AE 242
Aerospace Measurements
Laboratory
Sensors – electrical resistance change
In many transducers physical quantity, manifest as change
in resistance. Change in resistance can be measured as
change in current in the circuit or voltage across the
transducer. Current variation can be indicated by current
indicator and voltage variation can be indicated by voltage
indicator.
Current sensitive circuit Voltage sensitive circuit
2
Sensors – Thermistor
It is a semiconductor material and its resistance changes
as temperature changes. Sensitivity of these materials is
very high. Resistance can increase (PTC) or decrease with
increase (NTC) in temperature.
NTC – Negative
Temperature Coefficient
PTC – Positive
Temperature Coefficient
3
Current sensitive circuits
Let a transducer element whose variation in resistance can be expressed by a
factor k. Factor k can vary from 0.0 – 1.0 (0 % to 100%)
ei
By Ohm’s law, i0
Current in the circuit kR t R m
i0 i0Rm 1
Current is maximum
when k = 0 i max ei 1 k (R t / R m )
Rm is the resistance of the measuring
device
Current sensitive circuit 4
Current sensitive circuits
Let a transducer element whose variation in resistance can be expressed by a
factor k. Factor k can vary from 0.0 – 1.0 (0 % to 100%)
ei
By Ohm’s law, i0
Current in the circuit kR t R m
i0 i0Rm 1
Current is maximum
when k = 0 i max ei 1 k (R t / R m )
Rm is the resistance of the measuring
device
Current sensitive circuit 5
Voltage sensitive circuits
Let a transducer element whose variation in resistance can be expressed
by a factor k. Factor k can vary from 0.0 – 1.0 (0 % to 100%), Rb is ballast
resistance and Rt is transducer element
ei
By Ohm’s law, i
Current in the circuit R b kR t
Voltage across e i kR t e0 kR t / R b
e 0 i (kR t ) or
transducer R b kR t e i 1 kR t / R b
e0/ei is the measure of input and
kRt/Rb is the measure of output
6
Voltage sensitive circuit
Voltage sensitive circuits
as sensitivity, ratio of de 0 ei R t R b
change in output to change
in input
dk (R b kR t ) 2
Sensitivity can be studied d e i R t (kR t R b )
with respect to ballast
resistance, a user variable
dR b (R b kR t ) 3
Derivative will be zero when 1)
Rb = minimum sensitivity,
and 2) Rb = kRt maximum
sensitivity. Rb is a fixed quantity
and it will maximum for a
certain value of kRt
e0 kR t / R b
e i 1 kR t / R b
7
Voltage sensitive circuits
Potentiometer type in which total resistance remain same. Potential can
be measured with a low impedance or high impedance indicator. When
the indicator impedance is very high relative to Rp, negligible current will
be drawn from the source and voltage output is proportional to the
position of wiper (for a linear potentiometer). When RL is comparable
with RP, the output is non-linear.
kR p R L
R R p (1 k )
kR p R L
8
Voltage sensitive circuits
Potentiometer type in which total resistance remain same. Potential can
be measured with a low impedance or high impedance indicator. When
the indicator impedance is very high relative to Rp, negligible current will
be drawn from the source and voltage output is proportional to the
position of wiper (for a linear potentiometer). When RL is comparable
with RP, the output is non-linear.
kR p R L
R R p (1 k )
kR p R L
ei e i (kR p R L )
i
R kR p2 (1 k ) R p R L
e 0 e i iR p (1 k )
e0 k
e i 1 (R p / R L )k (R p / R L )k 2
9
Voltage sensitive circuits
At end point i.e. k=0 and k=1, error is zero. At other values of k, the
output will be always less compared to actual value.
Error eo ideal eo
k k 2 (1 k )
Error e i k ei
k (1 k )( R p
/ R L
)k 1 k (1 k ) ( R p
/ R )
L
10
Voltage sensitive circuits
Non-linearity can be reduced by
introducing end resistors. This
shifts the operation range and in
this range output is assumed
linear. Introduction of these
resistors reduces the range of
output voltage, this can be
improved by higher input voltage.
11
Small change in transducer resistance
Some resistance transducers show
very small change in their
resistance. Strain gage resistance
vary about 0.0001%. For the circuit
given, initial R1 = R2 = R0
R2 R0 ei
e0 ei ei
R1 R 2 R0 R0 2
12
Small change in transducer resistance
Some resistance transducers show
very small change in their
resistance. Strain gage resistance
vary about 0.0001%. For the circuit
given, initial R1 = R2 = R0
R2 R0 ei
e0 ei ei
R1 R 2 R0 R0 2
R 0 R
R2 = R0 changes by a small amount e 0 e 0 ei
R, and Output is R 0 (R 0 R )
13
Small change in transducer resistance
Some resistance transducers show
very small change in their
resistance. Strain gage resistance
vary about 0.0001%. For the circuit
given, initial R1 = R2 = R0
R2 R0 ei
e0 ei ei
R1 R 2 R0 R0 2
R 0 R
R2 = R0 changes by a small amount e 0 e 0 ei
R, and Output is R 0 (R 0 R )
1 1 R / R 0 ei R / 2R 0
e 0 e 0 e i 1
2 1 R / 2R 0 2 1 R / 2R 0
e i e i R 1
2 2 2R 0 1 R / 2R 0
14
Small change in transducer resistance
e i e i R 1
e 0 e 0
2 2 2R 0 1 R / 2R 0
R/2R0 << 1 the output can R
be approximated as
e 0 e 0 e 0 ei
4R 0
15
Small change in transducer resistance
e i e i R 1
e 0 e 0
2 2 2R 0 1 R / 2R 0
R/2R0 << 1 the output can R
be approximated as
e 0 e 0 e 0 ei
4R 0
For small variation in resistance it will be linear and it is advantageous.
Variation in small resistance and the output is at disadvantage. For a
120 strain gage change in resistance is 240 and it will change the
output in micro volts
e 0 (R / 4R 0 )e i R
10 6
e0 ei / 2 2R 0
Measurement is e0 + e0 and this will need a very precise instrument.
16
Small change in transducer resistance
Difficulty is to resolve voltage
change which is a small fraction of
output voltage.
17
Small change in transducer resistance
Difficulty is to resolve voltage
change which is a small fraction of
output voltage.
The difficulty can be removed by
measuring only the difference and
amplifying it.
R
e out e a e b e 0 ei
4R 0
18
Wheatstone bridge
Consist of four arms of resistors, a
detector and power supply source.
Two arms are voltage divider and
the detector finds the potential
difference. Bridge is balanced
when potential difference is zero
and no current flow through
detector. When bridge is balanced:
R1 R 3 R1 R 2
or
R2 R4 R3 R4
For the Wheatstone resistance bridge to be balance, the ratio of
resistances of any two adjacent arms must equal the ratio of resistances of
the remaining two arms, taken in the same sense.
19
Input and Output Configuration
20
Methods of Correction for Interfering
and Modifying Inputs
Wish to measure voltage applied to DC motor by displacement of a spring
connected to it. By design displacement can be made proportional to applied
voltage.
e1 DC
Motor
x0 ( K M 0 K SP )e1
x0 21
Methods of Correction for Interfering
and Modifying Inputs
x0 ( K M 0 iM 1FM ,D ,1 )( K SP iM 2 FM ,D , 2 )e1
Motor constant and spring constant are vulnerable to interfering input
x0 K '
M0
'
K e
SP 1 22
Methods of Correction for Interfering and Modifying Inputs
Difference voltage is Output of the spring is
amplified and it drives measured by feedback device
the motor which produces voltage
proportional to spring
displacement.
23
Methods of Correction for Interfering and Modifying Inputs
(ei e0 ) K AM K M 0 K SP x0
24
Methods of Correction for Interfering and Modifying Inputs
(ei e0 ) K AM K M 0 K SP x0
(ei K FB x0 ) K AM K M 0 K SP x0
25
Methods of Correction for Interfering and Modifying Inputs
(ei e0 ) K AM K M 0 K SP x0
(ei K FB x0 ) K AM K M 0 K SP x0
ei K AM K M 0 K SP (1 K FB K AM K M 0 K SP ) x0
K AM K M 0 K SP
x0 ei
1 K FB K AM K M 0 K SP
26
Methods of Correction for Interfering and Modifying Inputs
(ei e0 ) K AM K M 0 K SP x0
(ei K FB x0 ) K AM K M 0 K SP x0
ei K AM K M 0 K SP (1 K FB K AM K M 0 K SP ) x0
K AM K M 0 K SP
x0 ei
1 K FB K AM K M 0 K SP
1
Amplifier Gain is very large
x0 ei
K FB
27
Methods of Correction for Interfering and Modifying Inputs
1
x0 ei
K FB
By using a high gain amplifier in series effect of
interfering inputs is reduced by factor of amplifier gain.
High gain amplification is also susceptible to instability.
It also draws less power from the source. Power
required to drive motor is supplied by amplifier.
28
