A coplanar waveguide radial line stub resonator is experimentally characterized with respect to stub radius, sectoral angle, substrate thickness, and relative dielectric constant. A simple closed-form design equation which predicts the resonance radius of the stub is presented

Simons, R. N.

Taub, S. R.

English

NASA Technical Reports Server

N94-29503
COPLANAR WAVEGUIDE RADIAL LINE
STUB
R. N. Simons and S. R. Taub
Indexing terms: Waoeguldes, Resonators, Silicon
A coplanar waveguide radial line stub resonator is experi-
mentally characterised with respect to stub radius, sectoral
angle, substrate thickness and relative dielectric constant A
simple closed-form design equation, which predicts the reson-
ance radius of the stub, is presented
Introduction: Coplanar waveguide (CPW) technology is
emerging as a viable alternative to stripline and microstrip
line for monolithic microwave integrated circuits [1]. There
are several applications in which a CPW radial line stub res-
onator is necessary; these include: bias line filters requiring a
point of virtual RF ground, mixer and frequency multiplier
circuits that require a reactance to terminate the diodes and
the harmonics, respectively. In addition, a grounded CPW
p.-D H
N
- f--:- ___f_
Fill. ! Schematic diagramof CPW radial linestub
(GCPW) radial line stub resonator has application in oscil-
lator circuits for active antennas [2]. In general, the advan-
tages of a radial line stub over a straight 50f_ stub are the
smaller resonance length, wider bandwidth and smaller dis-
continuity reactance at the junction with the main line [3].
This Letter presents, for the first time, CPW and GCPW
radial line stub resonators, characterised by measuring the
resonance frequency. The resonance frequency is measured for
stubs with different radii, sectoral angles, substrate thicknesses
and substrate relative dielectric constants. A closed-form
design equation, which predicts the resonance radius of the
c
-3
-6
0
m -I0
-20
-30
-40
._c-50
stub, for a given set of parameters, is also presented.
Desion and fabrication: Fig. I shows a schematic diagram of
the CPW radial line stub resonator. The inner and outer
radius or the stub are denoted as R 1 and R2, respectively. The
sectoral-angle is denoted as 0. The CPW stubs are fabricated
on Duroid (relative dielectric constants _, = 6 and 10.5) and
on high resistivity silicon (e,= 11.7, /7= 5000 10000t_cm)
substrates. The GCPW stubs are fabricated on Duroid with
_, = 2"2. Three bond wires near the plane of discontinuity
ensure equal potential at all ground planes. The CPW centre
strip conductor with width S and slot width W, are chosen to
be compatible with the coaxial launchers of the Wiltron uni-
versal test fixture. Thus, the characteristic impedance Z0 of
the main line is 55Q.
Experimental results and closed-form equation: The measured
return loss and insertion loss of a CPW radial line stub are
compared with those of a straight CPW stub in Fig. 2. In this
experiment 0 and R2 for the radial stub are arbitrarily chosen
as 60° and 5-08 ram, respectively. The length L of the straight
stub is 7ram. The measurements show that for identical _, and
resonance frequency fo, the radius R z is 37% smaller than the
length L Further, the radial line stub has a wider bandwidth.
The bandwidth or the two structures as a function of the
attenuation is compared in Table 1. The excess loss defined as
Z ,l1- IS.I -IS2,1, and determined from the measured S
parameters, is small. It is of the order of 0.09 and 0-05 for the
radial line stub and straight stub, respectively.
A GCPW radial line stub with e, = 2.2, D = 0-254mm and
0 and R2 the same as for the CPW radial line stub, has a
much wider bandwidth. The characteristics for the GCPW
radial line stub are also included in Table 1. The excess loss is
of the order of 0.04.
Table ! PERCENTAGE BANDWIDTH OF STRAIGHT
AND RADIAL LINE STUB
Stub configurations
Attenuation S_raight CPW radial GCPW radial
dB % % %
10 18.3 25.7 58.1
20 5-6 8.0 15.8
30 I "6 2'5 3.5
For a CPW radial line stub, the measured f0 as a function
of 0 for a fixed R 2 is shown in Fig. 3. The fo decreases by 20%
as 0 increases from 30 to 90 °. It is also worth noting that Rt
does not remain constant but increases with 0. The excess loss
is small and decreases from 0-12 to 0.06 as 0 increases from 30
to 90".
5O
/.-5
0
g
g
I I I I 1 I
35 39 43 /..7 51 5-5
frequency, GHz 3 8
Fq. 2 Measured return loss and insertion loss of CPW radial line szub
and CPW straight stub
S=O.33mm, W=0.234mm, D=0.635mm, %=10-5, R,=
0'191 mm, R a = 5.08 mm, 0 = 60 _, i = 7mm
-- radial line stub
....... straight stub
20
i i i , • i i
I I I I / I I
30 40 50 60 70 80 90 I00
sector angle 0 , deg
Fig. 3 Measured resonance frequency of CPW radial line stub against
sector angle
S=0"33mm, W=0-234mm, D=O.635mm, %=10.5, R2=
5.08 mm
©Reprinted, with permission, from IEE Electronics Letters, vol. 29, no. 4, lBd) February L993, pp. 412-413.
55
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https://ntrs.nasa.gov/search.jsp?R=19940016030 2020-06-16T17:24:05+00:00Z
!O
g.
-3 O
10 ___ t • _ .... I t L I i J LL
100 101 I0z
fo' GHz
Fig. 4 Measured resonance frequency ooainst outer radius of radial
stub for 0 = 60 °
(i) GCPW:
1"3(a) $ = 0-518mm, W = 0.127mm, D = 0"254mm, s, = 2"2,
R_ = 0.Jmm
(ii) CPW:
O (b) S = 0-33ram, W = 0.234mm, D = 0-635mm, _,= 10.5,
R t = 0.191 mm
@ (c) S=0.33mm, W=0.185mm, D=0.254mm, t,=10.5,
R_ = 0.191 ram
V (d) S _ 0.508ram, W- 0.155ram, D = 0.635ram. E, =6, R,
0"Jmm
• (e) S=0.152mm, W=0-114mm, D=0.381mm, c,=ll.7,
R= = 0.092 mm
Fig. 4 shows the product of _(e,) and measured fo as a
function of R 2 for CPW and GCPW radial line stubs. By
curve fitting the measured data, the coefficients of a simple
closed-form equation to predict R 2 are determined using a
sigma plot. The equations for CPW and GCPW are as
follows:
log (R2)= Ct log [_/(e,)fo ]
+ C2 log (D) + C_ log (R_) + C,
Iog(Rz) = C 5 log ['_(t,)fo]
+ C_,[log (D) + log (R 1)]
where fo is in gigahertz, R j, R2, and D are in metres. The
coefficients were determined to be: C, =-1.0496, C z =
0.098375, Cs = -0-1401, C4 = -1.297, Cs =-0-82462 and
C_ = 0.21201, respectively. These equations are valid for the
geometry and the range of parameters given in Fig. 4. The
range of parameters considered are those typically used in
microwave circuit design. The standard error of the equation
is at most 0-18 and 0.01% for the CPW and GCPW, respec-
tively.
Conclusions: A CPW radial line stub resonator is experimen-
tally characterised in terms of its radius, _ctoral angle, sub-
strafe thickness and relative dielectric constant. A simple
closed-form design equation which predicts the resonance
radius of the stub for a given set of parameters is also present-
ed. The radial line stub, when compared to a straight stub, has
a wider bandwidth and shorter length.
Acknowledgment : The authors are thankful to P. G. Young for
fabricating the circuits on silicon substrates.
4th January 1993
R. N. Simons and S. R. Taub (Mail Stop 54-5, NASA Lewis Research
Center, 21000 Brookpurk Road, Cleveland, Ohio 44135, USA}
References
l *b'_Ag, M. (Ed.): IEEE 1991 Microwave and Millimeter-Wave
Monolithic Circuits Syrup. Dig. of Papers (91CH3016-3)
2 SlMONS,R. _, and L_ a. Q.: 'Planar dielectric resonator stabilized
HErlvlT oscillator integrated with CPW/aperture coupled patch
antenna'. IEEE M'I-I'-S Int. Microwave Syrup. Dig., I992, VoL I,
pp. 433-436
3 ATWAI'EV.,H. X.: 'The design of the radial line stub : A useful micro-
strip circuit dement', Microwave J., 1985, 2g, (I 1),pp. 149 -156
56


Coplanar Waveguide Radial Line Stub

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