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‘CPW-fed activc slot antennas’, IEEE Truns. Microw. Theory
Tech., 1994, 42, pp. 541-545
4 ROBERTSON. s.v, r i m , N.I., YANG, G., and KATEHI, L.P.: ‘A folded-slot
antenna for planar quasi-optical mixer applications’. 1993 IEEE
AP-S Dig., pp. 600-603
5 FORMA, G., and LAHEURTE. I.M.: ‘Compact oSci1hting loop antenna
with coplanar feeding’, Electron. Lett., 1996, 32, pp, 1633-1635
the two ground planes enclosing the whole structure is d. As is
well-known, the TEM phase constant of the line is given by: PITM
= od[Lc], where L and C are the inductance and capacitance
PUL of the line. Considering a situation where the quasi-TEM
(with k,,
being the
approach applies [4] and with P,EM < k,,
phase constant of the fundamental background parallel-plate
waveguide mode), the quasi-TEM mode will leak energy and will
then be characterised by a complex propagation constant kz = P
ja. The attenuation constant a can be related to the power transmitted along the line Pz by means of:
Closed-form evaluation of low-frequency
leakage losses in layered striplines
R. Marques, F. Mesa and M. Horno
Indexing terms: Strip lines, Leuky wuve untennas, CAD
A method is shown for obtaining a closed-form expression for the
radiation losses of a layered stripline as a function of the quasiTEM parameters of the line. This fast and simple formula is very
useful in all practical situations in which the electrical length of
the stripline cross-section is sufficiently small.
Introduction: Recently, it has been reported that the fundamental
quasi-TEM mode of some layered striplines becomes leaky at certain frequencies [l, 21. This behaviour appears whenever the quasiTEM mode of the stripline is faster than the fundamental mode of
the background parallel-plate waveguide [3]. At low frequencies,
the value of the phase constant of the fundamental quasi-TEM
leaky mode has been found to be well determined by the TEM
phase constant obtained from the static capacitance and inductance per unit length (PUL) of the line using the elementary transmission line theory [2]. This fact suggests the possibility of a
complete quasi-TEM theory of low frequency stripline leaky
modes, which could be very useful for CAD purposes.
Fig. 1 Cross-section of layered stripline
Provided that
PrEw and, therefore, if a is sufficiently small 121,
P, can be expressed as P, = 112ZrElvl~2,
with Z,,, being the quasiTEM impedance of tlhe line, Z,, = d[L/c]and Z is the total current intensity on the strip. Since the power losses are basically due
to the fundamental TM, waveguide mode radiating at an approximated angle 0 from the strip, it can be written that cos0 = pTE,bf/
[3] and thus d P / & = -2P,,sin0
(see Fig. 2) where P,, is
the power carried out by the 7’” waveguide mode at each side of
the strip. The attenuation constant in eqn. 1 is then given by
2 P ~ sin
~ v0 ~
The values of Z,,, and 0 can be extracted from a standard
quasi-TEM analysis of the structure [4], taking into account that
k,,, can be approximated by
= wd[L,C,] (since the TM,
mode becomes quasi-TEM as o --f 0), where Le and C, are the
inductance and capacitance of the background parallel-plate
with k, being the free-space phase constant. The remaining parameters of eqn. 2 can be evaluated in terms of the amplitude of the
TM, mode. This amplitude is computed assuming that the current
on the strip is well approximated by the quasi-TEM surface current distribution, JzrEM,obtained from the quasi-TEM analysis
and that the attenuation constant of the leaky mode can be
neglected in a zero-order approach. Under these assumptions, the
amplitude of the TMo is calculated considering that this mode is
excited by a surface current density J,(x, z) = Ji~E-~(?c)exp(-jp,)
on the strip. This deterministic problem is solved using the theory
of the excitation of modes in waveguides by known current
sources [5] (section 5.8). This theory must be adapted to this particular situation, where the presence of the propagation factor
along the z axis helps to simplify the problem. Additional simplifications are also imposed due to the assumed small
electrical size of the stripline cross-section. Once the amplitude of
the excited TM, mode has been obtained, the power flux, P,,,
carried by this mode is calculated in a straightforward manner.
, into eqn. 2, the attenuation constant can
After substituting P
be finally expressed as
with q2 = 1~,,~,,2 I $ . E ~ . Taking into account the frequency
dependence of the different quantities in eqns. 3 and 4, a shows a
quadratic dependence on the frequency in agreemcnt with the theory of field expansion in powers of frequency for the quasi-TEM
modes 141.
It should be noted that the validity of eqn. 4 is mainly restricted
by the small electrical size of the stripline cross-section, corresponding to the application range of the quasi-TEM approach.
Another important restriction is due to the presence of sin0 in the
denominator of eqn. 4, which would raise physically meaningless
infinity values of a as prEw approaches krM,. Our previous fullwave analysis results [:>]showed that, in that region, also the phase
constant of the leaky mode is not well approximated by P,),
at very low frequencies. Moreover, when the phase constant of the
leaky mode approaches k,.,,, the leaky mode does not properly
describe the radiation pattern of the stripline when it is fed by a
physical source 161. Consequently, the region of validity of eqn. 4
coincides with the region of most significance of the leaky mode.
Fig. 2 View ofpower transmitted by TM, mode
Theory: The structure under study is shown in Fig. 1, that is, an
inhomogeneous stripline with a layered isotropic lossless substrate
made of N dielectric layers of permittivity E, and height h,. The
total height of the layered substrate is h and the distance between
17th J u l y 1997
Vol. 33
No. 15
Table 1: Normali5ed phasc and attenuation constants of an airgap stripline with N 2
MESA, F., and MARQUES, R.: ‘Low-frequencyleaky regime in covered
noncoplanar multilayered strip-like transmission lines’, IEEE
Ti.uiis. iMicioii~.Theory Tech., 1996, MTT-44, pp. 1521-1525
S H l l i E S A W A . H , TSUJI. M , and OLINEII. A.A.: ‘Dominant mode power
leakage from printed-circuit waveguide’, Rudio Sei., 1991, 26, pp.
LIUDELL. I \ : ‘On the quasi-TEM modes in inhomogeneous
multiconductor transmission lines’, IEEE Trans., 198 1, MTT-29,
pp. 812-817
c c.: ‘Field and wave electrodynamics’ (McGraw-Hill
Inc.. 1965)
111 VALLO. c . MESA. F , and JACKSON, D K . : ‘Excitation of leaky
modes on multilayer striplines’. Proc. IEEE MTT-S Dig., 1996,
San Francisco. USA, pp. 171-174
0.635mm; I?,= (cl-h) = 0.445mm,
= E”
Frequency = 3.8GHz
M; =
6, E ,
= E = 2.6q1.
Numericul reszilts: To validate eqn. 4, the air-gap stripline pi-oposed in [I] is now analysed, although the structure has been
scaled by a factor of 0.1 to reduce the electrical size of the stripline
cross-section. Both the approximated quasi-TEM phase constant
and the attenuation given by eqn. 4, as well as the full-wave
results (computed following the method in [2])are shown in Table
1 for different values of the air-gap height ( / I ? = 6) at 3.8GHz.
Good agreement has been found between the two sets of data.
except for pi,, approaching /c,,,,~. Fig. 3 shows the quasi-TEM
and full-wave dispersion characteristics for a specific value of 6.
As expected, the good agreement at low frequencies deteriorates as
the electrical dimension of the stripline cross-section @/I,,)
increases, making the quasi-TEM approach inappropriate.
1 51
0 03
0 02
i x.
1L8/ ’
0 01
Fig. 3 Propugation diaructeristics of .structure imaIj.scd
6 = 0.075rnin
- ~
I - - d o 0 0
0 12
ruble I joi.
full-wave results
quasi-TEM result,
Conclusions: A useful closed-form expression has been provided
for the evaluation of radiation losses in layered striplines at low
frequencies. This formula expresses the attenuation constant as a
function of‘ the quasi-TEM paranictcrs of the structure. The range
of validity of this formula is then basically restricted to that of the
quasi-TEM approach.
A t l c r 7 o i ~ l ~ ~ d ~ fThe
~ z r nauthors
would like to thank the CICYT,
Spain (Project no TIC95-0447) for supporting this &ork
0 TEE 1997
E1c~ctronic.sLetters Online No: 19970895
IO June 1997
Silicon-on-sapphire MOSFET transmit /
receive switch for L and S band transceiver
R.A. Johnson, P.R. de la Houssaye, M.E. Wood,
G.A. Garcia, C.E. Chang, P.M. Asbeck and I. Lagnado
hidc.yiitgpterms: MOSFET, Transceivers
A single-pole double-throw transmit/receive switch has been
fabricated with MOSFETs in silicon-on-sapphiretechnology. The
switch has an insertion loss of 1.7dB and an isolation of > 30dB
at 2.4GHz. The switch was targeted for 2.4GHz operation, but is
broadband with only a 2.0dB inscrtion loss at 5GHz. The same
switch was also fabricated on SIMOX as a comparison. Owing to
capacitive losses to the substrate, the SIMOX switch had a much
higher insertion loss: 4.9dB at 2.4GHz and 6.2dB at 5GHz.
Improvements in silicon device performance, combined with low cost, are making silicon an increasingly attractive
technology for high frequency RF and microwave personal conimunication circuits. One such application is in monolithic transceivers operating in the 1.9 to 2.4GHz regime. Recently,
Rofougaran [I] and Porra [2] have reported Si MOS-based transceiver designs for 1 and 2GHz operation, respectively.
One circuit needed for this application is a transrnith-eceive
(TR) switch. This switch connects the transmitter power amplifier
to the antenna during the transmit mode and connects the antenna
to the receiver low noise amplifier during the receive mode. It is
important for this switch to have a low insertion loss while maintaining good isolation between the receiver and transmitter so that
the high power of the transmitter does not damage the sensitive
receiver input stage during the transmit operation. There have
been many papers reporting GaAs MESFET TR switches [3, 41.
In this Letter, we report the first silicon-on-sapphire (SOS) MOSFET based TR switch for operation at 1 1 GHz.
Silicon-on-sapphire (SOS) provides a variety of advantagcs over
bulk silicon, such as reduced parasitic capacitance, simplified
processing. elimiiialion of backgating and radiation hardness.
Moreover. SOS, or more generally silicon-on-insulator, is inherently advantageous over bulk silicon for switches because it avoids
the problem of drain-substrate current for large microwave signals. It is shown here that SOS can provide improved microwave
switch performance over SIMOX (and by implication, over bulk
K. Marc1ui.s. I?. Mesa and M. Homo (Microi~.uveG i ~ i i i ~Dcpmtnieiit
of E1eclronic.s und Ebctroniqpnetistn, Avtl. Reinu Meiceri‘es s/n. 41012
Seville, S p i n )
, and O L I N E R , A.A : ‘Proper
and impropcr dominant mode solutions for a stripline with an air
gap’. Rudio Sei., 1993, 28, (6), pp. 1163-1 180
N O I I I E M . D , W I L L I A M S ,J.. JACKSON, D.R
R‘ X
Fig. 1 Schemutic diugrurn uf circuit of’ SPDT swi1clz
17th July 1997
Vol. 33
No. 15
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