# Joint Design of Self-Tuning UHF RFID Antenna and Microfluidic Channel for
Liquid Sensing

Giulio Maria Bianco, and Gaetano Marrocco Paper supported by Project ECS
0000024 Rome Technopole, CUP B83C22002820006, NRP Mission 4 Component 2
Investment 1.5, Funded by the European Union – NextGenerationEU. Rome
Technopole Projects: ”Next-gen point of cares: chemical-physical sensors with
wireless interface for health monitoring in domestic settings” (Spoke 1;
Flagship Project 7) and ”Eco-friendly Electronic Labels for Food and Plastic
Waste” (Spoke 2; Flagship Project 3).G. M. Bianco is with the Department of
Civil Engineering and Computer Science Engineering, the University of Rome Tor
Vergata, Rome, Italy; e-mail<EMAIL_ADDRESS>Marrocco is
with the Department of Civil Engineering and Computer Science Engineering, the
University of Rome Tor Vergata, Rome, Italy.Manuscript received Month XX,
20XX; revised Month XX, 20XX.

###### Abstract

Microfluidic has been an enabling technology for over a decade, particularly
in the field of medical and wearable devices, allowing for the manipulation of
small amounts of fluid in confined spaces. Micro-channels can also be used for
wireless sensing thanks to the variations in antenna properties when the fluid
flows near it. However, up to now, microfluidic channels and sensing antennas
have always been designed separately; instead, since the liquid flow and the
antenna geometry both contribute to the overall performance, they should be
considered simultaneously when optimizing the antenna-microfluidic system. In
this paper, the joint design of the antenna and microfluidic channels is
investigated for liquid quantification. Self-tuning RFID microchips are
exploited to minimize communication degradation due to the increase of lossy
liquid amount over the sensing antenna while digitalizing the impedance
mismatch itself. To experimentally corroborate the joint design technique, two
different geometries are obtained and prototyped starting from a given
antenna-microfluidic layout by setting different goals for an optimization
function. The two flexible RFID prototypes returned performance in agreement
with the simulated ones, achieving a maximum sensitivity of about $20$ units
of the digital metric per milligram increase of water.

###### Index Terms:

Antenna systems, joint design, microfluidic, radio frequency identification,
self-tuning antennas, wireless sensing.

##  I Introduction

Microfluidic has been standing as one of the most impactful enabler
technologies for more than a decade, mostly thanks to the advancements in
medical and wearable devices [1]. Microfluidic channels allow for manipulating
a small amount of fluid in a confined space, the scale typically of a few to
hundreds of microliters, and they can be integrated into small devices for
performing even complex in-loco sensing [2], usually through electrochemical
sensors [3]. The adoption of microfluidic naturally involved wireless devices
in three main research paths: i) the development of antennas made of liquid
metal, usually exploiting microfluidic to achieve spatial reconfigurability
[4, 5, 6], and use of microfluidic ii) to acquire sensory data, eventually by
chemical reactions [7, 8, 9, 1], and iii) to produce variations in the
antenna’s properties for sensing scopes [10, 11, 12].

Concerning liquid and humidity sensing, remote monitoring based on variations
in antennas’ properties has been extensively investigated in recent years as
well, especially by means of RFID (radiofrequency identification) technology.
Several chipped [13, 14] and chipless [15, 16] solutions showed promising
sensitivity but suffered from a significant reduction in antenna gain and,
hence, in the reading distances. Thus, a peculiar kind of self-tuning RFID ICs
(integrated circuits) was proposed to complete sensing without sacrificing the
reading distances excessively [17]. Indeed, such microchips can compensate for
limited impedance mismatches and return a digital metric proportional to the
retuning effort.

Table I summarizes the main, recent papers on the joint use of antennas and
microfluidic including the maximum volume of liquid considered111When the
liquid volume was not reported directly in the reference, it was evaluated
from the geometrical parameters of the microchannel.. Although liquid sensing
is the main application of the research topic, the microfluidic subsystem has
always been considered divided from the microwave one so that one of the two
subsystems is designed only after having fixed the other. Therefore, the joint
design of the antenna and the microfluidic channels to achieve optimal
performance has never been investigated.

Figure 1:  Concept of a UHF RFID sensor-antenna with microfluidic for liquid quantification. The sensitive area of the system is constituted by the superposition of the microfluidic channel with the AA. TABLE I: Comparison between this research and recent works on microfluidic-antenna systems. Reference |  | Microfluidic role | Working | Maximum | Digitalized | Joint |
---|---|---|---|---|---|---|---
(Year) | Scope | (liquid quantity $\mu$L) | frequency | size | sensing | design | Description
This work | Remote sensing | Govern liquid |  |  $50$ mm $\times$ |  |  | Joint antenna-microfluidic
(2024) | (liquid quantity) |  flow ($1050$) |  $925$ MHz |  $20$ mm | Yes | Yes | design to govern performance
[18] | Remote sensing | Govern |  $3.12$ GHz to |  $140$ mm $\times$ |  |  | Metamaterial sensor for remote
(2022) | (water salinity) |  liquid flow ($6$) |  $3.59$ GHz |  $160$ mm | No | No | sensing of water salinity levels
[10] | Remote sensing | Govern |  $2.9$ GHz and |  $14$ mm $\times$ |  |  | Harmonic-based sensor with
(2020) | (liquid quantity) |  liquid flow ($630$) |  $5.7$ GHz |  $6$ mm | No | No | a micromachined liquid channel
[19] | Remote sensing | Govern |  $8.8$ GHz to |  $5$ mm $\times$ |  |  | Microwave-integrated sensor for
(2016) | (liquid characterization) |  liquid flow ($7$) |  $9.0$ GHz |  $12$ mm | No | No | liquid sample characterization
[11] | Remote sensing | Govern |  $4.2$ GHz to |  $13$ mm $\times$ |  |  | Substrate-integrated waveguide
(2016) | (ethanol quantity) |  liquid flow ($1$) |  $4.6$ GHz |  $19$ mm | No | No | for chemical sensing
[20] | Remote | Govern |  $840$ MHz to |  $95$ mm $\times$ |  |  | Biosensor with microfluidic
(2016) | biosensing |  liquid flow ($120$) |  $960$ MHz |  $8$ mm | No | No | and self-assembling antennas
[21] | Reconfigurable | Change |  $3.7$ GHz and |  $40$ mm $\times$ |  |  | Self-diplexing antenna based on
(2023) | antenna |  frequency ($75$) |  $5.9$ GHz |  $40$ mm | - | No | air- and liquid-filled pockets
[22] | Reconfigurable | Reconfiguring meta- |  $8$ GHz to |  $200$ mm $\times$ |  |  | Reconfigurable metasurface
(2022) | metamaterial |  metamaterial ($24375$) |  $13$ GHz |  $200$ mm | - | No | based on liquid metal injection
[23] | Reconfigurable | Reconfiguring |  $32$ GHz to |  $45$ mm $\times$ |  |  | Reconfigurable antenna
(2021) | antenna |  antenna ($703$) |  $35$ GHz |  $20$ mm | - | No | with fluidically-loaded lens
[24] | Reconfigurable | Reconfiguring |  $8$ GHz to |  $40$ mm $\times$ |  |  | Liquid metal alloy and micro-
(2021) | array |  metasurface ($216$) |  $32$ GHz |  $40$ mm | - | No | fluidics for a metasurface
[25] |  | Feed network |  |  $3$ mm $\times$ $2$ mm |  |  | Microfluidically-switched feed
(2018) | Beam steering |  switching ($395$) |  $30$ GHz | (single element) | - | No | for beam-steering

In this work, we propose a global design technique wherein the geometrical
parameters of the channel and those of the antenna are simultaneously
optimized by numerical simulations to quantify a liquid volume. Indeed, liquid
sensing is based on the flow of the liquid onto the antenna so that the
electromagnetic variations will be a function of the geometrical parameters of
both the antenna and the microfluidic shape. The gain degradation expected by
the liquid’s absorption of electromagnetic waves and the antenna detuning is
minimized thanks to a self-tuning UHF (ultra-high frequency) RFID IC.
Moreover, the flow of the liquid is governed by a microfluidic channel
superimposed on the AA (antenna impedance adapter) to dominate the detuning of
the antenna (Fig. 1). This sensing mechanism is digitalized and returned by
the IC, avoiding known issues in similar analog sensing approaches [26].
Accordingly, the joint design of the sensing antenna and the microfluidic
channel has to be conceived and validated to optimize the overall performance
of the system that is simultaneously function of both geometries.

The paper’s organization follows. Section II lists the most relevant symbols
used in this paper; afterwards, Section III recalls the known scientifical
background on the self-tuning RFID ICs and on microfluidics. The joint design
problem is formulated and then managed through a goal function in Section IV.
Section V presents a design example by numerical simulations, whereas the
relative experimental corroboration of the proposed design technique follows
in Section VI.

##  II Symbols

For the reader’s convenience, the most relevant symbols used in the remainder
of the paper are listed in this Section in order of appearance.

$C_{s}$ | Self-tuning capacitance step
---|---
$C_{0}$ | Self-tuning baseline capacitance
$C_{IC}\left(s\right)$ | Self-tuning overall capacitance
$s$ | Sensor code (SC)
$\omega$ | Frequency pulse
$B_{A}$ | Antenna susceptance
$s_{min}$ | Lowest value of the SC linear range
$s_{max}$ | Highest value of the SC linear range
$\Psi$ | Measurand
$\Delta s$ | Differential sensor code
$s_{0}$ | Reference value of the differential sensor code
$\boldsymbol{v}$ | Vector of variable geometrical parameters for the joint design
$a_{i}$ |  $i$-th variable geometrical parameter of the antenna
$c_{i}$ |  $i$-th variable geometrical parameter of the microfluidic channel
$\xi$ | Quantity of liquid in the microfluidic
$\xi_{0}$ | Unloaded condition of the microfluidic, viz., in the absence
| of liquid (initial state)
$\xi_{F}$ | Loaded condition of the microfluidic, viz., microfluidic filled
---|---
| with liquid completely (final state)
$F\left[\boldsymbol{v}\right]$ | Fitness function for the joint design, sum of $f_{i}\left[\boldsymbol{v}\right]$ functions
$w_{i}$ |  $i$-th weight of the fitness function $f_{i}\left[\boldsymbol{v}\right]$
$G_{\tau}\left(\xi\right)$ | Realized radiation gain in presence of liquid ($\xi$)
$S\left[\boldsymbol{v}\right]$ | Sensitivity of the antenna-microfluidic system
$c_{1}$ | Thickness of the microfluidic
$\varepsilon$ | Dielectric constant
$\tan\delta$ | Loss tangent
$a_{1}$ | Side of the $\Gamma$-match transformer parallel to the IC
$a_{2}$ | Side of the $\Gamma$-match transformer perpendicular to the IC
$c_{2}$ | Width of the microfluidic channel
$a_{3}$ | Width of the antenna’s conductor trace
$G_{IC}$ | Conductance of the integrated circuit
$c_{3}$ | Side of the microfluidic parallel to the IC
$c_{4}$ | Step of the microfluidic serpentine
$\rho_{l}$ | Density of the fluid

##  III Background

###  III-A Self-tuning RFID ICs

Self-tuning microchips modify their internal capacitance to maximize the power
delivered by the harvesting antenna to the IC itself [17, 27]. By assuming a
constant incremental step $C_{s}$ and denoting the baseline capacitance
$C_{0}$, they are modelled as a resistance in parallel to the variable
capacitance $C_{IC}\left(s\right)$ where $s$ is named _sensor code_ (SC),
which is an adimensional digital unit. The self-tuning equation determines the
actual value of $C_{IC}$ based on the frequency pulse $\omega$ and the antenna
susceptance $B_{A}$

$\left|\omega C_{IC}\left(s\right)+B_{A}\right|=0.$ (1)

Equation (1) is fully valid for a microchip-dependent SC range $s_{min}\leq
s\leq s_{max}$. If the antenna susceptance is a function of a measurand
$\Psi$, the SC can be exploited for sensing through (1) [28]:

$s\left(\Psi\right)=\textnormal{nint}\left\\{-\frac{1}{C_{s}}\left[C_{IC}\left(s_{min}\right)+\frac{B_{A}\left(\Psi\right)}{\omega}\right]\right\\}.$
(2)

Measurand-independent baselines can be removed by resorting to the
_Differential sensor code_ ($\Delta s$) w.r.t. a reference value $s_{0}$ [28].

###  III-B Microfluidic Channels

Microfluidic is a topic of research in the manipulation of microliters,
encompassing theoretical physics, numerical methods, fabrication, and
deployment [29]. Hereafter, the particular case of capillary pumps is
exploited. Capillary pumps are microchannels placed horizontally wherein the
liquid propagates by capillarity, and since there is no opposition from
gravity, the (ideal) capillary flow continues until the channel is completely
traversed thanks to the capillary forces [30]. In real microfluidic, hydraulic
resistances caused by the interaction with the channel’s walls oppose the
capillary rise, and the liquid will also flow downward due to gravity if it is
not opposed by any solid surface [30] (Fig. 2). Specifically, in this work, we
consider Whatman CF$4$ paper which tends to have variable flow rates due to
the structure of the paper fibers so that fixed liquid quantities might flow
to different positions each time.

Figure 2: Model of the fluid diffusion in paper-based microfluidic.

##  IV Joint Antenna-Microfluidic Design

In this section, the joint design technique is introduced and addressed
through a goal function.

###  IV-A Problem Formulation of the Joint Design

The goal of the joint design of the antenna and the microfluidic is, hence, to
quantify a small volume of water having the order of magnitude of a few
microliters while ensuring a stable reading range of the RFID sensor. To
achieve this objective, a self-tuning RFID IC and microfluidic channels can be
employed. Then, the problem is formulated as the optimal design of the
antenna-microfluidic pair to _i_) minimize the performance degradation due to
the increasing, lossy liquid, and _ii_) maximize the sensitivity of the
antenna’s response to the liquid quantity.

Let us assume that the antenna and microfluidic channels, including the
materials and placement of the RFID sensor, are parametrized by a vector of
variable geometrical parameters $\boldsymbol{v}$

$\boldsymbol{v}=\left\\{a_{1},...,a_{N},c_{1},...,c_{M}\right\\}$ (3)

where $\left\\{a_{1},...,a_{N}\right\\}$ are the antenna’s parameters, whereas
$\left\\{c_{1},...,c_{M}\right\\}$ are the microfluidic channels’ ones. The
hyperspace $\left\\{a_{1,min}\leq a_{1}\leq a_{1,max},...,c_{M,min}\leq
c_{M}\leq c_{M,max}\right\\}$ to be explored for finding the best solution is
naturally delimited by size and manufacturing constraints.

Therefore, the liquid quantity $\xi$ increases with time between the starting
and final instances of the phenomenon to be monitored. Hence,

$\xi_{0}<\xi<\xi_{F}$ (4)

being $\xi_{0}$ and $\xi_{F}$ the conditions of channel fully free and filled
with liquid, respectively. When the liquid increases, the susceptance’s
variations must be monotonic to perform sensing by self-tuning correctly

$\begin{split}B_{A}\left(\xi_{0}\right)<B_{A}\left(\xi\right)<B_{A}\left(\xi_{F}\right)\veebar\\\
B_{A}\left(\xi_{0}\right)>B_{A}\left(\xi\right)>B_{A}\left(\xi_{F}\right)\end{split}$
(5)

where $\veebar$ is the XOR (exclusive or) boolean operator. This must be
imposed when selecting the general antenna-microfluidic geometry to be
optimized in the given parameters’ space.

###  IV-B Boundary Conditions and Goal Function

The optimal layout can be determined by considering the initial ($\xi_{0}$)
and final ($\xi_{F}$) states of the sensor. Then, the optimization problem can
be formalized as the maximization of a three-term _fitness function (F)_ as
follows

$F\left[\boldsymbol{v}\right]=\left\\{\begin{array}[]{ll}\left(\sum_{i=1}^{3}w_{i}\right)^{-1}\sum_{i=1}^{3}w_{i}f_{i}\left[\boldsymbol{v}\right]\\\
\textnormal{if}\quad\left(f_{1}\land f_{2}\land f_{3}\right)\neq 0\\\
0\qquad\textnormal{elsewhere}\end{array}\right.$ (6)

where $\land$ is the AND boolean operator, and

$f_{1}\left[\boldsymbol{v}\right]=\left\\{\begin{array}[]{ll}\frac{s\left[\boldsymbol{v}\right]\left(\xi_{0}\right)}{s_{max}}\qquad\textnormal{if}\quad
s\left[\boldsymbol{v}\right]\left(\xi_{0}\right)\leq s_{max}\\\
0\qquad\textnormal{elsewhere}\end{array}\right.$ (7)
$f_{2}\left[\boldsymbol{v}\right]=\left\\{\begin{array}[]{ll}\frac{G_{\tau}\left[\boldsymbol{v}\right]\left(\xi_{0}\right)+G_{\tau}\left[\boldsymbol{v}\right]\left(\xi_{F}\right)}{2G_{0}}\\\
\textnormal{if}\quad\textnormal{min}\left(G_{\tau}\left[\boldsymbol{v}\right]\left(\xi_{0}\right),G_{\tau}\left[\boldsymbol{v}\right]\left(\xi_{F}\right)\right)\geq
G_{min}\\\ 0\qquad\textnormal{elsewhere}\end{array}\right.$ (8)
$f_{3}\left[\boldsymbol{v}\right]=\left\\{\begin{array}[]{ll}\frac{S\left[\boldsymbol{v}\right]}{S_{0}}\qquad\textnormal{if}\quad
S\left[\boldsymbol{v}\right]\geq S_{min}\\\
0\qquad\textnormal{elsewhere}\end{array}\right..$ (9)

The notation $s\left[\boldsymbol{v}\right]\left(\xi\right)$ indicates the
value of $s$ when the liquid in the channel is $\xi$ while considering the
$\boldsymbol{v}$ vector of parameters. $\left\\{w_{1},w_{2},w_{3}\right\\}$
are a set of weights, $S$ is the sensitivity, which is measured in SC units
over milligrams of liquid, $G_{\tau}\left(\xi\right)$ is the realized gain in
the presence of liquid’s volume $\xi$, $\left\\{G_{min},S_{min}\right\\}$ are
the minimum acceptable performance value that automatically discards solutions
if they are not met, and $S_{0}$ and $G_{0}$ are two normalization values such
that each addend of $F\left[\boldsymbol{v}\right]$ is comprised between $0$
and $1$. The sensitivity to the liquid quantity is defined as a function of
the overall weight of water in the sensitive area in loaded conditions
$\xi_{F}$

$S\left[\boldsymbol{v}\right]=\frac{\left|s\left[\boldsymbol{v}\right]\left(\xi_{F}\right)-s\left[\boldsymbol{v}\right]\left(\xi_{0}\right)\right|}{\xi_{F}\left[\boldsymbol{v}\right]}.$
(10)

The sub-term (7) imposes that the whole flow of interest is captured by the
antenna in the case of monotonically-decreasing susceptance222The case of
monotonically-increasing susceptance can be derived straightforwardly. so that
the dynamic range of the sensor is maximized, whereas the sub-term (8) imposes
a check on the reading distance of the RFID tag while the liquid increases.
The sensitivity to the liquid quantity, which depends on both the antenna
response and microfluidic geometry, is accounted for by (9) and (10). The
terms can be weighted according to the application’s needs. It is worth
highlighting that both the geometrical parameters of the antenna and
microfluidic affect all three fitness terms (7)-(9) due to the close
interrelationship between the microwave and the microfludic subsystems.

##  V Design Example

The joint design is demonstrated here with two antenna-microfluidic systems by
starting from the same general geometry and applying different weightings in
(6).

###  V-A System Layout and Parameters’ Space

(a) (b)

(c) (d)

Figure 3: System layout composed by an RFID sensor-antenna and microfluidic for liquid quantification. The sensitive area of the system is highlighted in red. (a) Exploded view with highlighted AA and $c_{1}$ parameter, and (b) above view with the highlighted sensitive area. Parametrization of the antenna-microfluidic system. (c) Geometrical parameters of the RFID antenna and the pair to be optimized $\left\\{a_{1},a_{2}\right\\}$. (d) Zoomed-in view of the system’s sensitive area and geometrical parameters of the microfluidic channels to be optimized $\left\\{c_{2},c_{3},c_{4}\right\\}$. $\left\\{a_{3},c_{1}\right\\}$ are fixed. TABLE II: Weights and parameters’ values. Geometry | $\mathbf{w_{1}}$ | $\mathbf{w_{2}}$ | $\mathbf{w_{3}}$ | $\mathbf{a_{1}}$ | $\mathbf{a_{2}}$ | $\mathbf{c_{2}}$ | $\mathbf{c_{3}}$ | $\mathbf{c_{4}}$
---|---|---|---|---|---|---|---|---
Sensitivity-opt. | $1$ | $1$ | $1$ | $0$ | $10.5$ | $2$ | $3$ | $0.3$
Gain-optimized | $0$ | $5$ | $1$ | $6$ | $5$ | $1.5$ | $9$ | $0$

The starting geometry and parameters’ space were selected by considering a
flexible RFID sensor for monitoring a small water content in a compact $50$ mm
$\times$ $20$ mm surface. The microfluidic has thickness $c_{1}=1$ mm and
comprises two identical ellipses (that are neglected in the electromagnetic
simulations) as collecting and waste pads’ sections and by a serpentine
passing on the antenna’s AA (Fig. 3(a,b)). In this example, the minimum volume
of liquid to be monitored is $10$ mm3 which is a microvolume suitable for
initiating monitoring the sweating rate during domestic fitness [31] depending
on the body area and exercise routine [32]. Ovoidal input and waste pads are
used as examples since the design of the pads to carry the liquid of interest
does not have any effect on the EM (electromagnetic) response of the antenna-
microfluidic system and it is, hence, outside the scope of this work.

The antenna geometry is a partially folded $\Gamma$-match dipole on a thin
layer of Kapton ($\varepsilon=3.5$, tan$\delta=0.0026$, thickness $0.125$ mm).
The antenna is made of a copper trace (thickness $35$ $\mu$m) and can host the
whole microfluidic within its area, including the collecting and waste pads.
The dipole length is such to match the conductance of the chosen self-tuning
IC (Magnus S3 by Axzon, conductance $G_{IC}=0.0482$ mS, capacitance ranging
between $1.9$ pF and $2.9$ pF).

The parameters’ space is such that the susceptance of the antenna moves around
the linear SC range at the working frequency of $925$ MHz, which is an
unlicensed UHF frequency commonly used for RFID applications in the United
States of America. The width of the microfluidic paper trace is also bound to
be larger than $0.5$ mm because of manufacturing constraints. The
parameterization of the whole antenna-microfluidic geometry is summarized in
Fig. 3(c,d). A $1$-mm gap hosts the IC, and the free parameters to be
optimized are the form factors of the $\Gamma$-match transformer
($\left\\{a_{1},a_{2}\right\\}$) and the microfluidic trace width ($c_{2}$),
whereas the copper trace width is fixed ($a_{3}=1$ mm) and the other variable
parameters of the microfluidic are functions of the free parameters as follows

$c_{3}=a_{1}+2a_{3}+1,$ (11)
$c_{4}=\max\left(0,\frac{a_{2}-a_{3}-0.5-4c_{2}}{3}\right).$ (12)

For $c_{4}=0$, the serpentine degenerates in a straight channel. Consequently,
given $\rho_{l}$ density of the fluid (for water, considered hereafter,
$\rho_{l}=1$ mg/mm3), the denominator in (10) is

$\begin{split}\xi_{F}\left[\boldsymbol{v}\right]=\min\\{\rho_{l}c_{1}c_{3}\left(a_{2}-a_{3}-0.5\right),\\\
\rho_{l}c_{1}c_{2}\left(4c_{3}+3c_{4}\right)\\}.\end{split}$ (13)

From (13), a suitable parameters’ space to monitor at least $10$ mm3 is given
by $0$ mm $\leq a_{1}\leq 8$ mm, $5$ mm $\leq a_{2}\leq 15$ mm, and $1$ mm
$\leq c_{2}\leq 2.5$ mm.

###  V-B EM Modeling of the Microfluidic

Hereafter, microfluidic is accounted for in electromagnetic models by an
increasing quantity of the fluid. The channel material and fluid dynamics are
assumed to be negligible; namely, the channel material does not significantly
affect the antenna’s susceptance, the transient regime of the liquid flow does
not interfere with the self-tuning mechanism of the IC, and the liquid front
propagates only along the direction of the microfluidics. These
simplifications are valid for a wide range of practical cases, like the use of
paper-based channels [33] for monitoring biological processes [34].

In the EM numerical simulations, therefore, the water ($\varepsilon=78$,
$\sigma=1.78$ S/m) fills the channel’s volume with a sharp liquid front. To
perform the simulation-measurement comparison of the filling percentage of the
channel despite the Whatman paper properties (Sec III-B), the weight of the
antenna-microfluidic system is used. The weight corresponding to the empty
channel was observed by adding water to the input pad until the sensitive
channel was reached; then, the weight corresponding to the $100\%$-filled
channel in the EM simulations was experimentally observed by adding more
liquid until a stationary value of the SC was achieved, viz., the lowest SC
level the system could return. Hence, the comparison between the simulated
(through liquid front) and measured (by weighting) filling percentages could
be drawn.

###  V-C Numerical Optimization

TABLE III: Simulated antenna performance. The normalization values are $G_{0}=2.50$ dBi and $S_{0}=19.4$ $\textnormal{mg}^{-1}$. Geometry | $\mathbf{F}$ | $\mathbf{f_{1}}$ | $\mathbf{f_{2}}$ | $\mathbf{f_{3}}$ | $\mathbf{s_{u}}$ | $\mathbf{s_{u}-s_{l}}$ |  $\mathbf{S}$ $\left[\mathbf{mg^{-1}}\right]$ |  $\mathbf{G_{\tau}\left(\xi_{0}\right)}$ [dBi] |  $\mathbf{G_{\tau}\left(\xi_{F}\right)}$ [dBi] |  $\mathbf{\Delta G_{\tau}}$ [dB]
---|---|---|---|---|---|---|---|---|---|---
Sensitivity-opt. | $0.83$ | $0.98$ | $0.50$ | $1.00$ | $501$ | $501$ | $19.4$ | $-0.8$ | $-11.8$ | $-11.0$
Gain-optimized | $0.66$ | $0.24$ | $0.77$ | $0.15$ | $121$ | $94$ | $3.0$ | $-1.0$ | $-2.3$ | $-1.3$
Figure 4: Flowchart detailing the two-step hierarchical grid search performed.
$\left\\{a_{1,O1},a_{2,O1},c_{2,O1}\right\\}$ are the optimum values of the
$\left\\{a_{1},a_{2},c_{2}\right\\}$ triplet found in the first search, and
$\left\\{a_{1,O2},a_{2,O2}\right\\}$ are the values of
$\left\\{a_{1},a_{2}\right\\}$ refined in the second grid search.

(a) (b)

Figure 5: Numerical optimization for the two different geometries to be
designed: (a) sensitivity-optimized and (b) gain-optimized. For each geometry
are shown, from the top to the bottom: the parameters’ space with the goal
function values evaluated in the points of the hierarchical grid and the
$c_{2}$ value of the optimal solution highlighted; the slice including the
best solution; the exploded numerical model of the antenna-microfluidic
system, omitting the antenna substrate and the ovoidal input and waste pads of
the microfluidic.

Simulated radiation gain, power transfer coefficient, realized gain and
differential SC

Figure 6: Simulated performance of the two layouts when increasing the filling
percentage of the sensitive areas. The numerical models of the loaded
sensitive areas are reported in the insets and are based on experimental
observation (see next Fig. 10).

Two geometries were jointly designed by using different sets of weights, and
they are hereafter referred to as (i) ” _sensitivity-optimized_ ” and (ii) ”
_gain-optimized_ ” solutions (Table II). The two different sets of weights
$\left\\{w_{m}\right\\}$ were considered to optimize the sensitivity in the
continuous detection of liquid (sensitivity-optimized layout) and preserve the
antenna gain and, consequently, the reading distance by accepting a lower
sensitivity (gain-optimized layout). As shown in the following, the second
setting will be suitable as a threshold sensor.

The parameters’ space was searched by using a hierarchical grid search, which
is a largely employed technique to address nonlinear problems in low-
dimensional spaces like the one under analysis [35, 36, 37]. The hierarchical
grid can be finely refined through subsequent searches near the area of the
maximum found value. For each optimization round, numerical simulations were
completed by using CST Microwave Studio Suite 2023 (frequency-domain solver,
single-frequency simulations), and then the results were given as input to a
Matlab R2022b script to perform the hierarchical grid search. The values
$\left\\{G_{0},S_{0}\right\\}$ were updated at each optimization round and set
to their maximum found on the grid. For the sake of completeness, the minimum
values to be met by the solutions in (8) and (9) were
$\left|G_{min}\right|=\left|S_{min}\right|=0$, thus making all explored
geometries acceptable. Fig. 4 details the two-step hierarchical grid used to
find the final antenna-microfluidic systems. In the end, the optimal
geometries were further assessed through a multi-frequency simulation covering
the frequency range $850-1050$ MHz to validate the joint design.

The numerical results of the joint design procedure for the two geometries are
reported in Fig. 5. From Table II, it is possible to see that the sensitivity
term in (9) has the highest impact on the overall value
$F\left[\boldsymbol{v}\right]$. The two antenna-microfluidic geometries differ
from each other and return performances in agreement with the design goals
(Table III). The sensitivity-optimized geometry returns $S\sim 20$ mg-1 at the
cost of a progressive reduction of the antenna gain while the serpentine is
being filled with liquid. Instead, the gain-optimized geometry keeps the
antenna gain near invariable (Fig. 6), achieving a
$G_{\tau}\left(\xi_{F}\right)$ value $9.5$ dB higher than the one of the
sensitivity-optimized layout, whereas the sensor-code changes only when the
filling percentage of the sensitive channel exceeds $75\%$ of the maximum
value and, hence, the device can be considered as a threshold sensor capable
of discriminating between the unloaded and nearly-fully-loaded microfluidic.

##  VI Prototypation and Measurements

(a) (b) (c)

(d) (e) (f)

Figure 7: Prototypes of the two antenna-microfluidic systems. Sensitivity-
optimized layout: (a) RFID antenna, (b) microfluidic channel, and (c) whole
system. Gain-optimized layout: (d) RFID antenna, (e) microfluidic channel, and
(f) whole system. Figure 8: Electromagnetic measurements of the antenna-
microfluidic system compared with the simulated ones (average over $5$
measurements). The working frequency of $925$ MHz is highlighted by a vertical
line and the standard deviation is not reported if it is lower than $0.5$ dB.

The two prototypes were fabricated by using a $35$-$\mu$m-thick copper layer
attached to a Kapton film as in the simulations and, then, cut by a milling
machine ($4$MILL$300$ATC by Mipec [38]). Based on the authors’ prior
experience with filter papers [7, 9] and the preliminary investigation we
reported in [39], the microfluidic was manufactured by manually superposing
two identical layers of Whatman CF$4$ filter paper (from [40]; single-layer
thickness at $53$ KPa: $482$ $\mu$m: water absorption: $49.9$ mg/cm2).

The filter paper was cut through a $40$W USB CO$2$ Laser Engraving Machine
Cutter (by Vevor [41]) having a position accuracy of $10$ $\mu$m and engraving
precision of $2500$ dpi. The designed microfluidic channel was connected to
two identical and ellipsoidal input and waste pads. The microfluidic was fixed
to the Kapton substrate by using a thin polypropylene tape without contacting
the conductor trace in any point since similar arrangements are known not to
alter the self-tuning sensing [17]. For the measurements, four antenna
prototypes (two per geometry) and twenty-two layers of filter paper (i.e.,
eleven double-layer microfluidic channels per geometry) were employed. Each
paper layer was cut by the laser cutter, and, by superimposing two layers, one
microfluidic prototype was obtained; then, the double-layer microfluidic
channels were utilized for single-use, whereas the antennas were not affected
from usage and could be used again after replacing the microfluidic channel
and some minutes of dry time. The antenna-microfluidic prototypes are shown in
Fig. 7.

As the first test, the realized gain was measured through a Tagformance
station (by Voyantic; linearly-polarized interrogation antenna AN-FF-WB; $55$
cm of interrogation distance) in the extreme conditions of unloaded and loaded
tags. Good agreement and stability were observed between measurements and
simulations in both conditions (Fig. 8), allowing for a theoretical reading
range $>1$ m when interrogating the tags with a circularly-polarized antenna
and $1$ W EIRP. Notably, the gain-optimized geometry achieves gain degradation
of just $\Delta G_{\tau}\simeq-1$ dB between the two boundary conditions in
contrast with a degradation $\Delta G_{\tau}\simeq-10$ dB in the case of the
sensitivity-optimized system layout.

Figure 9: Experimental set-up for the sensor code measurements with the highlighted reader-tag distance of $1$ m. |  |  |  |
---|---|---|---|---
$0\%$ | $25\%$ | $50\%$ | $75\%$ | $100\%$
|  |  |  |
Figure 10: Visual examples showing of the progression of coloured water into
the microfluidics sensitive channel (filling percentage) of the sensitivity-
optimized (above) and the gain-optimized (below) layouts.

(a)

(b)

Figure 11: Comparison between the simulated and measured $\Delta s$ values of the two geometries: (a) sensitivity-optimized and (b) gain-optimized. Cubic polynomial trend lines fitting the data read from the intermediate distance ($50$ cm) are reported with the corresponding R2 values. TABLE IV: Measured (meas.) performance of the prototypes and absolute value of the difference (diff.) with the simulated values. The measurements are averaged on the three reading distances. | $\mathbf{s_{u}}$ | $\mathbf{s_{u}-s_{l}}$ |  $\mathbf{S}$ $\left[\mathbf{mg^{-1}}\right]$ | $\mathbf{G_{\tau}\left(\xi_{0}\right)}$ | $\mathbf{G_{\tau}\left(\xi_{F}\right)}$ | $\mathbf{\Delta G_{\tau}}$
---|---|---|---|---|---|---
Geometry | Meas. | Diff. | Meas. | Diff. | Meas. | Diff. | Meas. | Diff. | Meas. | Diff. | Meas. | Diff.
Sensitivity-opt. | $489\pm 1$ | $12$ | $484\pm 27$ | $17$ | $18.8$ | $0.6$ |  $-1.8$ dBi |  $1.0$ dB |  $-11.7$ dBi |  $0.1$ dB |  $-9.9$ dB |  $1.1$ dB
Gain-optimized | $307\pm 13$ | $186$ | $98\pm 18$ | $4$ | $3.1$ | $0.1$ |  $-2.1$ dBi |  $1.1$ dB |  $-3.3$ dBi |  $1.0$ dB |  $-1.2$ dB |  $0.1$ dB

Afterwards, the sensing capability of the prototypes was assessed through a
M6e (by ThingMagic; $30$ dBm of interrogation power), the same AN-FF-WB
antenna from the measurements above, and custom software (from previous works
[17]) for the retrieval of the SC. Liquid quantity was increased by using a
micropipette (M1000 by QWork) and the weight was controlled by using a digital
scale (nominal resolution: $1$ mg) to check the system’s weight before
measurements (Fig. 9). A maximum error on liquid weight of $5\%$ was accepted
due to the imperfect manual pipetting. Three measurement distances ($30$,
$50$, and $100$ cm) were tested to investigate eventual effects of the
interrogation distance on the digital metric. $10$ SC samples were averaged
for the measurement-simulation comparison based on the convergence error
analysis in [28]. The differential SC from Sec. III-A was used to drop out IC-
dependent baselines. The simulations-measurements comparison was referred to
the filling percentage of the microchannels, measured by weighting (stable
$s_{l}$ achieved, adding more water did not cause any SC variation; $1050$ mg
for the sensitivity-optimized layout and $900$ mg for the gain-optimized
layout; weights measured after the water reached the sensitive channel). Red
food colorant was employed [9] in order to visually emphasize the water
quantity present in the microfluidic. Fig. 10 shows the fluid progressing
similarly to the EM numerical models in Fig. 6.

Despite the very different SC ranges used by the two geometries, good
measurement-simulation agreement is always observed (Table IV). Fig. 11
depicts the comparison with the data measured from the three distances,
showing good robustness of the $\Delta s$ metric when changing the
interrogation distance. The trend of the SC when increasing the water follows
a cubic trend line (R${}^{2}>0.99$) although the EM simulations did not
capture the phenomenon for the gain-optimized geometry due to the simplyfied
numerical model of the antenna-microfluidic system. As expected, the
sensitivity-optimized geometry exploited the largest sensor-code range,
achieving the best overall sensitivity ($S=18.8$ units of sensor code per
water milligram) at the expense of the radiation gain. The sensor code
response of the ”gain-optimized” geometry stays flat until the filling
percentage of the serpentine reaches $75\%$, in good agreement with the
simulation, with a variation of $\Delta s\simeq 100$ between the two extremal
loading conditions.

##  VII Conclusion

In this work, the joint design of an antenna and a microfluidic channel has
been proposed, formulated, and experimentally validated. When comparing the
design examples with the systems for wireless liquid sensing in Table I, our
examples monitored a larger quantity of fluid with the added benefits of
relying on a dedicated, digitalized metric [26]; on the other hand, the main
con of the proposed approach consists in the complexity of the EM modeling of
the microfluidics since inadequate modeling can result in design failure. In
the joint design, the balance between sensitivity and communication
performance can be easily modulated by properly selecting the optimization
weights, thus offering the flexibility to adapt the system to the specific
application of interest.

The design method proposed in this article can be used for optimizing UHF RFID
antenna-microfluidic systems to address open issues in healthcare, like point-
of-care devices for monitoring hyperidrosis [42] or sweating during domestic
exercise [31], and food sectors, like devices estimating food quality through
”drip loss” quantification [43, 44], eventually by using ad-hoc RFID totems
[45]. Yet, the microfluidic model we employed is simple and not representative
of more complex microfluidic circuits or fast flows of liquids; in this second
case, multiphysics simulators could be employed, to exploit the joint design
when the simple modeling described in Sec. V-B does not hold, for instance, to
account quantitatively for a significant wicking effect of the paper.
Moreover, the choice of the filter paper was not investigated throroughly and
was performed based on prior authors’ experience to complete the design
example. Furthermore, the quantity of the liquid to be monitored is only
governed by the microfluidic channel through the assumption that the input and
waste pads and the microfluidic path can carry the quantity of interest in the
sensitive area. Future research directions will address those open issues and
explore the deployment of jointly designed antenna-microfluidic systems to
exploit and refine the joint design technique.

## Acknowledgements

The authors thank Prof. Fabiana Arduini, Dr Vincenzo Mazzaracchio and Dr Luca
Fiore (all affiliated with the Department of Chemical Science and
Technologies, Tor Vergata University of Rome) for their fundamental
collaboration in fabricating the microfluidic channels.

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