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A 40-nm CMOS Complex Permittivity Sensing Pixel for Material Characterization at Microwave Frequencies

TL;DR: In this article, a compact sensing pixel for the determination of the localized complex permittivity at microwave frequencies is proposed, which comprises a square patch, interfaced to the material-under-test sample, that provides permittivities-dependent admittance.
Abstract: A compact sensing pixel for the determination of the localized complex permittivity at microwave frequencies is proposed. Implemented in the 40-nm CMOS, the architecture comprises a square patch, interfaced to the material-under-test sample, that provides permittivity-dependent admittance. The patch admittance is read out by embedding the patch in a double-balanced, RF-driven Wheatstone bridge. The bridge is cascaded by a linear, low-intermediate frequency switching downconversion mixer, and is driven by a square wave that allows simultaneous characterization of multiple harmonics, thus increasing measurement speed and extending the frequency range of operation. In order to allow complex permittivity measurement, a calibration procedure has been developed for the sensor. Measurement results of liquids show good agreement with theoretical values, and the measured relative permittivity resolution is better than 0.3 over a 0.1–10-GHz range. The proposed implementation features a measurement speed of 1 ms and occupies an active area of $0.15\times 0.3$ mm2, allowing for future compact arrays of multiple sensors that facilitate 2-D dielectric imaging based on permittivity contrast.

Summary (4 min read)

Introduction

  • On the biomedical side of the application spectrum, examples include blood glucose monitoring [6] and exvivo or in-vivo cancer detection and assessment [8], [9].
  • Conventional microwave permittivity measurement techniques, used to acquire the aforementioned literature data, employ expensive and bulky equipment such as vector network analyzers (VNAs) and probe or cavity sensors interfaced to the material-under-test (MUT) [12], [13].
  • Efforts towards miniaturization of microwave permittivity sensing systems have been mainly concentrated towards CMOS implementations because of the ultimate form factor that CMOS offers.
  • The paper is organized as follows; section II analyzes the basic principles behind the system architecture, including the near-field patch sensor, the RF impedance bridge it is embedded in, as well as the multi-harmonic IF down-conversion read-out concept.

II. SYSTEM ARCHITECTURE

  • To address the aforementioned application scenarios, it is desirable that the sensor features the following qualities: Broadband operation that allows flexibility in choice of fre- quency.
  • Complex material permittivity detection, i.e. ability to detect both real and imaginary part of the permittivity.
  • Suitability for embedding in a 2-D array for permittivity contrast imaging, implying small size and fast read-out.

A. Near-Field Sensor

  • The two simulated sensors occupy an area of 100×100 µm2 and a distance of 10 µm between fingers was chosen for the differential sensor.
  • The fact that it is not inherently bound to differential sensing also allows the use of more advanced driving schemes where multiple patches are used to inspect a sample.
  • Since permittivity relates to electric energy storage and loss ( ′ and ′′ respectively), the sensing element is expected to represent a lossy capacitor of which the reactive and resistive behavior will strongly depend on the real and imaginary part of the MUT permittivity, respectively.
  • Table I summarizes the parameters of the model in (1) extracted after least square fitting with the EM-simulated curves.

B. RF Impedance Bridge

  • Following the established analytical -to-Y model for the patch, a method of reading out the admittance is required.
  • Consider the RF impedance bridge shown in Fig. 4 with branch admittances Y0 and the load measurand YL deviating from a baseline admittance Y0, also known as 1) Bridge Analysis.
  • Formulating the bridge behavior as in (6) and (7) allows to present a linear relation between an output quantity (inverse of output) to the input quantity (weighted conductance and susceptance).
  • Fig. 5 shows how the two noise contributions (thermal and external) will vary versus the bridge output voltage.
  • Moreover, if the two drive signals are not exactly 180o outof-phase, a phase mismatch signal (vb,MM ) will appear in the output of the bridge.

C. Multi-Harmonic Down-Conversion

  • Therefore, the bridge is driven at multiple odd harmonics which will be downconverted to odd harmonics of fIF , after being mixed with the odd harmonics of LO, as shown in Fig.
  • Situated 2fIF apart, these harmonics can be isolated and analyzed, enabling characterization of the load at higher frequencies than the highest achieved by the fundamental drive, and at more than one frequency point at the same time.
  • Since the amplitude of the higher-order odd harmonics in the square wave reduces by at least 1/n compared to the fundamental, where n the harmonic, order a lower sensitivity is expected at these higher harmonics.
  • Nevertheless, useful information can still be acquired, contributing to the previously mentioned goal of redundancy.
  • In addition to the baseband products of the mixing process, crossmixing can create content close to the even harmonics of fRF (e.g. 3fRF−fLO).

III. CIRCUIT DESIGN

  • The authors discuss the specific implementation and integrated circuit design of the permittivity sensor based on the previously reported architecture.
  • The three circuit blocks comprising the sensor is the RF bridge, the down-conversion mixer, and the bridge and LO drivers that provide the square wave for multi-harmonic operation.

A. Double-balanced, Fully-Differential Bridge Design

  • The implemented sensing element is a square 100×100 µm2-patch implemented in the top ultra-thick metal of the CMOS stack (M7), with a nitride opening for direct interfacing with a MUT or used for probing.
  • This structure is EM-simulated in order to generate the RFM model of Fig. 3b, discussed in II-A, which is later used for calibration of the system.
  • Fig. 9 shows the simulated on/off parallel conductance and capacitance versus frequency for the switched capacitor (post-layout extraction).
  • Rd is placed between the bridge middle nodes (A, A′, B, B′) and ground in order to ensure a DC discharge path that sets the DC bias condition for the proper operation of the NMOS switches.
  • Therefore, an amplitude and phase measurement of the bridge output is required.

B. Down-Conversion Mixer

  • The topology implements a current-mode switching mixer that achieves low 1/f noise operation and high linearity [38].
  • If the value of RL is large enough, most of the drain current of the transistors will be transferred to the output, converting the bridge output voltage (vRF+, vRF−) to a differential current (iRF+, iRF−).
  • The transistor Qs sets the bias current, which is generally limited for two main reasons: a) the large resistor value limits headroom of Q1 and Q2, which is required for good linearity and b).
  • The output current of the gm stage is fed to a CMOS switching quad that performs the mixing action.
  • As expected, the noise figure of the third and fifth harmonic downconversion process deteriorates by at least as much as the conversion gain deterioration.

C. Square-wave Drivers

  • The bridge and LO drivers share the same topology that utilizes inverter amplifiers to achieve a square-wave rail-to-rail output.
  • Shown in Fig. 12, the driver consists of a self-biased inverter that sets the DC voltage of the input waveform to the desired mid-rail value by proper choice of the NMOS and PMOS size.
  • Two complementary copies of the input are created and a series of increasingly larger cross-coupled inverters further amplify the signal and ensure risefall edge alignment, thus minimizing phase imbalance.
  • In general, steeper edges (i.e. larger sized transistors and higher power consumption) minimize rise-fall mismatch accross PVT variations.
  • Finally, the simulated integrated phase noise (IPN) of the bridge driver, which contributes to the bridge output noise, is between -92 dBc at 1 GHz and -81 dBc at 5 GHz, for an integration bandwidth of 0.01-1 kHz.

A. Calibration

  • As discussed in II-B1 and summarized in (6) and (7), the real and imaginary part of the inverse bridge differential output are linear combinations of the weighted load conductance and susceptance.
  • Equations (6) and (7) hold true with the assumption that the bridge is perfectly balanced to the baseline load admittance, i.e. in the middle of the measured load range.
  • Provided they are available, the sensor load YL can be estimated by observing the respective chip output outm.
  • Their exact value remains unknown due to fabrication tolerances and modeling or simulation inaccuracies.

B. Accuracy and Resolution

  • A distinction should be made at this point between the accuracy and the resolution of the sensor.
  • The authors make use of tabulated permittivity values that originate from Debye models and that are accurate within 1% [39], [40].
  • Since the readout of the real and imaginary part of the bridge output is done by measuring amplitude and phase, the authors need to link the resolution of the amplitude and phase read-out to the noise level, and, from that, assess the expected system resolution.
  • As expected, a larger external integrated phase noise (IPN) and system noise factor (F) incurs a more noisy readout of both amplitude and phase.
  • Then, the calibration procedure is performed to evaluate the standard deviation of the permittivity and, hence, the resolution.

V. EXPERIMENTAL RESULTS

  • The reported design was incorporated in a test IC, fabricated in a 7-metal, 40-nm CMOS process, with an ultra-thick top metal option, used for the sensing element.
  • Using such an advanced technology node allows extension of frequency range, although is not expected to offer significant area advantages, due to the extensive usage of analog circuitry and passive elements.
  • The RF, LO, control and read-out part remains the same for liquid material measurement.
  • 15-nL micro-container with a 500-µm bottom opening was carefully placed on top of the chip so that it encloses the patch.
  • To avoid the formation of air bubbles, the liquid MUT was injected slowly into the micro-container by pointing a micro-needle towards the container walls.

A. Load Measurements

  • In order to verify the operation of the bridge and the calibration procedure described in sections II-B and IV-A, respectively, the patch was contacted by a probe (Cascade Z40-V-GSG-500) to a digitallycontrolled RF tuner (Maury MT982E) in order to allow loading of the bridge with various RF admittances.
  • Calibration is performed using a SOL wafer calibration kit for the probe while the source is driving the termination port of the RF tuner.
  • Inverting the measured reflection coefficient (Γ) provides the calibrated Γ of the measured load, therefore, its admittance YL can be calculated and expressed as a parallel combination of a capacitance CL and a resistance RL.
  • The lc signal is also used for synchronization of the ADC.
  • The difference of offset capacitance between these two settings is 724.7 fF , which agrees well with the simulated branch capacitance difference of 693.5 fF from the simulations (see section II-B).

B. Material Permittivity Measurements

  • A number of six liquid materials was available for permittivity measurement: de-ionized water, methanol, ethanol, 2-propanol (IPA), 1-butanol and air.
  • The variance of the measured amplitude and phase versus chip output at 1 GHz is shown in Fig. 20.
  • A very good agreement between prediction and measurement is seen in the output phase, which does not show a dependence on the bridge imbalance.
  • Therefore, to assess the permittivity resolution of the independent material , the standard deviation of 100 consecutive permittivity measurements is examined.

VI. CONCLUSION

  • The design, calibration and measurement of a compact 40-nm CMOS complex permittivity sensing pixel has been presented.
  • Table II summarizes the achieved performance of the sensor along with the results of previously published state-of-the-art integrated permittivity sensors.
  • To the best of the authors’ knowledge, this work features the smallest active area while achieving fast and precise operation over two decades of bandwidth.
  • These properties, along with its compact size, fast readout and broadband architecture, make it suitable for utilization as a pixel element in 2D permittivity-based imaging sensors for biomedical and industrial applications.

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Delft University of Technology
A 40-nm CMOS Complex Permittivity Sensing Pixel for Material Characterization at
Microwave Frequencies
Vlachogiannakis, Gerasimos; Pertijs, Michiel A.P.; Spirito, Marco; de Vreede, Leo C.N.
DOI
10.1109/tmtt.2017.2753228
Publication date
2018
Document Version
Accepted author manuscript
Published in
IEEE Transactions on Microwave Theory and Techniques
Citation (APA)
Vlachogiannakis, G., Pertijs, M. A. P., Spirito, M., & de Vreede, L. C. N. (2018). A 40-nm CMOS Complex
Permittivity Sensing Pixel for Material Characterization at Microwave Frequencies.
IEEE Transactions on
Microwave Theory and Techniques
,
66
(3), 1619-1634. https://doi.org/10.1109/tmtt.2017.2753228
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. XX, NO. X, MONTH 2017 1
A 40–nm CMOS Complex Permittivity Sensing Pixel for
Material Characterization at Microwave Frequencies
Gerasimos Vlachogiannakis, Student Member, IEEE, Michiel A. P. Pertijs, Senior Member, IEEE,
Marco Spirito, Member, IEEE, and Leo C. N. de Vreede, Senior Member, IEEE
Abstract—A compact sensing pixel for the determination of the
localized complex permittivity at microwave frequencies is proposed.
Implemented in 40-nm CMOS, the architecture comprises a square
patch, interfaced to the material-under-test (MUT) sample, that provides
permittivity-dependent admittance. The patch admittance is read out
by embedding the patch in a double-balanced, RF-driven Wheatstone
bridge. The bridge is cascaded by a linear, low-IF switching down-
conversion mixer, and is driven by a square wave that allows simultaneous
characterization of multiple harmonics, thus increasing measurement
speed and extending the frequency range of operation. In order to
allow complex permittivity measurement, a calibration procedure has
been developed for the sensor. Measurement results of liquids show good
agreement with theoretical values and the measured relative permittivity
resolution is better than 0.3 over a 0.1–10 GHz range. The proposed
implementation features a measurement speed of 1 ms and occupies
an active area of 0.15×0.3 mm
2
, allowing for future compact arrays
of multiple sensors that facilitate 2-D dielectric imaging based on
permittivity contrast.
Index Terms—bridge circuits, biomedical sensors, complex permittivity
measurement, integrated microwave circuits, microwave sensors
I. INTRODUCTION
B
ROADBAND dielectric spectroscopy at microwave frequencies
has been identified as a promising tool for a large number
of applications, ranging from the agricultural, food and automotive
industry to the biomedical domain [1]–[8]. This method relies on
the fact that the dielectric footprint of various materials of interest,
i.e their complex permittivity across frequency, varies in conjunction
with a parameter that needs to be detected or quantified.
To highlight a few examples, in agriculture, the complex permit-
tivity of fruits and vegetables has been correlated to changes in
temperature, water and inorganic material content [1]–[3], while in
the automotive industry, it is the preferred method for oil and fuel
quality inspection [4], [5]. On the biomedical side of the application
spectrum, examples include blood glucose monitoring [6] and ex-
vivo or in-vivo cancer detection and assessment [8], [9]. The latter
application is supported by measurements on bulk animal and human
tissue, suggesting that the permittivity of cancer tissue can vary by
up to 20% compared to healthy tissue [10], [11].
Despite the promising potential suggested by these studies, con-
ventional microwave permittivity measurement techniques, used to
acquire the aforementioned literature data, employ expensive and
bulky equipment such as vector network analyzers (VNAs) and probe
or cavity sensors interfaced to the material-under-test (MUT) [12],
[13]. These setups are not suitable for most practical application
scenarios, such as outdoor, remote-location measurements, and point-
of-care medical testing. Moreover, their high cost hinders potential
wider adoption of the technology.
This work was supported by the Dutch Technology Foundation
(STW/NWO), project INFORMER 13010.
G. Vlachogiannakis, M. A. P. Pertijs, M. Spirito and L. C. N. de Vreede
are with the Department of Electrical Engineering, Mathematics and
Computer Science, Delft University of Technology, The Netherlands,
2628CD Delft (e-mail: G.Vlachogiannakis@tudelft.nl, M.Spirito@tudelft.nl,
M.A.P.Pertijs@tudelft.nl, L.C.N.deVreede@tudelft.nl )
Miniaturization of sensors and measurement systems is, there-
fore, essential in order to leverage the true potential of microwave
permittivity sensing in real-life applications. Moreover, miniaturized
sensors can facilitate new applications that deviate from the bulk-
level measurement regime, such as the unexplored area of 2-D sensor
arrays for permittivity contrast measurement and visualization at
microwave frequencies. Such imaging functionality can prove useful
in a variety of applications such as:
(a) label-free, in-vivo cancer visualization as an assisting tool in
removal surgery [14],
(b) food and flower quality inspection for early detection of storage
disorders (e.g. browning, skin spots, etc),
(c) evaluation of drug penetration through the skin,
(d) non-destructive film coating testing in industry.
A differentiation should be made at this point between microwave
permittivity sensors and low-frequency permittivity/impedance sen-
sors, operating below 100 MHz. For the latter, arrayed imple-
mentations have already been implemented successfully [15], [16].
Nevertheless, motivation to move towards broadband microwave
frequency implementations still exists for two main reasons: i) in
order to achieve better penetration in the material-under-test (MUT)
and ii) to employ the higher redundancy implicit in acquiring a
permittivity dataset which is more complete and flexible in the
frequency domain. Such redundancy is directly linked to increased
sensitivity and specificity in biomedical applications.
To enable such imaging systems, focus has to be put on a fast read-
out, with acceptable resolution to fulfill the application requirement,
as well as the overall size of the sensor and its signal conditioning
circuitry, since this will determine its scalability in a dense array
towards a fine spatial resolution. Efforts towards miniaturization of
microwave permittivity sensing systems have been mainly concen-
trated towards CMOS implementations because of the ultimate form
factor that CMOS offers. Several microwave CMOS implementa-
tions during the last years have demonstrated accurate permittivity
readout [17]–[24]. Oscillator-based approaches exist, which are very
narrow-band, area-consuming and limited to measurement of the real
part of permittivity, thus are not suitable for implementation of a
broadband permittivity sensing pixel [17], [19], [22], [24]. Several
other implementations achieve an operation frequency range of at
least a decade by employing broadband down-conversion [18], [20],
[21], [23] or wide-band PLL-based architectures [22]. However, since
they are not meant for imaging applications, little optimization and
analysis has been done on the readout speed, resulting in potentially
long measurement times. Moreover, the active area still remains quite
large if implementation of a sub-mm-resolution imager is targeted.
In the following sections, we detail an integrated complex per-
mittivity sensor, suitable for use as an imaging pixel, which was
prototyped in 40-nm CMOS and occupies sub-mm
2
area while
achieving fast readout. The proposed sensor, briefly presented in
[25], features a single-ended patch sensing element, embedded in
a fully-differential double-balanced RF-driven impedance bridge. A
multi-harmonic measurement scheme is employed to extend the
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. XX, NO. X, MONTH 2017 2
(a) (b)
Fig. 1. 3D depiction of (a) a differential and (b) a single-ended patch sensing
element.
frequency range and increase the effective measurement speed. In
this work, we analyze the utilized sensing element in depth, and
develop a calibration procedure, based on the analysis of the RF
bridge. Moreover, the noise sources that contribute to the system
resolution limit are identified and their contribution is quantified.
Additional measurement data are complementing the preliminary
results reported in [25] that demonstrated the ability to measure
material complex permittivity. Independent measurements with the
sensing pixel loaded by a probe that offers a known termination are
used to validate the bridge transfer characteristic, while statistical
data of material measurements have been collected to evaluate the
permittivity resolution of the sensor when fundamental, third and
fifth harmonic are measured.
The paper is organized as follows; section II analyzes the basic
principles behind the system architecture, including the near-field
patch sensor, the RF impedance bridge it is embedded in, as well
as the multi-harmonic IF down-conversion read-out concept. Section
III describes the physical implementation of the permittivity-sensing
system in a 40-nm CMOS technology. In section IV, a calibration
procedure for the developed sensor is given and the resulting accuracy
and resolution are discussed. Experimental results are presented in
section V. Finally, conclusions are drawn in section VI.
II. SYSTEM ARCHITECTURE
To address the aforementioned application scenarios, it is desirable
that the sensor features the following qualities:
Broadband operation that allows flexibility in choice of fre-
quency.
Complex material permittivity detection, i.e. ability to detect
both real and imaginary part of the permittivity.
Suitability for embedding in a 2-D array for permittivity contrast
imaging, implying small size and fast read-out.
The proposed architecture consists of a near-field patch sensor, an
RF-driven impedance bridge in a double-balanced configuration and
a multi-harmonic, IF down-conversion scheme.
A. Near-Field Sensor
The sensing element translates the relative permittivity of the
material, expressed as a frequency-dependent complex number
?
(ω) =
0
(ω) j
00
(ω), into a lumped equivalent complex admit-
tance that can be read out by subsequent circuitry.
Previously reported CMOS permittivity sensors typically employ
differential capacitive sensing elements, similar to the one depicted in
Fig. 1a, implemented on the top metal of the CMOS metal stack, with
a passivation opening for direct contact to the MUT [17], [19]–[22].
These sensor types provide convenient access to both terminals (P +
and P in Fig. 1a) and are directly compatible with fully differential
read-out chains. However, due to their planar configuration, the
P+
P-
P+
Diff. cap. sensor
Normalized |E| (dB)
Patch sensor
Dif
f
f
f
f
f
f
-
-
-
-
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
++++++
+
+
+
+
+
+
+
+
+
+
+
++
+
+
+
++
+
+
+
++
+
Distance z from sensor (m)
z
100 m
10 m
Diff. cap
P
z
100 m
Patch
Fig. 2. EM simulation of normalized electric field magnitude versus vertical
distance from the sensor interface for two types of sensors both occypying the
same 100×100 µm
2
area: a single-ended patch and a differential capacitor
with 10 µm between fingers.
electric field is mainly concentrated in the vicinity of the sensor
surface, i.e the surface-MUT interface. On the contrary, the electric
field lines of a single-ended metal patch sensor, portrayed in Fig. 1b,
penetrate deeper in the MUT, thus allowing sensing further from the
sensor-MUT interface.
To demonstrate this, EM simulations were carried out to determine
the electric field as a function of vertical distance from the sensor sur-
face, using a commercial 3D EM simulation tool (Keysight EMPro).
The two simulated sensors occupy an area of 100×100 µm
2
and a
distance of 10 µm between fingers was chosen for the differential
sensor. A typical 40-nm CMOS metal stack was considered and the
EM simulation was carried out at 1 GHz, in a worst case scenario
where the sensor is interfaced to air (
?
= 1 j0). As seen in the
simulation results in Fig. 2, a much steeper decay of the electric
field is evident in the case of the differential sensor. At a distance
of 300 µm, the electric field magnitude is approximately 100 dB
lower than the maximum strength, whereas for the patch sensor this
reduction is in the order of 70 dB, a difference of 30 dB.
A patch sensor is, therefore, less sensitive to potential air-gaps,
since a smaller portion of the field is concentrated at the interface.
This property is desired in solid or semi-rigid material measurements
(e.g. biological tissue), but also in applications when a permittivity
contrast measurement deeper in the MUT is targeted. Although the
patch sensor is expected to provide a poorer isolation to neighboring
pixels, the fact that it is not inherently bound to differential sensing
also allows the use of more advanced driving schemes where multiple
patches are used to inspect a sample. Examples of such schemes
include multi-phase patch excitation, selective differential sensing
between different sensors and bootstrapping, i.e. driving neighboring
pixels without reading them in order to cancel capacitive scross-
coupling [26]. Based on the above, the patch configuration was
favoured as a sensing element in this implementation.
Fig. 3a shows the cross-section of the a square patch sensor
implemented on the top metal of a generic CMOS stack. When the
patch is in contact with air the patch node P is loaded by the parallel-
plate capacitance C
0
, formed between the top metal and the ground
plane. When interfaced to a MUT, the load will change depending on
the MUT complex permittivity. Since permittivity relates to electric
energy storage and loss (
0
and
00
respectively), the sensing element
is expected to represent a lossy capacitor of which the reactive and re-
sistive behavior will strongly depend on the real and imaginary part of
the MUT permittivity, respectively. Hence, the admittance Y
P
at the

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. XX, NO. X, MONTH 2017 3
ε*
Υ
MUT
(ε΄,ε΄΄)
MUT
Passiv.
Oxide
GND metal
Si Substrate
Y
P
C
0
P
6.7 μm
(a)
0 20 40 60 80
100
200
300
ε
C
P
(fF)
0 10 20 30 40
0
0.2
0.4
0.6
0.8
ε
G
P
/f (mS/GHz)
ε=40
ε′′=20
ε′′=0
ε′=1
ε′=10
ε′=30
ε′=80
ε′
(b)
Fig. 3. (a) Cross section of utilized patch sensing element and (b) equivalent
patch capacitance and conductance from EM simulations (solid lines) and
RFM model (dots) for various values of
0
and
00
at f = 1 GHz.
TABLE I
PARAMETERS OF LINEAR -TO-Y MODEL
Parameter Value
C
0
82.56 f F
α
r
2.745 f F
1
α
i
17.5 µS
1
· GHz
1
patch node can be expressed as a parallel combination of a material-
dependent admittance Y
MU T
G
MU T
(
00
) + jωC
MU T
(
0
) and the
baseline admittance Y
0
= jωC
0
, yielding Y
P
= Y
0
+ Y
MU T
.
In order to quantify the permittivity-to-admittance behavior of
the patch, a 3D model of a 100×100µm
2
patch on a realistic
representation of the available 40-nm CMOS stack, in direct contact
with a MUT, was simulated versus varying
0
and
00
. The solid lines
in Fig. 3b show the capacitance and conductance of node P versus
0
and
00
, for different values of
00
and
0
, respectively, at a simulation
frequency of 1 GHz. An explicit relation of capacitance to
0
and
conductance to
00
exists that can be linearly approximated by
Y
P
(
0
,
00
, ω) α
i
· ω ·
00
+ jω ·
C
0
+ α
r
0
, (1)
where α
r
and α
i
are real parameters. Note that the ω contribution in
the real part of the admittance results from the fact that conductivity
of the material is given by σ = ω
00
[27]. Table I summarizes the
parameters of the model in (1) extracted after least square fitting with
the EM-simulated curves.
Although the linear model is simple, intuitive and useful for
preliminary analysis, it is clear from the simulated results of Fig. 3b
that G
MU T
and C
MU T
also vary with
00
and
0
, respectively, an
effect not captured by (1). For the purpose of calibration, a rational
function model (RFM), fitted from EM simulations, can be used
to arrive to an analytical model, a methodology widely used in
permittivity measurements performed with open-ended coaxial probes
[13], [28], [29]:
Y
P
(
?
, ω) jωC
0
+
N
P
n=1
P
P
p=1
α
np
?
p
(jωa)
n
1 +
M
P
m=1
Q
P
q=1
β
mq
?
q
(jωa)
m
, (2)
Y
0
Y
0
Y
0
Y
0
+ Y
L
υ
b,o+
υ
b,o-
υ
i
Driver
υ
gen,n
Bridge
υ
dr,n
C
0
G
0
Δυ
b,o
υ
gen,n,o
υ
dr,n,o
υ
th,n,o
υ
gen,n,o
υ
dr,n,o
υ
th,n,o
υ
in
Fig. 4. Balanced impedance bridge, driven at RF frequency by a driver, with
annotated signals and noise sources contributing to the total noise at the output
of the bridge.
where a is a scaling parameter, set equal to the patch dimension,
and α
np
, β
mq
are N × P and M × Q real model parameters,
respectively. In order to find the parameters, eq. (2) is fitted with
parametric EM simulations across
0
,
00
and frequency. A fitted
model with N = P = M = Q = 4 is deemed sufficient since it
already achieves 1% maximum deviation from simulations over a
0.1-10 GHz frequency range.
B. RF Impedance Bridge
Following the established analytical -to-Y model for the patch,
a method of reading out the admittance is required. A Wheatstone
bridge [30], [31] is a widely adopted method of measuring or sensing
electrical impedance since it offers a quantification of impedance
variation relative to a constant baseline value, such as C
0
in the
case of the patch sensor. At RF frequencies, impedance bridges
have been widely used in broadband vector network analysis as
directional detection elements, as an alternative or complementary
to bi-directional couplers [32].
In this subsection, an alternative analysis of the AC-driven Wheat-
stone bridge with complex branch loads is presented. A mathematical
manipulation of the bridge equation is performed to extract useful
information for the calibration of the sensor. This analysis is later
verified by measurements of various known RF impedances in a
probed measurement environment. Moreover, the bridge output noise
is calculated to extract information about the minimum detection
limit.
1) Bridge Analysis: Consider the RF impedance bridge shown
in Fig. 4 with branch admittances Y
0
and the load measurand Y
L
deviating from a baseline admittance Y
0
. The bridge is excited at
a given frequency ω with a signal of amplitude v
in
, through bridge
driver that amplifies a signal v
i
of the same frequency. The differential

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. XX, NO. X, MONTH 2017 4
output voltage of the bridge can be found after straightforward circuit
analysis:
v
b,o
= v
b,o+
v
b,o
= v
in
·
Y
L
4Y
0
+ 2Y
L
, (3)
where Y
L
= G
L
+ jB
L
and Y
0
= G
0
+ jB
0
are the generic com-
plex representation of the admittances. A common approximation
is that, for small variations of the measured load admittance, i.e.
G
L
<< G
0
and B
L
<< B
0
, equation (3) denotes that the output
varies linearly with the measured load admittance:
v
b,o
v
in
·
Y
L
4Y
0
(4)
This approximation, however, can result in large errors in the
estimation of Y
L
. A more generic result that accounts for any value of
measured load is possible, irrespective of how much it unbalances the
bridge and without requiring any approximations. Indeed, assuming
that Y
L
6= 0, inverting (3) results in
1
v
b,o
=
1
v
in
2 +
4Y
0
Y
L
. (5)
Substituting for Y
0
and Y
L
yields
<
1
v
b,o
=
1
v
in
(2 + 4G
0
· G
Lw
+ 4B
0
· B
Lw
) (6)
and
=
1
v
b,o
=
4
v
in
(B
0
· G
Lw
G
0
· B
Lw
) , (7)
where G
Lw
:
= G
L
/|Y
L
|
2
and B
Lw
:
= B
L
/|Y
L
|
2
are defined as
the weighted load conductance and susceptance values, respectively.
Therefore, irrespective of deviation of Y
L
from Y
0
, the real and
imaginary part of the inverse bridge differential output are linear
combinations of the weighted load conductance and susceptance.
Formulating the bridge behavior as in (6) and (7) allows to present
a linear relation between an output quantity (inverse of output)
to the input quantity (weighted conductance and susceptance). In
this manner, an intuitive calibration procedure can be obtained that
is closer to the bridge operation, rather than utilizing high-order
polynomial fitting [18], [20], [21]. The calibration procedure is
described in detail in section IV-A.
2) Bridge Noise: In order to calculate the noise at the output of
the bridge, we can break it down into three uncorrelated components
shown in Fig. 4: thermal noise generated by the bridge resistive
elements (v
th,n
), flicker, shot and thermal noise generated by any
internal active elements driving the bridge (v
dr,n
), and input noise
to the bridge driver originating from the RF signal generator, either
external or internal (v
gen,n
). By applying superposition, the contri-
bution of each component to the output noise can be analyzed. The
total noise is thus the mean-square sum of these three components:
v
n,o
2
= v
2
th,n,bo
+ v
2
dr,n,o
+ v
2
gen,n,o
.
The thermal noise power at the differential output of the bridge is
given by
v
2
th,n,o
= 4kT
ω+∆ω/2
Z
ωω/2
<
1
4Y
0
+ Y
L
· (8)
= 4kT
ω+∆ω/2
Z
ωω/2
4G
0
+ G
L
(4G
0
+ G
L
)
2
+ (4B
0
+ B
L
)
2
· , (9)
where ω is the observation bandwidth. Since the complex per-
mittivity is translated to conductance and capacitance, the bridge
susceptance will essentially be that of a capacitance, i.e. B = ωC. In
addition, the observation bandwidth is typically much smaller than
RMS Noise
Power
Total
1
Thermal
External
1
Total
2
External
2
IPN
2
>IPN
1
Δυ
b,o,t1
Δυ
b,o,t2
Δυ
b,o
(log)
Fig. 5. Thermal and external noise contributions to the bridge output noise
versus bridge differential output voltage for different level of integrated phase
noise of the external source.
the frequency of interest (ω << ω) and thus we can safely neglect
the frequency variation of the integrated quantity:
v
2
th,n,o
4kT
4G
0
+ G
L
(4G
0
+ G
L
)
2
+ ω
2
(4C
0
+ C
L
)
2
ω. (10)
As will be analyzed in section III-C, a clipping buffer is used as the
bridge driver. Assuming a quiet power supply, the contribution of
noise from the bridge driver is in the form of cyclo-stationary phase-
modulated (PM) noise that results from up-conversion of thermal and
flicker noise to the frequency of operation [33]. This noise will be
scaled by the bridge similarly to the bridge drive signal v
in
and can,
therefore, be expressed as a function of the single-side-band (SSB)
phase noise of the driver, L
dr
, and the differential output (v
b,o
) of
the bridge:
v
2
dr,n,o
= 2
Z
ω
0
10
L
dr
(ω)/10
· v
2
b,o
· = IP N
dr
· v
2
b,o
, (11)
where IP N
dr
is the integrated phase noise of the driver up to the
measurement bandwidth ω. Similarly for the external generator
noise, any amplitude-modulated (AM) component is suppressed by
the buffer, but the PM noise will be propagated to the bridge through
a phase noise transfer of unity, since any timing variation in the input
of the switching buffer will be transferred directly to its output. As
a consequence, the contribution of the generator noise to the output
of the bridge can be expressed, identically to (11), as
v
2
gen,n,o
= IPN
gen
· v
2
b,o
, (12)
where IP N
gen
is the double sideband (DSB) integrated phase noise
of the generator within the measurement bandwidth ω.
Notice from (11) and (12) that the noise components related
to the bridge drive are proportional to the output power, which
suggests that the more balanced the bridge is, the less the external
noise contribution to the output. These contributions can be grouped
together into what we can call external noise contributions. Fig. 5
shows how the two noise contributions (thermal and external) will
vary versus the bridge output voltage. The total noise power, being
the mean-square sum of the two, is dominated by the external sources
when the bridge is unbalanced and is limited by the thermal noise
level when the bridge is close to balanced state. The transition point
between the two dominant noise regimes is denoted as v
b,o,t
in
Fig. 5 and is closer to the balanced state for an external source with
higher IPN.
In practice, the total noise is in many cases dominated by
the external sources since the phase noise levels of buffers and
generators are much higher than the thermal noise level of the
bridge, even for small bridge output voltages. As an example,
consider a realistic case of the RF bridge as in Fig. 4, with
G = 1 mS, C = 100 fF , G
L
= 0.01 mS and C
L
= 1 fF (1%
imbalance), driven at 1 GHz (ω = 2π · 1 G · rad/s) with an am-
plitude of v
in
= 1 V and read out at an observation time of 1 ms

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  • ...appearing from the driving buffer [5]....

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Abstract: We report on the development of a method for measuring the permittivity and conductivity of fluids inside a sealed tank (or a pipe) by using an embedded coaxial probe. Permittivity and conductivity in the frequency range 600 MHz to 6 GHz are determined from measurements of a complex reflection coefficient by using a vector network analyser (VNA) that is connected to the embedded probe via a coaxial cable. Substitution methods for calibration of an inaccessible probe are studied in this paper. These require the VNA with attached cable to be calibrated prior to connecting the cable to the embedded coaxial probe. Measurement of permittivity and conductivity of fluids inside sealed tanks and pipes is needed for monitoring industrial processes, such as fermentation. The authors’ requirement, however, was to allow monitoring of a tissue-equivalent liquid that is contained inside a sealed tank. This tank is a component of a commercial system for rapid, multiple-band measurement of the specific absorption rate (SAR) of mobile phone handsets. Monitoring of permittivity and conductivity is needed to ensure compliance with international standards for SAR measurement. The paper also presents data for a new broadband (600 MHz to 6 GHz) tissue-equivalent liquid that is based on an oil-in-water emulsion. It is demonstrated that over an extended period of time, the liquid is stable, and an embedded coaxial probe enables its properties to be monitored with the required accuracy.

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Proceedings ArticleDOI
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References
More filters
Journal Article
TL;DR: This expanded and thoroughly revised edition of Thomas H. Lee's acclaimed guide to the design of gigahertz RF integrated circuits features a completely new chapter on the principles of wireless systems.
Abstract: 53 ■ IEEE CIRCUITS & DEVICES MAGAZINE ■ NOVEMBER/DECEMBER 2005 THE DESIGN OF CMOS RADIOFREQUENCY INTEGRATED CIRCUITS, 2ND ED By Thomas Lee, Cambridge University Press, 2003. All-CMOS radio transceivers and system-on-a-chip are rapidly making inroads into a wireless market that, for years, was dominated by bipolar solutions. On wireless LAN and Bluethooth, RF CMOS is especially dominant, and it is becoming also in GSM cellular and GPS receivers. Hence, books that cover this widespread domain respond to a real need. The first edition of this book, published on 1998, was a pioneering textbook on the field of RF CMOS design. This second edition is a very interesting and upgraded version that includes new material and revised topics. In particular, it now includes a chapter on the fundamentals of wireless systems. The chapter on IC components is greatly expanded and now follows that on passive RLC components. The chapter on MOS devices has been updated since it includes the understanding of the model for the shorth-channel MOS and considers and discusses the scaling trends and its impact on the next several years. It has also expanded the topic of power amplifiers; indeed, it now also covers techniques for linearization and efficiency enhancement. Low-noise amplifiers, oscillators, and phase noise are now expanded and treated with more detail. Moreover, the chapter on transceiver architectures now includes much more detail, especially on direct-conversion architecture. Finally, additional commentary on practical details on simulations, floorplanning, and packaging has been added. The first edition of this book widely covered all the main arguments needed in the CMOS design context and provided a bridge between system and circuit issues. This second edition, which is upgraded and improved, is really useful, both in the industry and academia, for the new generation of RF engineers. Indeed, it is suited for students taking courses on RF design and is a valuable reference for practicing engineers. Of course, the arguments treated in the textbook lead up to low-frequency analog design IC topics. Hence, readers have to be intimately familiar with that subject. The book is divided into 20 chapters: 1) A Nonlinear History of Radio 2) Overview of Wireless Principles 3) Passive RLC Networks 4) Characteristics of Passive IC Components 5) A Review of MOS Device Physics; 6) Distributed Systems 7) The Smith Chart and S-Parameters 8) Bandwidth Estimation Techniques 9) High-Frequency Amplifier Design 10) Voltage References and Biasing 11) Noise 12) LNA Design 13) Mixers 14) Feedback Amplifiers 15) RF Power Amplifiers 16) Phase Locked Loop 17) Oscillators and Synthesizers 18) Phase Noise 19) Architectures 20) RF Circuits Through the Ages. Moreover, it contains over 100 circuit diagrams and many homework problems. Gaetano Palumbo

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"A 40-nm CMOS Complex Permittivity S..." refers background in this paper

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TL;DR: The dielectric properties of tissues have been extracted from the literature of the past five decades and presented in a graphical format to assess the current state of knowledge, expose the gaps there are and provide a basis for the evaluation and analysis of corresponding data from an on-going measurement programme.
Abstract: The dielectric properties of tissues have been extracted from the literature of the past five decades and presented in a graphical format. The purpose is to assess the current state of knowledge, expose the gaps there are and provide a basis for the evaluation and analysis of corresponding data from an on-going measurement programme.

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"A 40-nm CMOS Complex Permittivity S..." refers background in this paper

  • ...Note that the ω contribution in the real part of the admittance results from the fact that the conductivity of the material is given by σ = ω ′′ [27]....

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Book
05 Jun 2012
TL;DR: In this article, the authors present an expanded and thoroughly revised edition of Tom Lee's acclaimed guide to the design of gigahertz RF integrated circuits, which is packed with physical insights and design tips, and includes a historical overview of the field in context.
Abstract: This book, first published in 2004, is an expanded and thoroughly revised edition of Tom Lee's acclaimed guide to the design of gigahertz RF integrated circuits. A new chapter on the principles of wireless systems provides a bridge between system and circuit issues. The chapters on low-noise amplifiers, oscillators and phase noise have been significantly expanded. The chapter on architectures now contains several examples of complete chip designs, including a GPS receiver and a wireless LAN transceiver, that bring together the theoretical and practical elements involved in producing a prototype chip. Every section has been revised and updated with findings in the field and the book is packed with physical insights and design tips, and includes a historical overview that sets the whole field in context. With hundreds of circuit diagrams and homework problems this is an ideal textbook for students taking courses on RF design and a valuable reference for practising engineers.

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TL;DR: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed and appropriate Cramer-Rao bounds and maximum-likelihood estimation algorithms are derived.
Abstract: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.

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"A 40-nm CMOS Complex Permittivity S..." refers methods in this paper

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"A 40-nm CMOS Complex Permittivity S..." refers background in this paper

  • ...To highlight a few examples, in agriculture, the complex permittivity of fruits and vegetables has been correlated with changes in temperature, water, and inorganic material content [1]–[3], while in the automotive industry, it is the preferred...

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Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "A 40–nm cmos complex permittivity sensing pixel for material characterization at microwave frequencies" ?

Implemented in 40-nm CMOS, the architecture comprises a square patch, interfaced to the material-under-test ( MUT ) sample, that provides permittivity-dependent admittance.