IEEE MTT-V044-I12A (1996-12)

178 Pages·1996·21.894 MB·English

by  FANTOMASPING

IEEE T R A N S A C T I 0 N S O N

MICROWAVE THEORY
AND TECHNIQUES
A PUBLICATION OF THE IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY

DECEMBER 1996 VOLUME 44 NUMBER 12A IETMAB (ISSN 0018-9480)

[email protected]

PART I OF TWO PARTS

PAPERS
Development of a general symmetrical condensed node for the TLM method - V. Trenkic ; C. Christopoulos ; T.M. Benson 2129 - 2135
Modeling and performance of a 100-element pHEMT grid amplifier –
M.P. De Lisio ; S.W. Duncan ; Der-Wei Tu ; Cheh-Ming Liu ; A. Moussessian ; J.J. Rosenberg ; D.B. Rutledge 2136 - 2144
Hybrid method solution of scattering by conducting cylinders (TM case) - T. Roy ; T.K. Sarkar ; A.R. Djordjevic ; M. Salazar-Palma 2145 - 2151
Analytical dispersion analysis of loaded periodic circuits using the generalized scattering matrix - W.S. Best ; R.J. Riegert ; L.C. Goodrich 2152 - 2158
Dynamic shape of the depletion layer of a submillimeter-wave Schottky varactor - J.T. Louhi ; A.V. Raisanen 2159 - 2165
Order-recursive Gaussian elimination (ORGE) and efficient CAD of microwave circuits - P. Misra ; K. Naishadham 2166 - 2173
A coaxial 0.5-18 GHz near electric field measurement system for planar microwave circuits using integrated probes -
T.P. Budka ; S.D. Waclawik ; G.M. Rebeiz 2174 - 2184
Numerical simulation of the power density distribution generated in a multimode cavity by using the method of lines technique to solve directly for the
electric field - Huawei Zhao ; I. Turner ; Fa-Wang Liu 2185 - 2194
On the application of finite methods in time domain to anisotropic dielectric waveguides –
S.G. Garcia ; T.M. Hung-Bao ; R.G. Martin ; B.G. Olmedo 2195 - 2206
Accurate and efficient circuit simulation with lumped-element FDTD technique - P. Ciampolini ; P. Mezzanotte ; L. Roselli ; R. Sorrentino 2207 - 2215
Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media
Jiayuan Fang ; Zhonghua Wu 2216 - 2222
Analytical expansion of the dispersion relation for TLM condensed nodes - V. Trenkic ; C. Christopoulos ; T.M. Benson 2223 - 2230
Scattering of millimeter waves by metallic strip gratings on an optically plasma-induced semiconductor slab - K. Nishimura ; M. Tsutsumi 2231 - 2237
Electric screen Jauman absorber design algorithms - L.J. Du Toit ; J.H. Cloete 2238 - 2245
Analysis and linearization of a broadband microwave phase modulator using Volterra system approach - P. Celka ; M.J. Hasler ; A. Azizi 2246 - 2255
Application of a coupled-integral-equations technique to ridged waveguides - S. Amari ; J. Bornemann ; R. Vahldieck 2256 - 2264
Oscillator-type active-integrated antenna: the leaky-mode approach - Guang-Jong Chou ; C.-K.C. Tzuang 2265 - 2272
Intermodulation distortion in Kahn-technique transmitters - F.H. Raab 2273 - 2278
An analytical model for the photodetection mechanisms in high-electron mobility transistors –
M.A. Romero ; M.A.G. Martinez ; P.R. Herczfeld 2279 - 2287
Stokes phenomenon in the development of microstrip Green's function and its ramifications - D. Chatterjee ; R.G. Plumb 2288 - 2290
A fast algorithm for computing field radiated by an insulated dipole antenna in dissipative medium -
Lin-Kun Wu ; D. Wen-Feng Su ; Bin-Chyi Tseng 2290 - 2293
A fast integral equation technique for shielded planar circuits defined on nonuniform meshes –
G.V. Eleftheriades ; J.R. Mosig ; M. Guglielmi 2293 - 2296
Analysis of electromagnetic boundary-value problems in inhomogenous media with the method of lines - A. Kornatz ; R. Pregla 2296 - 2299
New reciprocity theorems for chiral, nonactive, and bi-isotropic media - C. Monzon 2299 - 2301

(end)
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44, NO. 12, DECEMBER 1996 2129
Development of a General Symmetrical
Condensed Node for the TLM Method
Vladica Trenkic, Member, IEEE, Christos Christopoulos, Member, IEEE, and Trevor M. Benson, Member, IEEE
Abstruct- A general symmetrical condensed node (GSCN) modeling of the capacitance and inductance of the medium
for the transmission line modeling (TLM) method, with six and preservation of impulse synchronism. In Section 111-A, the
different link line characteristic impedances, six stubs, and six
scattering matrix for the GSCN is derived from the equivalent
lossy elements is described for the first time. It unifies all the
network model [9], [lo], which formulates scattering in a
currently available condensed nodes into a single formulation
and provides the basis for the derivation of an infinite set of new node having six different link-line impedances, three open-
nodes, including nodes with improved numerical characteristics. circuit stubs, three short-circuit stubs, and six lossy elements
The GSCN is derived in two ways: 1) from an equivalent network for modeling electric and magnetic losses. Applying particular
model and 2) directly from Maxwell’s equations using central
constraints to the GSCN, the scattering matrices for all existing
differencing and averaging. The direct correspondence estab-
condensed nodes [1]-(81 and their parameters are derived from
lished between the GSCN TLM and a finite difference scheme for
Maxwell’s equations provides a rigorous theoretical foundation the formulation of the GSCN presented here.
for all available TLM methods with condensed nodes. A formal equivalence between the SCN TLM and the time-
domain finite-difference (FD-TD) method was first established
in [ll]. Recently, it was shown that the SCN TLM can
I. INTRODUCTION
T be derived directly from Maxwell’s equations applying the
HE SYMMETRICAL condensed node (SCN) [ll has
Method of Moments (MOM) [12]. The two above references,
been the basis of the three-dimensional (3-D) trans-
however, consider only the simple 12-port SCN, which cannot
mission line modeling (TLM) method for many years. To
model inhomogeneous and lossy media and is restricted only
allow for the modeling of general lossless materials and
to the cubic cells. More practical schemes, namely the stub-
nonuniform grading of the mesh cells, the basic 12-port SCN is
loaded SCN and the HSCN, were only very recently derived
augmented by three open- and three short-circuit stubs [ll. In a
directly from Maxwell’s equations, using central differencing
development of the SCN referred to as the hybrid symmetrical
and averaging [13]. A direct theoretical derivation of the Type
condensed node (HSCN) [2], the characteristic impedances of
I1 HSCN and the SSCN has not been presented in the literature
the link lines are varied to account for mesh grading and to
so far.
model magnetic properties of the mesh, and three open-circuit
In Section 111-B, we derive the GSCN directly from
stubs are used to make up for any deficit in the capacitance.
Maxwell’s equations, using principles established in [ 131. This
A complementary HSCN, denoted as the Type I1 HSCN [3],
derivation gives the same results for the field components in
was recently developed using different link-line impedances
the GSCN as obtained using the network model in Section
to model electric properties and short-circuit stubs to correct
111-A, thus offering further evidence of the soundness of
for any deficit in inductance. In a further recent development
the method. Since the symmetrical super-condensed node is
of the SCN, referred to as the symmetrical super-condensed
derived from the GSCN by removing stubs, a field-based
node (SSCN) [4]-[6], stubs are removed all together and all
theoretical foundation to the SSCN is also established for the
medium parameters are modeled by varying the characteristic
first time.
impedances of the link lines. Modifications of the SCN to
account for electric and magnetic losses are described in [7]
11. GENERALT LM CONSTITUTIVREE LATIONS
and [8] and can be readily applied to all other condensed nodes.
In this paper, we present the development of a general The total capacitance and inductance of the block of space
symmetrical condensed node (GSCN) that unifies all of the -w_ith linear dimensions Ax, Ay, AZ and material properties
existing condensed node schemes [ 11-[8] into a single scheme Z,p defined as diagonal tensors
and provides a template for the derivation of new nodes with
improved propagation properties. A general formulation of the -- Erx 0 0 Prz 0 0
link and stub parameters is presented in Section I1 that can be
used in connection with any TLM node. These parameters Prz
are determined by a set of 12 equations that ensure proper modeled by a TLM node, in the i direction are given as [14]
Manuscnpt received June 10, 1995; revised August 26, 1996. This work AjA k AjAIC
c;
was supported in part by the Engineenng and Physical Sciences Research = Eo&,,- Ai L; = POCLTZ- ai (2)
Council, U.K.
ingT, hUe naiuvtehrosirtsy aorfe Nwoittht inthgeh aDmep, aNrtGm7e n2tR oDf ENloetcttmncgahla amn,d U E.Kle.c tronic Engineer- where i,j ,I C E {x,y , Z} and i # j,I C. Equations (2) must hold
Publisher Item Identifier S 0018-9480(96)08478-5. for any TLM node, constructed by an arbitrary combination
0018-9480/96$05.00 0 1996 IEEE
2130 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL 44, NO 1
on these restrictions, we gi classification of the 3-D
TLM condensed nodes use ime-domain schemes.
1) Stub-loaded nodes use the same chara
for all link lines, which sets six co
L,,/C,, = const.
2) Hybrid nodes use e
that three extra conditions are given by L; = 0 or
Ci = 0. The other three conditions are obtained by
field components
the previous three spec1
teristic admittanceslimpedanceso f the link and stub lines must
be determined, and they ar as [15]
Fig 1 3-D TLM symmewical condensed node (SCN)
and stubs, and we refer to them as the general
TLM constitutive relations.
Consider the TLM symmetrical condensed node depicted in an 2-directed j-polarized link line and Yo,,Z ,,a re t
Fig. 1. Let the distributed capacitance and inductance of an z-
directed, j-polarized link line be denoted by indexes according
to their direction and polarization as C,, and Lz,.T he total
capacitance of an open-circuit stub and the total inductance of
contributing to the cell’s capacitance and
vely, in the a direction, are denoted as C;
and Li. The general TLM constitutive relations (2) applied to
the condensed node can be written as
ajak
+ c,,aj + c:
C~,A~C = EOEr,- (3)
Qa
In time-domain TLM, losses are modeled by inlroducing
matched stubs, loaded to the nodes at the scattering points [ 1
Their presence does not affect the general system of
The six equations defined in (3) and (4) by using all possible
Given the effective electric and magnetic conductiv
combinations of z,~,k E {x,y,z}, represent the basis for the
and in the 2 direction, the parameters
correct modeling of the medium using a generally graded TLM
are defined as 171, [8]
mesh with condensed nodes. They contain eighteen unknown
parameters, namely C,, and L,, of the six link lines, C; of
it stubs, and Li of the three short-circuit
re are 12 degrees of freedom that can be
lation of particular types of symmetrical
condensed nodes.
In time-domain TLM schemes, time synchronism must be (4) that the contributions t
maintained in the mesh, i.e., the time step At must be the same
throughout and therefore six more conditions are imposed in
six lossy elements, and
(5)
With these extra conditions, six degrees of freedom still remain
n solving (3)-(5). combination of stubs and
can be readily shown that the link line and stub parameters
of the existing 3-D time-domain condensed nodes can be
obtained by imposing different constraints to (3)-(5). Based two different approaches, namely: 1) an equivalent network
TRENKIC et al.: GENERAL SYMMETRICAL. CONDENSED NODE FOR THE TLM METHOD 2131
- -
16 17 18
1 0 0 i,,
2 0 -i,, 0
3 0 0 -i,,
4 if, 0 0
5 -ayz 0 0
6 0 i., 0
7 ", 0 0
8 -82, 0 0
9 0 i,, 0
10 0 -is, 0
11 0 0 i,,
S= -12 0 0 -iv,
13 0 0 0
14 0 0 0
-15 o o o O e,, e,, e,, O o e,, 0- o I o O h, 0 0 0
16 0 0 0 f z - f z 0 f z - f , 0 0 0 0 1 0 0 0 j, 0 0
17 O - f y O 0 0 f, 0 0 f u - f y O 0 0 0 0 0 j, 0
-18 fz O - f , O 0 0 0 0 0 0 f , - f , O 0 0 0 0 j,
19 IC,, IC,, 0 0 0 0 0 0 IC,, 0 0 IC,, E, 0 0 0 0 0
20 0 0 IC,, IC,, 0 0 0 IC,, 0 0 B,, 0 0 I, 0 0 0 0
-21 0 0 0 0 IC,, t,, IC,, 0 0 4, 0 0 0 0 E, 0 0 0
22 0 0 0 m,-m,O m,-m,O 0 0 0 0 0 0 n, 0 0
23 0 - m , O 0 0 my 0 0 mu-m,O 0 0 0 0
'24 m, 0 - m , O 0 0 0 0 0 0 m,-m,O 0 0
Fig. 2. Scattering matrix of the general symmetrical condensed node (GSCN). (The first row and column are not part of the matrix. They give the
port numbering for convenience.)
model and 2) central differencing and averaging of Maxwell's {(~,z,y),(y,~,z),(z,y,~)}T.h e equivalent voltage in the i
equations. direction, V,, is given by
A. Derivation from the Network Model
Scattering in a condensed node scheme is traditionally de-
rived by imposing unitary and other conditions on its scattering
matrix [l]. However, a network model introduced in [9] and and the equivalent current contributing to the magnetic field
generalized and validated in [lo] shows that scattering in in the i direction, Ii, is given by
condensed nodes can be conveniently described by scattering
equations derived directly from the set of "equivalent" shunt
and series circuits. For historical reasons and in order to allow
comparisons with previous nodes, we also present the complete where (%.A k) E {(TY , z),( Y,z ,2),( z,x,Y )}. The voltages
reflected to stubs and lossy elements are given as
scattering matrix for the GSCN. For the same reasons, we keep
the original node port numbering scheme [l], [15], although v; = v, - v;, (14)
more elegant numbering schemes described recently [ 171, [ 181 v,l;= LZ,, + v;, (15)
yield a more symmetrical form of the scattering matrix.
V,T, =v, (16)
In the notation used here a voltage coming from the negative
v;,
side of the node (assuming the origin of coordinates at the cen- = R*,L (17)
ter of the node) along an i-directed, j-polarized transmission where i E (2,y , z}.
line is denoted as Kn,, whereas a voltage coming from the Using the scattering equations (10)-(17), we obtain the
positive side of the same line is given as V,,, (i,j E {x,y , z} scattering matrix for the GSCN, given in Fig. 2. Because there
and i # j). Voltages on the open- and short-circuit stubs are are no incident voltages from lossy elements, the matrix S
V,, and V,,, whereas the voltages on electric and magnetic is written as a 24 x 18 matrix rather then a full 24 x 24
loss elements are V,, and Vm,. In all cases, voltages incident square matrix with zero columns 19-24. The elements of the
on the node have superscript i while reflected voltages have scattering matrix S shown in Fig. 2 are
superscript T.
By following the principles established in [9] and [lo], the azj =Qj - b,, - 4 3 b,, = Q,Ck3
+
complete scattering procedure in the GSCN can be described cZ3 = Q3 - b,, dZ3 - 1 4, = pkiz,
by the following equations:
fk =2(1 - Pk - uk) e,, = bk,
yn,= v, f IkZ,, - y;, (10) 9, =2(1 - Qj - w,) it, = d,,
ypj= v, F 42,, - yn, (11) h, = g, - 1 jk = 1 - fk
where the upper and lower signs apply, respectively, for k,, = ea, 1, =
QJ
indexes (i,j,k)E {(~,Y,~),(Y,~,~),(~an,d~ (,iY,j),}k )E mk =2uk nk = -mk (18)
2132 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TEC QUES, VOL 44, NO. 12, DECEMBE
with eliminating partitions of S related to the short-circuit stubs,
the scattering matrix of the HSCN 121, [3] is derived. The
(19) scattering matrix for the Type I1 can be derived
from 5 ’ by setting yZ, = Yk,, Y
(20) partitions related to the open-circ
The scattering matrix for th
GSCN by eliminating rowkolu
(21)
Yo, = Zsi, = 0. If a lossless medium is modeled, then
the SSCN scattering matrix i y the submatrix Sln,
with elements a,, = 1 - b,
C2, and d,, = Lt3, as derived
also for frequency-domain
impedances [20],[ 21].
B. Derivation from Maxwell’s Equations
where indexes i,j ,k take all possible combinations of x,y , z. We now derive the GSCN TLM scheme directly from
Maxwell’s equations, by employing a procedure similar to that
can be written in the following partitioned
form, where each submatrix represents one of the matrices used in 1131. Maxwell’s equations, written in the Cartesian
coordinate system, are given as
outlined in Fig. 2
1
dE, dHk
Pl(n12 x12) s(G1S2+xl?3l ) ’S(S1i2lnx 3) &Q&,,- dt 1~ d? - _adH_k’ - oe2E2
Six equations are contained in (2
is introduced as
The mapping given by (27) will be
The indexes In, os, ss, el, ml, indicating the physical purpose this subsection. It allows the rotation of dummy indexes
of each submatrix, stand for link line, open-circuit stub, short- i,j ,5 in an arbitrary exp
circuit stub, electric loss, and magnetic loss voltage ports, F(i,j,k ),F (j,k ,i ) and
respectively. The superscripts of the submatrices define their After performing coor
size. Some partitions can be removed from the matrix if stubs by
or lossy elements are not . For example, if short-circuit
stubs and lossy elements are not used in the node, all partitions
with indexes ss, el and ml can be removed from S giving a
15 x 15 matrix.
where k E {z, y, x}, Maxw
By removing lossy elements from the node, setting G,, = 0
ten as
and R,k = 0 in (21)-(24) and eliminating rows 19-24 in the
scattering matrix S, it can be shown that the lossless GSCN
conserves energy by confirming that STYS = Y 1191, where
Y is a diagonal matrix with elements corresponding to the
characteristic admittances of link lines and stubs.
The matrix S has identical structure to the scattering matrix
for the stub-loaded SCN [E].B y setting the characteristic
impedances of link lines equal to the intrinsic impedance of
the background medium, i.e., letting Z,, = 20,th e elements
of the CSCN and the SCN scattering matrix become equal, as
expected. If an homogeneous lossless medium is modeled on a
uniform mesh, then stubs and lossy elements can be eliminated
by setting Yo, = Z,, = G,, = R,k = 0 in (21)-(24) and the In this formulation, Y,Z
partition SI, of the matrix S becomes equal to the original sidered as coefficients i
12-port SCN matrix [l] with the elements a,, = e,, = 0 and to conveniently represent
b,, = d,, = 112. sions. They are chosen in
Similarly, by setting Z,, = Z,, and ZSk = 0, for all grees of freedom demand
combinations of indexes 2, j,k E {x,y , z}, i # j,k and (7)-(9), these coefficients
TRENKIC et al.: GENERAL SYMMETRICAL CONDENSED NODE FOR THE TLM METHOD 2133
the link and stub admittanceshmpedances of the GSCN. In the where the upper and lower signs, respectively, correspond to
derivation of the SCN presented in [12] these coefficients were the incident and reflected voltages.
not explicitly introduced since there were no stubs and all the A similar transformation which establishes a correspon-
link-line impedances were identical. dence between the electrical and magnetic field components
Following [ 131 we introduce mixed space-time coordinates at the cell center and the incident and reflected voltages on
as the open and short stubs is given as
&=i+Er;& =i-t" nr(l/a)K(c) = 2 . nv:;"
for k E {x,y,z} and rewrite (30) as n~(l/2)L(C)Z,z = T 2 * n q " . (33)
By substituting transformations (32) and (33) into difference
2
equations obtained from (3 1) we derive
+- aK
yo2 -+GeZV,=O
2 at
z,i ari
+ - + Rm;I; 0. These two equations represent, respectively, the charge and
2 7at the flux conservation laws in the i-direction [22].
By using central-differencing at point (n,p ,q , T) [13], where Another set of finite difference equations can be obtained
+
n is a time and p, q, r are space coordinates, a set of finite from (30) by using central differencing at point (n
difference equations can be obtained from (31). The space 1/2, P, 4,
coordinates of the cell's boundaries and the cell's center are
referred to as
(Pf i,q,r)= (x*'> (PAf = (I/*>
;,
(p,4,rf =(z*) (P,W)= (e).
The terms associated with the mixed coordinates (k are
differenced as, for example
whereas terms associated with vk are differenced as, for
example
+
- [n+(l/a)V,(k-) n+(l/z)lj(k-)Zkzl.
The terms associated with the time coordinate t^ are differenced
as, for example
av,
at^ -
- n+(l/Z)K(C) - n-(1/2)I/(C).
Similarly as in [13], we now introduce the variable transfor-
mation in order to establish relationships between the electric
and magnetic field components at the cell boundaries and the
incident and reflected voltages at the cell center:
2134 IEEE TRANSACTIONS ON MICROWAVE THEORY A
By substituting (37)-(39) into (36) we obtain which after using (33) gi
at the time step n as
+ qz+ +2 “et) [n+l%(C)- n%(C)I
+ + + n+lTpz)
= Ykz(n+lV;nzn +lVZpz) q z ( n + l ~ n z
These expressions are equivalent to (14) and (15) obtained
from the network model.
Because there are no incident
pulses “reflected” to these ele
-- - [n V‘ jnk - n V‘ gpk -nv;n3- tnVlpP+3n v,T, Therefore, the complete ering equations is
+
Em, . ~L(c)] given by (45)-(48), which
+ for the GSCN already de
-[n+lynk - n+lTJ;.& - n+lVlng n+lVZpj
+ presented in Fig. 2.
n+lV,,I. (41)
Finally, substituting (34) and (35) into (40) and (41) we
obtain voltages and currents at the center of the node at time The formulation of the g
step n as given here is derived both
and from Maxwell’s equations. T
in [lo] that the network mode
of decoupled series and shunt pplying the charge
which are equivalent to (12) and (13) derived from the network
model.
The scattering matrix for the GSCN can be derived by
averaging appropriate field components at point (n,p , q, T) condensed nodes into a sin
in the mixed coordinate system. The procedure is similar to can be derived from the
that used in [13]. For example, by averaging the component additional conditions to the
+
(% IgZ kz) with respect to qk we obtain
+
2[nV,(c) nIg(C)Zkz] foundation to all nodes contained in the formulation of the
+
-- [n-(l/z)V,(k+) n-(1,2)J3(k+)Zkz] GSCN. This gives for the first time a fie
+ + of the symmetrical super-condensed nod
[n+(l/z)V,(k-) n+(1/2)4(k-)ZkZl. (44)
be derived from the GSCN by removing all stubs and
Substituting (32) into (44) we derive a reflected voltage at the the theoretical foundation for any new GSCN-ba
time step n as node scheme with an arbitrary number of stubs an
link lines. Following the discussion about accuracy given in
+
Vlnz= K(.) .r,(C)Zkz - VZpz (45) [13], one may conclude th
where x(c) and I,(c) are defined from (42) and (43). Si&-
larly, by averaging the component (K IjZkz)w ith respect
- equations gives clear insight in
field components and the trans
model. All field compone
= K(c)- r;(C)Zkz- Vlnz. (46) of a cell at the time mo
transformation (28) and
ons for all link lines can be derived
in this manner and they are found to be in agreement with the
+
scattering equations (10) and (11) derived from the network n - 1/2, n l/2,. . . , by
and the excitation in the G
model.
Averaging V, and I, with r ect to t^ at the point (n,p,q , r)
The derivation of the
gives
+
2. nAz(c) = n-(l/z)A,(c) n+(l/z)A,(c) A E W,II
TRENKIC et al.: GENERAL SYMMETRICAL CONDENSED NODE FOR THE TLM METHOD 2135
the SSCN, requires the least computer storage and is the most [20] D. P. Johns, “An improved node for frequency-domam TLM-The
efficient but its implementation is more complicated due to ‘Distributed Node’,’’ Electron. Lett., vol. 30, no. 6, pp. 500-502, Mar.
1994.
the presence of link lines with different impedances. The only [21] P. Berrim and K. Wu, “A new frequency domain symmetrical condensed
reason why one should combine the complexity of such a TLM node,” IEEE Microwave Guided Wave Lett., vol. 4, no. 6, p__p .
scheme with the extra storage of stubs is to achieve better 180-182, June 1994.
J-22-1 J . L. Herring and C. Christoooulos, “The auulication of different
propagation characteristics. The possibilities opened up by meshing techIni ques to EMC problems,” in 9tIh_ A nnu. Rev. Prog. in
the GSCN formulation have been exploited to develop and Applied Comp. in EM, NPS Monterey, CA, 1993, pp. 155-762.
[23] V. Trenkic, C. Christopoulos, and T. M. Benson, “Advanced
implement the matched SCN (MSCN) [23] and the adaptable
node formulations in TLM-The matched symmetrical condensed
SCN (ASCN) [24]. These nodes use combinations of link node (MSCN),” in Proc. 12th Annu. Rev. Prog. in Applied Comp.
and stub parameters which offer improved accuracy and mini- Electromagn., Monterey, CA, Mar. 18-22, 1996, vol. I, pp. 246-253.
[24] -, “Advanced node formulations in TLM-The adaptable symmet-
mized dispersion error in modeling inhomogeneous microwave
rical condensed node,” IEEE Trans. Microwave Theory Tech., vol. 44,
circuits [23], [24]. no. 12, pt. 11, pp. 2473-2478, Dec. 1996.
REFERENCES
P. B. Johns, “A symmetrical condensed node for the TLM method,” Vladica ’Ikenkic (M’96) was born in Aleksinac, Yu-
IEEE Trans. Microwave Theory Tech., vol. MTT-35, no. 4, pp. 370-377, goslavia, in 1968. He received the Dipl.Ing. degree
Apr. 1987. in electncal engineering with computer science from
R. A. Scaramuzza and A. J. Lowery, “Hybrid symmetrical condensed the University of NiS, NiS, Yugoslavia, in 1992 and
node for TLM method,” Electron. Lett., vol. 26, no. 23, pp. 1947-1949, the Ph.D. degree from the University of Nottingham,
Nov. 1990. Nottingham, U.K., in 1995.
P. Bemni and K. Wu, “A pair of hybrid symmetrical condensed TLM Since 1992, he has been a Research Assistant,
nodes,” IEEE Microwave Guided Wave Lett., vol. 4, no. 7, pp. 244-246, Department of Electrical and Electronic Engineer-
July 1994. ing, University of Nottingham. His research interests
V. Trenkic, C. Christopoulos, and T. M. Benson, “New symmetrical include numerical modeling using the transmission
super-condensed node for the TLM method,” Electron. Lett., vol. 30, line modeling method and its implementation to
no. 4, pp. 329-330, Feb. 1994. electromagnetic compatibility and microwave heating problems.
-, “Generally graded TLM mesh using the symmetrical super- Dr. Trenkic received the IEE Electronics Letters Premium award in 1995.
condensed node,” Electron. Lett., vol. 30, no. 10, pp. 795-797, May
1994.
-, “Theory of the symmetrical super-condensed node for the TLM
method,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 6, pp.
1342-1348, June 1995.
P. Naylor and R. A. Desai, “New three dimensional symmetrical Christos Christopoulos (M’92) was born in Patras,
condensed lossy node for solution of electromagnetic wave problems Greece, in 1946. He received the Diploma in elec-
by TLM,” Electron. Lett., vol. 26, no. 7, pp 492493, Mar 1990. trical and mechanical engineering from the National
F. J. German, G. K. Gothard, and L. S. Riggs, “Modeling of materials Technical University of Athens, Athens, Greece, in
with electric and magnetic losses with the symmetrical condensed TLM 1969 and the MSc. and D.Phi1. degrees from the
method,” Electron. Lett., vol. 26, no. 16, pp. 1307-1308, Aug. 1990. University of Sussex, Sussex, U.K., in 1970 and
P. Naylor and R. Ait-Sadi, “Simple method for determining 3-D TLM 1975, respectively.
nodal scattenng in nonscalar problems,” Electron. Lett., vol. 28, no. 25, In 1974, he joined the Arc Research Project
pp. 2353-2354, Dec. 1992. of the University of Liverpool, Liverpool, U.K.,
V. Trenkic, C. Christopoulos, and T. M. Benson, “Simple and elegant and spent two years working on vacuum arcs and
formulation of scattering in TLM nodes,” Electron. Lett., vol. 29, no. breakdown while on attachment to the UKAEA
18, pp. 1651-1652, Sept. 1993. Culham Laboratories. In 1976, he joined the University of Durham, U.K.,
2. Chen, M. N. Ney, and W. J. R. Hoefer, “A new finite-difference as a Senior Demonstrator in Electncal Engineenng Science. In October 1978,
time-domain formulation and its equivalence with the TLM symmetncal he joined the Department of Electncal and Electronic Engineering, University
condensed node,” IEEE Trans. Microwave Theory Tech., vol. 39, no. 12, of Nottingham, Nottingham, U.K., where he is now Professor of Electrical
pp. 2160-2169, Dec. 1991 Engineering. His research interests are in electrical discharges and plasmas,
M. Kmmpholz and P. Russer, “A field theorehcal derivation of TLM,” electromagnetic compatibility,e lectromagnetics, and protection and simulation
IEEE Trans. Microwave Theory Tech., vol. 42, no. 9, pp. 1660-1668, of power networks.
Sept. 1994. Dr. Christopoulos received the IEE Snell Premium and IEE Electronics
H. Jm and R. Vahldieck, “Direct derivations of TLM symmetrical con- Letters Premum awards in 1995
densed node and hybrid symmetrical condensed node from Maxwell’s
equations using centered differencing and averaging,” IEEE Trans.
Microwave Theory Tech., vol. 42, no. 12, pt. 2, pp. 2554-2561, Dec.
1994.
D. A. Al-Mukhtar and J. E. Sitch. “Transmission-line matrix method
Trevor M. Benson (M’96) was bom in 1958. He
with irregularly graded space,” IEE Proc., pt. H, vol. 128, no. 6, p.p.. received the first-class honors degree in physics and
299-305,-Dec: G81.
C. Christoooulos, The TI ransmission-Line Modeling (TLM) Method. the Clark Prize in experimental physics from the
University of Sheffield, Sheffield, U K., in 1979 and
Piscataway: NJ: IEEE Press, 1995.
S. Akhtarzad and P. B. Johns, “Generalized elements for TLM method the Ph D degree from the same university in 1982.
of numencal analysis,” Proc. IEE, vol. 122, no. 12, pp 1349-1352, After spending over six years as a Lecturer at
Dec. 1975. University College, Cardiff, Wales, he joined the
P. P. M. So and W. J. R Hoefer, “A new look at the 3D condensed University of Nottmgham, Nottmgham, U.K., as a
node TLM scattering,” in IEEE Int. Microwave Symp. Dig., Atlanta, Ga, Senior Lecturer in Electncal and Electronic Engi-
June 1993, pp. 1443-1446. neering in 1989, was promoted to the post of Reader
V. Trenkic, T. M. Benson, and C. Christopoulos, “Dispersion analysis in 1994, and Professor of Optoelectronics in 1996.
of a TLM mesh using a new scattenng matnx formulation,” IEEE His current research interests include experimental and numencal studies of
Microwave Guided Wave Lett., vol. 5, no. 3, pp. 79-80, Mar. 1995. electromagnetic fields and waves with particular emphasis on propagation in
R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New ophcal waveguides and electromagnetic compatibility.
York: McGraw-Hill, 1992. Dr. Benson received the IEE Electronics Letters Premium Award in 1995
2136 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUE
ling and Performance of a
lement pHEMT Grid Ampli
Michael P. De Lisio, Member, IEEE, Scott W. Duncan, Member, IEEE, Der-Wei Tu, Cheh-Ming Liu,
Alina Moussessian, James J. Rosenberg, and David B. Rutledg
Abstruct- A 100-element hybrid grid amplifier has been fab-
ricated. The active devices in the grid are custom-made pseudo-
ransistor (pHEMT) differential-
for gain analysis and compare
rid includes stabilizing resistors
the grid has a peak gain of 10
a gain of 12 dB when tuned for
The maximum andwidth is 15% at 9 GHz. The
m~ni~unmois e figure is 3 dB. The maximum saturated output ljlput &=am
power is 3.7 W, with a peak power-added efficiency of 12%.
are a significant improvement over previous grid Output Beam
ed on heterojunction bipolar transistors (HBT’s).
E
I. INTRODUCTION
UASI-OPTICAL amplifiers combine the output powers
of many solid-state devices in free space, eliminating
the losses associated with waveguide or transmission- Fig 1 A gnd amplifier A honzontally polarized input beam is incident
line combiners. The first quasi-optical amplifier was a 25- from the left The output beam is vertically polarized and is radiated to the
nght The polarizers independently tune the output and input circuits
element grid amplifier [l]. A grid amplifier is an array of
closely-spaced differential pairs of transistors. Fig. 1 shows
the approach. A horizontally polarized input beam excites
rf currents on the input leads of the grid. This drives the report on the modeling and performance of a 100-element
transistor pair in the differential mode. Currents on the output X-band grid amplifier using pHEMT
leads produce a vertically polarized output beam. Metal-strip photograph of the assembled grid is sho
polarizers provide independent tuning of the input and output
circuits. Other types of quasi-optical amplifiers using patch
11. DEVICED ESCIUPTI
antennas [2]-[4], back-to-back integrated horn antennas [SI,
[6], folded slot antennas [7],a nd probe antennas [8] have
The differential-pair c
been demonstrated. The largest number of devices have been
Martin Laboratories.
incorporated in a 100-element HBT grid amplifier [9].
GaAs/InGaAs/GaAs pHEMT’s. The total gat
Recently, pHEMT technology has developed rapidly.
transistor is 100 pm distributed amo
Millimeter-wave pHEMT’s are capable of high gain, high
gates were defined by an
output powers, and low noise figure, making them the device
and a bi-level resist. Th structure is a
of choice for high-frequency applications [lo]-[ 121. Here we
double-doped heteros
Manuscnpt received April 10, 1995, revised September 13, 1995. ‘Ihs details about the devices can be found in [lo].
research was supported by the Army Research Office and Lockheed Martln
The differential pair chip layout is
Laboratories. M P De Lisio held NSF and AASERT fellowships
M P. De Lisio is with the Department of Electncal Engineering, Umversity sources of two pHEMT’s are tied to
of Hawaii-Mwoa, Honolulu, HI 96822 USA pair. Unlike the HBT’s in previous g
S W Duncan is with Sanders, a Lockheed Marti
terminal can be extern
03061 USA
D -W. Tu is with the Laboratory for Physical this gate control bias to
Maryland, College Park, MD 20783 USA. because the gate draws very little bias current. The 0.5-pF
C -M Liu is with the Rockwell Science Center, Rockwell Intemahonal
capacitor and 2-kR resistor are feedback elements to stabilize
Corp , Thousand Oaks, CA 91385 USA
A. Moussessian and D. B. Rutledge are with the Department of Electncal the pHEMT’s. The two 100-0 source resistors are intended to
Engineering, California Institute of Technology, Pasadena, CA 91 125 USA reduce common-mode gain. These resistors should not effect
J. J. Rosenberg is with the Department of Engineenng, Harvey Mudd
the differential-mode the overall
College, Claremont, CA 91711 USA.
Publisher Item Identifier S 0018-9480(96)08479-7. efficiency of the grid
001 8-9480/96$05 00 0 1996 IEEE
De LIS10 et al.: MODELING AND PERFORMANCE OF A 100-ELEMENT pHEMPT GRID AMPLIFER 2131
Fig. 2. Photograph of the amplifier grid. The grid is a 10 x 10 array of pHEMT differential pairs. The active area of the grid is 7.3 cm on a side.
7.3 mm
Fig. 4. The grid amplifier unit cell. The width of the input and output leads is
I
0.4 mm. The width of the meandering bias lines is 0.2 mm. Arrows indicate
Fig. 3. The differential pair chip layout. the directions of rf currents.
111. GRIDA MPLIFIERM ODELLING
is re-radiated from the vertical drain leads. Bias to the drain
An important advantage of grid amplifiers is that the unit and source is provided by the thin meandering lines. Gate bias
cell primarily determines the driving-point impedances seen is provided along the horizontal gate leads. The resistors in
by the device, while the power scales with the grid area. This the gate leads suppress common-mode oscillations and will be
allows one to optimize for gain and noise figure by the choice discussed later.
of the unit cell and to independently select the grid size to meet The assembled grid amplifier tuned for 10 GHz is shown
the total power requirement. Previous grid amplifiers [l], [9] in Fig. 5(a). The grid and polarizers are fabricated on Rogers
were designed empirically. We have developed a model for Duroid boards with a relative dielectric constant of 2.2. The
the grid amplifier that predicts its performance [13], [14]. output tuner is a Duroid board with E, = 10.5. A simple
The unit cell is shown in Fig. 4. The cell size is 7.3 mm transmission-line model for the grid amplifier is shown in
on a side. The input beam is coupled to the gates of the Fig. 5(b). For convenience, one-half of the unit cell is used in
transistors through the horizontal gate leads. The output beam the analysis, with the result that the characteristic impedances