SECTION 4:
MEASUREMENT FUNDAMENTALS
MAE 2055 – Mechetronics I
2
K. Webb
Electronic Measurements
MAE 2055 – Mechetronics I
Non-Disruptive Measurements
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The act of taking a measurement may change the
quantity being measured
True for both measurements of mechanical
properties and electrical properties
The key to making accurate measurements is
minimizing the disruption
Measurement system should be invisible to the
device-under-test (DUT)
K. Webb
MAE 2055 – Mechetronics I
Non-Disruptive Measurements
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
Consider measuring pressure inside a vessel
A
pressure sensor is placed in the wall of a the vessel
 If the sensor causes a leak, it will change the pressure
being measured

Say you want to measure flow rate in a pipe
A
flow meter (e.g. a turbine flow meter, flow nozzle,
or pitot tube) is placed in series with the flow
 If the meter presents excessive resistance to the flow
it will change the flow rate you are trying to measure
K. Webb
MAE 2055 – Mechetronics I
Measuring Electrical Parameters
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When working with electronic circuits the three
parameters we are most often concerned with are:
 Voltage
 Current
 Resistance
These parameters (and many more) can be
measured with common test equipment available in
the lab
K. Webb
MAE 2055 – Mechetronics I
Measuring Voltage
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Voltage is measured with a
voltmeter
Inserted into the circuit
between the nodes to be
measured
Very high input resistance
 Ideally,

Rin = ∞ Ω
Measure , V2, the voltage across
R2 in the following circuit
Connect voltmeter probes across
R2, between nodes to be
measured
Very low input current
 Ideally, Iin
K. Webb
=0A
MAE 2055 – Mechetronics I
Measuring Current
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Current is measured with an
ammeter
Inserted into the circuit in
series with the branch whose
current is being measured
Very low input resistance


Ideally, Rin = 0 Ω (short circuit)
Measure , I2, the current through
R2 in the following circuit
Break the circuit and reconnect
with ammeter probes, inserting
meter in series with R2
All (unaltered) branch
current flows through the
meter
K. Webb
MAE 2055 – Mechetronics I
Measuring Resistance
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Resistance is measured
with an ohmmeter
Connected across the
terminals of the device
being measured
Component disconnected
from circuit
Supplies a small current
and measures the voltage
K. Webb
Measure the resistance of R2
Disconnect R2, and connect
ohmmeter across the resistor
=
MAE 2055 – Mechetronics I
9
K. Webb
Electronic Measurement Instruments
MAE 2055 – Mechetronics I
Digital Multimeter - DMM
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www.agilent.com

Multi-purpose measurement instrument

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Voltage
Current
Resistance
Capacitance

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Frequency
Diode forward voltage
Transistor parameters
Temperature ...

Benchtop (more accurate) or handheld (portable) form factors

Connects to circuit under test with probes

Scalar measurements of DC or AC signals/parameters
K. Webb
MAE 2055 – Mechetronics I
DMM – inputs
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Inputs for
4-wire
resistance
measurements
Positive input
for voltage &
resistance
measurements
Positive input
for milliamp
current
measurements
Positive input
for voltage &
resistance
measurements
Positive input
for amp
current
measurements
Negative
input
www.agilent.com
K. Webb
Positive input
for current
measurements
Negative
input
MAE 2055 – Mechetronics I
Oscilloscope
12
www.agilent.com
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www.agilent.com
Displays voltage vs. time waveforms
Indispensible piece of equipment when working with
electronic circuits – scopes let you see otherwise invisible
electronic signals
Typically 2 or 4 channels connect to circuits with probes
Today’s scopes are digital as opposed to older analog
scopes
K. Webb
MAE 2055 – Mechetronics I
Scope Inputs
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Ch1, Ch2
input BNC
connectors


Coaxial BNC connectors are the input
connections to scope channels
Can connect to electrical signals with coaxial BNC
cables or with scope probes
K. Webb
MAE 2055 – Mechetronics I
Scope Controls
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Horizontal Control
sec/DIV
Vertical Control
V/DIV
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Scope waveforms plotted on a grid
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10 or 12 divisions along the horizontal (time) axis
8 divisions along the vertical (voltage) axis
Controls enable scaling of time and voltage axes


K. Webb
Vertical control (sensitivity or V/DIV) scales voltage axis
Horizontal control (sweep speed or time/DIV) scales time axis
MAE 2055 – Mechetronics I
Scope Controls – sensitivity (V/DIV)
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Sensitivity or volts per
division (V/DIV) control
adjusts the voltage step
between adjacent grid
lines on the vertical
(voltage) axis
Can adjust V/DIV setting
for each channel
independently
Offset control moves
0 V reference up and
down on screen
K. Webb
Ch1, Ch2
V/DIV
Controls
Ch1, Ch2
offset
Controls
Ch1, Ch2
input BNC
Connectors
MAE 2055 – Mechetronics I
Scope Controls – sweep speed (time/DIV)
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Sweep speed or time per
division (time/DIV)
control adjusts the
voltage step between
adjacent grid lines on the
horizontal (time) axis
Can adjust V/DIV setting
for each channel
independently
Delay control moves the
t=0 sec reference left and
right on screen
K. Webb
sec/DIV
Control
Delay
Control
MAE 2055 – Mechetronics I
Scope Controls – trigger level
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Sets the voltage level at which the scope
triggers
Trigger point of signal is placed at the
horizontal center of the screen (or left or
right)
Can select rising or falling edge trigger
Trigger coupling modes can provide stable
triggers for noisy signals
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AC coupling – rejects DC
High-frequency reject
Low-frequency reject
Noise reject
Trigger
mode/coupling
select
Trigger
Level
Control
Properly configuring the trigger enables
capturing infrequent events
K. Webb
MAE 2055 – Mechetronics I
Scope Controls – trigger level
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Trigger point is placed at trigger reference point –
usually the center of the horizontal (time) axis
Signal crosses trigger level voltage at center screen
Note how trigger level affects
waveform position on screen
Trigger reference point at center screen
Trigger level
= 50 mV
Trigger level
= -50 mV
K. Webb
MAE 2055 – Mechetronics I
Data Acquisition System
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Like a scope, captures a time record of measurements
May have hundreds of channels

Useful for acquiring large
amounts of data during
automated testing

Valuable for testing mechanical
systems

Interface and display through
external PC

Inputs provide signal
www.ni.com
conditioning for strain gauges,
thermocouples, and many other
types of sensors
Convenient post-processing of measured data in tools such as MATLAB

K. Webb
MAE 2055 – Mechetronics I
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K. Webb
Analog vs. Digital
MAE 2055 – Mechetronics I
Analog vs. Digital
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Analog signals are continuous in time and
amplitude
All physical phenomena – pressure, temperature,
velocity, strain, position, etc. – are analog in nature
 They

can take on any value at any time
Digital signals are discrete in time and amplitude
 They
can only assume a finite number of discrete
values at discrete instants in time
 Digital signals are representations of analog signals
that are easily stored and processed electronically
K. Webb
MAE 2055 – Mechetronics I
Analog vs. Digital – an example
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Temperature is an analog quantity – at any instant in time
it can assume any value
www.faqs.com

A mercury thermometer is an 
analog measure of temperature
– the mercury can be at any
height at any time
K. Webb
www.mdhb.com
A digital thermometer samples
the actual temperature at
discrete instants in time and
represents it with a finite
number of possible values
MAE 2055 – Mechetronics I
Digital Measurement System
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Analog
Analog
Input
Signal
Signal
Conditioning/
Amplification
Digital
Analog
to Digital
Converter
(ADC)
Digital
Data/Display
Processing
Digital
Data
Output/
Display
The analog input signal is converted to a
digital signal in an analog-to-digital
converter (ADC or A/D)
K. Webb
MAE 2055 – Mechetronics I
Analog-to-Digital Conversion
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Continuous-time and -amplitude analog signals are
converted to digital signals in A/D converters
Analog signal is sampled in time, generating a series of
discrete-time samples
Discrete-time samples are quantized – amplitudes are
mapped to a finite number of discrete amplitude
values
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A continuous range of input values maps to a single
quantization level
Resulting digital signal is discrete in both time and
amplitude
Digital signal is easily processed, stored, and displayed
K. Webb
MAE 2055 – Mechetronics I
A/D Conversion – sampling
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The first step in
converting from an
analog signal to a
digital signal is
sampling
Sampled signal is a
discrete-time
signal, but is still
continuous in
amplitude
K. Webb
MAE 2055 – Mechetronics I
A/D Conversion – quantization
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Next step is quantization
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Sampled signal becomes
a digital signal
The digital signal is
discrete in both time and
amplitude
Amplitude values of the
digital signal are
expressed as codes
# of A/D codes = 2N
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K. Webb
N = # of bits
10 bit A/D has 1024
distinct quantization
levels
Digital signal stored as
binary values
MAE 2055 – Mechetronics I
27
K. Webb
Measurement System Requirements
MAE 2055 – Mechetronics I
Instrument Requirements
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The two most important specifications for
oscilloscopes and data acquisition systems are
 Bandwidth
 Sample

Rate
These specifications determine what types of
electrical signals can be accurately measured
K. Webb
MAE 2055 – Mechetronics I
Bandwidth
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Bandwidth
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Defined as the frequency at which and analog input signal will
be attenuated by 3 dB by the measurement process
Places an upper limit on the frequency of signals which can be
accurately measured
Signals near and above instrument bandwidth will be
significantly attenuated
Ratio of the measured
amplitude to the input
amplitude (in dB)
K. Webb
BW = f3dB = -3 dB frequency
MAE 2055 – Mechetronics I
Sample Rate
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Sample Rate
 The
rate at which the measurement instrument
samples and digitizes the analog input signal
 Measured in Hz or in samples per second (Sa/sec)
 Inverse of the sampling period fs = 1/Ts
 Places an upper limit on the frequency (bandwidth) of
the input signal
 Can only accurately measure input signals whose
frequency is no more than half the sample rate
 Otherwise
K. Webb
aliasing will occur
f in 
fs
2
MAE 2055 – Mechetronics I
Sample Rate – aliasing
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Aliasing is a phenomena that results in a higher frequency
signal appearing as a lower frequency signal

Aliasing occurs due to failure to adhere to the Nyquist Criterion
Nyquist says that the sampling frequency must be at least twice
the maximum signal frequency

f s  2 f in

The Nyquist rate or Nyquist frequency is the minimum sampling
rate for which no aliasing will occur
f nyquist  2 f in
K. Webb
MAE 2055 – Mechetronics I
Aliasing – f = 10 Hz, fs = 8 Hz
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10 Hz signal sampled at 8 Hz
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Nyquist criterion violated
Aliased signal appears at 2 Hz
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K. Webb
MAE 2055 – Mechetronics I
Aliasing – f = 10 Hz, fs = 9 Hz
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10 Hz signal sampled at 9 Hz
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Nyquist criterion violated
Aliased signal appears at 1 Hz
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K. Webb
MAE 2055 – Mechetronics I
Aliasing – f = 10 Hz, fs = 10 Hz
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10 Hz signal sampled at 10 Hz
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Nyquist criterion violated
Aliased signal appears at DC (0 Hz)
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K. Webb
MAE 2055 – Mechetronics I
Aliasing – f = 10 Hz, fs = 20 Hz
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10 Hz signal sampled at 20 Hz
Nyquist criterion satisfied
Measured signal could appear, in theory, at DC – in practice, this
would rarely happen
K. Webb
MAE 2055 – Mechetronics I
Aliasing – f = 10 Hz, fs = 50 Hz
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10 Hz signal sampled at 50 Hz
Nyquist criterion satisfied
Frequency of sampled signal is the same as the analog signal
K. Webb
MAE 2055 – Mechetronics I