Fig. 1. From Maxwell’s equations in the toroidal coordinate system, we can express E,, E@,H,, and HO by E= and Hz in the hollow core region with a refractive index of n o as
“(
—
($pl 2 )1)
%)++’(W)2[*+PW2
1
– — noko
one can express Ej’) Ejl) .2
nokoT — u ()
(lo)
F
and Ejz) (i = 0,1, 2) as follows: 2
2 8f12 —E$~-’)_2 noko 8& rc0s6’ — —
‘okOT u () E(i-1)
noko )
“( T’ –j
aE(i)
;
(
r
)[
‘Oko
_._z_ ar
+—
Uf.lo
r
aH2(1)
—
ao
1
(11)
MIYAG1
: BENT
HOLLOW
WAVEGUIDES
WITH
ARRITRARY
_2
nokO
()
nOkOT
(12)
~ ‘“P”
&
phase constant
is a characteristic
T
with
understood account
negative
in the hollow
length,
say the
superscripts
Equations
18&l 2 is much
core
aE@) z
E:)
z
= 2n~k~
taken
(11) and (12) can be transformed
to (see Ap-
pendix)
– j2noko
into
(21)
J
and
using
dC
av
(21)
E~O)E~O)dS.
aE~O)/av and
Substituting
region, one obtains
8P1 E:)’ ds rcosd – — noko )
/(
into
12~08~21 [14].
(20)
~1
E(o) aE(l)
radius.
than
in the hollow
av
$[
in (11) and (12) are
smaller
z ~ zq@) _ @I) ~ z@l) ~(1)
using (16) and integrating
(13)
to be zero. In (10), it is already that
“
1
u2=(n~k~–f3~)T2 and
of tl~l by using in the straight
Constructing
aH(O
~+.
()[
Quantities
impedance
waveguide.
T 2 nOko 8E(i)
u is the transverse defined by
surface
[8].
the evaluation method E(o) and H (o), i.e., field distributions
only
)
.j;
are the normalized
respectively
We first mention
E~’-l)
“(
where region
and admittance,
u
()
ls& nokO rcos O——
where z=~ and y=~
2
nOkOT 2 8fi2 —Eji-zj
E~Z) = 2 ~
17
CROSS SECTION
aE$l)/av
the boundary
obtained
from
(14)
condition
(19),
one
obtains nokoT — u
2
( )(
–2
rcosd
()[
_
‘OkO
nokoT — u ()
E-o=z
–2
+
[
1
(14)
– ‘~o%-
)[
1“
equations
Similarly,
for
E~’) and
H~’) (i=
2H~i) +
!! () T
ll~o) v 2H~) – H~l)
v
2H$0) in the
one obtains
()
Spl jH;0J2 ds – j— ~E;O)H:O) dC up o 1 [ = noko
(
rcos8 – ~
E~j-1) +
j2nokoE~1-lJ
(16)
j2nokoH~i-1)
(1’7)
1
rcos 6H~0)2dS + j — up o
{f
noko )
2H~i) = 2noko8#2H$’-2)
~
(
H~j-l) + rcose – ~ noko )
Ex and
HX are simply
H,, HO, respectively. integrated
integrating
region,
0,1, 2) as
2E~i~ = 2nokot3&E~’-2)
–2n~k~ where
hollow
1
–2n~k~
v
r cos 0E~0)2dS
{/
(15)
follows : v ZE:E) +
= noko
1
, aH(O
of (11) and (12) into (5) and (6) leads to the
differential
1 E;O)H:O)dc dS -t- j— cocon~$
~~”)’
8/31 E$-l) – — noko ,)
aE(l)
noko~
;
(
ar
‘“p”
dfll
2 8/3, E(Z_2) — noko ‘
T2
Substitution
av
nokoT 2 rcose — u ( )(
–j
E;L-l)
noko ) aH:O
aEy
T2
_jz
Spl – —
with
calculated
Equations
the boundary E;o
— H:!)
(16)
conditions
up o = —z~
noko
by ET, Ee, and
and (17)
should
@con ~ X (22)+ @p. X (23), and using
By forming
be aH~O)
at C as
~jl)
a~
+[
(18)
~1
~ (o) aH(l)
z
H(o) aE (1)
a~
dC
H(l) aE(0)
+z~–z-&dC
!$[
H$l)
—
E:l)
. –
noko
_yTM
(h)po
(19)
—
~[ ~6’T E$JH;O) – E;O)H;l)]
1 dC = O
(24)
IEEE TRANSACTIONS ON MICROWAVS THEORY AND TECHNIQUES, VOL. MTT-33, NO. 1, JANUARY 1985
18
we arrive
Therefore,
at
nally ~~1
z ~[~~o~o~z
(
by
obtains
making
Ucon ~ X (28) + @p. X (29),
the expression
one
fi-
of 882 as follows:
@)2+ ~pOH;0J2 ] dS
+ j
[ E:O)H$Oj – E$O)H;O) dC 1}
#
= rloko
+ j
(J
2 rcos6J tJcon#=
(0)’+
dS
~poH:)2]
[
[ E;O)H;O)– E;O)H$) ] dS
J.
+ (.qtoH;O)Hjl)] dS + j
l_COS
4
8 [
E$O)H:O)– E:O)H;O)1 dC }0
(25)
+jJ
[EY(1)Hz(0)– H;JE$O)
Equation (25) shows that S~l can be evaluated from only the zeroth-order fields E (“)( E~O), E!), E~O)) and HI f“)( ~(o), IY?), H~O)), which makes the evaluation of ~~1 much
~impler
requiring
compared
the
with
first-order
O-O (1) It is clear that
the
conventional
perturbation
8&=
terms
b~l # O, it should
was
shown
properly
circular
method is sym-
waveguide,
i.e.,
that
the axial
phase
be described
by using
8~1 as well as S~2
[14]. Furthermore, bent
since we intend
waveguides
the evaluation of 8~2. Following a process similar
constant
~
to extend results for the
to any waveguide,
we proceed
to that used to obtain
(30) For circular
waveguides,
it is clear that (30) reduces to the
result obtained The bending
previously [8]. losses of the waveguides,
tion
a of the modes in the curved
constants
are simply
evaluated
i.e., the attenuawaveguides,
by
to
c$&,
i.e., integrating
(31) to the order of R ‘2. Finally, we mention
the validity
of (30) or (31). For the
~ Zq(o)
(26)
electric and magnetic fields, (7) and (8), obtained by the perturbation theory to describe the actual fields properly, it is necessary that the bending radius R is sufficiently large
@o ~ 2&@) – @2) ~ z~$o
(27)
and the zeroth-order solutions E(o) and u-U (o) are much larger than the first-order solutions E(1) and U-U ‘1). For the circular waveguides [8], the above condition leads to
E (o)~ 2E (2)– E9 z
z
and z
in the hollow
dS
of E(1) and
O when the waveguide
metric with respect to the plane x = O. In the asymmetric three-layered slab
1
region,
one obtains
R>>R where R ~ is defined
by
(33) –
j—
1
H:)&(o)
ucon~
4(
won:
rcose
—
and
o
E
(OJ
z
—1 aHi2)
a~
dC
R,
that the attenuation constant can be by the present method even when R
[15]. Therefore,
III.
(28)
we can expect
that
the
(32) and (33) are necessary for the present series to be valid.
A method
for evaluating
CONCLUSION the complex
propagation .-—
con-
stant has been developed for oversized, bent, hollow waveguides with arbitrary cross sections. The method simplifies
~:)H:O)]d~-~&4(rcose-*)~:O)E:O)dc} +*+:0)%%:2)%]dc (29)
+j—1 0/4
approaches conditions approach
~)E:O)H:O)dC}
E(2) (3H(0J z 2@Con; 4[ z dr 1
+
1
1
+ j—
and it was shown properly predicted
#J
MIYAG1: BENTHOLLOWWAVEGUIDES WITHARRITFWRY CROSS SECTION loss calculations was shown
relative
to the conventional
for the special case of circular
method,
waveguides
as
APPENDIX Let the angle between
[8]
[8]. [9]
v and r be +, one can express Ev
[10]
and ET as follows:
.(H
E:
For an arbitrary
=
Cos @
– sin ~
E,
sin +
Cos @
E.
scalar function
— —
eos + ( sin +
we finally
)
(Al)
– sin@ Cos @ )
aF ifr laF” —— [-1r N3
[13]
(A2) [14]
by making
[15]
Eq. (11) xcos@ – Eq. (12) Xsin+
(A3)
Eq. (ll)xsin+
(A4)
obtain
[11]
[12]
F, we obtain
[E) Therefore,
)(
-
+Eq.
(12) xcos+
M. Miyagi, K. Harada, and S. Kawakami, “Wave propagation and attenuation in the generaf class of circular hollow wavemides with uniform curvature,” IEEE Trans. Microwave Theoiy ‘Tech., VOL MTT-32, pp. 513-521, May 1984. L. Lewin, Theory of Waveguides. New York, Toronto: Wiley, 1975, pp. 105–111. A. E. ‘Karbowiak, “Theory of imperfect waveguides: The effect of wrdl impedance,” Proc. Inst. E/cc. Eng., vol. 102, pp. 698-708, Seut. 1955. C.’ Dragone, “High-frequency behavior of waveguides with finite surface impedance; Bell Syst. Tech. J., vol. 60, pp. 89-116, JaiL 1981. C. Dragone, “Attenuation and radiation characteristics of the HEII mode; IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 704-710. JuhJ 1980. I. V. Linden; “Asymptotic high-frequency modes of homogeneous waveguide structures with impedance boundaries,” IEEE Trans. Microwaue Theory Tech., vol. MTT-29, pp. 1087-1093, Oct. 1981. Y. Takuma, M. Miyagi, and S. Kawakarni, “Bent asymmetric dielectric slab waveguides: A detailed analysis: Appl. Opt., vol. 20, pp. 2291-2298, July 1981. M. Miyagi, K. Harada, Y. Aizawa, and S. Kawakarni, “Trrmsmission properties of circular waveguides for infrared transmission,” presented at SPIES Technicaf Symposium East ’84, Apr. 29-May 4, 1984, Arlington, VA.
(14) and (15), respectively. REFERf3NcES
[1]
E. Garmire, T. McMahon, and M. Bass, “Flexible infrared waveguides for high-power transmission< LEE-E J. Quantum Electron., vol. QE-16, pp. 23–32, Jan. 1980. [2] M. E. Marhic, L. I. Kwan, and M. Epstein, “ Opticaf surface waves ~ong a toroidaf metallic guide;’ Appl, Phys. Lett., vol. 33, pp. 609-%11, Oct. 1978. “[3] M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawaf=uni, “Fabrication of ~errnanium-coated nickel hollow wave.wsides for infrared transmission< Appl. Phys. Lett., vol. 43, pp. ~30-432, Sept. 1983. [4] T. Hidaka, T. Morikawa, and J. Shimada, ” Hollow-core oxide-glass cladding opticaf fibers for middle-infrared region,” J. Appl. Phys., vol. 52, pp. 4467-4471, July 1981. [5] E. A. J. Marcatifi and R. A. Schmeltzer, “Hollow metallic and dielectric wavegnides for long distance opticaf transmission and lasers:’ Bell $mt. Tech. J., vol. 43, pp. 1783-1809, July 1964. [6] E. Garrnire, T. McMahon, and M. Bass, “Propagation of infrared light in flexible hollow waveguides~’ Appl. Opt., vol. 15, pp. 145-150, Jan. 1976. [7] F. K. Kneubuhl and E. Affolter, “Infrared and submillimeter-wave waveguides,” in Infrared and Millimeter Waves (Sources of Radiation, vol. 1), K. J. Button, Ed. New York: Academic Press, 1979, pp. 235-278.
Mlyagi was born in Hokkaido, Japan, on December 12, 1942. He graduated from Tohoku University, Sendai, Japan, in 1965, and received the M.E. and Ph.D. degrees from the same university in 1967 and 1970, respectively. He was appointed a Research Associate at the Research Institute of Electrical Communication, Tohoku University, in 1970. From 1975 to 1977, on leave of absence from Tohoku University, he joined McGill University. Montreal. Canada where he was engaged ;n research on opticaf communications. Since 1978, he has been an Associate Professor at Tohoku University. His major interests are in opticaf communications, especially in developing IR waveguides for high-powered C02 lasers. He also carried out some works in electromagnetic theory, such as nonlinear wave nro~a~ation. Dr.’Mi~a~ is a member of the Institute of Electronics and Communication Engineers of Japan, the Optical Society of America, and the Arnericrm Institute of Physics. Mltsunobu
\
._-2Q-”
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-33, NO. 1, JANUARY 1985
Noise due to Pulse-to-Pulse Incoherence Injection-Locked Pulsed-Microwave Oscillators. Part II—Effects of Phase-Locking Dynamics DAN
Abstract
—me
in phase-locked includes
the
problem puked
dynamic
signaf-to-noise
ratio
y is the frequency correets
of noise due to partial
oscillators time
variation bandwidth
conjecture
MIETEK
pulse-to-pulse
LISAK,
of the phase-loekirrg to increase
process. as (yT)2,
and T is the pulse length.
of an exponential
dependence
AND P. THOMAS
II.
coherence
In particular, the anafysis
is investigated.
of such a system is found lucking
a previous
G. ANDERSON,
The where
This result
I
NJECTION for
If ~(t) denotes the (complex) amplitude variation of a single unit pulse, the total amplitude g(1) for a pulsed system consisting of (21V + 1) pulses can be written
on yT.
frequency
plays
systems
by
k=–
a doubly
providing
as well as by suppressing
beneficial a stable
the inherent
of the oscillator [1]. In addition to these well-known
role output
noise level
properties
for
a CW
oscillator system, injection locking also provides a stable initial phase for pulsed systems. This has an important noise-suppressing effect, since otherwise the randomness of the initial
phases for the individual
pulses would
to an excess noise, which could well prove noise process for the output signal [2], [3]. In a previous pulse-to-pulse ratios lock&g
work
[3], we analyzed
coherence
for achieving
in pulsed-oscillator
where
T is the pulse repetition
the mean phase (q). However, this approach is a dynamic
pulses,
tends
time
and ~~ denotes
phase of the k th pulse. In our previous
(1) the
study, we assumed
{@~ } to constitute a normal random process with an rms phase spread ((( A@)2))lz2. It was then shown that the normalized power spectrum GO(u) could be obtained by Fourier analyzing (1) together with a subsequent statistical averaging.
This yielded
give rise
‘0(’”)
= (2 N1+1)
(l@J)12)
the dominant =[pso(@)+(l-p)]
the importance
of
high signal-to-noise
where
G(LJ) and F(a)
respectively,
by assuming the initial
and
lF(&l)/2
are the transforms
SO(u) is the coherent sinz
phases ‘“(”)
pulses to have a random variation, norwith a phase spread ((A@) 2)1/2 around
locking
,
N
(2)
of g(t)
and j(t),
sampling
function
systems. The effect of the phase-
process was modeled
of the individual mally distributed
‘~N f(t–kl”)exp(i+~)
INTRODUCTION
LOCKING
oscillator
LEWIN
REVIEW OF PREVIOUS RESULTS
g(t)= I.
in
neglected
process, which
to improve
the fact
that
continuously,
the pulse-to-pulse
phase during
coherence
factor
zero. Thus, a more detailed tialysis of noise due to partial pulse-to-pulse coherence should include the dynamics of the phase-locking process. The purpose of the present work is to provide such an analysis.
P=exp(– We emphasized of the influence
0018-9480/85/0100-0020$01
by the phase spread
that (2) provides of partial
(4)
((@)2)).
a suggestive description
pulse-to-pulse
coherence
on the
power spectrum by being a weighted mean of a completely coherent part (pSo( w )) and a completely incoherent part (1 – p). III.
Manuscript received March 6, 1984; revised July 9, 1984. D. Anderson and M. Lisak are with the Institute for Electromagnetic Field Theory, Chalmers University of Technology, S-412 96 Goteborg, Sweden. T. Lewin is with Ericsson Radio Systems AB, P.O. Box 1001, S-431 26 Molndal, Sweden.
v is determined
as
by
mapping an initial maximum phase spread of 2 r on a phase interval 2A@(t) which is shrinking in time towards
(3)
z UT sin — 2
= (2 N1+1)
The weighting
l/2)uT]
[(~+
However, evolve equation
in
PHASE-LOCKING DYNAMICS
the phases of the individual time
according
to the dynamic
pulses
actually
phase-locking
[1] d+~(t) —= dt
.0001984
IEEE
Aao–ysin@k(t)
(5)
ANDERSON et al.: EFFECTS OF PHASE-LOCKING DYNAMICS
21
where Au. is the difference between the frequencies of the locking signal and the free-running oscillator, and y is the maximum
frequency
achieved.
tor together running
offset
y is determined with
the ratio
oscillator
for
which
locking
can
be
of the oscilla-
of the amplitudes
and the injected
The characteristic
locking
by the parameters
note
that
the initial
phases Ok must
of the free-
signal [1].
phase +~ is obtained
(M9Y}=
from (5)
as
be assumed
to be
randomly distributed over the interval [ – r, + m] with a constant probability function p (c$~) = l/(27r ). Furthermore @k and $1 are uncorrelated if k #1. Thus
(M)(w)> ,/#)&+m)
ifk+l (11)
ifk=l
9
{
and A(JO
sin~~.–— For
simplicity,
we will
(+;)
concentrate
=
on the case of exact
resonance ( ACJO= O), when the stable locking phase becomes 0~ = O. The phase variation during the locking process is obtained by solving (5), assuming an initial phase +~. The solution becomes particularly simple for small
k
77”
(6)
Equation (6) yields the dynamic time evolution phases of the individual pulses during the locking
of the process
towards the common phase +~ = O. In the Appendix, we briefly discuss the consequences allowing
for
nonresonant
locking
quality of the exponential ing variation (6). IV.
n+l’
The averaged power spectrum can again be suggestively presented as a sum of a coherent and an incoherent part, cf. (2). We find from (8) using (11) and (12)
POWER
SPECTRUM
‘0(’”)=
(2 N1+1)
OG@O
= [h1(@o(LJ)+h2(c+
of (14)
of the phase-lock-
IN THE PRESENCE OF
PHASE LOCKING
the phases of the individual
to (6), we can write g(t)
pulses vary according
the signal as, cf. (1)
=
y k=–
f(t–kT)lZk(t-kT)
V.
Although
[i~~exp(–yt)].
a power
the
Fourier
transform
unit pulse of length
series in the variable
(unaveraged)
1’=
power
~N k,l=–
of
(7),
assuming
~, and expanding
a
h ~( t) as
Z@kexp ( – yt), we obtain
spectrum
of
SIGNAL-TO-NOISE RATIO FOR STRONGLY PHASE-LOCKED PULSED SYSTEMS
(13)-(15) taking
the proper generalization dynamic phase locking.
(7)
where
rectangular
(m
(-om(qg’k-m,m(+
t
~=o
Equations (13)–(15) constitute our previous results to include
N
h~(t)=exp
(13)
where
“
When
h1(u)]lF(@)\2
processes and also the
approximation
DYNAMIC
, IG(LIJ)
(12)
if n is even.
+~, viz.,
+k(~)=+kexp(–yt).
By
if n is odd
o,
Y“
the
as
the
general
result
is in a physically
explicit,
for
the
power
suggestive form,
in view of the complicated
spectrum
it is not very
expressions
for hl( Q )
and h2(u). However,
in
degenerates stitutes
into
two
special
limits,
well-known
the
forms.
power
This
spectrum
fact
also con-
a check on the results.
i) In the limit of y~ ~ O, the phase-locking mechanism is not operating and we should regain the completely incoher-
~-,(~-w-
N
ent result. When
where we have introduced
the notation (9)
with l–exp[–(ia+ny)T]
and F’(o) order
which h2(o),
=
l–exp(–iu~)
is the spectrum
to proceed
1 1 – iny/o
of the rectangular
to the statistical
(
hl(~)+
&,m(~)=g”(@)d(@) g.(o)
y~ ~ 0, we obtain
averaging
(lo)
E k=O
implies
g.(u)s
1 for all n and 2
(–1)”
‘2k
(2k+l)!
that the coherent
)()
2 =
(16)
part vanishes, cf. (13). For
we find
hz(a)+
~
(–l)k
~2k2:1),
:O(-l)m(%)=l “ m—
k=O
(17)
unit pulse. In of IG ( o ) 12, we
= O
*
since
the
inner
sum is zero,
except
for
k = O when
it
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-33, NO. 1, JANUARY 1985
22
becomes
YT + O, GO(U)=
equal to one. Thus, in the limit
lF(a) 12, i.e.,
the completely
ii) In the limit
incoherent
result,
y~ -+ m, phase locking
and we should regain the completely When y~ ~ce, we obtain g.(a)=
as expected.
is instantaneous
coherent result. O for n # O and gO(u)
This
shows that
increase
with
the conjecture
y~
was too
2N = 6 X 104 and assuming dB. Thus,
in [3] of an exponential
optimistic.
Taking,
as in
y~ = 5 X 102, we obtain
our results demonstrate
that partial
[3],
S =92
pulse-to-pulse
=1, which implies that hi(a) ~1 and hz(a) al. Thus, the incoherent part of GO(co) vanishes and we regain the completely coherent result GO(u) = SO(o) IF( @) ]2, as we should. Most technically important situations involving pulsed
coherence could be an important noise source, which may well limit the performance of low-noise pulsed-oscillator systems. However, in this context it is appropriate to point out
phase-locked
properties
locked
in
locking
oscillators the
time,
can be considered
sense that l/y,
y~ >>1,
as strongi’y phase
i.e.,
cf. (6), is much
the characteristic
less than
the pulse
that
a major
difference
of pulsed
pending
on whether
or after
the rising
can be expected
phase-locked the locking
for
oscillator
the noise
systems,
signal is turned
edge of the oscillator
de-
on before
pulse. The results
duration time ~. Typical values for certain modern pulsedradar transmitter systems could be y =100 MHz and ~ =
presented in this paper are applicable to the case when the locking signal is introduced when the oscillator signal has
800 ns, implying that y~ = 5 X 102. In the case y~ >>1, g.(a) simplifies
reached
gn(ti)==is
to (gO(@) = 1)
1
n+
nyl–exp(–i~T)’
its maximum
the locking
O
(18)
signal
the oscillator proportional
that
hl(@)=l–ycot++(~)2
2y 2
UT cot—+~
lZ2(@)=l-y where the constants
~ () 2y
(19)
c: sin2 ( u~/2)
that
and
that
cl
signals, respectively)
the phase locking the
coherence first
noise
wards
~2k
c’=k:l(-l)k+’
(2k+l)~2’
with (22)
‘2=4%+4 The series defining
co=yo+lnr
provided
much
from
–l–
Ci(~)
to
partial
reduced
to the
analysis
assumes that
the
the phase-locking
by an exponential
decay
phase value, cf. (5). This simple that the initial final
locking
points
(23)
=0.65
phase does not deviate too phase.
the fact that we consider initial
interval
[ – 7T,m].
Actually,
this
ii) The analysis only considers the case of exact resonance AQO = O, whereas most realistic situations are charby Au. # O. these equa-
tion (5) as (Al) where
(24)
Equations (19) and (20) imply that the incoherent contribution to the power spectrum, in this limit, degenerates into white noise with a level determined by
con-
phases in the whole
where y. is Euler’s constant and Ci(x) denotes the cosine c1 converges rapidly and integral [4]. The series defining we find
to-
solution
In order to discuss the consequences of relaxing limiting assumptions, we rewrite the phase-locking
to yield
CI =0.60.
pulse-to-pulse
as compared
discuss two interesting
tradicts
acterized
COcan be rewritten
due
can be described
the locking
is valid, (21)
is very large. This im-
APPENDIX
dynamics
(2k);;+l)!
edge of
case.
i) The present c“=k:l(-l)k+l
level
In this Appendix, we will raised by the reviewers.
by
the rising
becomes much more efficient
is correspondingly
(20)
~in2 (@./2)
COand c1 are defined
plies
before
pulse, the effective locking bandwidth (being to the ratio of the amplitudes of the locking
and oscillator and we find
flat top value. On the other hand, if
is introduced
~ = yt and K = AuO/y.
We first consider Exact
the following
Resonance with Finite Initial
Exact solution
case. Phases
resonance requires K = O, in which case the full of (Al), subject to the initial condition +(0)= +.,
is [hl(ti)-h2(ti)]
lF(O)12=@=~.
(25) (A2)
In
particular,
spectrum
close to the main
peak
(u r .-k{”
shows
(19)
be expected.
Furthermore, independent
is swept
(23)
(18) follows
A(u+jQ)=A*(u–jQ)
could
when
Equation
lying
on the
lying
on the
computation, to a finite
(
f
the
infinite
dimension,
problem
A,,, _, AV, =O
k=–
(16)
i.e.,
N
(27)
axis; of poles of the determinant axis.
In principle NIZ could be found directly from the Nyquist plot of A( jco); however, the existence of such zeros is physically anomalous and numerically impossible, and will thus be disregarded (Nlz = O). No matter what the values of Nz and N[P, because of (22), A( ja) makes n counterclockwise encirclements of the
When
doing
physically
so, the integer
and numerically
N should be carefully
chosen if
accurate results are sought. The
Fourier expansions of the derivatives (11) must be truncated, too, by retaining a finite number ND of harmonics. Then (14) shows that, in order to approximately preserve the periodicity of (25) at least in the interval [0, @o], we must take
N–ND>>l
(28)
IEEE TRANSACTIONSON MICROWAVETHEORY
34
the degree of approximation value of the left-hand
being established
junctions
tives
may
driven be
functions
into
quite
harmonics
of
the
forward
broadbanded
appearing
in
the
order
AIO=Dm+
containing because
of
of
VOL.
MTF33, NO. 1, JANUARY 1985
{u+j(ti
+uO)}DIO+
Y(uO+u-ju)=O
p – n or Schot-
conduction,
device
TECHMQUES,
p + O), D~P = O (for m > 1), so that (32) reduces to
side of (28).
In some cases, such as circuits tky
by the actual
AND
the the
or, by the
exponential
A
equations.
(35)
deriva-
number
of
30 or more may be required
for
assumption
of
Dw+{u+j(~+
slowly
uO)}DIO
changing
perturbation
+Y(tiO)+~.
(~-ju)
=0
an accurate representation of the derivatives, which implies N >50 to obtain a 5-percent accuracy, according to (28). The numerical
problem
size of the truncated hundred. often
In practice,
such very stringent
be considerably
section.
then becomes very large, since the system (27) is of the order
can be dramatically method on a vector
requirements
improved processor;
We consider
by implementation in fact, the matrix
Free-Running
a steady-state
Y~(ti,
V)=
of the formula-
at
@ = UO.
quantity
~= v
advantage hardware,
~/2nF[P’cosx, rv~
–OVsinx]e-~xdx (37)
which is conventionally named “device (37) and the expansions (11), we get
Oscillator
Subject
to
&Y~(@,
admittance.”
V)=jDIO–
From
(38)
j2@O)D12
jexp(–
all derivatives
jaOt)]
i.e.,
can
be
in
reduced
time
(A1exp{j(ti+oO)t}]
Au(t)
[AVexp{j(u+tiO)t}]
=exp(ot).Re
with
respect
aYD
DW=Y~(LJo, Finally, Y,(to,
we define V)=
Dlz
V)+VW–
‘“0
ayD au -
(39)
—
the admittance
G,(~,
remember
Y~(uo, O). The stability analysis of (29) will be restricted to those perfundamental,
the
may
regime of the form
fi(t)=Re[~exp
the
evaluated
introduce
Perturbations
;(t)=Re [iexp(
turbations
being
now
EXAMPLES OF APPLICATION
A. Monochromatic Changing
derivative
We
of the solution
tion described above is ideally suited for taking of the high computational power of a vector especially for large-size problems.
Slow&
the
of one
released, as we will show in the next
In any case, the cost-effectiveness
III.
(36)
the
steady-state
V) = O, to obtain
from
equilibrium
condition
(36)
(31)
6J0.
(41) Due
the .s= k = 1 term
to (29) and (30), only
the solving system (17) is reduced to
(16),
so that
the eigenvalue
appears
equation
The
nonlinear
or
ay=
(32)
A(u+jti)=AIO=O. device
“device admittance” the general form
in
can be described
when
its time-domain
in terms
of a
equation
has
I2
u=Im
V—
=V
av
ayT au
The stability
~ a~Fmi+F’[F-’u,. ~=—[
. ., F’%]=0
(33)
av as was found
which is a particular case of (l). Just for the sake of clarity, in the following we will make use of the simplified expres-
ayT 2 da
condition 13GT
-
8BT 8G~ i?G~ 8BT —— —— av au – av aa
u 0 —— av au
8BT —— au
by Hansson
(43)
and Lundstrom
ously by Kurokawa [5] (the latter resistive nonlinear device).
[6] and previ-
for the case of a purely
sion: B. A4icrostrip –i(t)+F[u(t),
~]=O.
(34)
In
this
nonlinear From
(34) and (11), we obtain
Cm = – 1, C~P = O (for m or
Parametric
section, microstrip
cally illustrated
Frequency Divider
we apply network
the stability
analysis
whose topology
in Fig. 2. This circuit
to the
is schemati-
was designed
(in the
——. . RIZZOLI
AND
LIPPAFuNI
: PERIODIC
‘r
Y 3
2
STEADY-STATE
T 5
4
T t-’-l
RSGIMSS
1
6
J
1
7
T
35
9
11
8
7
10
13 12
T
T
m
A
A’ Fig. 2.
Transmission-line
A
model of microstrip frequency divider.
TABLE I MICROSTRIPDIMENSIONS n.
W,dth
(mm)
Ienqth
. .
(mm]
w~dth
Length
(ml
(m)
1
8.9
25.4
8
1.1
13.1
2
8.4
18.4
9
6.1
20.7
3
6.6
34.1
10
5.1
22.5
4
6.8
23.6
11
4.6
14.3
5
8.1
19.9
12
3.2
20.6
13
6
7.7
22,0
7
8.9
14.0
1.3 5UBSTRATE,
7.
Fig. 3.
Truncation
58
mm
with
band
an insertion
input
power
in Table diode the
centered
at 2.375 GHz
loss in the 4–6-dB
I in terms of microstrip
parameters
including
manufacturer’s
abrupt-junction
(input
parasitic
catalog
varactor
represented
steady-state
are, available Industries
describe
regime.
components
61
71
01
S1
101
111
solving
all
from Silicon
For
expansions
in (27), which
should
allow
6733-07).
according
device is a microwave
3, where
truncated
the Nyquist
error
of
about
waveforms;
in to
accuracy by the
at p = ~ ND. Taking
7 percent
the deviation
2N + 1. The deviation _i+l~[exP(=)-l]
101, then
(for
with
periodicity
of (25) in
the size of the truncated
is defined
system,
as A(0)
(46)
A(0) (44)
where Is
saturation
e
electron
x
slope (or ideality) Boltzmann’s
T
absolute
+ c c
TO DO
size solution
charge,
K~
factor
ND=
of current,
constant,
potential,
zero-bias
depletion-layer
(transition)
may
capacitance,
capacitance.
The varactor is unbiased’ and is thus drawn into forward conduction during a considerable fraction of the RF cycle. always
the calculations
definitely
no numerical
less than the diffusion
ill-conditioning
can be used to obtain tives;
from
A ~,p=Dop
show that the forward
ti~=l
potential,
is
explicit
expressions
+k@o)}Dlp forp=O,
for the deriva-
are then found
to be
-?l;Y(ti-ju+k@o), O otherwise.
intended
solutions~f
be required
a large-
based on the choices
use of 250 frequency to draw
points
the Nyquist
to show that our method
high numerical
in some critical
can
accuracy (which
cases), and
that
such
solutions may still be quite cheap when using a vectorized code on a supercomputer. We then briefly comment on the possible tradeoffs between numerical accuracy and computer
time requirements,
physical
accuracy
and on the impact
of this on the
of the solutions.
so that
can occur in (44). Thus, (44)
(14), the coefficients +{u+j((.’J
voltage
problem
in the ~ange [0, tie]
plots. This is mainly
diffusion
However,
spaced
indeed produce
diffusion
we first discuss in some detail
of the stability
35, N = 50, and making
evenly
temperature,
zero-bias
case, n = 1 in (25). The figure shows since, for the present that Ds 8.1 percent for the size of 101, which is considered satisfactory for practical purposes.
In the following,
current,
a
O ~ w < @o),
can be checked from Fig. from
~ = loo A(jtio)+
+[c.o(l-~)-y+c.oexp(~)]~=o
ten
were required
plots ,to be computed
to (28). This prediction we plot
purposes,
means a system of order
the range [0, @o] against
by [10]
35 harmonics
with a comparable
(11)
N =50 maximum
present
voltage and current ND=
the derivatives
Fourier
the
[9] were used in (4) to accurately
the equilibrium
compute
is given
and lengths;
in the time domain
61
OF TRUNCFITEO SYSTEM
error introduced when reducing the infinite system to a finite size.
the same conditions,
frequency),
geometry
(ALPHA
model DVH
by 2 in a
range at a nominal
widths
For the present case, the nonlinear varactor
divider
level of 9 dBm. The divider
41
DUROID
frequency 500-MHz
S1
24.4 I.
in [9]) to act as a frequency
21
SIZE
the way described
~ 19
(45)
Due to the exponential appearing in (44), the derivatives usually have a considerably broader bandwidth than
In proach
view
of
the implementation
on a vector
processor,
of the numerical
ap-
we note the following.
1) The passive network admittance appearing in (14) can be computed in parallel (in the pipeline sense) at all frequencies (Q -t ktio) by existing vectorized programs for microwave circuit analysis [11 ]. In this way, the time required for admittance calculations is reduced by more than one order of magnitude with respect to conventional computational
methods
on scalar macliines
[11].
IEEE
TRANSACTIONS
ON MJCROWAVE
THEORY
AND
TECHNIQUES,
POINT
MTT-33, NO. 1, JANUARY 1985
VOL.
N
— “.
Im (d) B
O>1
. . .“ should
read
●ul_
UO d
a’(z)
2 ds
~z(z)
1 Equation
(A15)
should
[
read
The
UO(S) = Ae-Js + Be+Js.
~R~ = 24 V are
spatial
of
in
of
assumes
the of
dc
effects
density
as the
is defined the
the
which
show
270°
ds
On page 1994, (A14)
includes
current
should
b(s)=~ 1‘[@l+*[*r
if the
out that
on the calculation
curves
region
to curve
is adequate
read
On page 1993, (All)
Taylor’s
expansion
take
straight
3. Here
in
(9) should
in
an inaccuracy the
Read equation,
A/en?,
dotted
instants
the field
two
space-charge
curve
the
electric
moving
first
we must
to 2000
replaces
curves changes
of the diode.
account
solid
The
be modified
thinks
is used. We should
conductance currents,
of time.
as the phase
must
Tiwari
that the Taylor’s
equation
increased
specific
equation
A V, has only a very small effect
the negative
and
the
of the classical
calculating
been
Read
The close agreement
modified
instants
2 are shown
Equation
Apparently,
only
demonstrates
paper.l
at successive of Fig.
of 4°.
AK
predict
expansion. tions
distance
the conditions
E at
Equation
(A19)
should
read
voltage
space
charge
180°
causes
upward. f@FERENCES
[1]C. [2]
A. Bracket, “The elernination of tuning induced burnout and bias circuit oscillations in IMPATT oscillators,” Bell Syst. Tech. J., vol. 52, pp.
Manuscript
received
Sept.
271-306,
The
are with
the Department
C.
A.
1973. Lee,
R.
L.
Batdorf,
dependence
of avalanche
2787-2796,
1967.
W.
processes
Wiegmarm, in silicon;’
and
G.
J. Appl.
Karrrinsky, Phys.,
vol.
“Time 38, pp.
425,
authors Engineering
1 M. MTT-30,
0018-9480/85/0100-0074$01
Center,
Abouzahra pp.
and
3, 1984.
University L,
1988–1995,
.00 @ 1984 IEEE
Lewin, Nov.
of Electrical of Colorado,
IEEE 1982,
Trans.
Engineering, Boulder,
Microwave
CO
Carrrpus
Box
80309.
Theoty
Tech,,
vol.
IEEE
74
TRANSACTIONS
ON MICROWAVE
~DC= Xa
z 1-1 0 >
S. C. Tiwari,
[3]
1.5 2000 =
state
A /cm2
0.4
THEORY
“Study
microwave
S.
C.
(Warsaw, [5]
> -4
G.
Khokle,
in
IMPATTS,”
Poland),
I /5”’
J.
[8] t
1
1
P. Dee,
V#~
the
and of
desigrr
of
Rajasthan,
solid
Jaipur,
and
M.
pp.
314-324,
J. H.
Leek,
in gallium
Sisodia,
“Effect
10th
“Nonlinear
Int.
J.
Farrayre,
GaAs
arsenide
L. Proc.
Pujari,
A.
of
M. in
Eur.
of
nonlinear
Microwave
Conf.
507-511.
oscillators,”
study 44,
and
for
ef feet
400
Goedbloed,
600
D.
[9]
E.
avalanche
Electron, and
IMPATT
region
analysis
1984.
B.
Kramer,
oscillator dependence
p-n junctions,”
Int.
J.
“Theoretical
efficiency,”
1973. “Temperature
when
charge
j~c
= 2000
on y while
A/cmz.
the dashed
The iine
“Noise
in
University,
Iglesias,
IMPATT,”
Xa = 0.4 #m of space
J.
Technological
1
I
Vrfz (w versus
operation
University
of
avafanche
Electron,
vol.
and
J.
Appl. brealc
25, pp.
539,
1968.
200
AV
on
thesis, and
pp.
J. Pribetich,
vol.
down
1980,
IMPATT
R. Hall
[7]
includes
effects
S.
Salmer,
Phys.,
0.5
,
MTT-33, NO. 1, JANUARY 1985
‘VOL.
Ph.D.
W.
experimental
2.
thermal
process
S. C. T1wari,
[6]
curve
of
devices,”
Tiwari,
avalanche
in Read
Fig.
TECHNIQUES,
1978, [4]
pm
,,0
@“
AND
J. C.
IEEE
IMPA’M
diode
Eindhoven,
Irvin,
Trans.
and
W.
Electron
oscillators,”
M.
S.
thesis,
1973. C. Niehaus, Devices,
vol.
“10 ED-22,
W
and pp.
12 W
200,
GaAs
1975
soLid
assumes
Corrections to “Theory and Application of Coupling Between Curved Transmission Lines” MOHAMED
ABOUZAHRA,
LEONARD
In the above paper}
2 CO)=
TR ~e
(MI)
FELLOW,
the following
On page 1990, (8) should
Z1(–
MEMBER,
LEWIN,
IEEE AND IEEE
corrections
should
be made.
read
–R@/h
2 Rfi .— Jh
_
( 0’
-10
-05
1.0
05
0
x [#nl) Fig.
3,
for
Electric
field
versus
VRF = 24 V and
from
90°
onstration order
to
results
to 270°
in steps
1 that
the classical
from
using
Read
modification
At
larger
which
takes
into
The
field
shown
in Fig.
terms
of (1) with
values
the computer
calcula-
increases
from into
this
to
drift
Fig.
the time
90°
the
lines
in
for
of
point while
the
it is crucial
in of
ER~ = VR~/ y w~, where
y,
effects,
2, in
which
line
phase
in
steps
when
and
The
sentence
then.
and
that
has (l),
the 4°.
the phase
y in y =1.
value
of
extemaf The
is near
~Z(z)
follows
~,,
our
current
read
(AS2)
should
read, “With
/3. L >>1
. . .“ should
read
●ul_
UO d
a’(z)
2 ds
~z(z)
1 Equation
(A15)
should
[
read
The
UO(S) = Ae-Js + Be+Js.
~R~ = 24 V are
spatial
of
in
of
assumes
the of
dc
effects
density
as the
is defined the
the
which
show
270°
ds
On page 1994, (A14)
includes
current
should
b(s)=~ 1‘[@l+*[*r
if the
out that
on the calculation
curves
region
to curve
is adequate
read
On page 1993, (All)
Taylor’s
expansion
take
straight
3. Here
in
(9) should
in
an inaccuracy the
Read equation,
A/en?,
dotted
instants
the field
two
space-charge
curve
the
electric
moving
first
we must
to 2000
replaces
curves changes
of the diode.
account
solid
The
be modified
thinks
is used. We should
conductance currents,
of time.
as the phase
must
Tiwari
that the Taylor’s
equation
increased
specific
equation
A V, has only a very small effect
the negative
and
the
of the classical
calculating
been
Read
The close agreement
modified
instants
2 are shown
Equation
Apparently,
only
demonstrates
paper.l
at successive of Fig.
of 4°.
AK
predict
expansion. tions
distance
the conditions
E at
Equation
(A19)
should
read
voltage
space
charge
180°
causes
upward. f@FERENCES
[1]C. [2]
A. Bracket, “The elernination of tuning induced burnout and bias circuit oscillations in IMPATT oscillators,” Bell Syst. Tech. J., vol. 52, pp.
Manuscript
received
Sept.
271-306,
The
are with
the Department
C.
A.
1973. Lee,
R.
L.
Batdorf,
dependence
of avalanche
2787-2796,
1967.
W.
processes
Wiegmarm, in silicon;’
and
G.
J. Appl.
Karrrinsky, Phys.,
vol.
“Time 38, pp.
425,
authors Engineering
1 M. MTT-30,
0018-9480/85/0100-0074$01
Center,
Abouzahra pp.
and
3, 1984.
University L,
1988–1995,
.00 @ 1984 IEEE
Lewin, Nov.
of Electrical of Colorado,
IEEE 1982,
Trans.
Engineering, Boulder,
Microwave
CO
Carrrpus
Box
80309.
Theoty
Tech,,
vol.
75
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TJ?.CHNJQUES,VOL. MTT-33, NO. 1, JANUARY 1985
The
sentence
just
before
(A20)
should
read,
rl = – Q and rz = + ~ and substituting then putting (A19) into (A12), we obtain.” In
(A20),
(different
Cl
and
C2 should
be
“Upon
UO (s)
into
replaced
by
choosing
In
(A19), and cl
and
the
above
the following
72
(A25)
should
R = +e-2J~O[ sin(2A~l).
read
= &
,-jfl,Ze-JAPJ~~e-”’2dt
_
(30) should
read
~eJPOZe-JA13
{
II(z
=
–
m)
=
–
j
A~~me2.f~O’-2hcz2
[&iT-,,Af*
lj
z a’(z)
.—
CO
The paragraph by – c and/or The
expression
(A22)
of i(z)
will
by – c and/or
(A24)
should
~z,
a(z’)
+ +e-2Jp0~ cos(2A/31)
} should
A/-? by – A/3 in (A22),
c replaced
Equation il(–
that follows
~_21pOz1e-JA~/;e-at2dt
read, “By
the solution be identical
replacing
to that
Equation
(31) should
read
A/3 by – A/3.”
D(z=
–m)
= –j{+*+r)e-2J~01
cos(2A~l)}.
read Consequently,
Fig.
9 on page 1101 should
,5.0-
Daw(.x) should
= e-x’~xe’~t, o
read
i2( – eo) = jA/3
r ~
7 ,o.o11
e“R@/h
+O(A/3)3.
.2 Ir
,. e-
to “Coupling
of Degenerate
DEEB
ABOUZAHRA,
LEONARD
LEWIN,
MEMSER, FELLOW,
Marmscrmrt
received
%utember
are with
th~ Department
auth&s Engineering
Center,
University
=2.54mm
c
= 0.2
cm
do = 0.05 1
2.4
=
-1
cm cm
w
“, /
to
.~ 70.0
IEEE, AND
80.0
,0.,
FREQUENCY
,.3..0
,,O.
,
,,
o
(GHz)
IEEE Fig.
The
a
w~h
60.0
MOHAMED
h
Modes on
Curved Dielectric Slab Seetions and Application Directional Couplers”
by the
r\
n /
Corrections
be replaced
figure.
with
(A25)
.
of 1(z)
co) = (A/3)2(~e-~8;zk
Equation
)
c
of (A2) can be
following
425,
~z
o
(
with
be made.
On page 1099, (29) should re;~d
Equation
found.
should
corrections
constants).
Equation I(z)
paper:
9.
Direcl
ivity
versus
frequency.
3, 1984. of ElectncaJ of Colorado,
Engineering, Boulder,
CO
Campus
Box
80309.
0018-9480/85/0100-0075$01
1M.
D,
MTT-28,
Abouzahra pp.
and
1096–1101,
.00 @ 1984 IEEE
L. Lewin, Oct.
1980.
IEEE
Trans.
Microwave
Theo.
Tech.,
vol.
75
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TJ?.CHNJQUES,VOL. MTT-33, NO. 1, JANUARY 1985
The
sentence
just
before
(A20)
should
read,
rl = – Q and rz = + ~ and substituting then putting (A19) into (A12), we obtain.” In
(A20),
(different
Cl
and
C2 should
be
“Upon
UO (s)
into
replaced
by
choosing
In
(A19), and cl
and
the
above
the following
72
(A25)
should
R = +e-2J~O[ sin(2A~l).
read
= &
,-jfl,Ze-JAPJ~~e-”’2dt
_
(30) should
read
~eJPOZe-JA13
{
II(z
=
–
m)
=
–
j
A~~me2.f~O’-2hcz2
[&iT-,,Af*
lj
z a’(z)
.—
CO
The paragraph by – c and/or The
expression
(A22)
of i(z)
will
by – c and/or
(A24)
should
~z,
a(z’)
+ +e-2Jp0~ cos(2A/31)
} should
A/-? by – A/3 in (A22),
c replaced
Equation il(–
that follows
~_21pOz1e-JA~/;e-at2dt
read, “By
the solution be identical
replacing
to that
Equation
(31) should
read
A/3 by – A/3.”
D(z=
–m)
= –j{+*+r)e-2J~01
cos(2A~l)}.
read Consequently,
Fig.
9 on page 1101 should
,5.0-
Daw(.x) should
= e-x’~xe’~t, o
read
i2( – eo) = jA/3
r ~
7 ,o.o11
e“R@/h
+O(A/3)3.
.2 Ir
,. e-
to “Coupling
of Degenerate
DEEB
ABOUZAHRA,
LEONARD
LEWIN,
MEMSER, FELLOW,
Marmscrmrt
received
%utember
are with
th~ Department
auth&s Engineering
Center,
University
=2.54mm
c
= 0.2
cm
do = 0.05 1
2.4
=
-1
cm cm
w
“, /
to
.~ 70.0
IEEE, AND
80.0
,0.,
FREQUENCY
,.3..0
,,O.
,
,,
o
(GHz)
IEEE Fig.
The
a
w~h
60.0
MOHAMED
h
Modes on
Curved Dielectric Slab Seetions and Application Directional Couplers”
by the
r\
n /
Corrections
be replaced
figure.
with
(A25)
.
of 1(z)
co) = (A/3)2(~e-~8;zk
Equation
)
c
of (A2) can be
following
425,
~z
o
(
with
be made.
On page 1099, (29) should re;~d
Equation
found.
should
corrections
constants).
Equation I(z)
paper:
9.
Direcl
ivity
versus
frequency.
3, 1984. of ElectncaJ of Colorado,
Engineering, Boulder,
CO
Campus
Box
80309.
0018-9480/85/0100-0075$01
1M.
D,
MTT-28,
Abouzahra pp.
and
1096–1101,
.00 @ 1984 IEEE
L. Lewin, Oct.
1980.
IEEE
Trans.
Microwave
Theo.
Tech.,
vol.
76
IEEE
TRANSACTIONS
ON MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-33
, NO.
1, JANUARY
1985
necessary
for
Patent Abstracts These
Patent
readers for
Abstracts
to determirte
a small
of
if they
fee by writing:
recently
issued
are interested U.S.
Patent
patents
are
in examining and
Trademark
Office,
Apr.
4,441,089
Change-Over
intended
to provide
the patent
in more
Box
the
detail.
minimum
9, Washington,
DC
Gianni BBC
Olgiati. Brown,
Boveri
& Company,
change-over
switch
a
Limited. Filed:
July
of patents
are avaiable
..;., ., . .. ,. .’
I
2di .:.: ‘~., ~, ,.:’:: fz .,. . . . . .’.. . .
dz Inventor:
.’.
.. . ‘. . .
Conductors
copies
20231,
2
3,1984
Switch for Coaxial
Assignee:
information
Complete
2, 19s1.
4,441,784 A&tract
—The
articulated
to
selectively ing
new
an inner
to one
element
and
tulip-shaped low
reflection.
the
axial
direction
conductor
and
other
conductors.
two
the
one
contacts,
aud other
of
thus
or
tufip-shaped as two-part
together,
pivoting
other
tube.
switching
contact, A
are
the
crank
is preferably
telescopic
loss
tube,
pushed
factor
into
for
is
pushing
necessary
1984
Coupler
for Light
Wave Guides Inventor:
Hans-Erdmann
Assignee:
International
Filed:
Apr.
30,
Korth. Business
Machines
Corp.
1981.
for
switching-over.
—A self-focussing
,4fmmact body 5
10,
in the
element
used as is
as
is pulled
connecting
Paraboloidal
connect-
designed
small and
Apr.
is
element
the
element
pivoted
which
connecting
between
unobtainable
the
the
element
conductors
movement,
re-extending
the
contacts
a hitherto
this
telescopic and
connects
inner
of one tufip-shaped For
a comecting
The
connecting-over,
contact.
designed
which
permitting
During out
the
having
Claims, 4 Drawing Figures
having
optical
configuration
are
connected
fibers
face
is
formed
formed
by
at (beam
gap
coupler
the bypass
optical
body
of
at or
the
axis
of
faces
of
two
couplers
plates,
be
the
A
or
may
alter
more
focus.
A
is
optical
be placed
the
flat
assembly
Different
etc.)
to
of
coupler
together.
filters,
added
a transparent One
point
symmetry.
bandpass may
includes
revolution.
near
to
fibers
fibers
a paraboloid
to the
spJitting
and
for
of
a normal
bringing
components interface
coupler
the
in
functions
of
an the
assembly.
10 Claims,
Drawing F@ures
8
ib
2b T I
I
30
A
Apr. 3,1984
4,441,091
4,441,785
Low-Loss
Leakage
Transmission
Apr.
Line Rotary
Inventors:
Shigeo
Nishida,
Assignee:
Hitachi
Cable
Filed:
July
1982.
tube
the wall
Mitsunobu
Miyagi,
Koichi
thickness
transmission
d2 of which
line
including
is selected
Fiber
a cylindrical
Inventor:
James
Assignee:
International
Filed:
Oct.
Abstract
the
dielectric
odd
integer.
to capture dielectric wall
dielectric
constant A loss auy
tubes
thickness
lost
constant
of the
of the materird
layer
may
wave
energy.
of different of each
dielectric
of the
which
be disposed In
tubes
5 Claims,
intemaJ
one
space
forms
around
the tube,
the
and
the cylindrical
embodiment,
constants
within
are coaxially
satisfying
the above
3 Drawing
Figures
tube,
is
tube
of cylindrical
arrauged
formula.
c*
n is a postive dielectric
a plurality
R. 29,
Petrozello. Business
Machines
Corporation
1981.
with
the
—Electronic
emitting
and
enter
utes
the light
elements el is the
Switch
dielec-
to satisfy
a tight
where
Optic
Mikoshiba.
Ltd.
—A low loss leakage
Abstract tric
22,
and
10,1984
detent
a rotary in the
diode
optic
drum.
Selecting
mechauicrdly
determines
emerge
from
mitted
through
output
where
they
the the
converted
signafs a fiber
A rotatable locations
the desired
into
the
orientation
conductive optic
drurrr
groups
of
to a photo
electronic
signrds
processing.
3 Claims,
in
6 Drawing
Figures
by
for
and
device. drum
of a
actuated
The and
or photo
normal
distrib-
conductive
light
the
of
group
by means
a
the diode
optic
of fight
of the drum drum
elements
by means
channels
by memrs
position
rotating
channel
light
fiber
to light through
output
or
by
are converted are channeled
switch.
to intended
signals
are
which
or laser
fiber
signals
switch
mechanism
signafs
diode
are
output trans-
transistor
electronic
1/0
IEEE
TRANSACTIONS
ON lvUCROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-33, NO. 1, JANUARY 1985
77
4,443,772
Apr. 17, 1984
Switching Microwave Bridge T Group-Delay Inventor:
Alfred
Assignee:
RCA
Filed:
Dec.
Abstract
two
narrow
gap
Monolithic
Microwave
Circuit with Integral Antema Inventors:
Ronald
Assignee:
Bafl
Filed:
June
Abstract array network,
—A
antenna. active
circuits
and
single
substrate
a
and
greater
between
connected
to
conductive
strip.
first
to
end
and
of
the
first
61Drawing
the
by
a
conductive two
conductor to provide fourth
relatively
other
apart
the first
The
‘a fifth
comprises
on
inductive
layer
conductors. by
form and spaced
two
the dielectric
second
7 CMms,
narrow
the gap between
ends
capacitor
Integrated
surface
end
over
and
grounded
one
than
adjacent
is disposed
the
a
in rnicrostrip
on
by a relatively
length
the
equalizer phme
oriented
together
overlies strip
delay
a ground
strips
connected
conductor
coupling 17,1984
group
having
conductive
layer
fourth Apr.
microwave
of substantially
dielectric
4,442~9f3
10, 1981,
substrate
surface strip
Schwarzmann. Corporation,
—A
a dielectric
Integrated Equalizer
strips.
A
strips.
A
capacitive
conductor
narrow
is
inductive
F@rr’es
Array 33)
J. Stockton
and
Robert
E.
Munson.
Corporation. 22,
1982.
monolithic
microwave
The
inchrdes
system
and/or
passive
microcomputer by
means
integrated radiati~g
semiconductor controller
of a controlled
1 Claim,
circuit
elements,
including feed
devices,
digitaf
simultaneously fabrication
13 Drawing
process
au
netw-ork, logic
incorporated
integral pha~ng interface on
a
sequence.
Fignres LIRU1 la
4,444,460
Apr.
Optical
Fiber
Substrate
Apparatus
Ruggedized
24,1984
Including
Optical
Fibers Inventor:
David
W.
Assignee:
Gould
Inc.,
Filed:
May
Abstract fibers turing
of
supported
interfacing
surface a lower
allow
partiaf
fiber
to aflow
melting assembly
of
point
portion softening fusing of
devices fibers.
may
areas
fiber
of
support
support
/42-/4
7i:Pt.
the
fiber
formed
fiber.
9
9’6
support
assembling
with
a rigid
assembly
along may
provide to a rigid
combinations
21 Drawing
which
Figures
opticaf
one
or
by molecufar
the
by
This
supported
in
and
assembly
fused
from
Au
fibers
to
rigidly
materiaf
materiaf
The
16 Claims,
,
the
matrxiaf
an optical be
support
in yrxtaposition
than
the
more provided
be fabricated
point
therebetween. the
of
may
or are
a rigid
of the fiber
melting
one
thereof
with
surface opticaf
comprising
opticaf opticaf
having,
making
are interfaced
rigidly outer
devices
a method
fibers
having
1981.
—Opticaf
and
optical
26,
Stowe.
the
material.
support
outer
materiaf
be heated surface
be cooled
a ruggedized support
material.
of
rigidly
such
The
a longitudinal
may
then
more
restruc-
of
below
to the the
fiber-optic Various supported
78
IEEE
TRANSACTIONS
4,445,097
Apr.
Microstrip
Transistor
with Dielectric
ON MICROWAVE
THEORY
Oscillator
Jean-Jacques Thomson-CSF,
Filed:
Sept.
Biasing
Magnet
Godart
and
Bernard
Le
Clerc.
Inventor:
Richard The
to one
in a very from due
end
situated
of
Thus,
high
to
a line
of
the
frequency
very
the
high
resonator
transistor power
resonator.
coupled
In
the
from
the
resonator
1, JANUARY
1985
1984
1,
Cap
A.
Stem.
United
States
the
wavelength
frequency
of America
the
as
Secretary
of the Army.
13, 1982.
which
the
circuit
from
the
is
line.
resonant
and for
upper
them.
above
to the
the
waveguide
vertex
legs. These
than
biasing
bonded
At
tuning
higher
positioned
the
and
dielectric
plate.
metal
extend
a cap
Y-junction
support
positioned
line
in turn
—A
Abstract dielectric
is connected along
open
varies
so as to frequency
gate
at a point
Aug.
by
temperature
maximum
end of the line,
a half
the
low
(3 to 10 GHz)
snd
case of a FET,
to
when
a very
oscillator
the other
resistor
is damped
with
available
to a dielectric
a discrete
oscillation
frequency
a dielectric
wavelength
through
the
using
the
at a qusrter
connected
Holder-Tuning
represented, Filed:
stabilization
NO.
Waveguide
Assignee:
14, 1981.
—A device
both
MTF33,
Circulator
Inventors:
coefficient
VOL.
May
for Dielectric
Resonator
Assignee:
benefit
TECHNIQUES,
4,446,448
24,1984
Stabilization
Abstract
AND
tie magnet.
circulator
adjacent
tuning
Preferably
circulator
bottom
of
legs are spaced the
tuning
jnnction.
The
lower
is provided
dielectric
magnet
of the support
from
cap
integral
afso serves
is centered
a are
the waveguides
legs are made
This
with
waveguides
with
as a holder
under
the junction
plate.
resonator. 8 Claims, 6 Claims,
4 Drawing
5 Drawing
F@mes
F&rres
8 6
I —
Aj
--Qii!i@ W
—
2’9
20
A?
%.
Apr.
Coupling Block Assembly Band-Reject Filter Inventor:
Frank
Assignee:
Electronics,
Filed:
Jan.
Abstract resonator coupling extends
2’?
coupling rod
and
adjusting the
disc
—A rod disc. the
with
Decker. Missiles
band-reject which
& Communications,
comprises
mounted
thrn
the
inner
resonator.
At
the end
Means
in
are provided
The
length the
filter
is
passes the
the disc. and
Ill, ,6
1984
Inc.
28, 1982.
rod into
24,
“,!
i4
-’
2+
4,445,100
30
frequency of
resonator
to
conductor
of
of the rod
to adjust rejected
the resonator
a resonator
proximity
rod
the distance
or by
co-axiaf
an
The
assembly
and
the resonator between
adjustable
assembly. there
is a
4,445,098
Apr.
the distance
by either between
Method
and Apparatus
Fast-Switching 5 Drawing
Pigrrres
24,1984
the resonator
can be adjusted
adjusting
rod.
3 Claims,
the
inside
by the filter
with
a co-axial
Microwave
Phase Shifter
Inventors:
Thomas
Assignee:
Electromagnetic
Filed:
Feb.
Abstract switching provided saturated bly and
partiafly
maintained shift
always
ferrite
circnits
Roberts.
is for
ferrite phase shifter. A first the ferrite in one of the toroids
with
for
any with
given only
of
the
only
one
for
in
state
switching
such
56 Drawing
at
least
time
states
one
79 Cfaims,
is provided between
switching
phase
method
toroids
given
reference
snd
conduit
ferrite
at any
apparatus
is provided
the
circuit
state new
an
A second
other
that
saturated provides
be achieved
states. the
A control
such
be achieved states
G.
Inc.
invention
in
states.
invention
cal phase
Roger
microwave switching
saturated
the
in the
may
present
and
Sciences,
present
saturated
second
Sharon
dual- toroid controllably
switching
partially
E.
19.1982.
—The a for
for
Dual-Toroid
such
that
that
any
for there
a reciprocal
operation
Figures
for
of
that for
fast-
each
first
toroids
desired
each
and
the
the
is a
controlla-
a saturated
controlling
one
operation such
of
circuit between
toroid.
are two phase toroid.
is
phase The
reciprostate
may
IEEE
TRANSACTIONS
ON MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-33,
NO.
1,
1985
JANUARY
79
-22
mom hsIMo#7
@ I
RATA RESET 2
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l_J
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2s
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+BEEE @
TRANSACTIONS
ON
MICROWAVE THEORY AND TECHNIQUES FEBRUARY
1985
A PUBLICATION
VOLUME
OF THE IEEE MICROWAVE
MTT-33
NUMBER
THEORY AND TECHNIQUES
m
2
(ISSN
0018-9480)
SOCIETY
@
PAPERS
Power-Handling Capabilities of Circular Dielectric Waveguide at Millimeter Wavelengths . . . . . . . . . . . . . . . . . . . . . D. G. Jablonski 85-115 -GHz Receivers for Radio Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. P. Woody, R. E. Miller, and M. J. Wengler Field Theory Design of Rectangular Waveguide Broad-Wall Metal-Insert Slot Couplers for Millimeter-Wave Applications ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Arndt, B. Koch, H.-J. Orlok, and N. Schroder 12-GHz-Band GaAs Dual-Gate MESFET Monolithic Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Sugiura, K. Honjo, and T. Tsuji Variational Analysis of Ridged Waveguide Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Y. Utsumi The Electric-Field Problem of an Interdigital Transducer in a Multilayered Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. M. van den Berg, W. J. Ghijsen, and A. Venema Computer Calculation of Large-Signal GaAs FET Amplifier Characteristics . . . . . . . . . . . . . . . . . . . . . A. Materka and T. Kacprzak Short Millimeter Wavelength Mixer with Low Local Oscillator Power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. W. Hant
SHORT
PAPERS
Exact Wave Resistance of Coaxial Regular Polygonal Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Terakado Analysis of the Transmission Characteristics of Inhomogeneous Grounded Finlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Beyer Phase-Matched Waveguide Using the Artificial Anisotropic Structure and Its Application to a Mode Converter ................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Mizumoto, H. Yamazaki, and Y. Naito A Design Methods of Bandpass Filters Using Dielectric-Filled Coaxial Resonators . . M. Sagawa, M. Makimoto, and S. Yamashita Conservation Laws for Distributed Four-ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. O. Schwelband R. Antepyan A Broad-Band Directional Coupler for Both Dielectric and Image Guides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. J. Collier An Iterative Moment Method for Analyzing The Electromagnetic Field Distribution inside Inhomogeneous Lossy Dielectric Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. F. Sultan and R. Mittra On the Graceful De radation Performance of Multiple-Device Oscillators . . . . . . . . . . . . . . . . . . . . . S. Sarkar and M. C. Agrawal ?
LETTERS
Comments on “EM Local Heating with HF Electric Fields” . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . M. J. Hagmann and K-M. Chen Comments about “On the Definition of Parameters in Ferrite-Electromagnetic Wave Interactions” . . . . E. M. A. Eid and L. Lewin
PATENT
ABSTRACTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .. N. R. Dietrich
Technical Compu(er-Aided
Design
L. BESSER
COMSAT General Integrated Syst. I I 31 San Antonia Rd. Palo Alto,
CA 94303
Submlllimeter
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Ferr\re.~
C. R. BOYD, JR. Microwave Appl]catlons Group 3030 Industrml Parkway Santa Maria, CA 93455 Mtcrowaue
Systems
F. IVANEK Farinon
Electric
Microwave High-Power
Te,-hmques
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Measurements
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Technical
Sysfems
Box 7728
RF Techniques
J. J. WHELEHAN, JR Eaton Corp. AIL Div Walt Whitman Rd Melwlle, NY 11747 M]crox,ace
Waue
Circuits
T ITOH Dep Elec. Eng. The Umv. Texas, Austin, Austin, TX 78712
LOW,Noise Techniques
Sci.
D. W. MAKI Hughes Aircraft Co. Bldg. 23 1/2019 3100 W. Lomita Blvd PO. BOX 2999 Torrance, CA 90509
MicrowaL1e
J. C. LIN Dept Bio -Eng. Univ. Ilhnois. Chlca~o BOX 4348 Chicago, IL 60680 MlcrowaL>e
Optics
Microwaoe and Millimeter-
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Committees
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LING
Res. Mallbu
Mallbu,
B. E. SPIELMAN U. S. Naval Res. Lab. 4555 overlook Ave. Washington, DC 20375
Labs. Canyon
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EDITORIAL
BOARD
Editor T, Itoh S. Adam A. T. Adams K. K Agarwal J, Amoss D. B. Anderson J. A, Arnaud J. R. Ashley A. E. Atia N. F. Audeh A. J. Bahr J. W. Bandler H. E. M. Barlow F. S. Barnes R. H. T. Bates E. F. Belohoubek P. Bhartia J. Bradshaw D. I. Breitzer M. Brodwin C. Buntschuh J. J. Burke H. Bussey K. J. Button C. A. Cam H. J. Carlin P. H. Carr K. S. Champlin W. S. C. Chang M. Chodorow J. Cit?rne S. B. Cohn R. E. Collin H. M. Cronson E. Cristal W. R. CurtIce J. B. Davies L. E. Davis M. E. Davis J. E. Degenford E. Derdinger L. E. Dickens
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