Michigan Aero305 Lab2

8/11/2019 Michigan Aero305 Lab2

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AE 305Laboratory 2:Non-steady-signal instrumentation

P.D. Washabaugh, J. Fishstrom, L.P. Bernal, T.B. Smith, and J.K. Edmondson

9 September 2014

PurposeThis 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 unknowncircuits. These circuits have a non-linear features. We will study the dynamic response of astructure using a reective distance sensor, and the acoustics of an air jet using a microphone andpressure gauge.

ConceptsNon-steady voltage excitation and measurement, frequencies and amplitude, aliasing, measure-ment accuracy and precision, instrument calibration, test matrices, circuit prototyping, and circuitcharacterization. Acoustics of a choked air jet.

SummaryYou will rst review some features of a laboratory function generator and an oscilloscope. Tobecome familiar with both of these instruments you will use the oscilloscope to calibrate the functiongenerator. An electrical breadboard with two passive circuits is provided. You will calibrate theirnon-steady voltage response as a function of input frequency and amplitude. The dynamic responseof a structure will be studied as a function of added mass. You will use a microphone and a pressuregauge 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; Reective Distance Sensor;microphone and pressure gauge.

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Important deadlinesLab 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 theprevious lab you measured the steady or static response of a device using instruments that arevery good at these types of measurements. While the steady response of a device is frequently acritical feature, the non-steady or dynamic response of a device can be even more important. Thedynamic or non-steady response of an instrument is more involved or complicated than the steadyresponse simply because of the introduction of another parameter, time. Time appears becausemost 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 inputand 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 withstandard instruments that are used to excite and measure a non-steady response. These include astate-of-the-art function generator and oscilloscope. Along the way you will be exposed to additionallaboratory processes and features of experimentation. For instance you will discover that theoscilloscope is an extremely versatile instrument that can be used to capture events that are tooquick for usual human response times. You will also nd that the function generator can be usedto 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 notethat 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 functiongenerator has some features akin to a power supply. Both a function generator and a power supplyproduce a voltage. You can think of a function generator as a power supply where you are wigglingthe voltage knob. Even though there are some similarities between a generator and a supply, thereare some signicant differences as well. For instance a power supply is optimized to provide aconstant voltage. A function generator is optimized to vary a voltage as a function of time at aprecise rate (i.e. frequency). As with most optimization problems, you lose something with thistime-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 labpower supply can generate 100 W of clean DC power. In contrast our function generator can onlydrive 200 mA of current at 10 V. This corresponds to 2 W. An almost universal symbol indicatinga 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 sinewaves, square waves, and triangle waves, e.g. see Figure 3. It also has the ability to be programmedto provide a wide variety of arbitrary or user specied waveforms. An image of the functiongenerator that well be using is shown in Figure 4.

In any signal generator you can adjust both the frequency f and the amplitude A. In some, youcan also adjust the offset o and the phase angle . (The phase is adjusted by a time-delay circuit.)These are graphically portrayed in Figure 5.

The function generator that youll be using has the ability to generate numerous other periodicsignals. For example you can modulate the base signals or generate arbitrary waveforms by alteringtheir amplitudes or frequencies, as shown in Figure 6. The sweep in frequency shown in Figure6(b) is especially useful to identify resonance.

Most function generators simply generate periodic signals . The function generator we will be usingcan also generate transient signals . Transient signals, e.g. see Figure 7, are initiated by some typeof trigger and after a prescribed delaypotentially zero in magnitudethe 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 2 A, period 1/f , d.c. offset o,and phase angle .


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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 shapeof this transient signal can be anything you wantwithin the capabilities of the generator. In thislab 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. Inothers words the signal that you see generated in Figure 5 actually has thousands of tiny steps. You just cant see them at a coarse resolution. However, if you examine the signal from the functiongenerator at a very high resolution in both amplitude and time you would see something likeFigure 8 a series of steps. These steps are related to the bit-resolution capabilities of the digitaldevice. These small steps are one of the most fundamental differences between analog and digitalinstruments. 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 thevoltage step is 10 mV.

resolution of the digital-to-analog (D/A) converters on the output stage of the instrument. Forinstance our function generator has a 14-bit D/A converter. What this means is that the voltagecan at best be divided into 2 14 or 16384 steps. If the voltage range is 20 Volts peak-to-peak (20Vpp), then the smallest voltage step you can expect to see is (20 / 214 ) 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 20MHz. For high-frequency instruments, this is not very impressive; however, it is usually plenty formost 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 wellas 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 thatthe oscilloscopes cousin is the voltmeter and not the multimeter. A multimeter has the abilityto measure current, resistance and other quantities, while a typical oscilloscope can only measurevoltage. If you want an oscilloscope to measure resistance or current, you usually have to providethe extra circuitry yourself. A symbol for an oscilloscope is shown in Figure 9.

There are other signicant differences between a voltmeter and a typical oscilloscope. While goodvoltmeters have a high input impedance (e.g. 10 M), the scope has a lower input impedance toterminate 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 dont know of a traditional symbol.

wires. In other words, oscilloscopes require more power from the circuit that they are testing thana multimeter. For example, most research-grade scopes have an input impedance of 50 with anoption for higher impedance such as 1 M. The scope you will be using has only a xed 1 Mimpedance. (The lack of a 50 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 M inputimpedance will protect the scope. A 50 input would get fried!)

This lower input impedance means that for a given voltage, the scope will draw signicantly morecurrent 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 oscilloscopeas a resistor and a capacitor, i.e. replacing the element in Figure 9, with the resistor and capacitorshowing 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 canpotentially inuence the system that is being measured. Note that most oscilloscopes are singleended. In other words the negative is internally attached to chassis ground. This ground is afrequent source of problems. On a differential voltmeter if you switch the positive and the negativeyou 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 well construct an active circuit that will besensitive to grounding through the oscilloscope.

The scope that well be using is shown in Figure 11. An oscilloscope is a display that is akin to anautomatic plotter. You can think of the scope as simply capturing processes that you are not quickenough to see with your own senses. This ability to both capture events and display them rapidlycan be critical. The capturing of the event is important because it forms the data from which youwill make decisions. The ability to display these results quicklyrather than wait minutes, hours


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or days for the resultsmeans that you can make rapid adjustments to a situation. For examplethink of an altimeter on the airplane. You want the altimeter to be accurate and precise, but youalso need the information in real time so you can make use of it while you are ying a craft.

Figure 11: Front panel of an Tektronix TDS2000 Series oscilloscope. Note four input channels anda 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 notworking because it is being asked to look at a signal that does not exist! For example, you cantell an oscilloscope to only look at voltages above 1 V, and if your signal is below 1 V, the scopewill not display it. In other words, unlike your voltmeter, the oscilloscope is not very good at usingauto-scale to nd your signalalthough your scope does have an auto-range button that cancapture certain signals, it is not perfect.

Another difficulty with an oscilloscope is when to look and how fast to look. Transient signalsrequire a proper trigger to avoid taking a measurement either too soon or too late. You have to becareful to make sure your scope is looking in a window to capture your signal. Consequently, youconstantly need to keep in mind how your scope is congured.

Scales

Consider the signal shown in Figure 12. There are two scales to worry about. The rst is thehorizontal scale or the time base. This scale is usually adjusted by a knob on the scope and ittells the scope how quickly to sample. The vertical scale tells the scope over what range to lookfor a signal and is also adjusted by a knob. There are analogues features on a digital voltmeter. Adigital voltmeter frequently has the ability to read at slow, medium, or fast rates the timebase is similar to this except that there are many more ranges to choose from, and the scope willactually record each individual readings (and display them) rather than average them into a singlenumber. 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 congured 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 entiresignal 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. Onolder scopes, the instrument would remain idle until a zero time condition was met. Once thiscondition was met, the instrument would wait the specied delay, and then record the voltages onthe input to the display at the proper reading rate (horizontal scale) and voltage range (verticalscale).

New digital scopes operate in a slightly different manner. They are persistently recording thevoltages 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 fromthe buffer. One consequence of this buffer is that the delay can be either positive or negativewith 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 observeevents 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 itreads on its input. In other words, as soon as the scope is done displaying a signal, it starts overand displays the next set of voltages without waiting. This is very useful if you have no clue as tothe properties of your signal.

Unfortunately, if you have a nice sine wave (e.g. see Figure 3(a)), except for the very special instancewhere your time base exactly matches the period of your signal, the sine wave would appear as inFigure 13. The reason for this confused display is that it is actually showing 5 or more traces of


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the signal in sequence very quickly. The scope is starting the display without any regard for whatis being measured on the input. Consequently, each time the display is initiated, the sine wave isat a different location in phase.

Figure 13: A typical display from an oscilloscope that is triggered to run continuously with notrigger level.

To correct this situation and get the scope to provide a stable display of the signal you need toset 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 mostcommon is to set a voltage level and a slope. The signal is read into the scope and when it detectsthe appropriate voltage level (say, a positive slope on the signal), the display is initiated. If thesignal source has a stable or constant phase, youll 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, sothat is every time it is nished 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 displayis nished, the trigger is turned off so that any subsequent input is ignored. Keeping the scoperunning is useful if the signal is periodic. Capturing a single event is useful if you are dealing withtransient events (i.e. events that dont repeat).

High-pass and low-pass lters, bandwidth

All devices that look at time varying signals have the ability to see (or measure) certain signalsand are blind (or are unable to measure) other signals. The capability of the instrument is mostusually dependent upon the frequency of the signal. If you provide a constant amplitude signal tothe instrument at some high frequency, the amplitude would seem to diminish. A point at whichthe 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 inFigure 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 examplea general-purpose scope might have a cut-off frequency of 20 MHz to 100 MHz. Signicantly moreexpensive scopes have frequency cut-offs that are as high as 100 GHz! This number is also calledthe bandwidth of the scope because an oscilloscope can measure signals down to 0 Hz (or DC) if properly congured. The scopes youll be using in this course are 100 MHz scopes.

Scopes also have the ability to insert several lters into the signal. These are typically called ACcoupling 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 willbe 60 MHz.). If AC coupling is selected, then a high-pass lter is inserted into the circuit. Thishigh-pass lter will have a lower cut-off frequency that is 10 Hz. It is specically used to removean unwanted DC component of the signal. This AC coupling would be used, for instance, tomeasure 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 instrumentsand how they are electrically terminated at each instrument can be criticalespecially as thefrequency of the signals increase. One way to connect signals is to use co-axial cables. These cablesprovide shielding of the primary signal line by wrapping the signal line in a conductor. The simplestshielded cable involves 2 conductors; one for the signal and one for the shield. Perhaps the mostcommon 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 twistedpairs of wires that are then shielded. For example Ethernet, USB cables, and IEEE 1394 cables


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(Sony I-Link and Apple Firewire) use multiple twisted pairs of wires that are shielded to transmitdigital signals over long distances.

In this lab you will be using co-axial cables because both the function generator and the oscilloscopehave co-axial cable connectors. The connectors that they use are called BNC connectors. A BNCconnector is a cable termination which is used primarily in labs and sometime in professionalstudios. The BNC connector has a thin central pin which is connected to the signal line and anouter rounded metal cylinder that is connect to the shield. The connector pushes onto its jack andtwists 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 isground. If you dont pay attention to this feature (and many do not) youll end up shorting yoursignal to ground. Fortunately many of your instruments have built-in protection for this type of error so it should not be catastrophic for your instrumenthowever it may be catastrophic for thedevice 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. Youcan refer to your text for details on these devices (e.g. Section 11.5 for Microphones, and Section6.1 to 6.6 for Pressure Transducers). You will use the pressure gauge to measure the pressure inthe plenum chamber before the air leaves the nozzle. You will use the microphone to measure thenoise that is generated by the ow. 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 ow showing small normal shocks in the vicinity of thenozzle. The Schlieren photographic technique displays regions of varying uid density. This is anactual image from one of our jets.

At low pressures the ow inside the chamber and outside the nozzle stays subsonic. However, if thepressure inside the plenum chamber is sufficiently large, the ow outside can become supersonic.This supersonic ow is characterized by large changes in uid density in the form of shocks andexpansions. These uid features are shown in Figure 16 which is a Schlieren photograph of the jet.It is important to note that the ow structures such as the normal shocks shown in Figure 16 onlyoccur when the air leaving the nozzle is supersonic. This occurs at elevated pressures. At lowerpressures, the ow is subsonic and the shocks would not appear.

The pressure gauge is used to measure the difference in pressure between the plenum and theambient 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 interiorso when the owapproaches sonic conditions compressibility effects may occur. In addition, since this nozzle onlyconverges (i.e. it is not a converging-diverging nozzle) you cant get supersonic ow in the nozzleitself. However, when the ow expands you can get supersonic speeds external to the nozzle! The

transition from subsonic ow to supersonic ow will lead to reasonably dramatic change in thecharacteristics of the noise produced from the nozzle.

The microphone is used to measure the noise from the jet mixing with the ambient air. It isimportant to keep the microphone directly out of the jet when performing this measurement becauseotherwise the microphone will detect the jet momentum and not the acoustic energy. Also, to geta good signal its a good idea to position the microphone 30-100 nozzle diameters downstreampointing at the nozzlekeeping 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 numerousissues here. First, the room does not have much acoustic treatment, so the microphone will hearall the fans in the ceiling. In addition, there will be potentially 5 nozzles running at once! Theseeffects will raise the noise oor or background noise level of your experiment.

3 Procedure

There are four main tasks in this laboratory. The rst task is to corroborate the performance of the function generator as measured by both the multi-meter and the oscilloscope. The second taskis to characterize the frequency response of a test circuit both as a function of frequency and asa function of amplitude. The third task is to examine the dynamic response of a simulated wing.The nal 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 requiresome 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 facilitatesubsequent testing.

3.1.1 Function generator

The function generator is a completely digital instrument. Cycling its power will return it to adefault state where it is generating a 1 kHz Sine wave at 100 mV peak-to-peak and the output isset for 50- impedance and turned off.

This default power-up state assumes that it is driving a 50- impedance. The instrument hasthis default setting because when you are dealing with non-steady signals, to reduce signal noiseproblems (i.e. signal reections on lines) you need to worry about the how cables are terminated.A 50 termination is frequently used. This function generator can be used to drive signals up to20 MHz where these termination issues can result in ringing in your measurements. At lowerfrequencies, (e.g. say < 50 kHz and below) termination is not usually a problem. An instrumentlike a voltmeter is a high impedance device, (e.g. input impedance > 1 M). There is a verygood reason for this high impedance; when you measure a voltage the high impedance simulatesan open circuit, thereby having a small effect on the circuit under test. Unfortunately, whatthis means is that when you measure the voltage coming out of the function generator with ahigh impedance voltmeter, you get a factor of 2 discrepancy between what the function generatordisplays as outputting and what the voltmeter will measure. The voltage value displayed is 2 timeshigher!

Since oscilloscopes are used to measure non-steady signals, historically they always had a 50- inputimpedance. Consequently when you took a function generator (that is expecting to drive a 50-impedance) and connect it up to a usual scope (with a 50- input impedance), the scope wouldprovide a measurement that corresponded to the function generators display. Unfortunately this50- input impedance can cause problemsespecially for students who are exploring creative uses


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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 resistor andplace 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. Usualresistors are rated at 1/4 to 1 Watt. The result of the above exercise is a blown input channel onthe scope! To try and remedy this problem the instrument makers have tried putting warnings onthe inputs or have provided an option for a high impedance input to the scope. The scope you willbe using only has a high impedance inputthis makes it more difficult to damage.

Consequently, to make your function generator compatible with both the voltmeter and the scopeyou have two choices:

1. You can remember that the function generator is trying to drive a 50- impedance. What thismeans is that anything that is displayed in terms of voltage on the generator (e.g. amplitudeand offset) is 1/2 of the actual voltage that is being generated. You can survive by doing thisbut 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 followingbuttons:

(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 rst 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 instrumentyou will go back to a 50- impedance. There is a way to store a state of the instrument if youhave to make these changes frequentlyhowever in the interest of education you need to be awareof how your instrument is congured!

The function generator is now ready for general use with high impedance devices. Unlike the powersupply, the function generator has limited current generating capability. If you now try to drive alow impedance circuit, say 50 , the actual voltage that is output will be lower than the displayedvalues.

On this instrument you have two ways to change the frequency, amplitude and offset. For exampleto change the frequency:

1. Select the proper input parameter (frequency, amplitude, or offset) by pressing the blue buttonunder the corresponding indicator. The indicator Freq, Amp, or Offset should highlightedand with vertical lines on both sides. In this case Freq should be highlighted and have verticallines 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, thenii. 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 theCANCEL option.

ii. Press the blue button for the correct units you are using. As soon as you press anyof 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 adjustthe 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 leftof the display will change to High Z Load . If High Z Load doesnt show the output impedanceis 50 and you should change it to high impedance.

Now that you have learned how to setup the signal generator, congure the signal generator to

produce a square wave of 1 kHz frequency and 100 mVpp amplitude. This will be very usefulto congure the oscilloscope. Please have your GSI verify that you have congured the signalgenerator 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 congure to makethe measurement that you want. The most difficult part of getting an oscilloscope to work is toget 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 isin a useable state, however it can be painful if someone has messed up the features. The followinginstructions are intended to show you some of the steps that are necessary to set-up the oscilloscopefrom 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 fromthe function generator (i.e. the 1 kHz, 100 mVpp square wave signal) to the channel 1 inputof the scope. Note that the function generator has two output jacks; use the one labeledOUTPUT.

3. To get the scope into a known useable state press the [AutoSet] button. This function willreset 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 conguration is shown in Figure 17. Please review all theelements of the display as illustrated in the gure.


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Figure 17: Oscilloscope display for the square wave signal test setup. Each element of the displayis labeled.

5. Note that the Channel 1 Menu gives information on the channel 1 status, which in this caseis: 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

conguration 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 Trigd .

7. Use the channel 1 vertical scale knob (Figure 18(a) shows the location of the knob within thevertical control group) to change the vertical scale and follow the changes in the Channel 1Status window at the bottom of the display.

8. Use the horizontal scale knob (Figure 18(b) shows the location of the knob with in thehorizontal control group) to change the horizontal scale and follow the changes in the TimebaseStatus window at the bottom of the display.

3.2 Calibration

You will be using the Oscilloscope and the Multimeter to calibrate or corroborate and characterizethe output of the function generator. You will learn some features of how the oscilloscope andthe multimeter measure unsteady signals. You will also learn about some of the limitations of theoscilloscope and function generator. To set up the calibration, proceed as follows:


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(a) Vertical (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 autorangefeature enabled. The multimeter will now measure the root-mean-squared (rms) voltage.

4. On the oscilloscope, using the default conguration (i.e. Press AutoRange ) previously de-ned, set up measurements as follows:


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(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 displayedisPk-Pk. The scope will now display the peak-to-peak voltage of the signal under theheading Value.

(d) Press the button to the right of Back to return to the Measure Menu. The scope willnow display the peak-to-peak voltage of the signal to the left of the uppermost screenmenu button.

(e) Press the next-lowest button of the screen menu to select CH1, and click through toselect RMS.

(f) As before, press the button to the right of Back to return to the Measure Menu. Thescope will now display the rms voltage of the data at the center of the display directlybelow the peak-to-peak voltage.

5. Here you will examine some aspects of how the time base on the oscilloscope needs to be setin order to obtain measurements. With the function generator providing a xed signal, varyhow 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 conrm 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 divisionand record the peak-to-peak and rms voltage as measured by the oscilloscope, and themultimeter. Make a note of the display changes on the oscilloscope.

i. 10.0 microsecondii. 50.0 microsecond

iii. 250.0 microsecondiv. 1.0 millisecondv. 5.00 millisecond

vi. 25.0 millisecondvii. 100 millisecond

viii. 500 millisecondix. 2.5 seconds

6. Next you will examine the frequency limits of both the oscilloscope and the multimeter. Varythe frequency on the function generator keeping its amplitude xed at 5 Vpp.

(a) In order to capture the signal on the oscilloscope you will have to adjust the time basefor each frequency. Use what you learned above. In order to get a good measurementyou need to have the waveform displayed on the screen.


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(b) At each frequency measure thei. peak-to-peak voltage and rms voltage using the oscilloscope when it is congured

with DC coupling;ii. peak-to-peak voltage and rms voltage using the oscilloscope when it is congured

with AC coupling; andiii. 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 resumedisplaying these measurements by pressing the Measure button.

(c) Examine the following frequencies:i. 10 MHz

ii. 1 MHziii. 100 kHziv. 10 kHzv. 1 kHz

vi. 100 Hzvii. 10 Hz

viii. 1 Hz

7. Since your oscilloscope has a faster frequency response than your function generator, you canuse 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 Vppamplitude.

(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-frequencypickup 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.


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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 propertieson the measurements that are being displayed.

3. Youll also discover some of the limitations of each of the instruments. For example, dependinghow the instruments are congured, 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 outputresponse of the circuits on the breadboard. Use the following procedure:

1. You have two circuits available from lab #1. Characterize circuit #2 rstit has a clippingbehavior that is extremely common. If you have time, characterize circuit #1 (i.e. circuit #1is optional).

2. Keep the function generator, oscilloscope and the multimeter in essentially the same cong-uration as above (i.e. you dont have to substantially re-setup the instruments, however youwill 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 shownin 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;


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Figure 20: Calibration of the circuit using the function generator, oscilloscope, and voltmeter. Thetwo oscilloscopes shown indicate the two input channels.


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(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 frequencymeasurements in (6) and (7) above. Make sure to note any differences in the output signalshape!

9. If you have time you may improve on the resolution of the above experiments by repeatingthe measurement and by adding frequency points. However, the above measurements will besufficient 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 thisis 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 conguration you may haveto 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 dynamicperformance. In addition, you can study the dynamics of the beam as a function of added mass.Proceed as follows:

1. Connect the Reective Distance Sensor to the oscilloscope and multimeter.

2. Congure the oscilloscope to detect the signal:

(a) One of your exercises is to adjust the time base and the amplitude to capture the signalyou 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,


5. Remove the magnet, cable and 50g pan, and then place both 50 g magnets on either sideof the beam at the root. (They should be touching the clamp that attaches the beam to itsright-angle bracket.) Again,


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6. Move the magnets by about 2 inches from the root toward the tip. As before,


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 multimeteryou can now characterize some features of the noise emanating from a jet. The steps required forthese measurements are:

1. Position the microphone roughly as shown in Figure 15:

(a) 2 downstream,(b) approximately 2 off the ow 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, andii. read the average voltage.

5. Turn on the air valve and adjust the pressure regulator:

(a) Adjust so the pressure gauge reads 4 psi.


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4 Lab preparation assignment

Name: Date:

Before you arrive at the lab you need to prepare. One way to prepare is to read and understandthe 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. Questionsare provided below. Please answer these questions on this sheet of paper and hand it in as youwalk 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 xed 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 yourlab time and to be more efficient. A checklist is, or a least the majority of a checklist is providedabove in the procedure. An example test matrix is provided below. Feel free to add material thatwas not anticipated in your lab notebook.


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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 s/div, check

Scope Vpp, check

Scope Vrms, check

Voltmeter Vrms, check

Main tests:

Time Scope Scope Voltmeter Commentsbase Vpp Vrms Vrms

(s/div) (V) (V) (V) .10.0 50.0 250.0 1.00 m5.00 m25.0 m100 m500 m

2.5


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Name: Date:


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Name: Date:

[Please note that this is a very complicated signal. Both the function generator and the oscilloscopeare digital devices, so you will see a superposition of two gures like Figure 8. Also, there will beelectrical noise present in the signal.]


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Characterization tests (circuit #1OPTIONAL)

Name: Date:


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Characterization tests (circuit #2)

Name: Date:


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Dynamic response of a wing

Name: Date:


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Characterization of an air jet

Name: Date:


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5 Lab results assignmentAn assignment written by each individual student is required for this lab. The assignment shouldfollow the guidelines below and answer the following questions. The assignment is due at the startof lecture on Tuesday, 16 September 2014.

Calibration tests

1. [5 pts] During tests with a constant input signal (1 kHz, 5 Vpp) and varying oscilloscopetime scale, the rms voltage measured by the oscilloscope at a very small time scale (shortertime/div) is smaller than the rms voltage measured by the multimeter. Briey explain why.

2. [5 pts] Plot the voltmeter measurement as a function of the excitation frequency. Note: Alog-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. Alog-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 callthis type of responsea High Pass or Low Pass lter?

8. [5 pts] What happens to the output waveform as the input amplitude is increased and whydoes it occur?

A simulated wing9. [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? Doesit increase or decrease the natural frequency?

11. [5 pts] What happens to the beams natural frequency when the mass is placed at the root?Is this consistent with your answer in (10)? Please explain.

Air jet noise12. [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, usinglogarithmic (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 explainin terms of choked nozzle ow and indicate on the graphs.

15. [10 pts] Note the recording student, other members of your lab group, and the bench (orbenches) you used.

1 Cutoff frequency is traditionally where a curve drops below 3-dB (or 50%) of full gain.


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6 Lab report

There is no report required for this lab.

References

[1] Agilent Technologies, Function Generator Specications and Operation.

[2] Agilent Technologies, Oscilloscope Specications and Operation.

Michigan Aero305 Lab2

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Transcript of Michigan Aero305 Lab2