JJ Systems Laboratory Background 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 various combinations of Transducers and signal processing systems that record the motion of the beam by picking up the signals supplied by the Strain Gauges based purely on the deformation of the beam due to its vibration.

Transducers A transducer is defined as a device that converts electrical energy into other forms of energy.

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

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 Combination Transducers.

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

The JJ System contains a number of these Transducers since not all of them are 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

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 and gets smaller in Cross Sectional Area. This will change the resistance of the wire (in fact increase). If the force applied is keeps the wire under its elastic limit , then this concept can be used to investigate the amount of force exerted on the wire from measuring its resistance.

It is known that Resistance R of a material depends on Length , Cross sectional area 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 fine wire , the grid pattern maximizes the amount of metallic wire subject to strain in the parallel direction.

The wide cross section of the gauge minimizes the the effect of shear strain and Poisson Strain .

The Gauge is bonded to a think backing, also known as a “carrier”. This is directly attached to the object such that the strain experienced by the Object is transferred directly 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 which decreases the Resistance. The sensitivity of the strain related to the Change in Resistance 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 Wheatstone Bridge.

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 the same input , the output of these are then taken from both voltage outputs.

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

This device measures the slightest change in current between both the voltage dividers.

If the Voltage Dividers have the exact same ratio

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

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

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

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

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

Add some more theory

Semi Conductor Strain Gage

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

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

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

This is due to the material property and the change in crystal structure as the strain is 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 replaced by a single piece of semiconductor material. The Semi-conductor material is either bonded 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 metallic strain 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 the impurity present.

The disadvantage however is that the variation of G against Resistivity of the material 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 the material 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 just being attached to the Object.

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

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

The effect of temperature is worse in a semi conductor Strain gage compared to metallic 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 the opposite direction to the actual strain gauge. This way if the strain gage on one side is under tension , the dummy gage on the other side will be under tension , both will produce 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 made from the same material it will have the same effect by the temperature since the temperature 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 piezocelectric material i.e. the sensing element in the accelerometer is a crystal which emits charge when subjected to a compressive force.

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

The output charge is proportional to the force .

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 from any 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 that can 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. A ferromagnetic core links the electromagnetic field of the primary coil to the secondary coils. Differencing the output of these two coils will result in a voltage thats 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 almost 0.5m.

The magnitude of Voltage induced is also maximum as it approaches the secondary coil (when entering the coil from either side , decreases to 0 in the middle where the transformer action between the primary and secondary coil are the same so that there will be no difference in voltage.

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 in one direction and 180 degrees out of phase in the opposite direction.

Variable Reluctance Magnetic SensorThe Variable Reluctance Magnetic Sensor converts mechanical motion to electrical energy without direct contact when placed near a Gear shaft , Rotor , Turbine or any 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 cylindrical magnetic material, typically made of ferrous material and is referred to as a pole piece.

A magnet is attached to the pole piece which creates a magnetic field around the pole 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 a potential difference is created (a sine wave). Since there is a gap of air between the sensor tip and the actual body , there will not be any current flow , however an electrical signal is tranmitted to a nearby An electrical signal is sent from the sensor tip. So when the Sensor tip is placed near a continously oscillating body it becomes very easy to measure the speed of the body since the speed of oscillation / rotation is directly proportional to the frequency of signals being sent.

The amplitude (sensitivity ) of the signal greatly depends on the air gap between the 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 measure the 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 coil when the core passes through the coil. The emf induced is directly proportional to the velocity of the body .

Low Pass Filter &Phase sensitive Detector A Low pass filter is a filter that separates low frequency signals from Signals that exceed 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 are reduced. The low pass filter can be of 2 configurations ( types)

Inductive Low Pass filter – The Impedance of the inductor increases with increasing frequency which prevents the high frequenciy electric signals to reach the load in the circuit.

Capacitive Low Pass filter – The Capacitance of the Capacitor decreases with increasing frequency, a low Impedance along side a parallely connected load tends to 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 two input 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 signals

Hence if the two input signals are given by :

where K is a constant.

Both the PSD and the Low pass filter are often used in combination to separate a specific 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

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

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

The Gain of the Voltage can be found using

Depending on the feedback path the Op-amp can be classified into Positive and Negative Feedback Amplifier. Similarly when the output signal is in the same direction 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.

In this Experiement the sensitivity of the LVDT was investigated by setting the Oscillator to 5kHz to obtain a 1.5V p2p primary excitation on channel 1. By Varying the range of the micrometer from 25 to 7.5 mm and obtaining readings for the peak to peak values for secondary voltages a set of values were obtained for increment of 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 the calculations below.

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

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

Setup the apparatus as shown below.

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

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

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

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

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

Note the observation and make a sketch of the waveform that corresponds to the 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 process signals from a transducer signal source.

Setup the Apparatus as shown below.

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

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

Connect the leads in such a way that the output of the psd passes through the Low Pass filter before reaching the Oscilloscope. Note the Output Voltage and 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 beam deflection. Note the waveform.

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

Setup the Apparatus as shown below.

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

Connect the output from the Accelerometer to the input to the charge amplifier using a short Co-axial lead. Note the magnitude and phase relationship of the ouput relative to the driving signal to the vibrating beam assembly.

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

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

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

Setup the Apparatus as shown below.

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 the readings on the oscilloscope for these input and output signals. This data will be used to calculate the gain.

Vary R1 & R2 to get the maximum gain of the op-amp, without clipping the signal. Note down the readings on the Oscilloscope. These will also be used later 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 the observations.

Results Experiment 1

From the experiment the minimum Peak to Peak Secondary Voltage that was obtained 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.

6 8 10 12 14 16 18 20 22 24 26

0

20

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Graph Showing displacement against Peak to Peak Voltage

Displacement (mm)

Vo

ltag

e (

mV

)

This can be calculated by

Experiment 2 – Observations

1. Both signals are in phase

2. When changing the Balanced supply from + to – Phase shift occurs by 180 degrees. It has a gain of -1.

19 20 21 22 23 24 25 26

0

10

20

30

40

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60

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f(x) = 10.4 x − 190.666666666667

Enlarged Graph of Secondary Voltage vs. Displacement

Displacement (mm)

Vo

ltag

e (

mV

)

3. When changing the Reference input from the -ve to the 0 degree terminal it becomes fully rectified. Peak to Peak 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

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

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

Experiment 3

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

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

After Phase Shifter is used : (Refer sketch below)

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 the remaining part of this experiment.

Experiment 4

Using The Voltage amplifier the following observation was made to the waveform when

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 :

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

Maximum Output 150mV

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

Experiment 5

To obtain the minimum and maximum gains using the op-amp , the resistors R1 and R2 should have the largest difference possible and the smallest difference possible correspondingly. 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 which referred to an overload. The Resistance was too high. Since the meter was able to measure 10M Ohm the Input Resistance is thought to be exceeding 10 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 output voltage.

This was done by displacing the beam using the micrometer. The results agreeing with 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. The graph produced a linear relations as expected from the LVDT. The Voltage decreased with decreasing Distance and started to increase specifically around 20mm. The residual Voltage 14mV occurred at a displacement of 17 mm . The Phase reverses its polarity between 20 and 17 mm which means the centre of the coil is positioned somwhere around that distance. The Readings themselves are not very accurate due to the noise interference present in the

room that affected the signals. The approximate sensitivities obtained from these graphs are still fairly acceptable.

Experiment 2

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

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

Whereas when the Lead are interchaged such that the Voltage across the input is negative. It can be seen that the shape of the output voltage stays exactly the same. However the Wave is 180 degrees out of phase. This means that there is a gain 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 it happens at 1.9V. Also noted that a phase shift occurs between the detected signal and the reference signal.Hence it can be deduced that the Phase Sensitive Detector not only detects and amplifies the input signal but also the Phase shift that occurs relative to the reference input . To correct this phase shift, the Phase shifter is used which means all signals are shifted in frequency by the reference frequency. All other frequencies that occur are attenuated such that they can not be detected by the Phase sensitive detector. When the phase shifter knob was adjusted , a fully rectified wave is obtained at maximum peak. The peak Voltage was 4.3V and the signal 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 the signal was sent to the Phase sensitive detector. The Peak voltage in this wave form was about close to 100mV. This system would not make a good measurement system in practise since the system had poor sensitivity besides this the output signal wasnt very clear and the signal was easliy disturbed by noise and other factors which was very undesirable.

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

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

Experiment 4

In this Experiment the piezoelectric accelerometer was connected to 2 different length coaxial cable connected to a charge amplifier and Voltage amplifier one after another.

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

0.5 radians out of phase with the output leading the input signal. However the lengths 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 feedback capacitance and the Charge input , which isnt really affected by the Cable Impedance since it is too low to detect.

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

Experiment 5

In this Experiment the minimum gain in the non-inverted operational amplifier was 1.13 which was about 13% . This was of course taken before clipping. Obtaining the clipping point seemed to be a bit of a problem and inaccuracies in this experiment can certainly be accounted by human errors. The input resistance of the Op-amp could not be measured as the Resistance was much too high. The Output resistor read 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 signal becomes too large such that the output current would be driven to its limit , clipping occurs. To prevent clipping a limiting network would be suggestible such that it identifies when the op-amp starts to become unstable.

ConclusionThe main aim of this Laboratory session was to investigate and understand the working 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 between Displacement and Voltage. However , the range was very limitied if a more accurate results is required , a beam with a much larger displacement could be used to obtain a bigger set of readings.

The Second Experiment was a bit more challenging a clear phase change could be observed when using the Phase Sensitive Detector. In the second part a clear rectified signal was obtained in both in and out of phase signals. This could only be accomplished with the use of a Phase shifter though to rectify the

Phase jump. The shape of the rectified waveform consisted of just peaks where every alternating peak 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 was much high than the negative peak. The unreliability of the equipment and its sensitivity made it hard to obtain readings but the end results were fairly acceptable.

The Third experiment was not very successful due to a fault Low pass filter. No accurate Readings could be obtained from this Experiment. When the beam was displaces the Low pass filter should have shown a low signal Corresponding to the vibration of the beam. In Reality , Although the Filter showed an initial Displaced signal due to the displacement of the beam , the Signal flicked back to 0. Even as a working system this would not be very useful for large displacements of beams since the Low pass filter can only respond to a limited range of signals.

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

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

The fifth Experiement was done using an Operational Amplifier. The minimum and maximum values for gain were obtained by adjusting to variable resistors. It was concluded that obtaining values close to theory wasnt very likely since the Resistance had to either be 0 or infinity. Although resistance can be increased to very large numbers , it is much harder to reduce Resistance to 0. However for practical Purposes , having a large enough difference between the two was just as effective.

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 its maintenance . Human Errors are very likely since a lot of readings and results required human intervention.

References http://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

Additional QuestionsExperiment 1

1.1 What is the cause of the residual Voltage ?

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

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

Experiment 2

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

When the signal from the reference input was positive the signal on the PSD became 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 Observation was either +1 or -1. This explains why there was no change in the amplitude or magnitude of the signal just a change in polarity.

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

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

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

Experiment 3

3.1 How 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 connected in parallel. As the frequency increases the Capacitors impedance decreases . The low impedance in parallel to a load resistance tends to short out high frequency signals.

◦ Inductivce Low Pass Filter

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

In this Experiment a Capacitive Low Pass Filter was used.

3.2 How 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 hence this investigation was not as precise. Theoretically the Low pass filter is calibrated to only allow the RMW of the peak voltage to pass through. The results recorded for this was 0.1V

Experiment 4

4.1 Explain 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 layer that 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 field that acts as a Faraday's cage i.e. complete block out any external static fields from the interior. When the signal in the cable is less prone to external interferences it can travel over greater distances without a disturbance which results in very low error rates , better output.

At the same time the coaxial cable has a much bigger bandwidth which means it can 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 an unshielded wire.

Experiment 5

5.1 Why 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 the signal thats being sent out is above or below this range then those signals get cut off and clipping occurs.

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

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

5.2 What 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 :

The minimum Value is can only be obtained when

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

5.3 In your report, redesign the op-amp to give a negative gain (inverting amplifier) , and then derive the relationship between the gains of the amplifiers 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 the signals. The Resistor R2 sends the output signal back to the negative input terminal. The difference in the polarity between the two signals means that they're completely out of phase as this signal superimposes on the incoming input signal , it reduces 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 current flowing from input to output through R1 and R2.

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

At this point :

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 the feedback signal increases , so does the input as it gets larger and larger since the output signal that is sent back through the feedback loop is positive and superimposes on the input.

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

We assume V- = V+

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