IEEE SENSORS JOURNAL, VOL. 12, NO. 6, JUNE 2012 2237
Distance Measurement With Inductive Coils
Gustavo Theodoro Laskoski, Sérgio Francisco Pichorim, and Paulo José Abatti
Abstract— Distance measurement is an important tool in sev-
eral applications. This article describes the development of a
resonant inductive sensor for short (few centimeters) distance
measurement. The sensor uses the principle of inductive coupling,
where a transmitter coil (TX) induces a voltage in receiver coil
(RX). The distance between TX and RX coils is determined as
a function of the amplitude of the induced signal. Both coils are
controlled by processing circuits and a microcomputer performs
information processing and stores the measured data. In a setup
for distances between 100–240 mm, experimental results showed
a maximum standard deviation (σ ) of 2.56 mm at 235 mm.
Index Terms—Distance measurement, inductive sensor, short
distance sensor.
I. I NTRODUCTION
I
N ORDER to find the laws governing the various changes
that take place in bodies as time goes on, measurement
systems must be able to describe these modifications and
have the ability to record them [1]. Because of this, several
types of sensors have been developed to quantify distance,
displacement, and other cinematic parameters. A particular
class of distance sensors are the field based ones, where
the intensity of a given energy field changes as a function
of distance [2]. In general, such sensors employ sound or
stationary magnetic fields for short (few centimeters) distance
measurements. Sound waves can be used to measure distance
between source and a specific object. However, obstacles
between source and object may affect sensor’s response. In
this situation, magnetic fields generated by permanent magnet
or coils (inductive sensors) can be considered more adequate,
because paramagnetic obstacles does not change sensor’s
response [2]. This characteristic is desirable in biomedical
applications, for instance, implanted devices employing coils
[3], where low frequency magnetic fields (in safety limiting
exposure conditions) does not present significant effect in
physiological tissues [4]. Therefore, inductive sensors are
being used in human or animal monitoring such as stomach
activity [5] and joint motion analysis [6]. In industrial envi-
ronment, inductive sensors are employed in mechanical appli-
cations (such as robotics systems) due to immunity against oil,
water and dirt [7].
Manuscript received November 22, 2011; revised December 27, 2011;
accepted January 10, 2012. Date of publication January 24, 2012; date of
current version April 27, 2012. This work was supported in part by the Brazil-
ian Coordination of Improvement of Personnel of Superior Level (CAPES)
and a grant from the Brazilian Council for Scientific and Technological
Development (CNPq) in Masters Scholarship under Project 562563/2008-3
from 2008 to 2010. The associate editor coordinating the review of this paper
and approving it for publication was Prof. Weileun Fang.
The authors are with the Graduate School of Electrical Engineer-
ing and Applied Computer Sciences, Federal University of Technology-
Paraná, Paraná 80230-901, Brazil (e-mail: gustavo_thl@yahoo.com.br;
pichorim@utfpr.edu.br; pjabatti@gmail.com).
Digital Object Identifier 10.1109/JSEN.2012.2185789
Fig. 1. Geometric representation of magnetic link, where transmitter and
receiver coils are arranged in the same radial plane.
Fig. 2. Geometric representation of Biot-Savart law applied to determine
B
of TX coil in a given point P, where δ, γ , and Φ are angles between d
l and
p, r
1
and p, r
1
, and d , respectively.
In this work an inductive sensor for distance measurement
is presented, including theoretical analysis, implementation,
tests, and results.
II. THEORETICAL ANALYSIS
The developed sensor is based on the principle of inductive
coupling between two coplanar coils. Fig. 1 shows a graphical
representation, where a transmitter coil (TX) with inductance
L
1
and radius r
1
induces a voltage in receiver coil (RX) with
inductance L
2
and radius r
2
.
The Biot-Savart law relates the variation of magnetic flux
density (d
B) in a given point P in space due to an electrical
current (i
1
) passing through a wire [8] as a function of a
segment of conductor (d
l ), which can be written as
d
B =
μ.i
1
. p.d
l
4π. p
3
, (1)
where μ is medium magnetic permeability and p is a vector
from d
l to P. Fig. 2 shows a geometric representation of
Biot-Savart law.
In this case, p (the module of p) can be defined as a function
of Φ according to the law of cosines
p =
2
r
1
2
+ d
2
- 2r
1
.d .cos (Φ). (2)
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