JJ Systems FINAL

8/7/2019 JJ Systems FINAL

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JJ Systems LaboratoryBackground Theory

The JJ System is used to investigate the motion of a vibrating beam.It is built around the beams with the use of electromagnets and variouscombinations of Transducers and signal processing systems that record the motionof the beam by picking up the signals supplied by the Strain Gauges based purelyon the deformation of the beam due to its vibration.

TransducersA transducer is defined as a device that converts electrical energy into other formsof energy.

Depending on what kind of energy it is converting , Transducers can be classifiedinto

Chemical Transducers electrodes,

Mechanical Transducers - E.g. Strain Gages , Accelerometers & Generators

Electromagnetic Transducers E.g. Antennas , Satellite dishes & LDRs

Nuclear Transducers E.g. The Geiger Mueller Tube

Pressure Transducers E.g. Microphones and Speakers

Thermal Transducers E.g. Thermocouples , thermistors and thermometers

Besides this they are also classified as Sensors , Actuators and CombinationTransducers.

Sensors detect signals and process them into another form whereas Actuators areperform an actions based on their input signals and energy supplied. CombinationTransducers both , detect and perform actions.

The JJ System contains a number of these Transducers since not all of themare going to be used in this experiment , only some will be discussed below.

Amongst these are :

Wire Strain Gauges

Semi conductor Strain Gauges

Piezoelectric accelerometer


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Linear Variable Differential Transducer

Variable Reluctance Magnetic Sensor

Electromagnetic velocity transducer

Wire Strain GaugesThe Strain Gauge works on the concept that when it is stretched it elongates andgets smaller in Cross Sectional Area. This will change the resistance of the wire (infact increase). If the force applied is keeps the wire under its elastic limit , then thisconcept can be used to investigate the amount of force exerted on the wire frommeasuring its resistance.

It is known that Resistance R of a material depends on Length , Cross sectionalarea and the resistivity

And the relationship is given by

Image 1 Source : http://www.sensorland.com/HowPage002.html

The image above shows an example of a Wire Strain gauge . This consists of a finewire , the grid pattern maximizes the amount of metallic wire subject to strain in theparallel direction.

The wide cross section of the gauge minimizes the the effect of shear strain andPoisson Strain .
http://www.sensorland.com/HowPage002.htmlhttp://www.sensorland.com/HowPage002.htmlhttp://www.sensorland.com/HowPage002.html


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The Gauge is bonded to a think backing, also known as a carrier. This is directlyattached to the object such that the strain experienced by the Object is transferreddirectly to the strain gauge.

the Gauge is much more sensitive in the vertical direction than it is in the horizontal

direction. The Gauge is then attached to an object ( the beam in our case)When the object stretches / deforms , the strain gauge stretches too whichdecreases the Resistance. The sensitivity of the strain related to the Change inResistance depends on the Gauge Factor and the relationship is given by :

Where G is the Gauge Factor , R is Resistance , L is Length and is the Strain.

The Typical Gage Factor for a metallic Wire is around 2.

To actually calculate the force , the Strain gauge is connected to a WheatstoneBridge.

Image 2 source : http://www.play-hookey.com/dc_theory/wheatstone_bridge.html

The concept of the Wheatstone Bridge is two voltage dividers that are fed with thesame input , the output of these are then taken from both voltage outputs.


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A very sensitive devide called a Galvanometer attached to both the outputs.

This device measures the slightest change in current between both the voltagedividers.

If the Voltage Dividers have the exact same ratio

R1 / R 2= R 3 / R x

Then the Bridge is said to be in balance and no current flows through theGalvanometer.

However, even the smallest imbalance will cause current to flow in the sensitiveGalvanometer.

So when Rx is replaced by a Strain Gauge of Resistance RG then the Resistance of the gage (DR) due to its extension can be related by

DR = G F. R G . e

The setup where just one Resistor is replaced by the Strain Gage is called QuarterBridge Configuration.

The sensitivity of the Wheatstone can be increased further by Replacing a secondResistor by the Strain Gage (Half-Bridge) or by replacing all the Resistors withStrain-Gages(Full Bridge).

Add some more theory

Semi Conductor Strain Gage


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Image 3 : http://zone.ni.com/devzone/cda/ph/p/id/226

Similar to the Metal (Wire) Strain Gage , the Semiconductor Strain Gage works onthe principles of changing Resistance with Strain.

In the case of the Semi-conductor however , the resistivity also changes withstrain along with the physical Dimensions.

This is due to the material property and the change in crystal structure as the strainis applied that affects the electron flow.

The Result is a much Larger Gage Factor (G) which is still given by

Image 3 shows a Semi conductor Strain gage where the thin wired coil is replacedby a single piece of semiconductor material. The Semi-conductor material is eitherbonded to the object , or if encapsulated

just attached by the encapsulation material.

The typical Range of the Gauge factors is 100 to 300 compared to 2 in metallicstrain gages.

Some of the materials that are commonly used include Germanium and silicon.The magnitude of the piezo-resistive effect in these crystals depends on theimpurity present.

The disadvantage however is that the variation of G against Resistivity of thematerial are not linear.

Effect Of Temperature on Strain GageThe Temperature has a very large effect on the reading given by the strain gage.

Since the Sensitivity of these devices are very high , the Thermal Co-efficient of thematerial definitely affects the output. Beside the heat caused by the object (Beam)due to deflection , sometimes this effect can also be seen as the strain gage is justbeing attached to the Object.

The system gives a reading without any deformation occuring , this is due to thechange in resistance caused by the change in Temperature and is also known asthermal output.


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Thermal Output tends to be the main error source in gage measurements in mostcases.

The effect of temperature is worse in a semi conductor Strain gage compared tometallic gage's since the coefficient of resistivity is very large.

The temperature sensitivity can be reduced using several ways.

One of the effective ways to do this , is by using two gauges.

A dummy gauge made of the same material is attached to the object in theopposite direction to the actual strain gauge. This way if the strain gage on one sideis under tension , the dummy gage on the other side will be under tension , both willproduce Difference in Resistances but one will be positive and one will be negative.This should be used in a Half bridge configuration. Since the dummy gauge is madefrom the same material it will have the same effect by the temperature since thetemperature coefficients are the same.

Piezoelectric accelerometerAn accelerometer is used to measure the acceleration , schock or vibration.

A piezoelectric Accelerator does the same by making use of a piezocelectricmaterial i.e. the sensing element in the accelerometer is a crystal which emitscharge when subjected to a compressive force.

The sensing element is covered in a well protective casing and in most casescontains a weight that comes into contact with the accelerator as soon as a force isapplied to the weight that causes it to drop.

The output charge is proportional to the force .


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Image-4 Source :http://www.stanford.edu/class/me220/data/lectures/lect10/lect_6.html

The sensing element is housed in a suitable sensor case to protect the meter fromany environmental conditions. The case is usually welded to prevent the entry of

dust , water etc to the crystal.Linear Variable Differential TransformerThe Linear Variable Differential Transformer is a electromagnetic Transducer thatcan convert rectilinear motion into a corresponding electrical signal (AC voltage).

The LVDT consists of a primary coil and two secondary coils wound on a coil form. Aferromagnetic core links the electromagnetic field of the primary coil to thesecondary coils. Differencing the output of these two coils will result in a voltagethats proportional to its motion

Image 5 source : http://www.macrosensors.com/lvdt_tutorial.html

The primary coil is supplied with an AC source and AC voltages are induced in the

secondary core by Faradays Law.LVDT's can be used to measure displacements from a millionth of a metre to almost0.5m.

The magnitude of Voltage induced is also maximum as it approaches the secondarycoil (when entering the coil from either side , decreases to 0 in the middle wherethe transformer action between the primary and secondary coil are the same sothat there will be no difference in voltage.
http://www.stanford.edu/class/me220/data/lectures/lect10/lect_6.htmlhttp://www.macrosensors.com/lvdt_tutorial.htmlhttp://www.macrosensors.com/lvdt_tutorial.htmlhttp://www.stanford.edu/class/me220/data/lectures/lect10/lect_6.htmlhttp://www.macrosensors.com/lvdt_tutorial.html


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After this it slowly increases as the core moves closer to the secondary coil.

The output voltage is in phase with the primary voltage source for displacement inone direction and 180 degrees out of phase in the opposite direction.

Variable Reluctance Magnetic SensorThe Variable Reluctance Magnetic Sensor converts mechanical motion to electricalenergy without direct contact when placed near a Gear shaft , Rotor , Turbine orany regularly moving device

It is strain based and typically measures pressure force or acceleration.

A variable reluctance sensor is composed of a winding wound around a cylindricalmagnetic material, typically made of ferrous material and is referred to as a polepiece.

A magnet is attached to the pole piece which creates a magnetic field around thepole piece front , the protruding magnet tip is known as the sensor tip.

When a ferrous material passes the sensor tip , it disrupts the magnetic field and apotential difference is created (a sine wave). Since there is a gap of air between thesensor tip and the actual body , there will not be any current flow , however anelectrical signal is tranmitted to a nearby An electrical signal is sent from the sensortip. So when the Sensor tip is placed near a continously oscillating body it becomesvery easy to measure the speed of the body since the speed of oscillation / rotationis directly proportional to the frequency of signals being sent.

The amplitude (sensitivity ) of the signal greatly depends on the air gap betweenthe sensor tip and the object , the speed of rotation and the material being used.

Electromagnetic Velocity TransducerAn electromagnetic Velocity Transducer like the name suggests, is used to measurethe velocity of a body.

The transducer itself is made from a permanent magnet core thats used as a

dynamic core for a stationary coil.The core is attached to the moving body whose magnetic field is cut by the coilwhen the core passes through the coil. The emf induced is directly proportional tothe velocity of the body .


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Low Pass Filter &Phase sensitive DetectorA Low pass filter is a filter that separates low frequency signals from Signals thatexceed the cut-off frequency of the filter. This means only a specific range of frequencies is allowed to pass through the filter while the rest of the signals arereduced. The low pass filter can be of 2 configurations ( types)

Inductive Low Pass filter The Impedance of the inductor increases with increasingfrequency which prevents the high frequenciy electric signals to reach the load inthe circuit.

Capacitive Low Pass filter The Capacitance of the Capacitor decreases withincreasing frequency, a low Impedance along side a parallely connected load tendsto short out the high frequencies in the circuit not letting it reach the load.

A Phase sensitive Detector is used to reduce noise on a signal. The Detector has twoinput signals assuming these are sinusoidal of nature and of similar frequency, the

output produced will be the cosine of the phase angle between those two signalsHence if the two input signals are given by :

v1= V 1 sin t v2= V 2 sin t

Then theouput voltageis given by :v0= KV 1 V 2 cos

where K is a constant.

Both the PSD and the Low pass filter are often used in combination to separate aspecific signal from the noise and amplify it by rectification.

Operational AmplifierAn operational amplifier is a dc differential amplifier that acts as an ideal voltage-controlled voltage source.

Image -6 source : http://holbert.faculty.asu.edu/ece201/opamp.html
http://holbert.faculty.asu.edu/ece201/opamp.htmlhttp://holbert.faculty.asu.edu/ece201/opamp.htmlhttp://holbert.faculty.asu.edu/ece201/opamp.html


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The Operational Amplifier can be modelled ideally with two supply terminals , oneoutput terminal and one ground terminal.

The Operational Amplifier , only amplifies the difference of voltage between the twoinputs and ignores those common to both.

The Gain of the Voltage can be found using

VoltageGain G =V out V i

Depending on the feedback path the Op-amp can be classified into Positive andNegative Feedback Amplifier. Similarly when the output signal is in the samedirection as the supply , the Op-amp is non-inverting and vice versa.

Different configurations of Op-amps can be used for different purposes.

Procedure

Experiment 1Set up the Equipment as shown below.


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In this Experiement the sensitivity of the LVDT was investigated by setting theOscillator to 5kHz to obtain a 1.5V p2p primary excitation on channel 1. By Varyingthe range of the micrometer from 25 to 7.5 mm and obtaining readings for the peakto peak values for secondary voltages a set of values were obtained for incrementof 2.5mm on the micrometer and its corresponding peak Voltages.

A glaph is plotted from these results to obtain a relationship between sensitivity ,Secondary Voltage and Micrometer setting which will be investigated further in thecalculations below.

Experiment 2This Experiment is used to investigate the Phase sensitive detector, its gain andamplifying properties.

A Phase shifter is also introduced in this experiement to compensate for slightvariations that occur in the phase.

Setup the apparatus as shown below.


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Set the Oscillator to 5kHzand adjust the control knob to obtain a 2V peak topeak signalas measured on channel 1 of the oscilloscope. Once the PSDreturns a gain value of +1 ( Input = Output) , move the lead connected to thePSD reference input from the positive terminal of the DC supply , into thenegative terminal. Note what happens to the output

To investigate the signal frequency of the supply when using a PSD , movethe lead connected to the input reference to the DC supply from the PSD , tothe 0 degree terminal of the Oscillator. Note the obeservation.

Move the lead from the 0 degrees to the 180 degrees terminal of theOscillator. Note the Obeservations.

Connect the leads in such a way that the PSD gets its reference from thePhase shifter , in order to compensate for the slight phase variations thathave been observed during the previous task.

Adjust the Phase shifter knob to obtain a perfect full rectified wave. Vary thephase shifter about this optimum setting and observe the variation in readingfrom the metre.

Note the observation and make a sketch of the waveform that corresponds tothe maximum meter output. Comment on the shape of the graph

Experiment 3This Experiment is study how the Low Pass filter can be used to optimally processsignals from a transducer signal source.

Setup the Apparatus as shown below.


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Set the Oscillator to 5kHz minimum and the phase shifter to 12 o'clock.

Displace the beam using the micrometer until a reasonable signal isobtained while moitoring the output from the PSD on the oscilloscope.

Connect the leads in such a way that the output of the psd passes throughthe Low Pass filter before reaching the Oscilloscope. Note the Output Voltageand the waveform.

Remove the micrometer and deflect the beam by hand. The displacement of the beam seen on the oscilloscope is directly proportional to the beamdeflection. Note the waveform.

Experiment 4This Experiment is to investigate the effect of the load Capacitance on a

Piezoelectric Accelerometer.



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Set the Oscillator Amplitude control knob to minimum and the frequenct controlknob to 7Hz.

Connect the output from the Accelerometer to the input to the chargeamplifier using a short Co-axial lead. Note the magnitude and phaserelationship of the ouput relative to the driving signal to the vibrating beamassembly.

Repeat the above step using a long coaxial lead. Note the magnitude andphase relationship relative to the driving signal to the beam assembly.

Replace the Charge amplifier by a Voltage Amplifier and repeat the first twosteps. Note the observations.

Experiment 5This Experiment is to provide a basic understanding of the principles and workingsof a non-inverting operational amplifier.



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Set the Oscillator to 5kHz, Oscilloscope Channel1 Y sensitivity to 0.5V/cm ,Oscilloscope Channel2 Y sensitivity to 5 V/cm, Oscilloscope time base to 50 s/cm& the Oscilloscope triggering from channel 1.

Vary R1 and R2 to obtain the minimum Gain for the op-amp. Note down thereadings on the oscilloscope for these input and output signals. This data willbe used to calculate the gain.

Vary R1 & R2 to get the maximum gain of the op-amp, without clipping thesignal. Note down the readings on the Oscilloscope. These will also be usedlater to calculate the gain.

After turning off the JJ-system, Using the meter that has been provided ,measure the Input and output Resistance of the op-amp. Note theobservations.

Results Experiment 1


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From the experiment the minimum Peak to Peak Secondary Voltage that wasobtained was :

14mV @ 17mm Displacement.

To find the Sensitivity , the gradient of the graph is required which can be found

using the most linear section of the Graph.

Displacement Phase P-2-Pmm rad V

25 1.7 7022.5 1.7 42

20 1.7 18

17 -0.2 1415 -0.3 42

12.5 -0.2 7010 -0.2 88

7.5 -0.2 110

6 8 10 12 14 16 18 20 22 24 260

20

40

60

80

100

120

Graph Showing displacement against Peak to Peak Voltage

Displacement (mm)

Voltage (mV)


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This can be calculated by

Sensitivity = yx

=70 18 mV 25 20 mm

= 10.4 V / m

The generalised sensitivity is givenby

G= Sensitivity.1

Primary Voltage

G = 10.4 . 11.5

= 6.93 m 1

Experiment 2 Observations

1. Both signals are in phase

2. When changing the Balanced supply from + to Phase shift occurs by180 degrees. It has a gain of -1.

19 20 21 22 23 24 25 260

10

20

30

40

50

60

70

80f(x) = 10.4x - 190.67

Enlarged Graph of Secondary Voltage vs. Displacement

Displacement (mm)

Voltage (mV)


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3. When changing the Reference input from the -ve to the 0 degreeterminal it becomes fully rectified. Peak to Peak V ch2 = 2 , 2.3 V

Image showing the PSD reference input switched from DC supply to 0 degrees of the 5kHz Oscillator.

4. When the lead is connected back to the 180 degrees terminal the

following bservation is made :Same peak-to-peak as before. The range is set to 1V and Peak occurs at 1.9V


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When using a phase shifter module the following graph shows the signal that wasoberved :


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The following figure is the result of trying to adjust thePhase shifter to obtain a fully rectified wave :

Experiment 3

Voltage remains the same where as different amplitude.Phase Shifter is used torectify the waveform

- Before Phase Shifter was used : (Refer sketch below)

After Phase Shifter is used : (Refer sketch below)


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During the peak voltage , the displacement on the micrometer is 10.56 mm

Due to a fault in the Low pass filter , further Results could not be obtained for theremaining part of this experiment.

Experiment 4

Using The Voltage amplifier the following observation was made to the waveformwhen

a. The short wire was used :

-Input Voltage 6V max amplitude setting for channel 1

- Output 100mV , output is lagging in phase

- maximum Amplitude for channel 2 of 20mV :


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b. The long wire was used :

The phase remains the same but amplitude of channel 2 descreases.

Maximum Amplitude of Channel 1 is 100mV

Using the Charge amplifier the following result was observed :

a. For a short wire :

Output is leading in terms of phase


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Maximum Output 150mV

b. For the long wire , the exact same output was observed !

Experiment 5


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To obtain the minimum and maximum gains using the op-amp , the resistors R1 andR2 should have the largest difference possible and the smallest difference possiblecorrespondingly. The Results were taken before the signal started to clip.

Minimum Gain:

Channel 2 = 1.7 V

Channel 1 = 1.5 V

Minimum Gain = Output / Input = 1.7 / 1.5 = 1.13

Maximum Gain :

Channel 1 = 1.5 V

Channel 2 = 21 V

Maximum Gain = Output / Input = 21 / 1.5 = 14

- The approximate Input Voltage when Clipping occurs = 25V

When measuring the input resistance the Meter displayed an OL Error whichreferred to an overload. The Resistance was too high. Since the meter wasable to measure 10M Ohm the Input Resistance is thought to be exceeding10 M Ohms.

Output Resistance was measured to be 161.3 K Ohms.

Discussions Experiment 1

The main task is Experiment 1 was to investigate effect of the LVDT on the outputvoltage.

This was done by displacing the beam using the micrometer. The results agreeingwith the theory showed that the Secondary Peak Voltage Was highest at the ends of

the Displacing coil and as it moved towards the centre the Value decreased. Thegraph produced a linear relations as expected from the LVDT. The Voltagedecreased with decreasing Distance and started to increase specifically around20mm. The residual Voltage 14mV occurred at a displacement of 17 mm . ThePhase reverses its polarity between 20 and 17 mm which means the centre of thecoil is positioned somwhere around that distance. The Readings themselves are notvery accurate due to the noise interference present in the room that affected the


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signals. The approximate sensitivities obtained from these graphs are still fairlyacceptable.

Experiment 2

In Experiment 2 the operationa and effect of the Phase sensitive detector and thePhase shifter were investigated.

When the input was set to 2V and the PSD connected. The output signal wasobserved to be just identical. Which means the PSD was behaving like an amplifierthat produced a gain of +1.

Whereas when the Lead are interchaged such that the Voltage across the input isnegative. It can be seen that the shape of the output voltage stays exactly thesame. However the Wave is 180 degrees out of phase. This means that there is again of -1 , which would be as expected since the ouput is negative.

It is also noted that the changeover in polarity does not happen at -1 in fact ithappens at 1.9V. Also noted that a phase shift occurs between the detected signaland the reference signal.Hence it can be deduced that the Phase Sensitive Detectornot only detects and amplifies the input signal but also the Phase shift that occursrelative to the reference input . To correct this phase shift, the Phase shifter is usedwhich means all signals are shifted in frequency by the reference frequency. Allother frequencies that occur are attenuated such that they can not be detected bythe Phase sensitive detector. When the phase shifter knob was adjusted , a fullyrectified wave is obtained at maximum peak. The peak Voltage was 4.3V and thesignal seemed to be much more accurate compared to the other noise affected

signals.Experiment 3

This Experiment was performed by displacing the beam by 10.56mm in which thesignal was sent to the Phase sensitive detector. The Peak voltage in this wave formwas about close to 100mV. This system would not make a good measurementsystem in practise since the system had poor sensitivity besides this the outputsignal wasnt very clear and the signal was easliy disturbed by noise and otherfactors which was very undesirable.

Since the low pass filter wasnt functioning properly , this experiement couldn't beverified properly. When the Low pass filter was used , it displayed maximum signalfor Displacement that flicked back to a straight line immediately before the beamsdisplacement could even be measured. It was suggested that this was due to afaulty capacitor present in the Capacitive Low filter that is unable to hold the chargewhich results in the flickering signal.


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From what could be seen by the Capacitive Low filter , IF the system has worked , itcould have been a good system to measure due to the direct linear responsebetween the change in signal and displacement that could be measures so easily.

Experiment 4

In this Experiment the piezoelectric accelerometer was connected to 2 differentlength coaxial cable connected to a charge amplifier and Voltage amplifier one afteranother.

When connected to the Charge Amplifier it could be seen that the two channelswere almost

0.5 radians out of phase with the output leading the input signal. However thelengths of cables did not make a difference to the output of the Charge amplifier.This is because the Charge amplifier output mainly depends on the feedbackcapacitance and the Charge input , which isnt really affected by the CableImpedance since it is too low to detect.

In the case of a Voltage Amplifier , the change due to length in wire becomes moreapparent. There is a change of phase between both wires that are much different .When the charge in the Accelerometer increases , the Voltage will decrease. Sincethe Impedance of the Charge Amplifier was too high the signal from theAcclerometer is reduced. On the other hand , since the Voltafe amplifier has a veryhigh sensitivity the Difference if the signal due to the difference in length of wirescan be clearly seen.

Experiment 5

In this Experiment the minimum gain in the non-inverted operational amplifier was1.13 which was about 13% . This was of course taken before clipping. Obtaining theclipping point seemed to be a bit of a problem and inaccuracies in this experimentcan certainly be accounted by human errors. The input resistance of the Op-ampcould not be measured as the Resistance was much too high. The Output resistorread a value of about 161.3 K Ohms.

In the ideal case The inpute and output resistors should have read infinity and 0.Comparitively the Gain was very small.

The Op-amp is designed with limited range of current flow , If the input signalbecomes too large such that the output current would be driven to its limit , clippingoccurs. To prevent clipping a limiting network would be suggestible such that itidentifies when the op-amp starts to become unstable.


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ConclusionThe main aim of this Laboratory session was to investigate and understand theworking principles of various Transducers withing the JJ System.

In the First Experiment working with the LVDT yielded a fair set of results which

definitely agreed with the theory displaying a linear Correlation betweenDisplacement and Voltage. However , the range was very limitied if a more accurateresults is required , a beam with a much larger displacement could be used toobtain a bigger set of readings.

The Second Experiment was a bit more challenging a clear phase change could beobserved when using the Phase Sensitive Detector. In the second part a clearrectified signal was obtained in both in and out of phase signals. This could only beaccomplished with the use of a Phase shifter though to rectify the Phase jump. Theshape of the rectified waveform consisted of just peaks where every alternatingpeak seemed to have a bigger amplitude. This was due to the fact the the signal

had been rectified and from the discussion it was known that the Positive peak wasmuch high than the negative peak. The unreliability of the equipment and itssensitivity made it hard to obtain readings but the end results were fairlyacceptable.

The Third experiment was not very successful due to a fault Low pass filter. Noaccurate Readings could be obtained from this Experiment. When the beam wasdisplaces the Low pass filter should have shown a low signal Corresponding to thevibration of the beam. In Reality , Although the Filter showed an initial Displacedsignal due to the displacement of the beam , the Signal flicked back to 0. Even as aworking system this would not be very useful for large displacements of beamssince the Low pass filter can only respond to a limited range of signals.

The Fourth Experiment consisted of investigating a piezoelectric accelerometerwith long and short cable by measuring the Signal via a Charge amplifier andVoltage Amplifier.

The result showed that for the Charge amplifier to show a significant variationbetween the two cables , the cable had to be much much longer than used ,toincrease the Resistance of the wire . In the case of the Voltage Amplifier the Signalwas picked up immediately and a significant change was seen. This concludes thatCharge Amplifiers are much more desirable for Applications to measure InputSignals Since the Length of the wire doesnt have a significant effect.

The fifth Experiement was done using an Operational Amplifier. The minimum andmaximum values for gain were obtained by adjusting to variable resistors. It wasconcluded that obtaining values close to theory wasnt very likely since theResistance had to either be 0 or infinity. Although resistance can be increased tovery large numbers , it is much harder to reduce Resistance to 0. However for


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practical Purposes , having a large enough difference between the two was just aseffective.

Overall the Experiment Was satisfactory and some key concepts and principles of transducers have been investigated and verified. The JJ system itself is a bit

outdated and considering that the accuracy of an instrument also depends on itsmaintenance . Human Errors are very likely since a lot of readings and resultsrequired human intervention.

Referenceshttp://www.allaboutcircuits.com/vol_2/chpt_8/2.html

http://www.transtekinc.com/products/LVDT.html

http://www.sensorland.com/HowPage003.html

http://www.wisegeek.com/what-are-transducers.htm

http://www.allaboutcircuits.com/vol_1/chpt_9/7.html

http://www.play-hookey.com/dc_theory/wheatstone_bridge.html

http://www.sensorland.com/HowPage002.html

http://zone.ni.com/devzone/cda/tut/p/id/3642

Lecture notes 2010-2011 Dr.N. Saffari

All these have been accessed between the 21/12/10- 20/01/1
http://www.allaboutcircuits.com/vol_2/chpt_8/2.htmlhttp://www.sensorland.com/HowPage003.htmlhttp://www.allaboutcircuits.com/vol_1/chpt_9/7.htmlhttp://www.play-hookey.com/dc_theory/wheatstone_bridge.htmlhttp://www.sensorland.com/HowPage002.htmlhttp://zone.ni.com/devzone/cda/tut/p/id/3642http://www.allaboutcircuits.com/vol_2/chpt_8/2.htmlhttp://www.sensorland.com/HowPage003.htmlhttp://www.allaboutcircuits.com/vol_1/chpt_9/7.htmlhttp://www.play-hookey.com/dc_theory/wheatstone_bridge.htmlhttp://www.sensorland.com/HowPage002.htmlhttp://zone.ni.com/devzone/cda/tut/p/id/3642


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Additional QuestionsExperiment 1

1.1What is the cause of the residual Voltage ?

Like discussed above the LVDT consists of two set of coils the primary and thesecondary that are wound around a core. Supplying the Primary coil with a ACSupply creates an electromagnetic field around the core. The Secondary coils arewound in series oppositon such that the Induced Voltage of one secondary coilrelative to the other is 180 degrees out lof phase. When the Center of the Core is inline with the centre of the electromagnetic field then the Secondary Voltage is equalin Magnitude but exactly out of phase which nulls the signal. i.e. the signalscancel each other out. This would be the ideal case.

However there is SOME residual voltage that occur due to varying magneticproperties of the material , Winding Capacitance & perhaps Disalignment of thecore.

Experiment 2

2.1Explain the reasons for your observations made with the balanced DC supplly connected to the reference connection ofthe phase sensitivedetector?

When the signal from the reference input was positive the signal on the PSDbecame positively rectified and when the reference on the input was 180 out pf phase then the signal on the PSD was inverted and rectified. The gain in each


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Observation was either +1 or -1. This explains why there was no change in theamplitude or magnitude of the signal just a change in polarity.

2.2Why do you need a phase shifter in this Experiment?

A Phase shifter is needed to shift the phase of the Voltage. This was used tocompensate for the slight variation in phase that occurred when the polarity of theinput was changed.

The Phase shifter , shifts the phase correctly out of 180 degrees so it can be pickedup by the PSD.

Experiment 3

3.1How does the filter operate and what are the components inside ?

Firstly there are two types of Low pass filters , one is a Capactive Low pass filter and

the other , an inductive Low pass filter. Capacitive Low pass filter

As the name suggest it comprises of a Capacitor and a resistor that are connectedin parallel. As the frequency increases the Capacitors impedance decreases . Thelow impedance in parallel to a load resistance tends to short out high frequencysignals.

Inductivce Low Pass Filter

This filter is made of Inductors and Resistors connected in series. The inductorsimpedance increases with increasing frequency. This high impedance in seriestends to block high-frequency signals from getting through the load Resistor.

In this Experiment a Capacitive Low Pass Filter was used.

3.2How is the amplitude of the output DC signal related to the amplitude of the input signal for the filter?

Since the low pass filter was faulty , results couldn't be obtained successfully hencethis investigation was not as precise. Theoretically the Low pass filter is calibratedto only allow the RMW of the peak voltage to pass through. The results recorded forthis was 0.1V

0.1

2= 0.0707 V

Experiment 4


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4.1Explain why you would use a coaxial cable rather than a normal 'unshielded' wire ?

Co-axial cable are made of an inner conductor surrounded by an insulating layerthat is again layered with a conductive shield. Compared to an unshielded wire the

advantage of the co-axial cable is that this design creates an electromagnetic fieldthat acts as a Faraday's cage i.e. complete block out any external static fields fromthe interior. When the signal in the cable is less prone to external interferences itcan travel over greater distances without a disturbance which results in very lowerror rates , better output.

At the same time the coaxial cable has a much bigger bandwidth which means itcan be used to transfer many signals with different frequencies at the same time.Which means the coaxial cable has a much larger throughput capacity than anunshielded wire.

Experiment 55.1Why does clipping occur, how can it be prevented when designin an op-

amp?

Clipping occurs when a device has a limited output range , such that when thesignal thats being sent out is above or below this range then those signals get cutoff and clipping occurs.

This means that beyond the threshold Voltage , a flat cut off can be seen on theoscilloscope.

Clipping can be avoided using negative feedback from the op-amp used to reducethe gain when the Peak exceeds the threshold Voltage. This can be done using aconditioned Loop where the Input signal is checked to ensure its within a givenrange which will then influence the feedback on the system.

5.2What values of R1 and R2 would give maximum and minimum gain of the amp, and why is this not possible in practise?

The maximum and minimum values of gain of an Operational Amplifier are 1 and 0.

The value of gain is given by :

Av= 1R2R1

Hence themaximumvalueof 1 can only beobtained when R 2= 0R1=

The minimum Value is can only be obtained when


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R2R1

= 1

Realistically Resistance can never be 0 or infinite which means there will always besome marginal error. However for applicational purposes these errors can beminimised to such small amounts that it doesnt affect the actual reading to a greatextent so that the effect can be taken to be almost negligible.

5.3In your report, redesign the op-amp to give a negative gain (inverting amplifier) , and then derive the relationship between the gains of theamplifiers and the two resistors for both these types of amplifiers?

Image source : http://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_inv.gif

In this design , a negative feedback loop will be used to invert and amplify thesignals. The Resistor R2 sends the output signal back to the negative input terminal.


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The difference in the polarity between the two signals means that they'recompletely out of phase as this signal superimposes on the incoming input signal , itreduces the overall gain.

When the Potential Difference between the input and output becomes 0 this means

that the Resistance R1 and R2 are the same such that there is an equal currentflowing from input to output through R1 and R2.

In this case The voltage flowing through the feedback loop is the same as theVoltage output which means the New Voltage input reduces to 0.

At this point :

V out V inp= IRV out 0 = IR 20 V inp= IR 1

ThereforeV out R 2

= V inp

R1= I

HenceV out V inp

= R 2

R1

For a non-inverting Amplifier

Image source : http://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gif

In this case the positive feedback will be used to amplify the signal , as thefeedback signal increases , so does the input as it gets larger and larger since theoutput signal that is sent back through the feedback loop is positive andsuperimposes on the input.

In this figure the Output signal is sent back through the feedback loop into thenegative terminal of the input terminal.

We assume V- = V+
http://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gifhttp://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gifhttp://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gifhttp://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gifhttp://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gifhttp://www.electronics-radio.com/articles/analogue_circuits/operational-amplifier-op-amp/op-amp_basic_non_inv.gif


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Since V ve= IR2

Where I =V out

R2 R1

Combing these gives : V ve=R2

R 2 R1V out

V ve= V ve= V inp

V inp =R 2

R2 R1V out

Which defines the gain asV inpV out

as Av= 1R2R1

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