Download Microstrip resonators for electron paramagnetic resonance

Microstrip resonators for electron paramagnetic resonance experiments
A. C. Torrezan, T. P. Mayer Alegre, and G. Medeiros-Ribeiro
Citation: Rev. Sci. Instrum. 80, 075111 (2009); doi: 10.1063/1.3186054
View online: http://dx.doi.org/10.1063/1.3186054
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REVIEW OF SCIENTIFIC INSTRUMENTS 80, 075111 共2009兲
Microstrip resonators for electron paramagnetic resonance experiments
A. C. Torrezan,1,2,a兲 T. P. Mayer Alegre,1,3,b兲 and G. Medeiros-Ribeiro1,c兲
1
Laboratório Nacional de Luz Síncrotron, Caixa Postal 6192, Campinas, São Paulo 13084-971, Brazil
Faculdade de Engenharia Elétrica e de Computação, UNICAMP, Campinas, São Paulo 13083-970, Brazil
3
Instituto de Física Gleb Wataghin, UNICAMP, Campinas, São Paulo 13083-970, Brazil
2
共Received 22 April 2009; accepted 2 July 2009; published online 31 July 2009兲
In this article we evaluate the performance of an electron paramagnetic resonance 共EPR兲 setup using
a microstrip resonator 共MR兲. The design and characterization of the resonator are described and
parameters of importance to EPR and spin manipulation are examined, including cavity quality
factor, filling factor, and microwave magnetic field in the sample region. Simulated microwave
electric and magnetic field distributions in the resonator are also presented and compared with
qualitative measurements of the field distribution obtained by a perturbation technique. Based on
EPR experiments carried out with a standard marker at room temperature and a MR resonating at
8.17 GHz, the minimum detectable number of spins was found to be 5 ⫻ 1010 spins/ GHz1/2 despite
the low MR unloaded quality factor Q0 = 60. The functionality of the EPR setup was further
evaluated at low temperature, where the spin resonance of Cr dopants present in a GaAs wafer was
detected at 2.3 K. The design and characterization of a more versatile MR targeting an improved
EPR sensitivity and featuring an integrated biasing circuit for the study of samples that require an
electrical contact are also discussed. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3186054兴
I. INTRODUCTION
Electron paramagnetic resonance 共EPR兲 is a spectroscopic tool employed in many areas of science, including
chemistry, biology, and physics, for the study of paramagnetic species.1 Traditional EPR systems employing waveguide X-band 共8–12 GHz兲 cavities and inductive detection
have sensitivity limited to about 1011 spins/ GHz1/2 at room
temperature2 and are not adequate for the study of samples
with smaller number of spins. As the minimum number of
spins Nmin depends on the cavity volume Vc, angular resonant frequency ␻0, and unloaded quality factor Q0 as Nmin
⬀ Vc / 共Q0␻0兲,1 a resonant structure that confines the microwave magnetic field in a smaller volume may increase the
signal-to-noise ratio 共SNR兲 at a given frequency.3–5
Unlike traditional EPR waveguide cavities operating in
the transverse electric 共TE兲 mode, on which both transverse
and longitudinal dimensions scale with frequency,
transmission-line resonators operating in the transverse electromagnetic 共TEM兲 mode have their resonant frequency set
only by the longitudinal dimension and the effective relative
permittivity of the medium ⑀ref. This enables the transverse
dimensions to be shorter than a half wavelength and the resonator volume to be reduced.
Similarly to a waveguide cavity, transmission-line resonators also allow a paramagnetic sample to be placed in a
position where the microwave electric field is minimum and
a兲
Present address: Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
b兲
Present address: Thomas J. Watson Sr Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.
c兲
Present address: Hewlett-Packard Labs, Palo Alto, CA 94304, USA.
0034-6748/2009/80共7兲/075111/6/$25.00
the microwave magnetic field is maximum. This is an important requirement for conductive samples in order to minimize
losses due to cavity loading. As an example, samples containing quantum dots6–8 present a challenge that requires a
more elaborate solution. Finding such a spot to place a
sample can be difficult in other common resonant structures
utilized in EPR setups such as a loop-gap resonator 共LGR兲.6,9
One of the simplest configurations of transmission-line
resonator is a microstrip resonator 共MR兲.10,11 This compact
structure can be easily fabricated by conventional lithography and allows the integration of other passive/active devices in the same substrate, for example, a dc bias network
for samples that require an electrical contact such as quantum dots.12 Other examples include a quadrature resonator to
produce circularly polarized waves to determine the g-factor
sign13 and spin transition selection rules,14 a Hall sensor for
simultaneous EPR and magnetization measurements,15 to
name a few. Pulsed EPR experiments can also benefit from
MRs due to their low quality factor. Besides the inductive
detection employed here, other spin-resonance detection
methods can take advantage of the MR structure such as
optical14 and current detections.
In this work we evaluate the performance of an EPR
system using a MR. The design of the resonator is presented
in Sec. II along with detailed calculation of resonator parameters of importance to EPR and spin manipulation such as
quality factor, filling factor, and magnetic field strength in
the sample region. Calculated microwave electric field and
magnetic field distributions are also presented. Section III
describes the characterization of the resonator, including a
perturbation technique to map the spatial distribution of the
field over the MR substrate. EPR experiments performed to
80, 075111-1
© 2009 American Institute of Physics
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075111-2
Rev. Sci. Instrum. 80, 075111 共2009兲
Torrezan, Mayer Alegre, and Medeiros-Ribeiro
FIG. 1. 共Color online兲 共a兲 Overview of MR and feed line. 共b兲 Picture of the
fabricated MR on an alumina substrate.
assess the minimum detectable number of spins at room temperature and to evaluate the functionality of the EPR setup at
low temperature are also reported in this section. In Sec. IV
we discuss the design and characterization of a MR for improved EPR performance and featuring an integrated biasing
circuit. In the conclusion session we summarize the main
findings of this work.
II. RESONATOR DESIGN
A. Simulation results
The MR consists of a strip conductor of width w, length
l, and thickness t, patterned on a substrate of relative permittivity ⑀r, thickness h, with a ground plane of thickness t, as
depicted in Fig. 1共a兲. The mode of interest is the fundamental
quasi-TEM with a half-wavelength longitudinal variation,
which corresponds to an axial mode index n = 1. The resonant frequency f 0 is given by f 0 = nc0 / 共2共l + ⌬l兲冑⑀ref兲, where
c0 is the speed of light in vacuum and ⌬l is a correction due
to the fringe electric field at the end of the resonator. The
fundamental mode as well as modes with an odd axial mode
index has a maximum magnetic field H1 and a minimum
electric field E1 in the middle of the MR, which is a suitable
location to place the sample. While the length l determines
the resonant frequency, the width w can be chosen to maximize the quality factor Q0. The gap g between the feed line
and the MR determines the coupling of the resonator and its
loaded quality factor.
The discontinuity in permittivity and the open structure
of the MR makes its analysis involved. Although analytical
expressions are available to estimate parameters such as ⌬l
and ⑀ref,16 a detailed design required the use of the finite
element method 共FEM兲 solver HFSS 共Ref. 17兲 for an adequate
modeling of the structure. For a compact cavity design, an
alumina substrate with permittivity ⑀r = 9.4 and thickness
h = 680 ␮m was employed. A loss tangent of 6 ⫻ 10−3 was
assumed for alumina in simulation.18 The other design parameters of the MR are l = 6.3 mm, w = 1 mm, g = 75 ␮m,
and a 2-␮m-thick Cu layer. According to the simulated resonance curve shown as a solid black line in Fig. 2共a兲, the
resonant frequency and quality factor of this structure are
f 0 = 8.27 GHz and Q0 = 76, respectively.
Both in simulation and experiment the unloaded quality
factor Q0 was computed from the reflection coefficient ⌫
data using Q0 = 共1 + ␬兲f 0 / ⌬f. In this expression, ␬ denotes the
coupling coefficient and ⌬f the frequency curve width at the
level where 兩⌫兩 = 共1 + ␬2兲1/2 / 共1 + ␬兲. For an undercoupled
resonator, one has ␬ = 共1 − 兩⌫共f 0兲兩兲 / 共1 + 兩⌫共f 0兲兩兲; for the overcoupled case, ␬ = 共1 + 兩⌫共f 0兲兩兲 / 共1 − 兩⌫共f 0兲兩兲.19 The Smith chart
FIG. 2. 共Color online兲 共a兲 Measured and simulated resonance curves of the
alumina MR with w = 1 mm and l = 6.3 mm. 共b兲 Simulated unloaded quality
factor Q0 as a function of the strip conductor width w at f 0 = 8.27 GHz
共resonator parameters: ⑀r = 9.4, h = 680 ␮m, g = 75 ␮m, and Cu layer thickness t = 2 ␮m兲.
representation 共not shown兲 of the calculated reflection coefficient indicated an overcoupled regime for this MR. The
variation of Q0 as a function of w at f 0 = 8.27 GHz is shown
in Fig. 2共b兲. For small values of w the ohmic loss is dominant, while for large values the radiation loss predominates.20
Both asymptotic cases lead to a decrease in Q0 with a maximum quality factor near the designed value w = 1 mm. The
calculated electric and magnetic fields on the top of the alumina substrate are presented in Fig. 3.
B. EPR considerations
Despite its low quality factor Q0, which is advantageous
for pulsed EPR, the magnetic field and EPR sensitivity in
MRs can be comparable to EPR systems employing cavities
with much higher Q0 due to the smaller MR volume. For a
sample placed on the center of the strip conductor, simulation results indicated that an input power of 1 mW generates
a microwave magnetic field B1 = ␮0H1 / 2 = 6 ␮T at the
sample in the rotating frame, where ␮0 is the vacuum permeability. This corresponds to a power-to-field conversion
factor of ⌳ = 0.2 mT/ W1/2. Other commonly employed resonators in EPR X-band setups have similar conversion factors
such as ⌳ ⬇ 0.3 mT/ W1/2 for cylindrical TE011 cavities1 and
⌳ ⬇ 0.5 mT/ W1/2 for LGRs and dielectric resonators.21 A
high conversion factor is desirable for faster spin operations
and less sample heating.
With regard to sensitivity, the performance of the MR
can be estimated by comparing with a similar EPR setup that
employs as a resonant structure an empty TE011 cylindrical
cavity with radius r and length lc = 2r:10
FIG. 3. 共Color online兲 Resonator magnetic and electric fields on the top of
the alumina substrate 共simulation parameters: input power= 1 mW and
f 0 = 8.27 GHz兲.
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075111-3
NminMR
Nmincyl
Rev. Sci. Instrum. 80, 075111 共2009兲
Torrezan, Mayer Alegre, and Medeiros-Ribeiro
=
共Q0␩兲cyl
,
共Q0␩兲MR
共1兲
where ␩ = 兰Vs兩H1兩2dV / 兰Vc兩H1兩2dV is the filling factor, with Vs
and Vc denoting the sample and cavity volumes, respectively.
The resonator filling factors were calculated from FEM
simulations considering an empty cylindrical sample, radius
180 ␮m and height 40 ␮m, located at the position of maximum H1 on the MR conductor. This represents the same
condition as in the room temperature EPR experiment described in Sec. III B. At f 0 = 8.27 GHz, the filling factor of
the MR was found to be ␩MR = 1.7⫻ 10−4. For a cylindrical
cavity operating at the same frequency, the calculated
parameters were Q0 = 32 900 and ␩cyl = 4.9⫻ 10−7 and are in
good agreement with results obtained from analytical expressions available elsewhere.1 These numbers imply that
NminMR / Nmincyl ⬇ 1 and indicate a sensitivity on the order of
1011 spins/ GHz1/2 at room temperature for both configurations.
III. EXPERIMENTS
A. Resonator characterization
The MR was fabricated using standard optical lithographic techniques on a 680-␮m-thick polished alumina
substrate covered by a 2-␮m-thick Cu layer coated with a
200 nm Au film. A picture of the fabricated resonator is
shown in Fig. 1共b兲. The thickness of the metallic layer is
greater than twice the skin depth of copper at 8.27 GHz. The
employed modulation of the static magnetic field B0 on the
order of few kilohertz can easily reach a sample under the
strip conductor due to the open configuration and electrically
thin conductive layers of the MR at this modulation frequency. Special arrangements to permit the penetration of the
modulated field through the walls of cavities, for example,
by inserting slots in the waveguide walls,22 are not needed
here.
The resonance curve of the fabricated resonator was
measured using a vector network analyzer, model Anritsu
37347D, and the result is shown as a solid red line in Fig.
2共a兲. The measured resonant frequency f 0 = 8.14 GHz is in
fair agreement with the simulated value 8.27 GHz. The quality factor of the cavity was measured to be Q0 = 60, which is
close to the calculated value.
The field distribution on the MR surface was evaluated
by means of a cavity perturbation technique.23 Perturbing a
resonator in a region dominated by the electric field produces
a downshift in the resonant frequency if the resonator volume is reduced due to the perturbation. The electric field
strength in this region is related to the frequency shift by
E2 ⬀ 1 − 共␻ / ␻0兲, where ␻ and ␻0 are the perturbed and unperturbed frequencies, respectively. An opposite effect
should be observed in a region of high magnetic field.24 The
perturbing object used in the mapping consists of a
300-␮m-diameter metallic needle aligned in the z-direction
and located 250 ␮m above the MR surface. Two step motors
were used to move the needle over the MR surface. The
measured field distribution is shown in Fig. 4 and qualitatively agrees with the simulated one. A small upshift in the
FIG. 4. 共Color online兲 Simulated electric field distribution 兩Ez兩2 and measured field distribution as a function of 1 − 共␻ / ␻0兲. Both distributions were
taken at z = 250 ␮m above the top of the alumina substrate.
resonant frequency could also be observed in the central part
of the MR where the magnetic field is maximum.
B. EPR experiments
The EPR spectrometer built in order to evaluate the
minimum detectable number of spins is shown in Fig. 5. It
consists of a water-cooled copper magnet with an external
coil for magnetic field modulation, a solid-state microwave
source Agilent 83731B stabilized by a rubidium atomic
clock, and a heterodyne system with a lock-in detector
SR830 to measure the reflected signal from the MR. The
remaining components of the spectrometer are specified in
the caption of Fig. 5. The sample used in the experiment at
room temperature was a standard marker 1,1-diphenyl2picrylhydrazyl 共DPPH兲, volume 3.94⫻ 10−12 m3, and it
was placed in the middle of the MR on the strip conductor, a
region of minimum electric field as observed in the measured
field. As the spin density of DPPH is 2 ⫻ 1027 spins/ m3,25
the total number of spins of the sample was Nspin = 7.9
⫻ 1015 spins.
The measured electron paramagnetic resonance of DPPH
at 300 K is shown in Fig. 6共a兲. The corresponding SNR,
defined as the ratio of the peak-to-peak signal amplitude to
the root-mean-square value of the noise, was found to be
FIG. 5. 共Color online兲 Schematic of the EPR spectrometer. 共1兲 Microwave
source 共Agilent 83731B兲. 共2兲 Rubidium atomic clock 共Stanford Research
FS725兲. 共3兲 Lock-in amplifier 共Stanford Research SR830兲. 共4兲 Power divider
共Midisco MDC2289兲. 共5兲 Power meter 共Anritsu ML238A兲. 共6兲 Directional
coupler 共Pasternack MDC3228–22兲. 共7兲 Circulator 共Pasternack PE8404兲. 共8兲
rf amplifier 共AML Communications AML818P3501–2W兲. 共9兲 Mixer 共Marki
Electronics M10818LA兲. 共10兲 Home-built power amplifier. 共11兲 0.7 T watercooled copper magnet 共Bruker B-M4兲 driven by a current source 共Danfysik
858兲.
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075111-4
Rev. Sci. Instrum. 80, 075111 共2009兲
Torrezan, Mayer Alegre, and Medeiros-Ribeiro
FIG. 6. 共Color online兲 共a兲 Measured EPR signal of DPPH sample
共experimental parameters: microwave power= 9.3 mW, B1 ⬇ 19 ␮T,
f 0 = 8.17 GHz, sample at 300 K, magnetic field modulation frequency
= 5.3 kHz, lock-in amplifier filter settings: time constant= 30 ms, roll-off
= 24 dB/ octave, and ENBW= 2.604 Hz兲; 共b兲 Measured EPR signal of Cr
dopants in a semi-insulating GaAs wafer 共experimental parameters: f 0
= 7.92 GHz, sample at 2.3 K, and magnetic field modulation frequency
= 7.5 kHz兲.
SNR= 30 000 and the peak-to-peak linewidth ⌬Hpp
= 0.3 mT, in agreement with values reported for DPPH.1 The
experimental minimum detectable number of spins Nmin_exp
was determined by:25
Nmin_exp =
1
Nspin
,
SNR ⌬Hpp冑ENBW
共2兲
where ENBW is the equivalent noise bandwidth of the
lock-in amplifier. From the parameters of the filter set for the
experiment, time constant of 30 ms and roll-off of 24 dB/
octave, one had ENBW= 2.604 Hz,26 yielding Nmin_exp = 5
⫻ 1010 spins/ GHz1/2. This sensitivity is comparable to EPR
setups using waveguide cavities as it was suggested by the
numerical calculations in Sec. II B.
The functionality of the EPR system was also tested at
low temperature. In this condition, the sample consisted of a
semi-insulating GaAs substrate with Cr impurities and it was
positioned at the midpoint of an alumina MR with resonant
frequency of 7.92 GHz. At low temperature, the Cr impurities become paramagnetic and the characteristic multiplet
Cr spin resonance27 could be detected at 2.3 K as shown in
Fig. 6共b兲.
FIG. 7. 共Color online兲 MR including feed line and biasing circuit.
FIG. 8. 共Color online兲 共a兲 Measured and simulated resonance curves of the
GaAs MR with w = 200 ␮m and l = 3.2 mm. 共b兲 Simulated unloaded quality
factor Q0 as a function of the strip conductor width w at f 0 = 14.95 GHz
共resonator parameters: ⑀r = 12.9, h = 365 ␮m, g = 40 ␮m, and Au layer thickness t = 1.5 ␮m兲.
IV. RESONATOR WITH INTEGRATED BIASING
CIRCUIT
As the microwave magnetic field scales as H1 ⬀ 冑Q0 / Vc,
the small MR volume compensated its low quality factor,
yielding a high filling factor and a sensitivity similar to EPR
setups using a high-Q0 cavity. Better performance may be
obtained by increasing the resonator filling factor. Following
this guideline, an improved MR design was made and is
presented in Fig. 7. This design utilizes a GaAs substrate
with permittivity ⑀r = 12.9 and thickness h = 365 ␮m, covered by a 1.5-␮m-thick Au layer. The GaAs substrate was
selected due to its higher permittivity, allowing a further reduction in the resonator size, and by the fact that GaAs substrates are utilized in many mesoscopic devices where the
study of spin-related phenomena is of interest. A loss tangent
of 2 ⫻ 10−4 was used for GaAs in simulation.28 The resonator
parameters l = 3.2 mm, w = 200 ␮m, and g = 40 ␮m were
tailored for f 0 = 15 GHz and maximum Q0 as shown in
Fig. 8.
A dc bias network was also included, allowing EPR experiments in samples that require biasing such as quantum
dots. The biasing circuit consists of a radial stub, dimensions
rdc = 1.36 mm and ␪ = 26.5°, and a quarter-wavelength transformer with line width wdc = 30 ␮m. The circuit is located in
a region of minimum electric field, as shown in the calculated field distribution in Fig. 9, in order to minimize any
interference in the resonance curve.
The measured resonant frequency f 0 = 14.97 GHz is in
good agreement with the simulated value 14.95 GHz, while
the measured unloaded quality factor Q0 = 60 is close to the
calculated value 96. Unlike the alumina cavity, the GaAs MR
was found to be undercoupled. The measurement was per-
FIG. 9. 共Color online兲 Resonator magnetic and electric fields on the top of
the GaAs substrate 共simulation parameters: input power= 1 mW, f 0
= 14.95 GHz, w = 200 ␮m, l = 3.2 mm, h = 365 ␮m, g = 40 ␮m, and Au
layer thickness t = 1.5 ␮m兲.
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075111-5
Rev. Sci. Instrum. 80, 075111 共2009兲
Torrezan, Mayer Alegre, and Medeiros-Ribeiro
FIG. 10. 共Color online兲 Simulated electric field distribution 兩Ez兩2 and measured field distribution as a function of 1 − 共␻ / ␻0兲. Both distributions were
taken at z = 100 ␮m above the top of the GaAs substrate 共parameters: f 0
= 10.05 GHz, w = 1 mm, l = 4.37 mm, h = 365 ␮m, g = 70 ␮m, and Au
layer thickness t = 1.5 ␮m兲.
formed directly on a GaAs wafer by means of a coplanar-tomicrostrip transition29 and a coplanar probe connected to a
vector network analyzer, model HP8510C. The main advantage of this transition is a virtual ground provided by the
radial stub, which has dimensions ls = 885 ␮m and ws
= 100 ␮m. This simplifies the fabrication process since no
via holes are required to connect the coplanar and microstrip
grounds. Comparison between measurements in MRs with
and without the dc network showed no perturbation in the
resonance curve due to the inclusion of the biasing circuit.
The field distribution was measured in a resonator built
on the same 365-␮m-thick GaAs substrate but with different
parameters, l = 4.37 mm, w = 1 mm, and g = 70 ␮m. The
measured resonant frequency of this MR is 10.05 GHz and
the quality factor Q0 = 50. The field distribution was measured at z = 100 ␮m from the MR surface and the result is
presented in Fig. 10. Similar to the map obtained for the
alumina MR, regions of high electric field were observed at
the ends of the resonator while a region of high magnetic
field was identified at the central part. However, additional
perturbation was noticed in the surroundings of the GaAs
MR.
The field confinement provided by the smaller resonator
volume contributed to a sixfold improvement in the powerto-field conversion factor to ⌳ = 1.3 mT/ W1/2 in the rotating
frame according to FEM simulations. An improvement of
two orders of magnitude in the MR filling factor was also
verified from calculations using the same sample volume as
in the alumina cavity, leading to ␩GaAs = 1.7⫻ 10−2. Based on
the experimental minimum detectable number of spins for
the alumina MR, the measured parameters Q0 and f 0 of both
MRs, and their simulated filling factors, the sensitivity of the
GaAs MR was estimated by means of Nmin_GaAs / Nmin_Al2O3
= 共Q0 f 0␩兲Al2O3 / 共Q0 f 0␩兲GaAs. This indicates that the GaAs
MR has the potential to achieve a sensitivity of about
109 spins/ GHz1/2 at 300 K.
V. CONCLUSIONS
In this work we evaluated experimentally the performance of an EPR setup using a MR. Utilizing a standard
marker at 300 K and a MR resonating at 8.17 GHz, the
sensitivity of the setup was determined to be 5
⫻ 1010 spins/ GHz1/2. The low MR unloaded quality factor
Q0 = 60, useful for pulsed EPR experiments, was compen-
sated by its high filling factor, yielding a sensitivity comparable to EPR systems using cavities with much higher quality
factors such as waveguide cavities. The functionality of the
EPR setup was also evaluated at low temperatures where a
Cr-doped semi-insulating GaAs was utilized to demonstrate
Cr-related spin resonance at 2.3 K using a MR tuned to 7.92
GHz. Scans of the field distribution performed over the MR
substrate confirmed that the samples were located in a region
of minimum electric field. MRs are easy to fabricate and
allow the integration of components close to the paramagnetic sample in a single substrate. An example of such integration was implemented using an integrated dc bias, which
allows an electrical contact to the resonator without cavity
loading. An improved MR design with higher filling
factor and operating at 15 GHz was also explored. The
power-to-field conversion factor of this design reached
⌳ = 1.3 mT/ W1/2 in the rotating frame according to simulations and the sensitivity was theoretically estimated to be
109 spins/ GHz1/2 at 300 K.
ACKNOWLEDGMENTS
We acknowledge the financial support from FAPESP
Process No. 04/01228-6, SPM Brazil network, CNPq, and
HP-Brazil. The authors are grateful to M. H. Piazzetta and A.
L. Gobbi from the microfabrication facility at LNLS for assisting with the fabrication of the resonators and CCSUNICAMP for the use of the vector network analyzer. A.C.T.
acknowledges the receipt of a CAPES fellowship and an
IEEE MTT-S Undergraduate/Pregraduate scholarship.
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