Implementation of high quality‐factor on‐chip tuned microwave resonators at 7 GHz

Abstract

We report on the design, analytical modeling, numerical simulation, fabrication, and experimental characterization of chip-scale microwave resonators that exhibit high quality-factors (Q-factors) in the microwave frequency range. We demonstrate high Q-factors by tuning these microwave resonators with the film capacitance of their LC tank circuits rather than the conventional approach of using external capacitors for tuning. Our chip-scale resonator design further minimizes energy losses and reduces the effect of skin depth leading to high Q-factors even for significantly reduced device areas. Using our new design methodology, we observe that despite the higher resonance frequency and smaller chip size, the Q-factor is improved compared with the previous literature using traditional approaches. For our 540 μm × 540 μm resonator chip, we theoretically compute a Q-factor of 52.40 at the calculated resonance frequency of 6.70 GHz and experimentally demonstrate a Q-factor of 47.10 at the measured resonance frequency of 6.97 GHz. We thus achieve optimal design for microwave resonators with the highest Q-factor in the smallest space for operation at 6.97 GHz. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 497–501, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24103

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IMPLEMENTATION OF HIGH QUALITY-
FACTOR ON-CHIP TUNED MICROWAVE
RESONATORS AT 7 GHz
Rohat Melik1,2and Hilmi Volkan Demir1,2
1Department of Electrical and Electronics Engineering,
Nanotechnology Research Center, and Institute of Materials Science
and Nanotechnology, Bilkent University, Ankara 06800, Turkey
2Department of Physics, Nanotechnology Research Center, and
Institute of Materials Science and Nanotechnology, Bilkent University,
Ankara 06800, Turkey; Corresponding author: volkan@bilkent.edu.tr
Received 20 June 2008
ABSTRACT: We report on the design, analytical modeling, numerical
simulation, fabrication, and experimental characterization of chip-scale
microwave resonators that exhibit high quality-factors (Q-factors) in the
microwave frequency range. We demonstrate high Q-factors by tuning
these microwave resonators with the film capacitance of their LC tank
circuits rather than the conventional approach of using external capaci-
tors for tuning. Our chip-scale resonator design further minimizes en-
ergy losses and reduces the effect of skin depth leading to high Q-fac-
tors even for significantly reduced device areas. Using our new design
methodology, we observe that despite the higher resonance frequency
and smaller chip size, the Q-factor is improved compared with the pre-
vious literature using traditional approaches. For our 540 ?m ? 540
?m resonator chip, we theoretically compute a Q-factor of 52.40 at the
calculated resonance frequency of 6.70 GHz and experimentally demon-
strate a Q-factor of 47.10 at the measured resonance frequency of 6.97
GHz. We thus achieve optimal design for microwave resonators with the
highest Q-factor in the smallest space for operation at 6.97 GHz. © 2008
Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 497–501, 2009;
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI 10.1002/mop.24103
Key words: microwave; resonators; quality-factor; tuning; fabrication
1. INTRODUCTION
High quality-factor (Q-factor) resonators are required for good
performance in applications such as microwave devices, mobile
phones, radars, wireless universal serial buses (USB), and wireless
local area networks (WLAN). In such applications, on-chip reso-
nators are preferred because they reduce power consumption,
prevent connection losses, and facilitate on-chip integration. These
lead to compact, low-cost systems. However, it is difficult to
produce chip-scale, small-size resonators that exhibit high Q-
factors at high frequencies. In general, smaller resonators yield
lower Q-factors. To date, microwave resonators based on on-chip
spiral coils have been successfully demonstrated, with unloaded
Q-factors of inductors up to a maximum of 40 at 5 GHz [1] and 50
at 2 GHz [2], which would further be reduced for operation at
higher frequencies [1, 2]. In these studies, to realize resonators
using these inductors, external capacitors are used to tune the
inductors, which undesirably increase the effective device area and
decrease the resonator Q-factor. The use of such an externally
connected capacitor further results in longer propagation times and
fewer operating channels for communication. It has also previ-
ously been shown that higher Q-factors can be achieved using
cavity geometries. But this then comes at the cost of significantly
increased size, resulting in much larger chips (as long as several
millimeters on one side) [3] and in more complicated fabrication
steps. Therefore, these are not ideal methods to obtain a compact
and high Q-factor microwave resonator operating at a high fre-
quency. In addition to the need for a high-frequency, high-Q
resonator, there is a strong demand for bio-implant resonators in
medical applications that would satisfy the biocompatibility con-
straints [4]. In this work, with the motivation to address the need
for compact high-Q bioimplantable microwave resonators, we
develop and demonstrate on-chip biocompatible resonators with
high Q-factors of about 50 in the microwave frequency range,
despite their chip-scale, small size (sub-millimeter on one side).
In the literature, Q-factors are typically stated in unloaded
cases, excluding the external loading effects [5, 6]. In this article,
we report the measured Q-factors including the loading effects and
the associated losses instead of merely citing unloaded Q-factors.
Thus, we present the worst case Q-factor values, with the probe
loading and related losses all included. Furthermore, we imple-
ment the resonator aiming for a minimal device size while oper-
ating with a high Q-factor at a high frequency. To do so, we
develop a new design methodology that reduces the effect of skin
depth in attaining high Q-factors. In our device, although the metal
layer is very thin, we can achieve high Q-factors because of our
new design approach. The area of our microwave resonator is
demonstrated to be as small as 540 ?m ? 540 ?m while the
Q-factor is still kept high at 47.10, which is not possible with
previous approaches in the literature.
The resonator architecture is based on a spiral coil structure
with a few turns tuned with the on-chip capacitance to obtain the
highest Q-factor from the smallest lateral chip size. This approach
relies on minimizing energy losses in the coil and also on using the
film capacitance for tuning. We develop a two-port circuit model
design for our on-chip coil. We support our analytical model with
numerical simulations. Our analytical model obtains targeted res-
onance frequencies that are very close to the resonance frequencies
we obtained with numerical simulations and those that are later
measured experimentally on our fabricated chips.
Although we implement our resonator chips using a standard
microelectro-mechanical-systems (MEMS) fabrication procedure,
we design them to be compatible with complementary metal oxide
semiconductor (CMOS) processing, while also using only biocom-
patible materials. Our resonators are of a size (a half millimeter by
a half millimeter with 100 nm thick metal lines) to possibly be
fabricated in large quantities, at a low per-unit cost, by standard
CMOS processes and conveniently be integrated on-chip with
CMOS electronics.
In this article, we present the design, analytical modeling,
numerical simulation, fabrication, and experimental characteriza-
tion of such compact high-Q microwave resonators. The rest of
this article is organized accordingly as follows. We first present the
theoretical background in Section 2 and then describe the micro-
fabrication of our on-chip resonators and their experimental char-
acterization along with our theoretical analysis in Section 3 and
finally conclude in Section 4.
2. THEORETICAL BACKGROUND
We develop our circuit model for a spiral coil starting with the
circuit model of a general transmission line [7]. We consider the
coil as being composed of many transmission line segments in
serial connection [8]. For each of these transmission lines, with
half of their capacitance terminated both at the beginning and the
end of each segment, we put together all of these transmission line
segments and include the admittance to ground through the dielec-
tric capacitance and substrate to construct the coil [9]. For further
simplification, we convert this coil model into a conventional
circuit that matches the coil structure. The circuit conversion is
illustrated step by step from Figures 1(a)–1(c). In the literature,
one of the ports is commonly taken as ground especially for the
analysis of the measured S parameters, which significantly simpli-
fies the analysis [10]. In our case, we produce the final circuit
DOI 10.1002/mopMICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 2, February 2009
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model using two ports as shown in Figure 1(d). We perform all of
our analytical modeling, analytical simulations, and designs based
on this final two-port circuit model representation. The standard
way of calculating a resonator Q-factor is based on measuring the
3-dB bandwidth ratio of S21magnitude [11], which is different
from calculating an inductor Q-factor by measuring reflectivity
after grounding one port of the circuit.
To calculate the circuit components for the coil model, we use
the equations listed together for convenience in Table 1. These
equations relate our structural design parameters to the circuit
components of our coil resonator (and thus to the resonator spec-
ifications). Our on-chip microwave resonator consists of metal
layers (Au) that make up the spiral coil structure and the insulator
layers (Si3N4) that isolate the metal layers from each other and the
substrate (Si). In our circuit model, LSis the inductance of the
spiral coil; Cfilmis the capacitance of the dielectric thin film
between the coil and the substrate; CSiis the capacitance from the
coil trace to the substrate for a half turn; CSis the capacitance
between adjacent coil segments; RSiis the resistance of the sub-
strate; and RSis the resistance of the spiral coil. Additionally, in
Table 1, in the inductance Eq. (1), Lselfis the self-inductance, M?
and M?are the positive and negative mutual inductance, respec-
tively; and in the coil resistance Eq. (6), ? is the skin depth.
Moreover, device design parameters used in these equations in-
clude the total length of the spiral coil (l), the metal width (w), the
separation between metal lines (s), the dielectric thin film thickness
(tfilm), the coil metal thickness (t), the total length and width of the
resonator chip (LCand WC), and the number of turns (N).
In Table 1, the inductance parameters LS, Lself, M?, and M?are
calculated [12]. For calculating CSiand RSi, experimental charac-
terization results are used in the method given in Lee [13]. For RP
and CP, the relations in Bahl [4] are utilized. We obtain RPand CP
through the circuit conversion from Figures 1(b) and 1(c). Here RP
and CPrepresent the combined impedances of RSi, CSi, and Cfilm.
RPis particularly important for the computation of substrate losses
and CPis significant for the resonance frequency and the self-
resonance factor.
Our design guidelines rely on the objective of maximizing
Q-factor of our on-chip microwave resonators. Thus, the Q-factor
definition is important. The Q-factor of a resonator is defined in the
most general sense in Eq. (13) [14]:
Q ? 2?
energy stored
energy loss in one oscillation cycle
(13)
The empirical form of this Q-factor definition is presented in Eq.
(12) in Table 1. However, this equation does not identify the
lumped elements that store energy and those that dissipate energy.
Therefore, it does not provide guidance on how to increase the
Q-factor. For that reason, in our design methodology, we utilize
the definition of the Q-factor of the inductor (rather than the entire
LC tank circuit of the resonator). We can obtain the resonator
Q-factor using both the inductor Q-factor (Qind) and capacitor
Q-factor (Qc) as given in Ludwig and Bretchko [11]:
1
Qind
affect Qcvery much. However, Qindis directly affected by geo-
metrical design and the material selection. As a result, we can
maximize the resonator Q-factor by using the classical resonance
definition and the methods to increase Qind. The inductor Q-factor
is given by Eqs. (14) and (15) [15].
1
Qres
??
1
Qc. Structural design and material selection do not
Qind? 2?peak magnetic energy ? peak electric energy
energy loss in one oscillation cycle
(14)
Qind?
R
?L?1 ??
?
?o?
2?
(15)
The open form of this equation is presented in Eq. (10) in Table 1,
which explicitly shows the design factors that affect the inductor
Q-factor (i.e., the elements that store energy and those that dissi-
pate energy). As shown in Eqs. (14) and (15), Qindis proportional
to the difference between peak magnetic energy and peak electric
energy, and the resonance frequency is the one where these two
energies are equal, i.e., where the inductor’s Q-factor is zero. This
is the point where the tank circuit has the minimum transmitted
power. Equation (11) of Table 1 gives the basic definition of the
Figure 1
driving the conventional circuit of the coil with two ports in (a), then
consider one of these ports to be grounded in (b), from which we obtain the
common representation of a parallel RLC circuit in (c). Unlike other
approaches, here we expand this model further into a simple two-port
circuit representation in (d) to be used for all of our analytical simulations.
Our circuit model conversion: We first consider a source
TABLE 1
Circuit Components from Design Parameters
List of Empirical Equations Used to Calculate
LS ? ? Lself? ? ? M?? ? ? M??
(1)
Cfilm ?
?o?rlw
tfilm
(2)
CSi ? 0.5lwCsub, where Csub ? 1.6 ? 10?10F
cm2
(3)
CS ?
?0lt
s
(4)
RSi ?
2
lwGsub, where Gsub ? 0.4
1
?cm2
(5)
RS ?
?l
w? ? ?1 ? e
2?
??0, where ? ? 2?f
1
?2Cfilm
1 ? ?2?Cfilm? CSi?CSiRSi
1 ? ?2?Cfilm? CSi?2RSi
2RP
2RP???
2?
1
??
(6)
? ? ?
(7)
RP ?
2RSi
?
RSi?Cfilm? CSi?2
Cfilm
2
(8)
CP ? Cfilm
2
2
(9)
Qind ?
?LS
RS
?
?LS
RS?
2
? 1?RS
2? CS?
LS
??1 ?
RS
CP
? ?2LS?
CP
2
? CS??
(10)
f0 ?
1
2??LC
f0
?f
(11)
Q ?
(12)
498
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Page 3

resonance frequency f0, which corresponds to the point where Qind
is zero and alternatively to the point where the transmitted power
is minimum. When using the numerical or experimental data, we
compute the resonance frequency from the point of minimum
transmitted power. Because the device we fabricate is an on-chip
resonator that does not require any tuning with an external capac-
itor, we calculate the Q-factor theoretically as given in Eq. (12) of
Table 1.
3. EXPERIMENTAL CHARACTERIZATION AND ANALYSIS
We design our devices to have a resonance frequency in the
microwave frequency range in accordance with the criterion of
maximum feasible Q-factor while maintaining the minimal size for
targeted biomedical applications. To maximize the Q-factor of our
microwave resonator, we construct our design methodology based
on maximizing the inductor’s Q-factor. As discussed in Section 2,
Qindexplicitly includes the effect of design parameters on reso-
nance and identifies the energy loss and storage elements. Given
these guidelines, we set the device parameters. Table 2 summa-
rizes two of our designs to demonstrate the effect of different
design parameters for comparison purposes.
We use silicon as substrate and Au as metal layer as they are
biocompatible (so that our resonator can be used as bio-MEMS
sensors in future applications). We directly lay down the first metal
layer used for contacts directly on the substrate to decrease sub-
strate losses. We choose the Si3N4thin film, which is also bio-
compatible while featuring a low loss tangent (as low as 5 ? 10?4)
and a high dielectric constant (as high as 8) in the microwave
frequency range. The low loss tangent significantly decreases the
loss, whereas the high dielectric constant increases the dielectric
film capacitance. To increase the resonance frequency and Qind
and to make a compact resonator, we reduce the resonator chip
area; LCand WCare thus as short as possible. By increasing the
metal width (w), we decrease the sheet resistance and, hence,
increase the Q-factor. An increase in the metal width with constant
spacing between metal lines (s) increases the lateral area; we thus
optimize the metal width and spacing, considering the Q-factor and
compactness. The higher the metal spacing is, the lower the
resonance frequency is. Generally, although smaller metal spacing
increases Qind, one should also consider the effect of the ratio
between w and s. This ratio should not be too large; otherwise, the
parasitic capacitance eventually decreases Qind. The first design
with 10 ?m spacing features higher Qindbecause the w/s ratio of
the other device is too large and thus the parasitic capacitance
decreases the Q-factor.
In Figure 2, we show Qindcomputed for both designs (with s ?
10 ?m and s ? 5 ?m). Here, we observe that the maximum
inductor Q-factor of the first design with s ? 10 ?m is higher than
that of the second one with s ? 5 ?m. At resonance frequencies,
their inductor Q-factors cross the zero line; the first design with
s ? 10 ?m has a resonance frequency of 6.70 GHz, and the second
design with s ? 5 ?m has a resonance frequency of 7.00 GHz.
High-Q factor in our designs is achieved because we use the
capacitance of the dielectric thin film between the coil and the
substrate for on-chip tuning and obtain an all on-chip, small-size
microwave resonator. In fact, because we use the high dielectric
capacitor instead of an external capacitor, the spiral inductor is
utilized the way that a cavity resonator would be. Thus, we obtain
a high Q-factor, comparable to the results of cavity resonator
studies, but here without sacrificing the small chip area. Therefore,
this study effectively combines two different approaches: The
spiral inductor concept and cavity resonator design techniques. In
addition, considering the factors that reduce the losses and enhance
the Q-factor by a careful inspection each of the circuit parameters
in Figure 1(a), the losses are minimized and the Q-factor is
maximized at a resonance frequency of 7 GHz. Also, if we further
modify our resonator design to operate at even higher frequencies,
the chip size becomes smaller and the Q-factor is enhanced be-
cause of our design methodology, which is again different from the
traditional approaches.
The first step in the fabrication procedure includes standard
lithography and liftoff directly on a Si substrate to lay down the
first metal layer made of Au with a thickness of 0.1 ?m. We then
deposit a Si3N4thin film using a plasma-enhanced chemical vapor
deposition (PECVD) system; this film is 0.1 ?m thick. To pattern
the Si3N4film, we perform a second lithography to open vertical
interconnection areas using a wet etching process with HF (hy-
drofluoric acid). In the subsequent Au metallization step, we erect
the interconnection layer. In the third lithography and Au metal-
lization steps, we construct the top coil and contact pads and finally
obtain our on-chip microwave resonator. Figure 4 summarizes our
process flow to fabricate our devices and shows one of the fabri-
cated devices. We characterize these fabricated devices using a
vector network analyzer (HP8510C). We calibrate our setup using
TABLE 2Our Device Design Parameters
Design
LC(?m)
WC(?m)
Nw (?m)
s (?m)
tfilm(?m)
t (?m)
1
2
540
520
540
520
2
2
100
100
10 0.1
0.1
0.1
0.15
Figure 2
[Color figure can be viewed in the online issue, which is available at
www.interscience.wiley.com]
Qindcomputed for our designs with s ? 10 ?m and s ? 5 ?m.
Figure 3
microwave resonators shown in cross-sectional view at the stages of (a)
metallization on the substrate, (b) dielectric film coating, (c) film patterning
(wet etching), (d) interconnect metallization, and (e) final top coil metal-
lization, along with (f) a top-view micrograph of our fabricated device.
[Color figure can be viewed in the online issue, which is available at
www.interscience.wiley.com]
The process flow for the microfabrication of our on-chip
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499

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the ISS (impedance standard substrate). In our measurements, we
take 801 points and perform 128-point averaging both in calibra-
tion and measurement.
Figures 4 and 5 show the S21parameters (in dB) that are
experimentally measured and numerically simulated (in CST Mi-
crowave Studio) together for our first and second designs (s ? 10
?m and 5 ?m), respectively. We measure the Q-factors of the
microwave resonators from the 3-dB bandwidth ratio of the S21
magnitude by taking transmission measurements [11]. Therefore,
we obtain the loaded Q-factor including the external effects, which
is different from calculating the Q-factor of an inductor alone by
measuring reflectivity after grounding one port of the circuit. We
observe sharp dips in the transmitted power at the resonance
frequencies both in Figures 4(a) and 5(a). We measure the reso-
nance frequencies (where S21is minimum) to be 6.97 and 7.12
GHz for our first and second designs, respectively. These experi-
mental results match very well with the theoretical values of 6.70
and 7.00 GHz. Our theoretical and experimental results are sum-
marized in Table 3.
To clearly illustrate 3-dB bandwidth measurements, Figures
4(b) and 5(b) depict the same experimental S21data presented in
Figures 4(a) and 5(a), zooming in the resonance regions. As can be
clearly seen in Figures 4(b) and 5(b), we measure ?f of the first and
second devices to be 148 and 178 MHz; these closely match the
numerically calculated ?f values of 128 and 169 MHz, respec-
tively. Using Eq. (12), we then experimentally obtain Q-factors for
the first and second devices of 47.10 and 38.48; these are also in
close agreement with the numerical results of 52.40 and 41.30,
presented in Table 3.
Here, it is worth noting that we take all of our measurements
loaded with standard microwave probes on the chips and then
extract the Q-factors from these measurements in the loaded case
including the losses coming from the probes. For example, for
cavity resonators [5, 6], typically unloaded Q-factors are cited;
these are calculated using the relation
1
Ql
?
1
Qu
?
1
Qe, where Qu
is the unloaded Q-factor, Qlis the loaded Q-factor, and Qeis the
external Q-factor. In these works, Quand Qeare larger than Ql. In
our case, we obtain and cite only the loaded Q-factors (Ql) in our
experiments by placing the microwave probes on the chips and
measuring the S21parameters with the probes. In our experimental
characterization, the minimum point of this S21measurement gives
the resonance frequency f0; the points that are 3 dB above this
minimum point give the 3-dB frequencies (f1and f2); the differ-
ence between f1and f2gives the 3-dB bandwidth ?f; and finally the
ratio of f0to ?f gives the loaded Q-factor as in Eq. (12), which is
also explicitly shown on the plots of Figures 4(b) and 5(b).
Figure 4
ical simulation of S21parameter and (b) zoom-in experimental S21data to
illustrate the resonance frequency f0and the 3-dB bandwidth ?f. [Color
figure can be viewed in the online issue, which is available at www.
interscience.wiley.com]
For our first device, (a) experimental measurement and numer-
Figure 5
numerical simulation of S21parameter and (b) zoom-in experimental S21
data to illustrate the resonance frequency f0and the 3-dB bandwidth ?f.
[Color figure can be viewed in the online issue, which is available at
www.interscience.wiley.com]
For our second device, (a) experimental measurement and
TABLE 3
Frequencies, 3-dB Bandwidths, and Quality-Factors of Our
Devices
Theoretical and Experimental Resonance
f0(GHz)
?f (MHz)
Q-factor
Theory Experiment Theory Experiment Theory Experiment
Device 1
Device 2
6.70
7.00
6.97
7.12
128
169
148
178
52.40
41.30
47.10
38.48
500
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Therefore, the Q-factors cited here present the worst case with
probe loading (and thus related losses) included in the measure-
ments and extraction of the Q-factors.
Using our new design approach, we also increase the Q-factor
by decreasing the device size and increasing the resonance fre-
quency as also stated in Eq. (10). However, with the conventional
design techniques, the Q-factor would rather decrease with in-
creasing frequencies. In our experimental study, after achieving a
considerably high Q-factor at 7 GHz using a small footprint of 540
?m ? 540 ?m, we further modify our design for LC? 270 ?m,
WC? 270 ?m, N ? 2, w ? 50 ?m, s ? 5 ?m, tfilm? 0.1 ?m, and
t ? 0.1 ?m. We use our analytical model to predict the operating
resonance frequencies, and we find out that the Q-factor is further
improved despite the smaller chip size, while the resonance fre-
quency is increased (13.08 GHz), as shown in Figure 6. This is a
unique feature of our self-tuning design methodology, which is not
possible with the traditional approaches.
The loaded Q-factors experimentally obtained with our all-on-
chip microwave resonator using our new design methodology in
this work are considerably larger than the current state-of-the-art
for similar-size microwave resonators that are implemented with-
out cavity geometries in traditional approaches. The excellent
agreement between our experimental measurement results and
theoretical simulation results (both analytical and numerical) ver-
ifies our theoretical models and techniques.
4. CONCLUSIONS
We have designed, fabricated, and demonstrated 540 ?m ? 540
?m on-chip microwave resonators working at 6.97 GHz with a
Q-factor of 47.10. These hold great promise for use as high-Q
chip-scale microwave resonators in different high-frequency ap-
plications, e.g., in implant RF sensors. To achieve high Q-factors,
our design methodology focused on tuning the on-chip coil induc-
tance with the increased on-chip dielectric thin film capacitance
and minimizing energy losses. Also, we developed a two-port coil
model representation, which we verified with our experimental
results and numerical simulations. This model allows us to design
and implement all-on-chip resonators whose resonance frequen-
cies and Q-factors are precisely set and controlled with the device
parameters in the design phase. As an interesting feature in our
design approach, the effect of skin depth on the Q-factor is
relatively reduced. Additionally, if our resonator design is modi-
fied to operate at an increased frequency, the chip size becomes
smaller and the Q-factor is enhanced, which is again a different
feature from the traditional approaches. Here in this study, the
well-known spiral geometry, which is commonly utilized in in-
ductors, is implemented as an all-on-chip microwave resonator for
the first time.
ACKNOWLEDGMENTS
This work is supported by the European Science Foundation (ESF)
European Young Investigator Award (EURYI) and the Turkish
National Academy of Sciences (TU¨BA) Distinguished Young Sci-
entist Award (GEBI˙P), and TU¨BI˙TAK EEEAG 105E066,
105E065, 104E114, 106E020, 107E088, and 107E297, and EU
IRG MOON 021391. The authors are pleased to acknowledge Dr.
N. Kosku Perkgoz, Dr. Z. Dilli, A. Kocabaçs, and D. C ¸alıçskan for
useful editing, discussions, experimental training, and support.
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Figure 6
can be viewed in the online issue, which is available at www.
interscience.wiley.com]
Qindcomputed for our design with LC? 270 ?m. [Color figure
DOI 10.1002/mopMICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 2, February 2009
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