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Design of Multi-channel Fringing Electric Field Sensors for Imaging Part I: General Design Principles









Design of Multi-channel Fringing Electric Field Sensors for Imaging
Part I: General Design Principles

X. B. Li, S. D. Larson, A. S. Zyuzin, and A. V. Mamishev
Sensors, Energy, and Automation Laboratory (SEAL)
Department of Electrical Engineering
University of Washington
Campus Box 352500, Seattle, WA 98195-2500 USA
shellyli@u.washington.edu

Abstract: Multi-channel electric field sensors are used for
electrical impedance and capacitance tomography applications.
In cases where only one-sided access can be accommodated,
fringing electric field sensors (FEF) sensors are used. The general
design principles of multi-channel fringing electric field sensors
are discussed in this paper. Analysis of the figures of merit of
FEF sensors, such as penetration depth, signal strength,
measurement sensitivity, and imaging resolution, are presented.
The effects of design parameters on sensor performance are also
evaluated. The qualitative design principles described in this part
of the paper provide intuitive guidelines for the simulation-based
design optimization procedure to be presented in the second part
of the paper.
INTRODUCTION

Multi-channel capacitive sensors are widely used for material
property imaging. For such applications, the major goal of
sensor design is to achieve high measurement sensitivity, high
signal strength, and high imaging resolution and speed. Design
parameters include electrode geometry, electrode and substrate
material, number of electrodes, and positioning of guard
electrodes.
The finite sensor head area makes it impossible to
achieve all of the design goals simultaneously. Designing
multi-channel sensors for imaging is, therefore, an iterative
process of determining the optimal set of design parameters.
The quantitative optimization process can be based either on
analytical models [1] or on numerical simulations [2]. This
paper focuses on the qualitative effect of design parameters on
sensor performance. Evaluation of the qualitative effect aids
the quantitative optimization process by providing intuitive
design guidelines.
Among all of the design parameters, electrode geometry
is the major determining factor for sensor performance.
Sensors of various geometries were designed previously for
imaging applications. For example, a multi-segment
interdigital fringing electric field (FEF) sensor array was used
for multi-phase interface detection in [3]; a multi-segment
cylindrical sensor was used to image continuous flows of
materials within a pipeline [4]; a helical wound electrode
sensor and a concave electrode sensor were developed for void
fraction measurements [5]. The choice of sensor geometry is
usually dictated by the requirements of the application. In the
cases where the sample can be accessed only from one side,
FEF sensors can be used. Several such applications are being
studied at the SEAL lab of the University of Washington.
They include online measurement of moisture content in food
products, pharmaceutical products, and paper pulp, as well as
curing process monitoring of the resin transfer molding
process.


This paper focuses on the design principles of multi-
channel FEF sensors. The effects of electrode geometry on the
performance of individual channels of interdigital FEF sensors
is analyzed in [6], but it was not in the context of imaging
applications, where imaging resolution and speed are of
concern. However, some of the issues addressed in the present
paper are not specific to FEF sensors, and the corresponding
results can be applied to designing multi-channel imaging
sensor of other types.
FIGURES OF MERIT
Penetration depth, measurement sensitivity, dynamic range,
signal strength, and noise tolerance are the figures of merit
usually used to evaluate the performance of multi-channel
FEF sensors. For imaging applications, imaging resolution
and speed of the sensor are also considered. The figures of
merit of FEF sensors are analyzed in detail in the following
sections.
Penetration depth
There is no consensus on the definition of penetration
depth for FEF sensors. One way to evaluate effective
penetration depth is to measure the position at which the
difference between the current value and asymptotic (sample
infinitely far from the sensor) value of sensor terminal
impedance equals to 3% of the difference between the highest
and the lowest values of the terminal impedance. The quantity
is denoted as
3%
[7]. Throughout this paper, this definition is
adopted. Conceptually, it is an effective measure of how
quickly the electrical field generated from the sensor decays as
the distance from the plane of sensor electrode increases.
Figure 1 provides an example where the penetration depth of
an interdigital FEF sensor is evaluated using the above method.
Capacitance values are normalized to the scale between 0 and
100%.
Penetration depth is determined mainly by the geometry
of the sensor electrodes. For an interdigital sensor, penetration
depth
3%
is roughly proportional to its spatial wavelength .









Spatial wavelength is defined as the distance between the
centerlines of neighboring fingers of the same type (e.g.
driving or sensing electrodes). Figure 2 shows the cross-
sectional view of

an interdigital sensor. In Figure 2, the
parameters l
1
, l
2
, and l
3
represent three different ways of
connecting the electrodes. The letter D represents the
driving electrodes, S represents the sensing electrodes and
G represents the ground electrodes. In the table below the
cross-sectional view of the sensor in Figure 2, each row
corresponds to one of the three connection schemes; each
column corresponds to the types of connection for the
electrode directly above the column used in the different
connection schemes. For l
1
, an ac voltage signal is applied to
every other electrode and the current/voltage at the un-driven
electrode is measured. For l
2
and l
3
, several un-driven fingers
are chosen as ground electrodes and only the current/voltage at
the sensing electrodes is measured. The ground electrodes are
either connected to ground or kept at the same voltage
potential as the sensing electrodes by using unity gain buffer
amplifiers. The spatial wavelength of the sensor is increased
(
3
>
2
>
1
) by using different connection schemes. As a result,
sensor penetration depth is also increased. The variable sensor
penetration depth obtained from the different connection
schemes provides the sensor with access to different layers of
the test specimen.

Figure 1. Evaluation of the effective penetration depth
3%
of an FEF
sensor.





Figure 2. Cross-sectional view of a fringing electric field sensor with
multiple penetration depth excitation patterns.
Measurement Sensitivity
Measurement sensitivity is defined as the slope of the sensor
measurement curve, namely the ratio of the change in sensor
output relative to the change in the measured physical
parameter. The non-uniformity of the field distribution of FEF
sensors makes their measurement sensitivities position-
dependent. As illustrated in Figure 1, sensitivity decreases
exponentially with increasing distance from the plane of
sensor electrodes.
Electrode area is another major factor that determines
measurement sensitivity. For a fixed spatial wavelength,
greater electrode area means higher measurement sensitivity.
Dynamic Range
Sensor dynamic range is defined as the ratio between the
largest and the smallest sensor output [8]. Its value is
determined by the sample under test and should be within the
measurement range of the interface circuit. The lower end of
the circuit measurement range is determined by the sensitivity
of the circuit, while the higher end is determined by factors
such as the input common mode range of the operational
amplifiers on the circuit.
Signal strength
The output signal for imaging applications is usually weak.
The signal strength of FEF sensors decays exponentially with
increasing distance to the sample. For non-contact
measurements, the output signal is usually very weak. This
requires that the interface circuit has high measurement
resolution. To relax the requirement on the circuit, the distance
between the sensor and the sample should be minimized.
Signal strength can also be improved by increasing amplitude
of the input driving signal. To avoid distortion, the sensor
output has to lie within the measurement range of the interface
circuit.
Noise tolerance
Guard electrodes are usually used to shield FEF sensors from
noise disturbances. This includes both the guard ring on the
top of the sensor substrate and the backplane under the sensor
substrate. Proper positioning of these guard electrodes is
crucial for design optimization. Special attention must be paid
to the connection of the guard electrodes to avoid stray
capacitances and ground loops. The driven-guard technique is
always used to remove or reduce stray capacitances [9].
Imaging Resolution
A straightforward method to produce an image of material
properties is to let each measurement channel of the sensor