technologies to implement the fog 7-b.pdf · digital ramp is used to drive the nonreciprocal...

1GYROSCOPESfrom: 'Electro-Optical Instrumentation' by S.Donati, 2004, © Prentice Hall (USA)

The three technologies shared by all types of FOGs are:• Micro-optics: consists in using conventional optical components,

and free space propagation; it offers the widest choice of componentsbut bottleneck is conjugation to fiber. Though useful in prototypes, micro-optics is not suitable for devices deployed in the field.

• All-Fiber: consists in modifying appropriately pieces of fiber to fabri-cate components. Examples are PZT-modulator, polarizers, etc.

Good for low insertion loss, has a limited choice of offered devices.• Integrated Optics (IO) this technology puts all required functions

together, integrated on a single chip. May perform functions like(i) passive functions (with SoS or silica-on-silicon), (ii) passive and modulation functions (lithium niobate or LiNbO3) (iii) active functions (compound semiconductors like GaAs and InP)- IO guides require pigtailing and incur in an extra coupling loss,but has the advantage of batch fabrication and reproducibility

Technologies to implement the FOG


Examples of IO technology for the FOG: an integrated, minimum-configuration FOG with3x3 coupler in SoS; (bottom) a lithium niobatechip implementing the splitting and PM functionsof a normal FOG.Called iFOG, the deviceperformances equal thoseof the best all-fiber FOG, but now performances are consistently obtained withhigh (≈95%) yield.

FOG in IO technology

SLED

PD

Li Nb O 3

launch couplerexit coupler

chipphase modulators

+V

-V

0 fiber coil to external

SoS substrate

3x3 coupler

PD1

SLED

PD2


A ring laser gyro (RLG) in a planar waveguide of large radius (≈1 cm) was proposed by Donati Giuliani Sorel (Alta Freq. 9, p.61, 1997). Rings fabric-ated in both GaAlAs and InP/InGaAs have shown (Opt Lett03, JQE04, APL04) alternate oscillator and bistability regimes, and strong locking.

RLG in SL technology


other attempts have dealt with the triangular cavity with end-cleaved mirrors (Ballantyne 1999 and 2004) and the double-ring variant (Oshinski 2004 and 2005), yet scattering was too large to permit free oscillation of the two counterpropagating modes required for operation

RLG in SL technology


Because the loop gain is large and negative, the phase difference is keptdynamically zero by the feedback loop, or φS–Φ=0. Output is then read from the drive voltage Vdr as φS=Φ=f(Vdr).

The Closed-Loop FOG

SLED

+Vbb

-A lock-in amplifier

driver

front-end

oscillator

PZT

ω m

ref

driveφS

nonreciprocalphase shifter

Φ

measVdr

ω m

output

comp

P0

R

sin ( )-0φS −Φ

In the closed-loopFOG, the lock-inoutput is fed back after amplificationand conversion toa nonreciprocalphase shifterΦ=f(Vdr), where f is the phase shiftertransfer function.


In the digital-readoutclosed-loop FOG, a digital ramp is used todrive the nonreciprocalSagnac-zeroingmodulator. Each phasestep increases the phase by an incrementΔφ equal to the least-significant-bit (LSB). If in the transit time T the phase modulation

Closed-Loop FOG: the serrodyne approach

SLED

+Vbb

lock-in amplifier

front-end

-A

PZT

oscillatorωm

ref

sensing

φS

meas

Vdrω m outputcomp

P0

R

PZT

zeroing modulator

modulator

clock (VCO)

step sequence generator

sawtoothgenerator

gate

Φ

Δφ

T

Φ

t

changes by M steps or Φ=M Δφ, (and φS-Φ =0), the Sagnac phase isread out as φS= MΔφ. A VCO clock fed by Vdr gives the pulsefrequency, and the sawtooth generator the underlying ramp waveformproviding the synchronism to validate the output through a gate.


♦ advantage of digital readout is the increase of resolution byaveraging. If LSB phase increment is a bare Δφ=0.1 mrad, yetthe corresponding Ω=100 deg/h is not so small. But, if measurementtakes, say 0.1 ms, we can average on 104 of them in 1-s and improvethe resulting error by √104=102, going down to Ω=1 deg/h. And, the statement is true if random noise is larger than 1 LSB.

♦ In the digital closed-loop configuration, the frequency passbandrequired to the phase modulator is not simply ≈1/T of the open-loopreadout, but probably about ≈ 20..50/T because the ramp and multistep features that we need to preserve.

♦ This leads to prefer the IO approach based on lithium niobate forimplementing the digital closed-loop.

♦ In conclusion, after ten years of maturation, the FOG has evolved toits best level with the digital closed-loop configuration, and got agood acceptance in space applications (AHRS of low-orbit satellites,and gyro-compass) and other niches (oil drilling, rocket spin control)

FOG serrodyne approach - 2


A typical closed-loopFOG with 0.5 deg/h zero bias and 0.06 deg/√h random noise, uses 200-m of high birefringence fiber, a Peltier-controlled SLEDand a custom IC togenerate and control the staircase zeroing ramp(courtesy of SEL, Germany)

a typical commercial FOG


Satellite Applications of FOGs

Space FOGshave beendesigned as the sensor forAHRS (attitudeheadingreferencesystem) of telecommuni-cation satellitesof the IRIDIUM series

The Iridium World Satellite Service


♦ The R-FOG uses the fiber coil as a ring resonator. The PZT modulator keeps the total path length locked to the resonance peak, and senses the Sagnac phase shift by an added ac modulation.

♦ Responsivity increases by a factor F, the resonator finesse. ♦ In the R-FOG we get the same responsivity of a normal FOG but use

a fiber F=2√R/(1-R) [typ. F≈100] times shorter than in FOG, and hopefully provides less noise.

Other approaches: the R-FOG

PZT PHASE MODULATOR

LAUNCH COUPLER

POLARIZATION CONTROL & FILTERSLED

PHOTODIODE

CW

CCW

fiber coil (hi-bi)


♦ The 3x3 FOG is the gyroscope or minimum-part-count FOG. ♦ Requires just the fiber coil (a normal fiber, shorter than in a normal

FOG), a SLED source, two photodiodes, and the 3x3 coupler. ♦ To dispense of fiber splices, the coupler is fabricated directly using

the pigtails of the SLED and of the fiber coil.

The 3x3 FOG for the Automotive

100-m SMR fiber on a 20..30-mm coil

3x3 COUPLER

SLD pigtail

PD1

SLED

PD2

coil pigtail

coil pigtail


We may assume that the splitting ratio is 1/3 in power (and 1/√3 in field), equal forall ports. Then, because of symmetry, two outputs shall be in-phaseand the other at 90° to satisfythe conservation of power (sum of squares) .As also the sum of vectorsequals the input vector, the

Properties of the 3x3 coupler

E2C

E0

E1C

ED

ED

E1C

E2C

E0

60°

30°

0

21

phaseshifts are 30, 30 and 60 deg. As we see from figure, we can write:TD = ED /E0 = (1/√3) exp –i 60°

T1C = E1C/E0 = T2C = E2C/E0 = (1/√3) E0 exp +i 30°


Let us now analyze the fields EPD1 and EPD2 collected at PD1 and PD2, which are EPD1 = E1CC +E2CD and EPD2 = E1CD +E2CC .We can write the terms in this equation as:

E1CC= E1C exp–iφS T1C E2CC= E2C exp+iφS T2C

E2CD = E2C exp+iφS TD E1CD = E1C exp–iφS TD

E1CC

1CE

0E2CE

2CDE

Fields in the 3x3 FOG

ED

E1C

E2C

E0

1CC 2CDEE +

2CC1CD+ EE

DE

2CCE

1CDE

2CC

E

1CD

E

DE

φS


Signal in the 3x3 FOG

By inserting in previous equations, we get: EPD1= E1C exp-iφS T1C +E2C exp+iφS TD

= (E0/3) [exp i(+60°-φS)+exp i(-30°+φS)] andEPD2= E2C exp+iφS T2C+E1C exp-iφS TD

= (E0/3) [exp i(+60°+φS)+exp i(-30°-φS)] The photodetected current is the square mean value, I= ⟨E2⟩, or:

IPD1=2 (E0/3)2 [1 + cos (90°-2φS)] = 2 (E0/3)2 (1+ sin 2φS)IPD2=2 (E0/3)2 [1 + cos (90°+2φS)] = 2 (E0/3)2 (1- sin 2φS)

By computing the difference IΔ=IPD1- IPD2 of outputs, we suppress the dc term and get a signal proportional to the sine of Sagnac phase φS:

IΔ = 4 (E0/3)2 sin 2φSA typical 3×3 FOG is made by a 30-mm diameter fiber coil with 100 m of single mode fiber. Performance is: baseline drift ≈0.05 deg/s, NEΩ≈0.01 deg/s (at B=10 Hz), linearity error <0.5% up to Ω≈200°/s.


velocity Ω along the y-axis, a Coriolis force FC = 2m Ω xv is developedalong z-axis. Measuring the z-displacement with a suitable sensor, the result is traced back to Ω. (right): MEMS gyro has a mass m suspendedwith a spring hinge, and a comb expansions along the x- and z-axis. The x-axis combs serve to actuate the mass by electrostatic force. The z-axiscombs have a capacitance that varies with opposite sign as the mass moves along z, and is the electrical readout of the z-displacement.

The MEMS Gyro and Other Approaches

kz

r

actuator

actuator

X

ZY

FC

v = v x

Ω = Ω y

z

kx/2

kx/2

rx/2

rx/2

m z-displacement sensor

actuator

FC

Ω

X

ZY

v

combs

readout combs

+ΔC -ΔC

m

Fx

(left) An MG is basedon the Coriolis’ force acting on a sensingmass m. Mass issuspended by springsand an actuator puts itin vibration (along x-axis). When the MG rotates at an angular


rotor displaces the rotor vertically (out of plane). The finger capacitance is measured to sense this displacement.

MEMS gyro

A typical MEMS gyrois made by a Si-rotorsuspended on substrateand free to oscillate around the centralhinge. Comb fingerslocated at the fourcorners allowelectrical excitation of the oscillatory motion. An angular velocity Ωin the plane of the


Noise equivalent angular velocity NEΩ versus measurementbandwidth B for a MEMS gyro as limited by the mechanical-thermal noise, NEΩ = ω3/2 (4kmTB)1/2 /2Q3/2F0Data is for m=2μg and ω=10 kHz.

MEMS gyro performance

101

102

10 3

104

0.1 1 10 100 1kbandwidth B (Hz)

NEΩ (deg/h)

Q = 10

100

1

300

30


Automotive FOG

the Magneti Marelli RoutePlanner

The Route Planneris an automotivenavigation system basedmainly on beaconing on GPS broadcast signals.Yet, when operating in downtowns with tallbiuldings, in tunnels or othershielded locations, the system calls for a backup. This is provided by the gyro(MEMS or PG) with typicalsensitivity of 10-100 deg/h and 100 rad/s dynamic range


A hybrid MEMS with optical readout of the displacement alongthe z-axis by means of selmix interferometry, or MOEMS, can alleviate the design requirements and help improve NEΩ.

A hybrid readout, MOEMS gyro

M

kz

r

LDPD

actuator

actuator

X

ZY

FC

v = v x

Ω = Ω y

z

kx/2

kx/2

rx/2

rx/2


Other examples of gyros developed for robotics, alltraceable to a mechanical gyro based on Coriolis' force are:

♦ The piezoelectric gyro (PG), in which both excitation and readout are obtained through the piezoelectric effect.The PGs may take different configurations, yet all use aninexpensive material (like a quartz crystal or a piezoceramic),and provide excitation/readout through cross-axes electrodesobtained by metallization. About performances of the PGs,data are, of course, compliant with the thermal noise limits.Typical sensitivity of commercial products is 0.2..1 deg/s and the dynamic range is 50 to 200 deg/s.

♦ The ion-beam gyroscope (IBG) uses an atomic beam (Ne, Ar) that is aimed to a 4-quadrant receiver. Relatively bulky (4-cmdia X 10-cm length) it achieves performances close to the PG.

Other Mechanical Gyros


In the tuning fork PG, fork oscilla-tes along v, and sensing is alongFc; angular velocity Ω is measuredin the plane of the fork. In the wine glass resonator, the tube vibrates in an elliptical-shaped flexure, and with arbitraryinclination (here ±45°). Whenexcited by ac voltages at resonantfrequency, a ±Ω applied along the tube axis makes the ellipse rotate CW or CCW . Comparing the S1-S3 and S2-S4 gives Ω.The resonating quartz triangle usesPZT transducers and a quartzblock to improve Q and response.

subs

trate tuning fork

sense

piezo

excitation

v

Ω

Fc

S1

S2S3

S4S2S3

cross section x-x

xx

vΩFc

S1

S2

quartz block

piezoceramics

oscillator

S3

A+-

out

S1

S3 S2

Types of piezo gyros (PGs)


The ion-beam gyroscope (IBG) uses a beam of noble gas atoms(or molecules) for a drift in the interelectrode space. The beamis subjected to Coriolis' force FC = 2m Ω x v. Hence, when aimedto a 4-quadrant receiver it senses the ΩX and ΩY componentsperpendicular to tube axis. The IBG is bulkier than other gyrosand achieves performances similar to PGs.

Ion-beam gyroscope (IBG)

bypass

source

S1

S2 molecularbeam

vΩ

technologies to implement the fog 7-b.pdf · digital ramp is used to drive the nonreciprocal...

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