The document provides details about three experiments conducted using instrumentation and control systems lab equipment: 1. The first experiment investigates strain gauges and how metal foil gauges can be used to measure strain. A linear relationship was observed between position and output voltage. 2. The second experiment uses a Wheatstone bridge circuit to determine the value of an unknown resistor. The measured value matched closely with the theoretical value. 3. The third experiment studies a linear variable differential transformer (LVDT) and how it can convert mechanical displacement into an electrical output signal. Graphs of AC and DC output versus core position showed the expected linear relationship.

1. Indian Institute of Space Science and Technology
Thiruvananthapuram
AV 335
Instrumentation
And
Control Systems
Lab
Submitted By:
Akhil Jaiswal (SC11B001)
Amal Jyothis V (SC11B004)
Anand Kumar (SC11B006)

2. Experiment No. 1
Strain Gauges
Objective:
To investigate the application of variable length transducer principle to strain guage transducers.
Equipments Required:
Instrumentation module, linear transducer, strain guage, power supply, dc voltmeter
Theory:
Metal Foil Gauges
Instead of using a fine wire filament for the
resistive element of the gauge, this type of
strain gauge uses a very thin metal foil which
is etched to give the zigzag pattern. For a
metal foil strain gauge a rolled Constantan foil
between 2µm and 10µm thick is normally
used. This is bonded to the backing material,
which may be any of those described
previously for the wire gauges and a photo
etching process similar to that used in printed
circuit manufacture is employed to produce
the required pattern.
Foil gauges may be mass produced more easily than wire gauges, and allow a better utilization of a given
area as the cross section is rectangular which gives a better cross section/surface area ratio. The width
at each end of the loop is often increased to reduce the sensitivity to transverse strain. The gauge factor
is typically 5% - 10% higher than for a comparable wire gauge, which leads to smaller gauges. They can
be used to measure higher strains than wire gauges, and are more robust, making them progressively
more and more popular when a choice between the two types is made.
It is possible to construct transducer which uses the principle of variation in length of a resistive path to
give a variation in the resistance of the transducer element. Also, variation in the cross-sectional area of
a resistive element will cause a change in the resistance of the element and this principle can be applied
to transducers.
Another method of increasing the length of a resistive element is by physically stretching it. Let us see
what happens when this is done and whether this method can be used as the principle of operation of a
transducer.

3. When a rectangular bar of material is stretched by the application of a tensile force along its axis, not
only will the bar increase in length, but it will also decrease in cross-sectional area.
The amount by which the bar is elongated is related to the amount that its width and depth decrease by
a factor which is known as Poisson’s Ratio.

Lateral contraction per unit breadth
Longitudinal extension per unit length
For materials such as steel, aluminum, copper and other metals Poisson’s Ratio lies between about 0.25
and 0.35.
Circuit Diagram:
Procedure:
1) Set the micrometer to 10mm
2) Use the slide to push the gauge operating rod against the left-hand stop and note the slide scale
reading.
3) Move the slide to the right until there is just no pressure on the operating rod and again notes the
scale reading.

4. 4) Set the slide to the midway point of the two readings and lock the slide. The strain gauge should now
be in middle of its operating range.
5) On the WSB set R1=R2=1K
6) Switch on the power supply.
7) Select a 10V range on the meter and set a gain of 100 on the operational amplifier.set the
potentiometer, R49, to mid-scale and adjust RS on the WSB until the meter reads as near to zero.
8) Now adjust R49 to give an exact zero, increasing the meter sensitivity and re-adjusting R49 alternately
until you have a zero setting on the most sensitive range available.
Observation:
Micrometer Setting (mm)
-0.5
-1.0
-1.5
-2.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
1.0
Output Voltage (mV)
0.2
0.4
0.6
0.8
1.0
0.8
0.6
0.4
0.2
-0.1
-0.3
-0.5

5. Result:
The graph was obtained between position and output voltage.
Inference:


The graph was almost linear as expected.
Hysteresis was observed and due to losses we could not get a closed curve.

6. Experiment No. 2
Wheatstone bridge
Objective:
To find the value of resistance of a given resistor using a Wheatstone bridge
Apparatus Required:
Instrumentation module, Power supply, DC Voltmeter
Theory:
The general arrangement of Wheatstone bridge circuit is shown in the figure below. It is a four arms
bridge circuit where arm AB, BC, CD and AD are consisting of resistances P, Q, S and R respectively.
Among these resistances P and Q are
known fixed resistances and these two
arms are referred as ratio arms. An
accurate and sensitive Galvanometer is
connected between the terminals B and
D through a switch S2. The voltage
source of this Wheatstone bridge is
connected to the terminals A and C via a
switch S1 as shown. A variable resistor S
is connected between point C and D.
The potential at point D can be varied by
adjusting the value of variable resistor.
Suppose current I1 and current I2 are
flowing through the paths ABC and ADC
Figure 1 Wheatstone Bridge
respectively. If we vary the electrical
resistance value of arm CD the value of current I2 will also be varied as the voltage across A and C is
fixed. If we continue to adjust the variable resistance one situation may comes when voltage drop across
the resistor S that is I2.S is becomes exactly equal to voltage drop across resistor Q that is I1.Q. Thus the
potential at point B becomes equal to the potential at point D hence potential difference between these
two points is zero hence current through galvanometer is nil. Then the deflection in the galvanometer is
nil when the switch S2 is closed.
Theoretically, we have the equation for the circuit as (P/R) = (Q/S).
Procedure:
1) Circuit in the module is setup as given in the figure.
2) Resistance value of P, Q and R are set as 10 kilo ohms.
3) Power supply of 15 V is given at point A and point C is grounded.
4) Resistor, S is varied accordingly to get zero current in the galvanometer.

7. 5) Value of resistor S is noted down for the zero current through the galvanometer.
Result:
The value of resistor S comes out to be around 9.71 kilo ohms. Theoretically, this value should be 10 kilo
ohms.
Inference:
There may be errors in the value of resistance obtained due to :
 Internal resistance of the power supply

Resistance of connecting wires.

Insufficient sensitivity of the galvanometer.

8. Experiment No. 3
Linear Variable Differential Transformer
Objective:
To study linear variable differential transformer (LVDT), typical characteristic of measuring devices and
possible applications.
Apparatus Required:
Linear transducer, instrumentation module, LVDT, Power Supply, two beam oscilloscope, dc voltmeter
Theory:
 Electromagnetic Induction:
Whenever there is a change in flux linkage through an electric conductor, a voltage is induced in the
conductor. In case of LVDT, an object of ferromagnetic material is moved within the flux path which in
effect changes the reluctance of the flux path and brings about the change in flux linkage. Thus
mechanical energy (used in moving the ferromagnetic material) is directly converted into electrical
energy. The induced voltage is used as a measure of the motion.
 Construction:
LVDT consists of a cylindrical, insulating, non-magnetic form that has primary coil in the mid segment
and a secondary coil symmetrically wound in the two end segments. The two secondary coils are
connected in series opposition, so that the Core potentials induced in the two coils segments oppose
each other. A core of ferromagnetic material is inserted coaxially in the cylindrical form without actually
touching it.
 Working:
The primary coil is energized by AC supply voltage. As a result AC voltage of same frequency is induced
in the secondary windings. When the core moves, the reluctance of the flux path changes and hence the
flux linkage with two secondary windings changes. Since the two secondary coils are connected in series
opposition, it is seen that the net induced voltage is zero (Vo = Vs1 - Vs2; Vs1 = Vs2; Vo = 0) when the
core is at the centre in between the two secondary windings.
This position is known as ’Null position’. Also, since the secondary windings are connected in series
opposition, the LVDT provides direction as well as magnitude displacement. At steady state, the
amplitude Vo of the induced voltage is proportional, in the linear region, to the core displacement. Note:
An error known as ’zero error’ is present in some differential transformer i.e. a non-zero reading at the
null position. The main reasons for the zero error are non uniformities in the windings, harmonic
components in the primary signal, nonlinearities in the device. The LVDT is a transducer which converts
mechanical energy into electrical energy i.e. we get output in terms of voltage. Transduced energy levels
are generally weak and often need conditioning. The signal conditioning is achieved by analog

9. transducer amplifier which we connect to the LVDT. The signal conditioning associated with the
differential transformers includes filtering and amplification. Filtering is necessary to reject the noise i.e.
to achieve high signal to noise ratio of the o/p signal. Amplification is necessary to achieve signal
strength for data acquisition and processing.
For ac output-
For dc output-
Procedure:
1) In the oscilloscope, set the time base 1µs/div & the vertical sensitivities to 2V/div to display a
few cycles of the output waveform and the oscillator waveform.
2) Move the ferrite core through the body of the transducer by pressing the rod against the return
spring. Observe the secondary output waveform on the oscilloscope.
3) Using the micrometer move the core through the coils in 1mm steps, recording the output at
each step, to a final setting of 25mm on the micrometer.
4) The phase change at null position should be 180®.
5) Plot the graph of output against position for the whole the whole range of movement.

10. Observations:
Position (mm)
AC Output
(mV)
DC Output
(mV)
3
3.6
3.5
3.5
2.8
6.4
4.0
2.2
6.5
4.5
2.0
6.7
5.0
2.5
7.5
5.5
3.0
6.8
6.0
3.0
-2.3
6.5
2.8
-2.3
7.0
2.9
-2.3
7.5
3.4
-2.2
7.8
4.0
2.1
Result:
The graph was obtained between position and output (Both AC and DC output)

11. Inference:


Central region of both graphs are linear.
Linear region for DC output graph is much more than the linear portion in AC output graph.