fundamentals of engineering supplied-reference handbook - Ventech!

MEASUREMENT
Definitions:
Transducer – a device used to convert a physical parameter
such as temperature, pressure, flow, light intensity, etc. into
an electrical signal (also called a sensor).
Transducer sensitivity – the ratio of change in electrical
signal magnitude to the change in magnitude of the physical
parameter being measured.
Resistance Temperature Detector (RTD) – a device used to
relate change in resistance to change in temperature.
Typically made from platinum, the controlling equation for
an RTD is given by:
( )
RT= R0 ⎡
⎣1+α T −T0
⎤
⎦ , where
RT is the resistance of the RTD at temperature T (measured
in °C)
R0 is the resistance of the RTD at the reference temperature
T0 (usually 0° C)
α is the temperature coefficient of the RTD
Strain Gauge – a device whose electrical resistance varies in
proportion to the amount of strain in the device.
Gauge factor (GF) – the ratio of fractional change in
electrical resistance to the fractional change in length
(strain):
∆RR ∆RR
GF = = , where
∆L ε
L
R is the nominal resistance of the strain gauge at nominal
length L
∆R is the change in resistance due the change in length ∆L
ε is the normal strain sensed by the gauge.
The Gauge Factor for metallic strain gauges is typically
around 2.
Wheatstone Bridge – an electrical circuit used to measure
changes in resistance.
+
V IN
−
R 1
R 2
− V O
Wheatstone Bridge
MEASUREMENT AND CONTROLS
+
R 3
R 4
87
If R1R4 = R2R3 then V O = 0 V and the bridge is said to be
balanced. If R1 = R2 = R3 = R and R4 = R+∆ R where
∆R � R , then
∆R
VO ≈ ⋅ VIN.
4R
SAMPLING
When a continuous-time or analog signal is sampled using a
discrete-time method, certain basic concepts should be
considered. The sampling rate or frequency is given by
f s =
∆t
1
Shannon's sampling theorem states that in order to
accurately reconstruct the analog signal from the discrete
sample points, the sample rate must be larger than twice the
highest frequency contained in the measured signal.
Denoting this frequency, which is called the Nyquist
frequency, as f N , the sampling theorem requires that
f > 2 f
s N
When the above condition is not met, the higher frequencies
in the measured signal will not be accurately represented
and will appear as lower frequencies in the sampled data.
These are known as alias frequencies.
Analog-to-Digital Conversion
When converting an analog signal to digital form, the
resolution of the conversion is an important factor. For a
measured analog signal over the nominal range [VL ,VH],
where VL is the low end of the voltage range and VH is the
nominal high end of the voltage range, the voltage
resolution is given by
V −V
ε V =
n
2
H L
where n is the number of conversion bits of the A/D
converter with typical values of 4, 8, 10, 12, or 16. This
number is a key design parameter. After converting an
analog signal the A/D converter produces an integer number
of n bits. Call this number N. Note that the range of N is
[0 , 2 n – 1]. When calculating the discrete voltage, V, using
the reading, N, from the A/D converter the following
equation is used.
V = ε V N+ VL
Note that with this strategy, the highest measurable voltage
is one voltage resolution less than VH, or VH − ε V .