PHYS 352
What the Course is About
  Overview of Measurement Systems
  Transducer Characteristics
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Learning Objectives
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core “unique” engineering physics course
measurement, instrumentation → transducers
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general characteristics of transducers
survey of different types of transducers for a variety of purposes
experiment (engineering) design
noise, amplifiers, filters, data acquisition, (digital)
signal processing
radiation detectors, radiation safety, nuclear
instrumentation and analytical techniques
exposure to MATLAB and LabView in the laboratory
physicists and engineers want to learn how to design
measurement systems in order to, for example:
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to build better experiments
to design control systems (always involves measurement)
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More Learning Objectives
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you tell me what you want to learn from this
course – send me an e-mail and tell me!
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I’m the “tour guide”
I want your PHYS 455 thesis projects to not
suck!
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we will try a case study approach to engineering design
by examining past 455 thesis designs
Teaching/Learning through Inquiry
I’m keeping 2010 course content on the web
page, like last year’s assignments and
solutions.
  I’ll flag when NEW material is posted and/or
when there are updates for 2011.
  That way, you will be able to and will read
through material prior to coming to lecture.
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then, I don’t have to lecture you and I can be here
to answer your questions
if you don’t ask me questions…I will ask you
questions
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Measurement Systems
block diagram of a measurement system
physical
effect
e.g. amplifiers,
filters
transducer
signal transmission
line
signal conditioning
electronics
e.g. amplifiers,
filters
ADC could
be here
signal conditioning
electronics
data acquisition
and display
analog-to-digital
conversion
digital signal
processing
noise may enter or may be present
in any element of the system
we will examine almost all of
these aspects in this course
Transducer
  translates
a measured physical effect into
a voltage or current signal with a
magnitude related to the quantity being
measured
  e.g. Hall probe, hot-wire anemometer,
capacitance level probe, photodiode light
meter, vacuum pressure gauge, antenna
  transducer specs often include the
following characteristics…
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…but first, let’s consider the familiar
  the
liquid-in-glass thermometer as a
transducer
relies on thermal expansion of liquids with
temperature [physical property]
  works between the freezing and boiling point
of the liquid [range of the transducer]
  slow due to the thermal conductivity of glass
and heat capacity of the liquid [response
time]
  calibration done at fixed reference points;
relies on thermal expansion being linear
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some content from Sayer
Transducer Characteristics
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accuracy: It is the conformity of an indicated value to an
accepted standard, or true value. It defines the limit the errors
will not exceed when the instrument is used under stated
operating conditions.
resolution: The smallest difference between measured values
that can be discriminated. For example, it corresponds to the last
stable figure on a digital display.
calibration: The degree to which an instrument is known to
conform to an accepted standard is termed as its calibration.
Both the accuracy and reliability of an instrument depends on its
construction and on how well it holds its calibration.
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e.g. The liquid-in-glass thermometer gives a liquid height that
corresponds to the temperature. Calibration converts the liquid
height measured by ticks on the glass into temperature. The
thermometer may be accurately calibrated to a standard; but if the
glass flows over time, the thermometer distorts and may not hold its
calibration.
An instrument with high resolution might make a precise
measurement that is not accurate because it is poorly
calibrated.
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Characteristics cont’d
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repeatability: The repeatability is the agreement among a
number of consecutive measurements of the output for the same
value of the input – under the same operating conditions and
when approached from the same direction.
reproducibility: It is known as the agreement among repeated
measurements of the output for the same value of the input over
a period of time under the same operating conditions and when
approached from either direction.
hysteresis: The effect in which a measured value differs for the
same value of the input if the input is applied in an increasing
direction versus a decreasing direction, is called hysteresis.
Hysteresis
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examples where it can occur
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magnetism
mechanical coupling (static friction)
gear backlash
photoconductive cells “light history effect”
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Characteristics cont'd
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linearity: For successive equal increments of the input, the
linearity is the deviation of the plotted transducer output from a
straight line. This is often defined in terms of a percentage of the
maximum or full scale output.
sensitivity: It is the ratio of the change in the magnitude of the
output to the change in the input which caused it after the steady
state has been reached.
The slope of the linearity curve is the sensitivity.
which is more linear?
which has higher sensitivity?
More on Linearity
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differential linearity: quantity y related to quantity x; a small
increment of the effect in x gives a small increment in the
response in y and if those steps are uniform, that's referred to as
differential linearity (how constant is the slope?)
integral linearity: is the relation of y to x over a range, typically
expressed as percent of full scale
  independent, zero-based (fixed zero), terminal or end-point
(fixes both ends)
terminal
independent
differential linearity of an ADC
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Transducer Characteristics cont’d
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noise: Noise (in the transducer) consists of signals generated
within the transducer, independent of the input signal, which
contribute to the output. Such signals may be intrinsic to the
transducer (for example, due to thermal fluctuations of carrier
concentrations in a semiconductor), or be generated by interaction
with the environment (for example, by RF pickup).
threshold: The minimum value for which a noticeable or
measurable response is produced. A relevant consideration
especially for active elements (as opposed to passive). May be
related to noise characteristics of the transducer in which case it is
called the…
noise floor: The lower limit of what can be measured set by the
noise levels of the transducer.
saturation level: The maximum input level before significant
non-linearities in the output appear.
maximum input: The highest input signal which gives a
calibrated output. This level can be set due to saturation, damage
to the transducer, safety, output signal degradation.
dynamic range: The ratio of the maximum input signal to the
noise floor or threshold. Often reported in decibels:
DR = 10 log10(Max/Min)
(how it changes versus time)
Dynamic Characteristics
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response time: it is the time interval between a change in the
measured quantity and the time an instrument reads a new
equilibrium value, often defined in terms of three characteristic
times:
dead time (tD): time during which a new signal or variation in a
signal cannot be detected due to some physical characteristic of
the system or the transducer
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example: a Geiger counter fires when a particle/radiation enters the
tube and during the time the Geiger counter is producing a signal,
another particle/radiation entering the tube is not observed because
the counter is in the middle of responding to the first one
rise time (tR): the time taken by the instrument to respond to a
step change in a measured quantity, often defined as the time
taken to change from 10% to 90% of the final value.
settling time (tS): the time required for an instrument to attain
a stable reading within a stated percentage of its equilibrium
output, often taken to be the time to the first minimum of the
oscillation
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Plot of Time Response
at time t = 0, the input physical quantity makes a step change
output level
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rise
time
Steady-State Frequency Response of a
Transducer
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a transducer produces a sinusoidal output (within its operating
range) in response to a sinusoidal input [eventually, in steady
state, after some transient response that can be ignored mostly]
there will be a maximum (and often a minimum) frequency at
which the transducer can respond
if the input varies faster, with a higher frequency, than the
transducer can respond to, the transducer output will be reduced
the frequency at which the output signal is decreased to half of
the nominal output is described as the “corner frequency” or the
−3dB frequency
bandwidth: the difference between the maximum and minimum
3dB frequencies of the transducer
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Electrical Modelling of Transducers
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transducers produce electrical signals – they act electrically
either as voltage sources, current sources, or their
resistance or capacitance might change as a function of the
quantity being measured: V(Q), I(Q), R(Q), C(Q)
thus, in addition to understanding how transducers respond
to the effect being measured (the physics), you need to
understand the electrical behaviour
most generally, there will be a frequency dependence
there can be noise sources intrinsic to the transducer
starting point is an equivalent circuit:
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usually the source model includes output resistance and
capacitance
Equivalent Circuit for a Transducer:
General Example
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the quantity being measured is light intensity and the transducer
outputs a voltage
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V(Q) physical effect produces ideal voltage source
that depends on quantity Q being measured
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Ro output impedance
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Vo actual transducer voltage output
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Io actual transducer current output
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Co output capacitance
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intrinsic noise in the transducer
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Summary
  we
examined some of the general characteristics
of transducers
  understanding these helps us choose the
appropriate transducer for the required
measurement system
  understanding these helps us estimate possible
systematic errors related to transducer properties
  transducers are electrical: measurement system
is thus amenable to “basic” circuit analysis once
an equivalent circuit source model describes the
electrical behaviour of the transducer
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