Linear variable differential transformer

Dr. Muhammad Shafique

HOD Biomedical Engineering

Faculty of Engineering and Applied Sciences

Riphah International University, Islamabad

24-04-2014

Biomedical Sensors (Contd)

Displacement measurement Inductive sensor

Inductance is the property of a conductor by which a change in current flowing through it induces a voltage (EMF) in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance)

An inductance L can be used to measure displacement by varying any three of the coil parameters:

L =n2 G

Where: n = number of turns of coil G = geometric form factor = effective permeability of the medium Each of these parameters can be changed by mechanical means

Displacement measurement (2) Inductive sensor

This device works on the principle that alterations in the self-inductance of a coil may be produced by changing the geometric form factor or the movement of a magnetic core within the coil

The change in inductance for this device is not linearly related to displacement

Self inductance

Mutual inductance


The application of these devices in measuring cardiac dimensions, monitoring infant respiration, and ascertaining arterial diameters

The linear variable differential transformer (LVDT) is widely used in physiological research and clinical medicine to measure pressure, displacement, and force

The LVDT is composed of a primary coil (terminals ab) and two secondary coils (ce and de) connected in series

The coupling between these two coils is changed by the motion of a high-permeability alloy slug between them

The two secondary coils are connected in opposition in order to achieve a wider region of linearity


In operation, the LVDTs primary winding is energized by alternating current of appropriate amplitude and frequency,

known as the primary excitation. The LVDTs electrical output signal is the differential AC voltage between the two secondary windings, which varies with the axial position of the core within the LVDT coil


LVDT


Advantages and disadvantages of LVDT:

Linear variable differential transformer characteristics include linearity over a large range, a change of phase by 180o when the core passes through the center position, and saturation on the ends Specifications of commercially available LVDTs include sensitivities on the

order of 0.5 to 2 mV for a displacement of 0.01 mm/V of primary voltage, full-scale displacement of 0.1 to 250 mm, and linearity of 0.25%

Sensitivity for LVDTs is much higher than that for strain gages

A disadvantage of the LVDT is that it requires more complex signal processing instrumentation.

Displacement measurement (7) Capacitive sensors

The capacitance between two parallel plates of area A separated by distance x is:

=

Eq. 1

Where = dielectric constant of free space = relative dielectric constant of the insulator (1.0 for air)

The displacement is monitored by changing the separation between the plates


The sensitivity K of a capacitive sensor to changes in plate separation x is found by differentiating

=

Eq. 2

The sensitivity increases as the plate separation decreases

Comparing Eq. 1 and 2:

=

Eq. 3

The percent change in C about any neutral point is equal to the per-

unit change in x for small displacements


In the design of a monopolar capacitive, one plate of a capacitor is connected to the central conductor of a coaxial cable and the other plate is formed by a target (object)


How to measure the varying capacitance?

The capacitance microphone is an excellent example of a relatively simple method for detecting variation in capacitance


This is a dc-excited circuit, so no current flows when the capacitor is stationary (with separation x0), and thus v1 = E

A change in position x = x1 xo produces a voltage vo = v1 E

The output voltage Vo is related to x1 by

()

1 ()=

+ 1 . 4

Where = RC Typically R is 1Mohm and thus the readout device must have a high (10 M or higher) input impedance They are better for microphone (f>20Hz) but not adequate for most of the

physiological parameters

For a 1 cm2 capacitance sensor, R is 100 M. Calculate x, the plate spacing required to pass sound frequencies above 20 Hz.

= 8.85x10-5

= 1x10-4


Answer:

Displacement measurement (13) Piezoelectric sensors

Piezoelectric (piezo=press) effect is the generation of electric charge by a crystalline material upon subjecting it to stress

The effect exists in natural crystals, such as quartz (chemical formula SiO2), and poled (artificially polarized) man-made ceramics and

some polymers, such as polyvinylidene

flouride.


To pick up an electric charge, conductive electrodes must be applied to the crystal at the opposite sides of the cut

As a result, a piezoelectric sensor becomes a capacitor with a dielectric material which is a piezoelectric crystal

The dielectric acts as a generator of electric charge, resulting in voltage V across the capacitor

If electrodes are formed with a complex pattern, it is possible to determine the exact location of the applied force by measuring the response from a selected electrode

The piezoelectric effect is a reversible physical phenomenon. That means that applying voltage across the crystal produces mechanical strain


Piezoelectric sensors are used to measure physiological displacements and record heart sounds

The total induced charge q is directly proportional to the applied force f

q = kf

where k is the piezoelectric constant,


The change in voltage can be found by assuming that the system acts like a parallel-plate capacitor where the

voltage v across the capacitor is charge q divided by

capacitance C

For a piezoelectric sensor of 1 cm2 area and 1 mm thickness with an applied force due to a 10 g weight, the output voltage v is 0.23 mV and 14 mV for the quartz and barium titanate crystals, respectively


Typical output signal of piezoelectric device

Study more

http://www.macrosensors.com/downloads/misc/LVDT-Basics.pdf

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Linear variable differential transformer