TU3B-7
Modeling
of
Quasi-Optical
Arrays
Polly Preventza,'
Blythe
Dicknian,'
Eniilio
Sovero,2 Michael
P.
De
Lisio?
James
J.
R~enberg,~
David
B.
Rutledge'
Department
of
Electrical
Engineering,
California
Institute
of
Technology,
Pasadena,
CA
91
125
2Rockwell
International
Science
Center,
Thousand
Oaks,
CA
91358
3Departnient
of
Electrical
Engineering, University
of
Hawai'i
at
MEnoa,
Honolulu,
HI
96822
4Departnient
of
Engineering, Harvey Mudd
College,
Claremont,
CA
9171
1
Abstract-
A
model
for
analyzing quasi-optical
grid
ampliiers
based
on
a
finite-element
electro-
magnetic simulator
is
presented. This
model
is
deduced
from
the
simulation
of
the
whole
unit
cell
and
takes into
account
mutual
coupling
ef-
fects.
By
using
this
model,
the
gain
of
a
10
x
10
grid amplifier
has
been accurately predicted.
To
further
test
the
validity
of
the
model
three
pas-
sive structures
with
different
loa&
have
been
fabricated
and
tested
using
a new
focused-beam
network
analyzer that
we
developed.
I. INTRODUCTION
Two techniques have been
reported
for
the
modeling
of
quasi-optical
system..
.
The
first
technique
aFsurnes
an
infinite array,
allowing
the
grid
to
be analyzed with
a
single
unit
cell
with synmietry
planes
[l].
The
unit
cell
of
an
amplifier grid
is
shown
in
Fig.
1.
De
Lisio
et
al.
[I]
developed
a transniission-line niodel
for
this
unit
cell where
the
metal
strips are
analyzed
by
the
method
of
nionients.
The
model
is
shown
in
Fig.
2
and it
overpredicts
the
gain
by
3dB.
Mutual
coupling
between
the
lines is neglected.
Fig.
1.
Unit
cell
of
a 100-element
,
10-GHz
grid amplifier
[
11.
The
input
beam is
coupled
to
the
gates
of
the
transistor
through
the
horizontal
gate leads.
The
output
berun
is re-
radiated
from
the
vertical
drain
leads.
The
thin
meandering
lines
provide bias
to
the
drain and
source.
0-7803-5135-5/99/$10.00
0
1999
IEEE
15
1
I
I
I
I
I
-.
Fig.
2.
(a)
The
unit-cell
transmission-line
model.
The
input,
output
leads
and
the
bias
lines are modelled
as
in-
ductors.
(b)
Grid
amplifier
gain
versus
frequency.
The
second technique
121,
uses
the
method
of
nio-
nients
to
simulate
the
full grid
and
includes
the
edge
effects
of
the
array.
This
niodel
uses
a
simplified
grid
layout
without
complicated
nietal shapes
like
meander-
ing
lines.
It
also
overpredicts
the
gain
by
as
much
as
3dB.
563
1999
IEEE
MTT-S
Digest
Advancement
in
finite-element
analysis techniques,
such
as
Ansoft’s
High
lirequency
Structure
Simulator
(HFSS),
allow
an
accurate
and
fast solution
for
the
electromagnetic
modeling
of
arbitrarily-shaped,
pm
sive,
three-dimensional
structures.
Two
new
modeb
that
are
an
extension
of
the
unit-cell trammimion-line
niodel
and
include
mutual
coupling
effects
are
devel-
oped based on
HFSS
simulations.
The
first niodel
iR
a
lumped-element equivalent circuit
of
the
unit
cell.
The
rsecmd
niodel finds
the
full
scattering parameters
in
an
approach
that
is similar
to
the
calibration
of
a
vector
network
analyzer. In
this
paper,
we
show
that
the
new
niodeLs
agree
very
well
with
previously published
mea-
surements
[l].
Comparison
between
measurements
of
pawive
arrays
and
siiniulatiom
further
validate
the
new
niodels.
11.
MODELING
OF
THE
UNIT
CELL
The
empirical trammimion-line
equivalent
circuit
used
in
[l]
to
model
the
unit
cell
is shown
in
Fig.
2(a).
The
input
and output
leads
of
the
grid
are
modelled
as
inductors.
The
meandering
bias
lines
are
modelled
as
a
shunt inductance.
The
numerical values
of
these.
reac-
tive
elements are
computed
by
&st using
the
niethod
of
moments
to
approximate
the
surfmecurrent
distribu-
tion
and then the
induced
emf
niethod
[3]
to
calculate
the
impedances
of
the
elements.
This
technique ana-
lyzes
single elements
of
the
unit
cell,
thereby
neglecting
coupling
effects
between
these
elements.
Two
new
models
have
been developed
based on
HFSS
simulations
of
the
whole
unit
cell.
The
first
niodel,
shown
in Fig.
3,
accounts
for
the
cmpling
be-
tween
the gate
lead
and
the
biar,
lines
and
predicts
a
gain
that
is
only
0.5dB
higher
than
measured.
Other
parasitic elements
such
as
the
inductance
of
the
bond
wires
and the
finite conductivity
of
the
metal
are
ah
included
in
the
simulation.
The
wcmd
technique, anal-
opus
to
the
calibration
of
a network
analyzer, directly
utilizes
data
obtained
from
HFSS
two-port
siniulatiom.
Siniulatiom
of the
unit
cell
are carried
out
for
matched,
short
and
open terminations
placed
at
the
active
de
vice
location.
Therie
three
twwport ,+parameter
files,
Go
can
then
be
ud
to
find
the
three-port
s
parameter
matrix
of
the
grid,
ellm
el2m
313
3
=
(
e;;;
%)
(1)
where
(2)
e21n
+
e210
-
2e21m
333
=
e210
-
e21n
r---i
-$;
r---,
*I
5
----
Theoly
i,
I
I
I
,[I
I
Frequency,
GHz
(b)
Fig.
3.
(a)
Lumped-element
equivalent
circuit
deduced
from
HFSS.
Lb
and
L,
are
the
inductancw
of
bias
lins
and
gate
radiating lead,
respectively,
and
M
is
the
mutual
in-
ductance
between
them.
(b)
The
measured amplifier
gain
is
within
O.lidI3
of
the
theoretical
prediction.
This procedure
is done
twice, once
for each polariza-
tion.
The
resulting
pair
of
*matrices
is
incorporated
into the
overall
amplifier
niodel
as
shown
in
Fig.
4(a).
564
3-port
Equivalent
output
circuit
Lw-4
-+
/
I
%port
Equivalent
Stabilising
Input
Circuit
Resistance
-15
-
8
9
11
Frequency,
GHz
(b)
Fig.
4.
(a)
The
scattering-parameter
model.
(b)
The
niea-
surd
amplifier
gain
conipared
with
theory.
Fig.
6.
Passive
array. The
black
lines
are
metal and
the
shaded
area
is
the
location
of
the
devices
and
the
various
tenninations.
111.
PASSIVE
STRUCTURES
To validate
the
use
of
HFSS
in
the
design
of
the
grid
aniplifers,
three
23
x
23-element
passive
structures
with
short
circuits,
open
circuits
and
7s-SI
terniinations
have
been
modelled
and
tcsted
(Fig.
S).
The
layout
is very
Fig.
6.
Quasi-optical meamrenient
network
analyzer.
0
Theory
Fig.
7.
Traminission and
reflection
nieacrurements
of
a
2.5-
cm
polysterene
slab
(er=2.45).
similar
to
the
topology
of
a
grid
amplifier.
The
arrays
were
fabricated
by
Rockwell
International
Science Cen-
ter. The substrate
used is
a
0.63bmm
thick,
75nml
diameter
GaAs
wafer.
The
size
of
the
array
is chosen
to
be
larger
than
the
beaniwaist.
IV.
MEASUREMENTS
We
extended
the
lens-focused
reflectometer,
devel-
oped
by
Gagtion
[4],
to
a
full
two-port
system.
The
apparatus
is
shown
in
Fig.
G.
It
uses
two
bi-convex
lenses
with a
30-cm
diameter and
focal
length
to
fe
cus
the
bean1
to
a
spot
at
the
measurement
plane.
Two
corrugated
feed
horns driven
by
an
HP8722D
vec-
tor
network analyzer
are
used
to
transniit
and
receive
the
gaudan
beam.
The
calibration
standards
for
the
network analyzer
were
a
short
(a
large
sheet
of
alu-
minum
at
the
measurement
plane),
an
offset
short
and
a
match
(a
large section
of
absorber
at
some
distance
from
the
measurement
plane).
To
check
the
calibra-
tion,
measurements
were
made
on
a polysterene
slab.
Fig.
7 shows excellent
agreement
between
simulation
565
Fig.
8.
Simulated
and
measured
scattering
parameters
of
the
passive
array
with
short-circuit terminations.
The
solid
line
shows
the
measurement.
Fig.
9.
Simulated
and
measured
scattering
parameters
of
the
passive
array
with
7551
terminations.
The
mlid
line
shows
the
measurement.
and
measurement. Gating
liw
been
wed
to
eliniinate
niultiple
reflections
from
the
lenses
and
horns.
Comparison
between
the
scattering parameter
model
and
niemurenients
for
the
passive
arrayR
are
shown
in
Fig.
8, 9
and
10.
Agreement
is
good:
V.
CONCLUSION
We
have
presented
two
new
models
for
the
design
of
quasi-optical
grid aniplifiew
bmed on
Ansoft’s
HFSS.
These
models account
for
mutual
coupling
between
the
lines
of
the
grid
and
for
parasitic inductances.
The
niodeLs
were
used
to
accurately
predict
the
gain
of
a
I
\\\\
i,
----_.
40
GHZ
Fig.
10.
Simulated and
measured
scattering
parameters
of
the
passive
array
with
open-circuit
terminations.
The
solid
he
shows
the
measurement.
10
x
10
grid
amplifier. Finally,
the
scattering
parani-
eter
model
was
validated
by
measuring
the
scattering
parameters
of
three
passive
arrays
with
different
tern&
nations.
V.
ACKNOWLEDGMENTS
The
authors
appreciate
the
support
from
the
Arniy
Research
Office
through
the
Caltech Quasi-Optic
Power
Combining
MURI.
VI.
R.EFERENCES
[l]
Michael
P.
DeLisio,
Scott
W.
Duncan,
Der-Wei
Tu,
Cheng-Ming
Liu, Alina
Mous.sessian,
James
J.
bnberg
and
David
B.
Rutledge,
“Modeling
and
Perforniance
of
a 100-Element
pHEMT Grid
Ampli-
fier,”
IEEE
%ns.
on
Micmwave
Theory
and
Tech.,
(dd),
No.
12,
pp.
2136-2144,
Dec.
1996.
[2]
M.A.
Suniniew, C.E.
Christoffemn,
A.I.
Khalil,
S.
Nhawa,
T.W. Nutemn,
M.B.
Steer
and
J.W.
Mink,
“An
Integrated Electromagnetic
and
Non-
linear Circuit
Simulation Environment
for
Spatial
Power
Combining
Systems,”
1998
IEEE
MTT
S
Int.
Microwave
Symp.
Dig.
(2),
pp.
168-176.
ledge,
“A
100-MESFET
Planar
Grid
Oscillator,”
Ieee
%na.
on
Micmwave
Theory
and
Tech.,
(39),
pp.
823-826,
1994.
[4]
D.R.
Gagnon,
“Highly
Sensitive
Measurements
With
a Lens-Focused
Reflectometer,”
IEEE
%na.
on
Micmwave
Theory
and
Tech.,
(39),
pp.
2237-2240,
Dec.
1991.
[3]
Z.B.
PopoviC,
R.M. Weikle,
M.Kirn,
D.B.
Rut-
~
566