Michigan Aero305 Lab2

AE 305—Laboratory 2:
Non-steady-signal instrumentation
P.D. Washabaugh, J. Fishstrom, L.P. Bernal, T.B. Smith, and J.K. Edmondson
9 September 2014
Purpose
This is an introduction to instrumentation that is frequently employed to excite and detect non-
steady voltages and currents. These instruments are used to characterize the response of unknown
circuits. These circuits have a non-linear features. We will study the dynamic response of a
structure using a reflective distance sensor, and the acoustics of an air jet using a microphone and
pressure gauge.
Concepts
Non-steady voltage excitation and measurement, frequencies and amplitude, aliasing, measure-
ment accuracy and precision, instrument calibration, test matrices, circuit prototyping, and circuit
characterization. Acoustics of a choked air jet.
Summary
You will first review some features of a laboratory function generator and an oscilloscope. To
become familiar with both of these instruments you will use the oscilloscope to calibrate the function
generator. An electrical breadboard with two passive circuits is provided. You will calibrate their
non-steady voltage response as a function of input frequency and amplitude. The dynamic response
of a structure will be studied as a function of added mass. You will use a microphone and a pressure
gauge to study some features of the noise produced by an air jet.
Instrumentation
Function Generator; Oscilloscope; Voltmeter (non-steady measurement features), electrical bread-
board prototyping kit; a circuit with linear and non-linear elements; Reflective Distance Sensor;
microphone and pressure gauge.
1
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Important deadlines
Lab preparation assignment: Hand in to GSI before your lab section.
Lab notebook: Upload to CTools at end of your lab section.
Lab results assignment: Due at start of lecture, 16 September 2014.
Report: No lab report required for this lab.
1 Introduction
As discussed earlier, an instrument can be characterized by its input-output response. In the
previous lab you measured the steady or static response of a device using instruments that are
very good at these types of measurements. While the steady response of a device is frequently a
critical feature, the non-steady or dynamic response of a device can be even more important. The
dynamic or non-steady response of an instrument is more involved or complicated than the steady
response simply because of the introduction of another parameter, time. Time appears because
most physical processes are rate dependent. In others words events do not occur instantly, but
they take time to evolve.
When examining the dynamic characterization of an instrument we retain our earlier block diagram,
except now the input and the outputs are functions of time. A typical schematic showing the input
and output of a generic device or black box is shown below in Figure 1.
Figure 1: A typical schematic showing the input and output of a generic device.
Here you will perform the next step in a characterization process. You will become familiar with
standard instruments that are used to excite and measure a non-steady response. These include a
state-of-the-art function generator and oscilloscope. Along the way you will be exposed to additional
laboratory processes and features of experimentation. For instance you will discover that the
oscilloscope is an extremely versatile instrument that can be used to capture events that are too
quick for usual human response times. You will also find that the function generator can be used
to similarly excite events that are very fast. They both can be used to calibrate other instruments.
You will also be exposed to some of the practical aspects of this instrumentation. For instance, the
inputs to an oscilloscope are frequently single-ended, rather than differential as in a multimeter.
There is also quite a bit of effort required to set the instruments to capture the events of interest.
The issues here involve scaling and triggering of the instruments.
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2 Background
To prepare for this lab you need to know a few things about the equipment that you will be using.
Here a short summary is provided. More details are provided in separate attachments. Please note
that in this lab we will be using only the most basic features of the instruments.
2.1 Function generator
The purpose of a function generator is to provide a signal that can vary in time. A function
generator has some features akin to a power supply. Both a function generator and a power supply
produce a voltage. You can think of a function generator as a power supply where you are wiggling
the voltage knob. Even though there are some similarities between a generator and a supply, there
are some significant differences as well. For instance a power supply is optimized to provide a
constant voltage. A function generator is optimized to vary a voltage as a function of time at a
precise rate (i.e. frequency). As with most optimization problems, you lose something with this
time-varying capability and that is power. Function generators have very little current capability.
A lab power supply can easily provide 2-3 A of current at voltages of up to 30 V. Thus our lab
power supply can generate ∼ 100 W of clean DC power. In contrast our function generator can only
drive 200 mA of current at 10 V. This corresponds to 2 W. An almost universal symbol indicating
a function generator in a circuit diagram is shown in Figure 2.
Figure 2: Traditional symbol for a function generator.
Modern function generators come in various types. The one that we will be using is a state-of-
the-art laboratory function generator. It has some usual features. For instance it can produce sine
waves, square waves, and triangle waves, e.g. see Figure 3. It also has the ability to be programmed
to provide a wide variety of “arbitrary” or user specified waveforms. An image of the function
generator that we’ll be using is shown in Figure 4.
In any signal generator you can adjust both the frequency f and the amplitude A. In some, you
can also adjust the offset o and the phase angle φ. (The phase is adjusted by a time-delay circuit.)
These are graphically portrayed in Figure 5.
The function generator that you’ll be using has the ability to generate numerous other periodic
signals. For example you can modulate the base signals or generate arbitrary waveforms by altering
their amplitudes or frequencies, as shown in Figure 6. The sweep in frequency shown in Figure
6(b) is especially useful to identify resonance.
Most function generators simply generate periodic signals. The function generator we will be using
can also generate transient signals. Transient signals, e.g. see Figure 7, are initiated by some type
of “trigger” and after a prescribed delay—potentially zero in magnitude—the signal is generated
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(a) Sine wave (b) Square wave (c) Triangle wave
Figure 3: Example waveforms from a function generator.
(a) Front panel (b) Rear panel
Figure 4: Front and back views of our Agilent 33220A Arbitrary Waveform generator.
Figure 5: Sinusoidal waveform, showing the peak-to-peak amplitude 2A, period 1/f, d.c. offset o,
and phase angle φ.
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(a) Amplitude modulation (b) Frequency modulation
Figure 6: Examples of amplitude-modulated and frequency-modulated sinusoidal waveforms.
for a certain duration. Since this function generator can produce arbitrary waveforms, the shape
of this transient signal can be anything you want—within the capabilities of the generator. In this
lab we will not exercise this transient capability, but you should know that it is available.
Figure 7: Example of a transient or burst signal.
Since this function generator is a digital instrument, it actually produces signals in discrete steps. In
others words the signal that you see generated in Figure 5 actually has thousands of tiny steps. You
just can’t see them at a coarse resolution. However, if you examine the signal from the function
generator at a very high resolution in both amplitude and time you would see something like
Figure 8 —a series of steps. These steps are related to the bit-resolution capabilities of the digital
device. These small steps are one of the most fundamental differences between analog and digital
instruments. Note that capacitance and noise in both the generator circuit and the measurement
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circuit will blur this image. The discrete steps in the generator are intimately tied to the bit
Figure 8: Details of an ideal digital signal. Here the time step in the signal is ∼ 10 ms, while the
voltage step is 10 mV.
resolution of the digital-to-analog (D/A) converters on the output stage of the instrument. For
instance our function generator has a 14-bit D/A converter. What this means is that the voltage
can at best be divided into 2
14
or 16384 steps. If the voltage range is 20 Volts peak-to-peak (20
Vpp), then the smallest voltage step you can expect to see is (20/2
14
) V or 1.22 mV.
Function generators are graded on their frequency range, amplitude capability, and (in the case of
digital instruments) their bit resolution. This function generator can generate frequencies up to 20
MHz. For high-frequency instruments, this is not very impressive; however, it is usually plenty for
most mechanical tests. This generator also has the very unusual capability (for a function generator)
to produce a constant signal. Since it can generate a wealth of pre-programmed waveforms as well
as arbitrary ones, it is an extremely versatile instrument.
2.2 Oscilloscope
In the same way that a function generator is the dynamical cousin of the power supply, the os-
cilloscope is the cousin of the voltmeter (e.g. see Section 4.15- 4.16 of Holman). Please note that
the oscilloscope’s cousin is the voltmeter and not the multimeter. A multimeter has the ability
to measure current, resistance and other quantities, while a typical oscilloscope can only measure
voltage. If you want an oscilloscope to measure resistance or current, you usually have to provide
the extra circuitry yourself. A symbol for an oscilloscope is shown in Figure 9.
There are other significant differences between a voltmeter and a typical oscilloscope. While good
voltmeters have a high input impedance (e.g. 10 MΩ), the scope has a lower input impedance to
terminate spurious waves properly, thus preventing energy from bouncing off ends of the signal
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Figure 9: A symbol for an oscilloscope. I don’t know of a ‘traditional’ symbol.
wires. In other words, oscilloscopes require more power from the circuit that they are testing than
a multimeter. For example, most research-grade scopes have an input impedance of 50 Ω with an
option for higher impedance such as 1 MΩ. The scope you will be using has only a fixed 1 MΩ
impedance. (The lack of a 50 Ω option helps to prevent accidents that damage the scope. e.g. if
you accidentally use the scope to measure 110 V AC from a wall power outlet, the 1 MΩ input
impedance will protect the scope. A 50 Ω input would get fried!)
This lower input impedance means that for a given voltage, the scope will draw significantly more
current than a typical voltmeter. To limit the power being dissipated in the scope, they usually have
a lower voltage range than a multimeter. You can think of the input impedance of the oscilloscope
as a resistor and a capacitor, i.e. replacing the element in Figure 9, with the resistor and capacitor
showing in Figure 10.
Figure 10: An equivalent circuit for an oscilloscope showing the effect of resistance R and capaci-
tance C on the circuit under test.
It is very important to note that any instrument that is used to measure a physical property can
potentially influence the system that is being measured. Note that most oscilloscopes are single
ended. In other words the ‘negative’ is internally attached to chassis ground. This ground is a
frequent source of problems. On a differential voltmeter if you switch the positive and the negative
you simply invert the signal being measured. However if you do this on a scope, you can short the
positive signal to ground! Consequently, you need to be very careful and keep track of the ground
line when you use an oscilloscope. In a later lab we’ll construct an active circuit that will be
sensitive to grounding through the oscilloscope.
The scope that we’ll be using is shown in Figure 11. An oscilloscope is a display that is akin to an
automatic plotter. You can think of the scope as simply capturing processes that you are not quick
enough to see with your own senses. This ability to both capture events and display them rapidly
can be critical. The capturing of the event is important because it forms the data from which you
will make decisions. The ability to display these results quickly—rather than wait minutes, hours
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or days for the results—means that you can make rapid adjustments to a situation. For example
think of an altimeter on the airplane. You want the altimeter to be accurate and precise, but you
also need the information in ‘real time’ so you can make use of it while you are flying a craft.
Figure 11: Front panel of an Tektronix TDS2000 Series oscilloscope. Note four input channels and
a separate trigger.
The trick to using an oscilloscope is to keep track of its display, That is, you need to keep track of
where the oscilloscope is ‘looking’ for information. Frequently an oscilloscope appears to be ‘not
working’ because it is being asked to look at a signal that does not exist! For example, you can
tell an oscilloscope to only look at voltages above 1 V, and if your signal is below 1 V, the scope
will not display it. In other words, unlike your voltmeter, the oscilloscope is not very good at using
‘auto-scale’ to find your signal—although your scope does have an ‘auto-range’ button that can
capture certain signals, it is not perfect.
Another difficulty with an oscilloscope is when to look and how fast to look. Transient signals
require a proper trigger to avoid taking a measurement either too soon or too late. You have to be
careful to make sure your scope is looking in a window to capture your signal. Consequently, you
constantly need to keep in mind how your scope is configured.
Scales
Consider the signal shown in Figure 12. There are two scales to worry about. The first is the
horizontal scale or the ‘time base.’ This scale is usually adjusted by a knob on the scope and it
tells the scope how quickly to sample. The vertical scale tells the scope over what range to look
for a signal and is also adjusted by a knob. There are analogues features on a digital voltmeter. A
digital voltmeter frequently has the ability to read at “slow,” “medium,” or “fast” rates the time
base is similar to this except that there are many more ranges to choose from, and the scope will
actually record each individual readings (and display them) rather than average them into a single
number. Similarly the vertical scale is akin to the “manual mode” on a voltmeter.
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Figure 12: A transient signal. To capture this signal the scope must have the horizontal (time base)
and vertical (voltage) scales configured properly (i.e. range and offsets) as well at the trigger level.
On the scales you also have the ability to offset the display. For instance you can move the entire
signal on the display vertically with an “offset” or “position” knob. This is shown in Figure 8.
There is also a corresponding ability to offset the display in the horizontal direction by a delay. On
older scopes, the instrument would remain idle until a “zero time” condition was met. Once this
condition was met, the instrument would wait the specified delay, and then record the voltages on
the input to the display at the proper reading rate (horizontal scale) and voltage range (vertical
scale).
New digital scopes operate in a slightly different manner. They are persistently recording the
voltages on the input and store them in a buffer. When the “zero time” condition is met, the
display can either capture new data from the input, or the scope can also take information from
the buffer. One consequence of this buffer is that the “delay” can be either positive or negative
with respect to where ‘zero time’ is set. This ability to set the zero time condition at the end of
a signal is especially useful in transient tests like failure analysis (where you would like to observe
events leading up to failure) or shock tube testing (where you would like to measure the pressure
just before and after a shock wave). This delay is not shown in Figure 12.
Trigger
The trigger is the way you set “zero time” in a scope. The simplest trigger is to tell the scope to
run continuously no matter what! What this means is that the scope is displaying everything it
reads on its input. In other words, as soon as the scope is done displaying a signal, it starts over
and displays the next set of voltages without waiting. This is very useful if you have no clue as to
the properties of your signal.
Unfortunately, if you have a nice sine wave (e.g. see Figure 3(a)), except for the very special instance
where your time base exactly matches the period of your signal, the sine wave would appear as in
Figure 13. The reason for this confused display is that it is actually showing 5 or more traces of
AE 305 — Lab 2 Fall 2014 10
the signal in sequence very quickly. The scope is starting the display without any regard for what
is being measured on the input. Consequently, each time the display is initiated, the sine wave is
at a different location in phase.
Figure 13: A typical display from an oscilloscope that is triggered to run continuously with no
trigger level.
To correct this situation and get the scope to provide a stable display of the signal you need to
set the time the display starts, (i.e. ‘zero time’) to some feature of the input signal. This is done
through a more sophisticated trigger. There are lots of types of triggers but one of the most
common is to set a voltage level and a slope. The signal is read into the scope and when it detects
the appropriate voltage level (say, a positive slope on the signal), the display is initiated. If the
signal source has a stable or constant phase, you’ll get a just a single sine wave on the display.
Scopes have many other interesting features. You can tell them to keep triggering, i.e. to “run,” so
that is every time it is finished with the display the trigger is re-enabled and triggers immediately.
Or you can tell it to run just once. When it runs once, after a trigger event and the display
is finished, the trigger is turned off so that any subsequent input is ignored. Keeping the scope
running is useful if the signal is periodic. Capturing a single event is useful if you are dealing with
transient events (i.e. events that don’t repeat).
High-pass and low-pass filters, bandwidth
All devices that look at time varying signals have the ability to see (or measure) certain signals
and are blind (or are unable to measure) other signals. The capability of the instrument is most
usually dependent upon the frequency of the signal. If you provide a constant amplitude signal to
the instrument at some high frequency, the amplitude would seem to diminish. A point at which
the amplitude reduces is called an upper cut-off frequency. Similarly, in some instruments, as the
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frequency is reduced, the signal will again reduce at some point called the lower cut-off frequency.
This dependence of the amplitude of the measured signal as a function of frequency is shown in
Figure 14.
Figure 14: Typical features important to the performance of an oscilloscope.
The upper cut-off frequency is usually prominently displayed on the front of the scope. For example
a general-purpose scope might have a cut-off frequency of 20 MHz to 100 MHz. Significantly more
expensive scopes have frequency cut-offs that are as high as 100 GHz! This number is also called
the bandwidth of the scope because an oscilloscope can measure signals down to 0 Hz (or DC) if
properly configured. The scopes you’ll be using in this course are 100 MHz scopes.
Scopes also have the ability to insert several filters into the signal. These are typically called “AC
coupling” or “DC coupling.” With “DC coupling,” the scope will have a lower cut-off frequency of
∼ 0 Hz and an upper cut-off frequency that is the maximum of the instrument. (For us, this will
be 60 MHz.). If “AC coupling” is selected, then a high-pass filter is inserted into the circuit. This
high-pass filter will have a lower cut-off frequency that is ∼ 10 Hz. It is specifically used to remove
an unwanted DC component of the signal. This “AC coupling” would be used, for instance, to
measure the small oscillatory ripple on a DC power supply.
2.3 Shielded cables and adapters
When you are dealing with non-steady signals the cabling that is used to connect the instruments
and how they are electrically terminated at each instrument can be critical—especially as the
frequency of the signals increase. One way to connect signals is to use co-axial cables. These cables
provide shielding of the primary signal line by wrapping the signal line in a conductor. The simplest
shielded cable involves 2 conductors; one for the signal and one for the shield. Perhaps the most
common co-axial cable system is “Cable TV” which uses this type of cable.
Alternate methods to transmit high frequency signals involve more wires. These can involve twisted
pairs of wires that are then shielded. For example Ethernet, USB cables, and IEEE 1394 cables
AE 305 — Lab 2 Fall 2014 12
(Sony I-Link and Apple Firewire) use multiple twisted pairs of wires that are shielded to transmit
digital signals over long distances.
In this lab you will be using co-axial cables because both the function generator and the oscilloscope
have co-axial cable connectors. The connectors that they use are called BNC connectors. A BNC
connector is a cable termination which is used primarily in labs and sometime in professional
studios. The BNC connector has a thin central pin which is connected to the signal line and an
outer rounded metal cylinder that is connect to the shield. The connector pushes onto its jack and
twists down and to the side to lock it in place.
It is important to note that frequently an instrument will ground the shield on the BNC connector.
This is especially important when you are converting from say “banana plug” to a BNC connector.
One side of the BNC to banana plug adapter is labeled with a “GND” to indicate which pin is
ground. If you don’t pay attention to this feature (and many do not) you’ll end up shorting your
signal to ground. Fortunately many of your instruments have built-in protection for this type of
error so it should not be catastrophic for your instrument—however it may be catastrophic for the
device you are testing!
2.4 Microphone, pressure gauge, and choked nozzle
Finally in this lab you will use a microphone and a pressure gauge to characterize a cold air jet. You
can refer to your text for details on these devices (e.g. Section 11.5 for Microphones, and Section
6.1 to 6.6 for Pressure Transducers). You will use the pressure gauge to measure the pressure in
the plenum chamber before the air leaves the nozzle. You will use the microphone to measure the
noise that is generated by the flow. This is shown below in Figure 15.
Figure 15: A schematic showing the nozzle, pressure gauge, microphone and jet.
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Figure 16: A Schlieren image of the nozzle flow showing small normal shocks in the vicinity of the
nozzle. The Schlieren photographic technique displays regions of varying fluid density. This is an
actual image from one of our jets.
At low pressures the flow inside the chamber and outside the nozzle stays subsonic. However, if the
pressure inside the plenum chamber is sufficiently large, the flow outside can become supersonic.
This supersonic flow is characterized by large changes in fluid density in the form of shocks and
expansions. These fluid features are shown in Figure 16 which is a Schlieren photograph of the jet.
It is important to note that the flow structures such as the normal shocks shown in Figure 16 only
occur when the air leaving the nozzle is supersonic. This occurs at elevated pressures. At lower
pressures, the flow is subsonic and the shocks would not appear.
The pressure gauge is used to measure the difference in pressure between the plenum and the
ambient atmosphere. You can use this information to determine the air speed in the nozzle.
This is not a very fancy nozzle in that it has sharp corners on the interior—so when the flow
approaches sonic conditions compressibility effects may occur. In addition, since this nozzle only
converges (i.e. it is not a converging-diverging nozzle) you can’t get supersonic flow in the nozzle
itself. However, when the flow expands you can get supersonic speeds external to the nozzle! The
transition from subsonic flow to supersonic flow will lead to reasonably dramatic change in the
characteristics of the noise produced from the nozzle.
The microphone is used to measure the noise from the jet mixing with the ambient air. It is
important to keep the microphone directly out of the jet when performing this measurement because
otherwise the microphone will detect the jet momentum and not the acoustic energy. Also, to get
a good signal it’s a good idea to position the microphone 30-100 nozzle diameters downstream
pointing at the nozzle—keeping it out of the jet.
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Finally, the lab that you will perform will not be in an ideal environment. There are numerous
issues here. First, the room does not have much acoustic treatment, so the microphone will hear
all the fans in the ceiling. In addition, there will be potentially 5 nozzles running at once! These
effects will raise the ‘noise floor’ or background noise level of your experiment.
3 Procedure
There are four main tasks in this laboratory. The first task is to corroborate the performance of
the function generator as measured by both the multi-meter and the oscilloscope. The second task
is to characterize the frequency response of a test circuit both as a function of frequency and as
a function of amplitude. The third task is to examine the dynamic response of a simulated wing.
The final task is to examine the acoustic performance of a cold air jet.
3.1 Preliminary instrument setup
Both the function generator and the oscilloscope are quite complicated instruments that require
some preliminary steps to get them into a state to make them useful for any particular measurement.
The purpose of this preliminary step is to make sure both instruments are in state to facilitate
subsequent testing.
3.1.1 Function generator
The function generator is a completely digital instrument. Cycling its power will return it to a
default state where it is generating a 1 kHz Sine wave at 100 mV peak-to-peak and the output is
set for 50-Ω impedance and turned off.
This default power-up state assumes that it is driving a 50-Ω impedance. The instrument has
this default setting because when you are dealing with non-steady signals, to reduce signal noise
problems (i.e. signal reflections on lines) you need to worry about the how cables are terminated.
A 50 Ω termination is frequently used. This function generator can be used to drive signals up to
20 MHz where these termination issues can result in “ringing” in your measurements. At lower
frequencies, (e.g. say < 50 kHz and below) termination is not usually a problem. An instrument
like a voltmeter is a high impedance device, (e.g. input impedance > 1 MΩ). There is a very
good reason for this high impedance; when you measure a voltage the high impedance “simulates”
an open circuit, thereby having a small effect on the circuit under test. Unfortunately, what
this means is that when you measure the voltage coming out of the function generator with a
high impedance voltmeter, you get a factor of 2 discrepancy between what the function generator
displays as outputting and what the voltmeter will measure. The voltage value displayed is 2 times
higher!
Since oscilloscopes are used to measure non-steady signals, historically they always had a 50-Ω input
impedance. Consequently when you took a function generator (that is expecting to drive a 50-Ω
impedance) and connect it up to a usual scope (with a 50-Ω input impedance), the scope would
provide a measurement that corresponded to the function generators display. Unfortunately this
50-Ω input impedance can cause problems—especially for students who are exploring creative uses
AE 305 — Lab 2 Fall 2014 15
for instruments! For example, a persistent problem has been the attempt to measure line voltages
(e.g. usual AC voltages of 120Vrms from a typical power socket). If you take a 50 Ω resistor and
place it across the “hot” and the “neutral” of a power socket you will draw about 2.5 Amps of
current. This corresponds to several hundred Watts of power that need to be dissipated. Usual
resistors are rated at 1/4 to 1 Watt. The result of the above exercise is a blown input channel on
the scope! To try and remedy this problem the instrument makers have tried putting warnings on
the inputs or have provided an option for a high impedance input to the scope. The scope you will
be using only has a high impedance input—this makes it more difficult to damage.
Consequently, to make your function generator compatible with both the voltmeter and the scope
you have two choices:
1. You can remember that the function generator is trying to drive a 50-Ω impedance. What this
means is that anything that is displayed in terms of voltage on the generator (e.g. amplitude
and offset) is 1/2 of the actual voltage that is being generated. You can survive by doing this
but I do not recommend it.
2. You can set up the function generator to drive a high impedance circuit. When you do this,
the function generator will display the correct voltages. You do this by pressing the following
buttons:
(a) From the power on state press the Utility button.
(b) Press blue button under the display Output Setup. This is the third blue button from
the left.
(c) Press the blue button under Load High Z to highlight High Z. This is the first button
from the left.
(d) Press the blue button under DONE to enable the high impedance and go back to the
main display.
You should be aware that these changes are not permanent. If you cycle the power on the instrument
you will go back to a 50-Ω impedance. There is a way to store a state of the instrument if you
have to make these changes frequently—however in the interest of education you need to be aware
of how your instrument is configured!
The function generator is now ready for general use with high impedance devices. Unlike the power
supply, the function generator has limited current generating capability. If you now try to drive a
low impedance circuit, say 50 Ω, the actual voltage that is output will be lower than the displayed
values.
On this instrument you have two ways to change the frequency, amplitude and offset. For example
to change the frequency:
1. Select the proper input parameter (frequency, amplitude, or offset) by pressing the blue button
under the corresponding indicator. The indicator Freq, Amp, or Offset should highlighted
and with vertical lines on both sides. In this case Freq should be highlighted and have vertical
lines on both sides. This is the default power-up state of the display.
2. You have two ways of adjusting the frequency:
(a) Using the “knob”:
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i. use the [<] and [>] buttons to adjust the highlighted digit on the display, then
ii. use the physical knob on the display to adjust the numerical value of this digit.
(b) Entering the number directly:
i. Use the numeric keypad on the front panel of the instrument to enter the frequency.
Note that as soon as you press a number the display changes to show units and the
CANCEL option.
ii. Press the blue button for the correct units you are using. As soon as you press any
of the blue buttons the display goes back to waveform parameters input.
3. To adjust the amplitude, you would highlight Amp and proceed as in step 2 above; to adjust
the offset, you would highlight Offset and again repeat step 2.
4. Press the output oval button to enable the output. The Output Off indicator at the top left
of the display will change to High Z Load. If High Z Load doesn’t show the output impedance
is 50 Ω and you should change it to high impedance.
Now that you have learned how to setup the signal generator, configure the signal generator to
produce a square wave of 1 kHz frequency and 100 mVpp amplitude. This will be very useful
to configure the oscilloscope. Please have your GSI verify that you have configured the signal
generator correctly before you move on to the next section.
3.1.2 Oscilloscope
Oscilloscopes have a large number of features that can be used to measure various properties of
signals. Unfortunately this same versatility can make the instrument difficult to configure to make
the measurement that you want. The most difficult part of getting an oscilloscope to work is to
get a signal to be displayed. The oscilloscope that you are using is digital. However it has the
property that when you cycle the power it remembers its previous state! This is good if the scope is
in a useable state, however it can be painful if someone has messed up the features. The following
instructions are intended to show you some of the steps that are necessary to set-up the oscilloscope
from a relatively arbitrary state.
1. Make sure that the oscilloscope is turned on. The power button is on the top of this unit.
2. Connect a signal into channel 1. For instance: using a BNC cable, connect the output from
the function generator (i.e. the 1 kHz, 100 mVpp square wave signal) to the channel 1 input
of the scope. Note that the function generator has two output jacks; use the one labeled
OUTPUT.
3. To get the scope into a ‘known’ useable state press the [AutoSet] button. This function will
reset many, but not all, features on the scope. For instance if there is a signal on channel 1,
it will rescale both the vertical and horizontal axes to provide a good display.
4. Press the Run/Stop button and the yellow button labeled 1 to show the Channel 1 Menu.
The oscilloscope display in this configuration is shown in Figure 17. Please review all the
elements of the display as illustrated in the figure.
AE 305 — Lab 2 Fall 2014 17
Figure 17: Oscilloscope display for the square wave signal test setup. Each element of the display
is labeled.
5. Note that the Channel 1 Menu gives information on the channel 1 status, which in this case
is: Coupling DC, Bandwidth Limit OFF, Volts/Div Coarse, Probe 1X Voltage, and Invert
(off). You can change the status using the buttons immediately to the right of the display.
You could change these settings if you like, but make sure that you return to the default
configuration shown in Figure 17 after you are done.
6. Press the Run/Stop button; the acquisition status indicator at the top of the display will
change from STOP to triggered Trig’d.
7. Use the channel 1 vertical scale knob (Figure 18(a) shows the location of the knob within the
vertical control group) to change the vertical scale and follow the changes in the Channel 1
Status window at the bottom of the display.
8. Use the horizontal scale knob (Figure 18(b) shows the location of the knob with in the
horizontal control group) to change the horizontal scale and follow the changes in the Timebase
Status window at the bottom of the display.
3.2 Calibration
You will be using the Oscilloscope and the Multimeter to calibrate or corroborate and characterize
the output of the function generator. You will learn some features of how the oscilloscope and
the multimeter measure unsteady signals. You will also learn about some of the limitations of the
oscilloscope and function generator. To set up the calibration, proceed as follows:
AE 305 — Lab 2 Fall 2014 18
Operating Basics
!"#$%$"& '() *) + , -./ Positions a waveIorm vertically.
() *) + , - 01&2/ Displays the Vertical menu selections and toggles the display
oI the channel waveIorm on and oII.
34561 '() *) + , -./ Selects vertical scale Iactors.
05%7/ Displays waveIorm math operations menu and toggles the display oI the
math waveIorm on and oII.
8"9$:"&%56 ;"&%9"6#
*<475&&16 =">16 -<475&&16 =">16
!"#$%$"&/ Adjusts the horizontal position oI all channel and math waveIorms.
The resolution oI this control varies with the time base setting. (See page 87,
Window Zone.)
!"#$% To make a large adfustment to the hori:ontal position, turn the !"#$%"&'()
*+(), knob to a larger value, change the hori:ontal position, and then turn the
!"#$%"&'() *+(), knob back to the previous value.
8"9$:/ Displays the Horizontal Menu.
31% %" ?19"/ Sets the horizontal position to zero.
34561/ Selects the horizontal time/division (scale Iactor) Ior the main or the
window time base. When Window Zone is enabled, it changes the width oI the
window zone by changing the window time base. (See page 87, Window Zone.)
14 TDS2000C and TDS1000C-EDU Series Oscilloscope User Manual
(a) Vertical
Operating Basics
1 menu) button and then push the top option button to cycle through the
Vertical (channel) Coupling options.
In some lists, you can use the multipurpose knob to select an option. A hint
line tells you when the multipurpose knob can be used, and an LED by the
multipurpose knob lights when the knob is active. (See page 15, !"#$ %#&
'(#)*(+ ,$))(#-.)
Action: The oscilloscope displays the type oI action that will immediately
occur when you push an Action option button. For example, when the Help
Index is visible, and you push the Page Down option button, the oscilloscope
immediately displays the next page oI index entries.
Radio: The oscilloscope uses a diIIerent button Ior each option. The
currently-selected option is highlighted. For example, the oscilloscope
displays various acquisition mode options when you push the Acquire Menu
button. To select an option, push the corresponding button.
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TDS2000C and TDS1000C-EDU Series Oscilloscope User Manual 13
(b) Horizontal
Figure 18: Oscilloscope horizontal and vertical controls.
1. Use BNC cables and BNC T-adapter provided to construct the circuit shown in Figure 19.
Figure 19: Calibration of the function generator using the voltmeter and the oscilloscope.
2. On the function generator,
(a) press the sine button to select a sine wave signal,
(b) set the amplitude to “5.000 Vpp”, and
(c) Check that the frequency is 1.000,000,0 KHz (the power-on default).
3. On the multimeter, set the meter to display/measure VAC. Be sure to keep the autorange
feature enabled. The multimeter will now measure the root-mean-squared (rms) voltage.
4. On the oscilloscope, using the ‘default configuration’ (i.e. Press AutoRange) previously de-
fined, set up measurements as follows:
AE 305 — Lab 2 Fall 2014 19
(a) Press the Measure button to show the Measure Menu.
(b) Press the top button of the screen menu to select “CH1” as the “source.”
(c) Press the button to the right of “Type.” The Menu option displayed below this will
change from “None” to “Freq.” Continue pressing this button until the option displayed
is“Pk-Pk.” The scope will now display the peak-to-peak voltage of the signal under the
heading “Value”.
(d) Press the button to the right of “Back” to return to the Measure Menu. The scope will
now display the peak-to-peak voltage of the signal to the left of the uppermost screen
menu button.
(e) Press the next-lowest button of the screen menu to select “CH1,” and click through to
select “RMS.”
(f) As before, press the button to the right of “Back” to return to the Measure Menu. The
scope will now display the rms voltage of the data at the center of the display directly
below the peak-to-peak voltage.
5. Here you will examine some aspects of how the time base on the oscilloscope needs to be set
in order to obtain measurements. With the function generator providing a fixed signal, vary
how this signal is measured with the oscilloscope. On the oscilloscope, set the following:
(a) Adjust the Volts/Div scale to 1.00 V per division.
(b) Adjust the horizontal scale to 250 microseconds per division.
(c) To confirm that everything is set-up properly you should see:
i. a sine wave on the oscilloscope;
ii. a peak-to-peak voltage on the oscilloscope of approximately 5.0 V;
iii. an rms voltage on the oscilloscope of approximately 1.75 V;
iv. an rms voltage on the multimeter that should also be approximately 1.75 V.
(d) Vary the time base (or time scale) on the oscilloscope to the following times per division
and record the peak-to-peak and rms voltage as measured by the oscilloscope, and the
multimeter. Make a note of the display changes on the oscilloscope.
i. 10.0 microsecond
ii. 50.0 microsecond
iii. 250.0 microsecond
iv. 1.0 millisecond
v. 5.00 millisecond
vi. 25.0 millisecond
vii. 100 millisecond
viii. 500 millisecond
ix. 2.5 seconds
6. Next you will examine the frequency limits of both the oscilloscope and the multimeter. Vary
the frequency on the function generator keeping its amplitude fixed at 5 Vpp.
(a) In order to capture the signal on the oscilloscope you will have to adjust the time base
for each frequency. Use what you learned above. In order to get a good measurement
you need to have the waveform displayed on the screen.
AE 305 — Lab 2 Fall 2014 20
(b) At each frequency measure the
i. peak-to-peak voltage and rms voltage using the oscilloscope when it is configured
with DC coupling;
ii. peak-to-peak voltage and rms voltage using the oscilloscope when it is configured
with AC coupling; and
iii. rms voltage using the multimeter.
Once you have switched coupling modes (by pressing the yellow “1” button, then select-
ing the coupling mode at the uppermost button of the screen menu), you can resume
displaying these measurements by pressing the “Measure” button.
(c) Examine the following frequencies:
i. 10 MHz
ii. 1 MHz
iii. 100 kHz
iv. 10 kHz
v. 1 kHz
vi. 100 Hz
vii. 10 Hz
viii. 1 Hz
7. Since your oscilloscope has a faster frequency response than your function generator, you can
use it to visualize the discrete nature of the signal coming from your function generator.
(a) Re-set the function generator to provide a 1 kHz frequency sine wave with a 5 Vpp
amplitude.
(b) Focus in on the details of the signal coming from the function generator.
i. Set the horizontal resolution of your oscilloscope to a time base of 100 nanosecond
per division.
ii. Set the vertical resolution of your scope to a resolution of 2 millivolts per division.
(c) In order to improve the signal-to-noise ratio, try some (or all) of the following steps:
i. Remove the multimeter from the circuit, running a single uninterrupted coaxial cable
from the function generator to the oscilloscope. This will reduce radio-frequency
pickup on your signal line.
ii. Use signal averaging:
• press the “Acquire” button to show the Acquire Menu; and
• press the button to the right of ”Averages” until the signal stabilizes.
Either 16 or 64 should work well as a number of averages for this signal.
(d) Freeze the signal by pressing the “Run/Stop” button, and describe the waveform.
i. What is the approximate vertical magnitude (in voltage) of the steps?
ii. What is the approximate horizontal magnitude (in time) of the steps?
8. Restart acquisition, return to the Acquire Menu and return to the “Sample” mode.
Note:
1. The instructions above assume that you are using channel 1 on the oscilloscope.
AE 305 — Lab 2 Fall 2014 21
2. Keep in mind the purpose here is to learn how each instrument works. In particular the os-
cilloscope needs some care to properly record the signal. The scope only calculates properties
on the measurements that are being displayed.
3. You’ll also discover some of the limitations of each of the instruments. For example, depending
how the instruments are configured, they are incapable of measuring the signal.
3.3 Characterization of circuits
Making use of the calibration of the function generator we can now test the input and output
response of the circuits on the breadboard. Use the following procedure:
1. You have two circuits available from lab #1. Characterize circuit #2 first—it has a clipping
behavior that is extremely common. If you have time, characterize circuit #1 (i.e. circuit #1
is optional).
2. Keep the function generator, oscilloscope and the multimeter in essentially the same config-
uration as above (i.e. you don’t have to substantially re-setup the instruments, however you
will be re-wiring the external connections).
3. On the oscilloscope:
(a) Enable both channel 1 and channel 2 on the oscilloscope.
(b) Make sure both of them are DC coupled.
(c) Make sure they both have the same vertical scale of 1 volt/div.
(d) Depending on which channel you place the output, you may need to adjust the voltage
measurement functions (e.g. Vpp and Vrms) to measure the output of the circuit.
4. Use the BNC cables and BNC T-adapters provided to construct the following circuit shown
in Figure 20.
5. With the function generator set at 5 volts peak-to-peak,
6. Set the frequency of the function generator to:
(a) 1 Hz
(b) 10 Hz
(c) 100 Hz
(d) 1 kHz
(e) 10 kHz
(f) 100 kHz
(g) 1 MHz
7. At each frequency in (6):
(a) record the peak-to-peak and rms input voltage as measured by the oscilloscope;
(b) record the peak-to-peak output voltage as measured by the oscilloscope;
AE 305 — Lab 2 Fall 2014 22
Figure 20: Calibration of the circuit using the function generator, oscilloscope, and voltmeter. The
two oscilloscopes shown indicate the two input channels.
AE 305 — Lab 2 Fall 2014 23
(c) record the rms output voltage as measured by the multimeter;
(d) examine the difference between the input signal and the output signal; and
(e) note the phase difference between the two signals.
(f) You can either estimate the phase difference between the two signals, or,
(g) you can use the [Cursor] feature on the scope to actually measure a time difference
between two events on the screen.
(h) Note the shape of the two signals.
8. With the function generator set at 20 volts peak-to-peak, repeat the voltage and frequency
measurements in (6) and (7) above. Make sure to note any differences in the output signal
shape!
9. If you have time you may improve on the resolution of the above experiments by repeating
the measurement and by adding frequency points. However, the above measurements will be
sufficient to answer the questions in the post-lab assignment.
Note: Usually, the input is on channel 1 and the output is on channel 2. The main reason for this
is that the oscilloscope is triggered off channel 1. The input signal is a ‘cleaner’ and ‘known’ signal.
Using a known clean signal usually avoids triggering problems. In this configuration you may have
to change the oscilloscope measurement setup to measure Vpp and Vrms in channel 2.
3.4 Frequency response of a beam
In lab #1 you examined the steady response of a beam. Here you can quickly examine the dynamic
performance. In addition, you can study the dynamics of the beam as a function of added mass.
Proceed as follows:
1. Connect the Reflective Distance Sensor to the oscilloscope and multimeter.
2. Configure the oscilloscope to detect the signal:
(a) One of your exercises is to adjust the time base and the amplitude to capture the signal—
you may want to ‘pluck’ or tap the beam to get it vibrating.
(b) Turn on the frequency measurement function to display the frequency of the signal.
3. With no mass attached to the beam,
(a) tap the beam to get it vibrating, and
(b) record the frequency of the motion on the scope.
4. Add the magnet, cable and 50g pan to the beam to act as a load. Then,
(a) tap the beam to get it vibrating, and
(b) record the frequency of the motion on the scope.
5. Remove the magnet, cable and 50g pan, and then place both ∼ 50 g magnets on either side
of the beam at the root. (They should be touching the clamp that attaches the beam to its
right-angle bracket.) Again,
AE 305 — Lab 2 Fall 2014 24
(a) tap the beam to get it vibrating, and
(b) record the frequency of the motion on the scope.
6. Move the magnets by about 2 inches from the root toward the tip. As before,
(a) tap the beam to get it vibrating, and
(b) record the frequency of the motion on the scope.
7. Repeat step (6) until you get the magnets to the tip of the beam.
3.5 Noise from a jet
Given your knowledge of the oscilloscope and the AC measurement capability of the multimeter
you can now characterize some features of the noise emanating from a jet. The steps required for
these measurements are:
1. Position the microphone roughly as shown in Figure 15:
(a) 2” downstream,
(b) approximately 2” off the flow centerline, and
(c) oriented toward the nozzle.
2. Using the BNC connectors and a BNC T-adapter:
(a) connect the microphone to the multimeter (AC voltage measurement);
(b) connect the microphone to channel 1 of the oscilloscope; and
(c) turn on the microphone.
3. Adjust the instruments:
(a) Make sure the multimeter measures AC voltage
(b) Make sure the oscilloscope:
i. measures the Peak voltage,
ii. measures the RMS voltage, and has
iii. the time base and amplitude adjusted to measure the signal.
4. Make sure the air valve is turned off:
(a) Read the pressure gauge (it should be zero).
(b) Read the multimeter.
(c) Adjust the oscilloscope if necessary, then
i. read the peak voltage, and
ii. read the average voltage.
5. Turn on the air valve and adjust the pressure regulator:
(a) Adjust so the pressure gauge reads 4 psi.
AE 305 — Lab 2 Fall 2014 25
(b) Read the multimeter.
(c) Adjust the oscilloscope if necessary, then
i. read the peak voltage, and
ii. read the average voltage.
6. Adjust the pressure regulator:
(a) Increase the pressure reading by 2 psi.
(b) Read the multimeter.
(c) Adjust the oscilloscope if necessary, then
i. read the peak voltage, and
ii. read the average voltage.
7. Repeat (6) until you reach 40 psi.
AE 305 — Lab 2 Fall 2014 26
.
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AE 305 — Lab 2 Fall 2014 27
4 Lab preparation assignment
Name: Date:
Before you arrive at the lab you need to prepare. One way to prepare is to read and understand
the associated laboratory materials. Another helpful activity is to critically evaluate what you are
going to attempt, in particular it is useful to ask yourself or at least formulate questions. Questions
are provided below. Please answer these questions on this sheet of paper and hand it in as you
walk into your lab section. Each question is worth 2 pt of your lab.
Questions [2pts each]
1. What does a function generator do?
2. What does an oscilloscope do?
3. What is the default output impedance of the function generator?
4. What is the fixed input impedance of the oscilloscope used in this lab?
5. What is the speed of sound (in m/s) at typical FXB lab conditions (738 Torr and 22.1
◦
C)?
Again, another helpful activity is to write out tables or append a checklist to help organize your
lab time and to be more efficient. A checklist is, or a least the majority of a checklist is provided
above in the procedure. An example test matrix is provided below. Feel free to add material that
was not anticipated in your lab notebook.
AE 305 — Lab 2 Fall 2014 28
.
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AE 305 — Lab 2 Fall 2014 29
Calibration tests (1)
Name: Date:
Proper set-up:
Function generator:
Frequency = 1 kHz, check
Waveform = sine wave, check
Amplitude = 5 Vpp, check
Oscilloscope:
Vertical scale of 1.00 V/div, check
Horizontal scale of 250 µs/div, check
Scope Vpp, check
Scope Vrms, check
Voltmeter Vrms, check
Main tests:
Time Scope Scope Voltmeter Comments
base Vpp Vrms Vrms
(s/div) (V) (V) (V) .
10.0 µ
50.0 µ
250.0 µ
1.00 m
5.00 m
25.0 m
100 m
500 m
2.5
AE 305 — Lab 2 Fall 2014 30
Calibration tests (2)
Name: Date:
AE 305 — Lab 2 Fall 2014 31
Calibration tests (3)
Name: Date:
[Please note that this is a very complicated signal. Both the function generator and the oscilloscope
are digital devices, so you will see a superposition of two figures like Figure 8. Also, there will be
electrical noise present in the signal.]
AE 305 — Lab 2 Fall 2014 32
Characterization tests (circuit #1–OPTIONAL)
Name: Date:
AE 305 — Lab 2 Fall 2014 33
Characterization tests (circuit #2)
Name: Date:
AE 305 — Lab 2 Fall 2014 34
Dynamic response of a ‘wing’
Name: Date:
AE 305 — Lab 2 Fall 2014 35
Characterization of an air jet
Name: Date:
AE 305 — Lab 2 Fall 2014 36
5 Lab results assignment
An assignment written by each individual student is required for this lab. The assignment should
follow the guidelines below and answer the following questions. The assignment is due at the start
of lecture on Tuesday, 16 September 2014.
Calibration tests
1. [5 pts] During tests with a constant input signal (1 kHz, 5 Vpp) and varying oscilloscope
time scale, the rms voltage measured by the oscilloscope at a very small time scale (shorter
time/div) is smaller than the rms voltage measured by the multimeter. Briefly explain why.
2. [5 pts] Plot the voltmeter measurement as a function of the excitation frequency. Note: A
log-log plot would be appropriate here, but trendlines would not.
3. [5 pts] From your tests above what is the upper cutoff frequency
1
of the multimeter?
4. [5 pts] What is the difference between “DC” and “AC” coupling on the oscilloscope?
5. [5 pts] When the oscilloscope sampling rate is larger than the frequency of the input signal,
is the oscilloscope display always an accurate representation of the input signal? Justify your
answer.
Circuit characterization tests
6. [10 pts] Plot the input and output behavior of circuit #2 at both high and low voltages. A
log-log plot of gain (ratio of output to input) would be appropriate.
7. [5 pts] What is the frequency response of the non-linear circuit (#2) and what do you call
this type of response—a “High Pass” or “Low Pass” filter?
8. [5 pts] What happens to the output waveform as the input amplitude is increased and why
does it occur?
A simulated wing
9. [10 pts] Plot the natural frequency of the beam as a function of mass position.
10. [5 pts] What is the general effect of adding mass to a pure mass-dashpot-spring system? Does
it increase or decrease the natural frequency?
11. [5 pts] What happens to the beam’s natural frequency when the mass is placed at the root?
Is this consistent with your answer in (10)? Please explain.
Air jet noise
12. [5 pts] Plot the noise amplitude generated by the jet as a function of input pressure, using
linear scales for both axes.
13. [5 pts] Plot the noise amplitude generated by the jet as a function of input pressure, using
logarithmic (base 10) scales for both axes (i.e., a a log-log plot).
14. [5 pts] What happens in the vicinity of 15-20 psi plenum pressure for the jet? Please explain
in terms of choked nozzle flow and indicate on the graphs.
15. [10 pts] Note the recording student, other members of your lab group, and the bench (or
benches) you used.
1
Cutoff frequency is traditionally where a curve drops below 3-dB (or 50%) of full gain.
AE 305 — Lab 2 Fall 2014 37
6 Lab report
There is no report required for this lab.
References
[1] Agilent Technologies, Function Generator Specifications and Operation.
[2] Agilent Technologies, Oscilloscope Specifications and Operation.