[Q] Explain with neat diagram how electrical pressure transducer based on

principle of variable resistance, inductance, capacitance are developed for

converting the deflection or stress developed in elastic elements into
corresponding electrical signal?
 
ANS:
Electrical Pressure Sensor: Pressure Transducer either converts the pressure into
mechanical movement or into an electrical output.

The typical pressure sensor has three functional blocks:

 Pressure is sensed by mechanical elements such as plates, shells, and tubes that are
designed and constructed to deflect when pressure is applied. This is the basic
mechanism converting pressure to physical movement.

 The main types of sensing elements are Bourdon tubes, diaphragms, capsules, and
bellows.

 The physical movement is transduced to obtain an electrical or other output.

 ELASTIC DISTORTION METHOD:

This pressure measuring method is based on the idea that deformation of an elastic material is
directly proportional to the pressure being measured.
There are mainly three sensor types that are used in this method of measuring pressure:
Bourdon-tubes, diaphragms and bellows.

 ELECTRICAL METHODS
Electrical methods used for measuring pressure utilize the idea that dimensional changes in a
wire affect the electrical resistance to the conductor. These devices that use the change in
resistance of the wire are called strain gauges. Other electrical sensors include capacitive
sensors, inductive pressure transducers, potentiometric transducers.
 ELASTIC DISTORTION METHOD:

This pressure measuring method is based on the idea that deformation of an elastic material is
directly proportional to the pressure being measured.
There are mainly three sensor types that are used in this method of measuring pressure:
Bourdon-tubes, diaphragms and bellows
Examples of these elastic element pressure sensors are shown here.
 Bourdon Tube Gauge: The principle behind all Bourdon tubes is that an increase in
pressure on the inside of the tube in comparison to the outside pressure causes the oval or
flat shaped cross-section of the tube to try to achieve a circular shape. This phenomenon
causes the tube to either straighten itself out in the c-type or spiral cases or to unwind
itself for the twisted and helical varieties. This change can then be measured with an
analog or digital meter connected to the tube. Tube materials can be changed accordingly
to suit the required process conditions. They are also portable and require little
maintenance; however, they can only be used for static measurements and have low
accuracy. Types of Bourdon tubes include C-type, spiral (a more coiled C-type tube),
helical and straight tube Bourdon tubes.

 Bellows: Bellows elements are cylindrical in shape and contain many folds. They deform
in the axial direction (compression or expansion) with changes in pressure. The pressure
that needs to be measured is applied to one side of the bellows (either inside or outside)
while atmospheric pressure is on the opposite side. Absolute pressure can be measured by
evacuating either the exterior or interior space of the bellows and then measuring the
pressure at the opposite side. Bellows can only be connected to an on/off switch or
potientiomenter and are used at low pressures.

 Diaphragms: Diaphragm elements are made of circular metal discs or flexible elements
such as rubber, plastic or leather. The material from which the diaphragm is made
depends on whether it takes advantage of the elastic nature of the material, or is opposed
by another element (such as a spring). Diaphragms made of metal discs utilize elastic
characteristics, while those made of flexible elements are opposed by another elastic
element. These diaphragm sensors are very sensitive to rapid pressure changes. Examples
of diaphragms include flat, corrugated and capsule diaphragms. They can measure
fractional pressure differences over a very minute range (say, inches of water) (elastic
type) or large pressure differences .Diaphragm elements are very versatile -- they are
commonly used in very corrosive environments or with extreme over-pressure situations.

ELECTRICAL METHODS

Electrical methods used for measuring pressure utilize the idea that dimensional changes in a
wire affect the electrical resistance to the conductor. These devices that use the change in
resistance of the wire are called strain gauges. Other electrical sensors include capacitive
sensors, inductive pressure transducers, potentiometric transducers.

 Conversion by resistance variation:

STRAIN GAUGE:
The strain gauge detects changes in pressure by measuring the change in resistance of a
Wheatstone bridge circuit. In general, this circuit is used to determine an unknown electrical
resistance by balancing two sections of a bridge circuit such that the ratio of resistances in
one section (R3/R2) is the same as that in the other section(R4/R1), resulting in a zero
reading in the galvanometer in the center branch. One of the sections contains the unknown
component of which the resistance is to be determined, while the other section contains a
resistor of known resistance that can be varied.

The strain gauge places sensors on each of the resistors and measures the change in resistance
of each individual resistor due to a change in pressure. Resistance is governed by the equation

Where:  ρ = resistivity of the wire

L = length of the wire
A = cross-sectional area of the wire.
A pressure change would either elongate or compress the wire; hence a compression sensor is
needed on one resistor and an elongation sensor on the other. To control the effects of
temperature (a wire would also either elongate or compress with a change in temperature), a
blank sensor would be placed on the remaining two resistors.
The Wheatstone bridge circuit is shown below:

The output voltage of a bridge circuit is given as follows.

Where e: Voltage output

E: Exciting voltage
R1: Gauge resistance
R2~R4: Resistance of fixed resistors

The strain gauge is connected to a strain meter, which provides Wheatstone bridge circuit
and exciting input voltage. The strain is measured on a digital or analog display of the
strain meter.
 Conversion by capacitance variation:

CAPACITIVE
A capacitive sensor consists of a parallel plate capacitors coupled with a diaphragm that is
usually metal and exposed to the process pressure on one side and the reference pressure on
the other side. Electrodes are attached to the diaphragm and are charged by a high frequency
oscillator. The electrodes sense any movement of the diaphragm and this changes the
capacitance. The change of the capacitance is detected by an attached circuit which then
outputs a voltage according to the pressure change. An example of a capacitive pressure
sensor is shown on the right.

The capacitance of two parallel plates is given by:

   C = µA/d

where:
µ = dielectric constant of the material
between the plates

A = area of the plates

d = spacing between the plates

 INDUCTIVE
Inductive pressure sensors are coupled with a diaphragm or a Bourdon tube. A ferromagnetic
core is attached to the elastic element and has a primary and 2 secondary windings. A current
is charged to the primary winding. When the core is centered then the same voltage will be
induced to the two secondary windings. When the core moves with a pressure change, the
voltage ratio between the two secondary windings changes. The difference between the
voltages is proportional to the change in pressure.
 An example of an inductive pressure sensor utilizing a diaphragm is shown below.

For this kind of pressure sensor, taking Chamber 1 as the reference chamber with a reference
pressure P1 coming into the chamber and the coil being charged with a reference current.
When the pressure in the other chamber changes, the diagphragm moves and induces a
current in the other coil, which is measured and gives a measure of the change in pressure.
These may be used with any elastic element (though, it is typically coupled with a diaphragm
or a bourdon tube). The pressure reading generated will be determined by voltage calibration.