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8/10/2019 Basic Working of Fog
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BASIC WORKING OF FOG
8/10/2019 Basic Working of Fog
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S AGNAC EFFECT:-
• Light beams propagating in opposite direction experiences a path length difference , w
proportional to the rotation rate.
The wave travelling in direction of rotation is clock
wise wave, which will travel more path.
is the distance that the mirror has moved in that same time
The wave travelling in opposite direction of
rotation is counter clock wise, which will travel
less path.
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Time difference between the two waves is:
The phase shift produced between the two waves is,
Sagnac effect in a medium,
Where the velocity of light and velocity of a medium must be taken into
consideration.
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the speed of light should be increased when "dragged" along by the water
decreased when "overcoming" the resistance of the water
Fizeau equation for speed of light is given as
Magnitude of drag was very much lower then expected by Fizeau.
Differential length of Sagnac effect in a medium is identical to that of in vacuum
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TWO BEAM INTERFEROMETRY:
Sagnac effect can be observed in this phenomenon, the
phase shift produced between the two light waves due to
rotation is similar to that of Sagnac phase shift.
• Output fed to detector, the detector try to estimate the
optical intensity as a function of omega which is also a
function of differential length.
OPTICAL FIBER IMPLEMENTATION:-
• The 3 mirror system is replaced by an optical fiber to
improve the sensitivity of the interferometer.
• By implementing N turns, the corresponding diff-
length , phase shifts are enhanced by N times.
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P ASSIVE RESONATOR METHOD:-
Light with a frequency f enters the resonator at one mirror, along
directions and exits at other mirror.
In absence of rotation resonance frequencies are identical due tochange in perimeter.
In case of rotation the perimeter observed by both wave are differ
which will in turn create a frequency difference.
In case of optical implementation the perimeter is changed by n ti
, which will reduce the frequency difference.
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RING LASER GYRO:-
• Optical amplifier included into the resonator.
• In absence of rotation the laser frequency remains
constant.
• In presence of rotation, the time differencebetween the waves introduces slight change in
frequency.
• A beat pattern of waves is observed at the output
side.
Problems in fibre optic implementation:-
•
Simultaneous bi-directional lasing is not possible.
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IMPLEMENTATION OF TWO BEAM INTERFEROMETRY FIBER OPTIC
GYRO:-
• In absence of rotation output of detector is
maximum, and output drops with omega.
• To identify the magnitude and direction ofrotation phase modulator is introduced at the
coupler.
• If PSD output is directly used, it is called open-
loop.
• If PSD output is used to generate the phase
shift which is fed back to optic chip, it is calledthe closed loop.
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Other non reciprocal sources:
1. Polarization effects.
2. Back reflection.
3. Temperature effect.4. Offset errors of electronic devices.
Parameters that influence the closed loop operation:-
1. Source wavelength changes
2. Temperature control over the coil
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IMPLEMENTATION OF PASSIVE RESONATOR FIBRE OPTIC GYRO:-
• Counter clock-wise wave was detected bydetector 1 and used in locking the laser
frequency at the resonance.
• Clock- wise wave was detected by detector 2
and used to identify magnitude and direction
of gyro.
• By closing the second loop it is possible tochange the laser frequency in clock wise. Which
can produce a precise frequency difference
between both the waves.
• Other non reciprocal effects still exists…..
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Closed loop approach.
• A phase difference is introduced to nullify the total phase differenc
between the interfering optical waves.
• Advantages in closed loop approach rotation signal is independe
optical intensity and gain of electronic components.
• Disadvantage in this is identifying the exact electronic optical elem
that produces the phase shift.
• Generally frequency shifters and phase modulators are used to
produce the required phase shift.
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Phase modulator is located at asymmetrical position in gyro loop.
T is the transit time.
To avoid gyro switching between + or – 90deg, a phase bias of 90
is fed to change the operating point.
Ideal form of producing the phase difference is a continuous phas
ramp in time.
By varying the phase ramp the differential phase can be varied.
which in turn helps making the net difference zero.
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• Producing infinite phase ramp is not possible. So
to avoid that problem periodic ramp with finite
duration is used.
• The output of phase modulator is taken as the gyrooutput. This approach is called gated phase
modulation approach.
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FREQUENCY SHIFTER
Frequency shifter is placed at one end of gyroscope loop.
Both the waves are induced with frequency shift. The shift in the f
induces a differential phase shift = . is the transit time of light through the fibre.
In a closed loop gyro we always try to maintain the total differential
shift zero. i.e.:- Δ = +Δ =0.
Where the frequency becomes Δf=Δ/2 and Δf=(DΩ/nλ ).
Observations:-1) diff. freq depends on the D, n, λ but not on the optical intensity and
electronic components.
2) Scale factor similar to the RLG.
3) Dependence on ‘n’ causes instability of scale factor for a high rotati
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ANALOG SERRODYNE PHASE MODULATION:-
Different waveforms are used for the modulation
1. Saw tooth wave
2. Asymmetric triangular wave
Saw tooth wave for phase modulation:-
1. It should have a large frequency band width to accommodate th
modulated wave.
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CONT…
The diff. phase shift produced during time period Δ(t)=2f
Basing on fm(freq of saw tooth wave ) or T(time period of ramp sign
one can calculate the rotation rate i.e. Δf=(DΩ/nλ ).
Caution: finite fly-back time will introduce errors in the scale factor.
Drawback: demand of high bandwidth cannot be introduced in the f
optic.
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SINUSOIDAL MODULATION:
Sinusoidal approximation of saw tooth wave is applied to the
gyroscope. In turn it produces a sine phase diff modulated wave.
But, it is not useful at constant rotation rate.
Solution: if the negative half cycle of sine is turned of and we can
produce time averaged signal which can be used null the rotation
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ASYMMETRIC TRIANGULAR WAVEFORM:
Triangular waveform with asymmetry in time is used.
The operating point of gyro is made to alter between two symmet
points.
Two differential phase shifts induced for two time periods.
i.e.: Δ=2(m) / T1 and Δ= - 2(m) / T2.
The rotation rate is given as (r)= (T1-T2)/(T1+T2).
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CONT…
Observations:
1. measurement of rotation does depend on modulation amplitudthe transit time.
2. Scale factor is independent of the refractive index.
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OPEN LOOP APPROACHES:-
They do not use phase shifters but they need the quadrature pha
information. (i.e. differential phase shift values of sine and cosine
between two waves.)
Basic method by sinusoidal modulation, where detector current is
proportional to cosine(r) and sine(r) harmonics.
Basic method lacks accuracy and complex in measurement.
Other methods :
1. Synthetic heterodyne
2. Digital phase locked loop
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Synthetic heterodyne:-
• It converts the rotation information into phases of low frequency
signal.
• By amplitude modulation operating at (Fm) of detector current it
produces sidebands signals of Fm.
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CONT..
Band pass filter generates output at frequencies 2Fm
i.e. : I1=(IK/2)cos(2*Fm*t+(r)) and I2=(IK/2)cos(2*Fm*t-(r
By using these two signals one can measure the rotation rate.
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DIGITAL PHASE LOCKED LOOP:
Optical phase shift is measured by closed- loop digital electronic
circuit. The spacing between the pulses reflects the optical phase shift.
Phase shift equation= (r)= tan^-1[Sx (2/T)/Cx(2 /T)]
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THANK YOU
source
detector
Fibre coil
Phase modulator
Fb
GATE
PSD
Servo
Adjustablephase
modulator