Digital instrumentation principles 1
DIGITAL INSTRUMENTATION PRINCIPLES
WHY DIGITAL?
- Transducers: analog output.
- Analog to digital:
- precision
- values not changed during processing
- signal processing using micro-processing.
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Electrical Measurement notes, Thesis of Electrical Engineering
Different types of analog and digital instrument
Typology: Thesis
2017/2018
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Digital instrumentation principles
DIGITAL INSTRUMENTATION PRINCIPLES
WHY DIGITAL? - Transducers: analog output.- Analog to digital:
- precision- values not changed during processing- signal processing using micro-processing.
Digital instrumentation principles
Analog signal is converted into a digital signal: sampling and hold.
Digital instrumentation principles
Delay on switching from hold to sample (acquisition time).
Binary digits 1 or 0,
o
'1' (high): Vcc down to +2V,
o
'0' (low): 0V up to +0.8V
Digital instrumentation principles THE SAMPLING THEOREM
“A continuous signal can be represented completely by, and reconstructed
from, a set of instantaneous measurements or samples of its voltage which aremade at equal spaced times. The interval between such samples must be less thanone-half of the period of the highest-frequency component in the signal”.
Convert an analog signal into digital samples and convert them back into
original signal provided the number of samples per second is more than twicethe highest frequency in the signal.
Digital instrumentation principles
Instrumentation signal is a varying voltage
(not a regularly repeating
waveform).
By Fourier analysis, any such shape can be shown to be a summation of aconstant term (DC voltage) and sine waves of various amplitudes andfrequencies.
Digital instrumentation principles
ANALOG TO DIGITAL CONVERSION
1.
Single-slope or single-ramp A/D converter
. Simple. Cheap. Comparatively slow. Inaccuracy
Digital instrumentation principles .
Accuracy is unaffected by drift (upward and downward ramps are affected equally).
. High-frequency noise disappears in the integration. Changes in the analog input signal during the integration period are averaged out.. Slow speed (digital voltmeters and applications does not require fast conversion).
Digital instrumentation principles
3. Successive-approximation A/D converter
Faster than the ramp type
Set 1 starting from MSB,
Compare: < analog, retain 1, else =0,
Continue to lower bits
Digital instrumentation principles .
n-bit converter requires (2n-1) comparators (additional bit doublescomparators).
. Single integrated circuit chip.. Limit is 11 bits (12-bit resolution=two 11- bit chips in series). 8-bits is a more usual size (255 comparators, 20 million A/D conversions per
second.
Digital instrumentation principles A/D Consideration:
Saturation error (full scale, upper/lower limits)
Resolution and quantization error
full scale/
n
Conversion errors (non-linearity, zero-offset, scale error)
Sample rate
Signal conditioning for A/D conversion (prevent aliasing: filter removes >fs/2)
Digital instrumentation principles
Digital instrumentation principles .
types
. resolution. speed
(settling time:
time it takes for a full scale input to be converted to within
half of the least significant bit (1/2 LSB
. The number of bits also determines the resolution.. Each additional bit in the binary number doubles the number of steps in the
graph, and so halves the (theoretical) maximum error in the output voltage.
. The actual maximum error depends also on the stability of the reference
voltage applied to the chip and the stability of the resistors in the switchingcircuit
Digital instrumentation principles
. Never get absolutely perfect reproduction of the input signal at the output. Process of sampling changes a smooth analogue curve into an approximation
composed of steps made up of horizontal and vertical lines
. Superimpose the approximation onto the original curve will show the divergence
between them is a maximum at the sharp corners of the steps
. By working from sample voltages, noise is introduced (
quantization noise)
. Lower quantization noise: reduce the height of the steps by increasing the number
of voltage levels at which the LSB changes by 1, and this will require more digitsin the digital conversion of the voltage samples.
Digital instrumentation principles Example:
Question 4: (20 marks) – Final 2001^ Consider the circuit in a temperature measurement below. The A/D is a 5-bit
successive-approximation A/D converter type with an analog span of 0 to 10V, findthe input voltage of the A/D converter. The thermistor, R
T
, has a resistance of 2K at
O
C and the coefficient
β
is assumed to be constant at 1650, find temperature of the
thermistor.
)
T
T (
T
e
R
R
1 0
1
0
−−−−
ββββ
====
_ +
1M 1M
10M
10M
12V
5-bitA/D0-10V
4.7K
4.7K
4.7K
R
T Ot
C=?
MSB LSB
1 0 0 1 1
?
V
V