Simulation of Enhanced Ring Resonator with PZT for Microwave Gyroscope Application

Transcription

1 Simulation of Enhaned Ring Resonator with PZT for Mirowave Gyrosope Appliation Sandeep Kommineni 1, Swarna Bai Arniker 2, and Rambabu Kammili 3 1 M.Teh Student, Shool of Eletronis Engineering, Vellore Institute of Tehnology, Vellore, Tamilnadu, India. 2 Sientist E, Head SDSD, Diretorate of Laser Systems, Researh Centre Imarat, Hyderabad, Andhra Pradesh, India. 3 Sientist G and Diretor Laser Systems, Researh Centre Imarat, Hyderabad, Andhra Pradesh, India. 2 arniswarna@rilab.in Abstrat. Ring Laser Gyrosope belongs to the lass of Optial Rotation sensors in the field of inertial navigation systems. Despite its high auray it has suffered from lak of dynami range and as well lak of sensitivity at low rotation rates popularly known as lok-in. Mirowave gyrosope (MG) with Clokwise and Counter lok wise mirowaves propagating inside the mirostrip Ring resonator an provide required beat frequeny for eliminating lok in problem thus overoming insensitivity problem at low rotation rates. By means of a piezoeletri transduer inside the ring resonator whih the hanges the resonant frequeny and provides the desired ontrol on the required frequeny differene i.e., beat frequeny. Thus MG ats as a preise rotation sensor, and has wide appliations. This paper presents the simulation results of enhaned Ring resonator, and Inter-digital transduer frequeny response in standalone mode. Further it is proposed through simulation results that the Integrated Enhaned Ring Resonator with PZT in turn generates two resonant frequenies and their frequeny differene i.e., beat frequeny will be a measure of rotation rate being sensed. A omparative simulation result of Mirowave gyrosope and RLG are also presented. Keywords: Mirowave gyrosope, Ring resonator, Piezoeletri transduer, Surfae aousti wave, Rotation sensors, Simulation. 1. Introdution Ring Laser Gyrosope (RLG) is onsidered as one of the most reliable and preise sensor till date for high auray inertial navigation systems and in other appliations as well. RLG works on the priniple of Sagna effet [1]. Laser beam is split into two and one beam is made to irulate in the lokwise diretion inside a triangular or square avity formed by mirrors/prisms and other beam in the ounter lok wise diretion within the same avity. Both beams interfere and form a fringe pattern. The shift of fringe pattern δp is the rotation of the body aording to the equation (1). δp = 4 A (1) λo * where is the angular rate in rad/se, A is the total area enlosed, λ o is the wavelength of the laser soure used and is veloity of light in free spae. It is obvious from equation (1) that as the area of the avity inreases the fringe shift is more, thus the sensor an detet low rotation rate also and hene resulting in inreased sensitivity. Many attempts were made by researhers to inrease the sensitivity of the RLG as given in [2 6]. Various innovative tehniques that were suessful in inreasing the sensitivity inlude eliminating the external effets like magneti field, thermal gradients, ating on the RLG; Mehanial dithering to overome dynami lok-in; Use of dispersive elements in the optial path; Changing the shape of the avity to pentagonal shape; Inreasing the path of the one of the beams by bringing out this beam from the avity and traversing it extra distane outside the avity and resending this beam bak to the avity. These tehniques require additional external hardware and assoiated alibration from time to time. Even though these tehniques ahieved Corresponding author Elsevier Publiations 2013.

2 Simulation of Enhaned Ring Resonator with PZT for Mirowave Gyrosope Appliation Figure 1. Enhaned ring resonator. better sensitivity but not to the required extent. This motivated us to survey for alternate gyrosope tehnologies and arry out simulation studies and analyse their results. Mirowave gyrosope was proposed theoretially [7] and laimed of ahieving higher order sensitivity. This is proposed on the basis of Sagna effet in a mirowave ring resonator. The differene in frequeny of the two ounter propagating beams was the measure of rotation. Surfae aousti waves affeting the beams inside the ring resonator reates more frequeny differene resulting in inreased beat frequeny thus overoming lok-in problem and inreased dynami range. 2. Mirowave Gyrosope Components From simulation point of view the basi building blok of a Mirowave gyrosope is the ring resonator and the ritial element that enhanes the sensitivity is the SAW based delay line whih is realised using Inter-Digital Transduers (IDT). 2.1 Ring resonator The ring resonator is a transmission line in a losed loop. It onsists of two feed lines for oupling power into the resonator through oupling gaps. The ondition for resonane is its irumferene should be equal to integral multiple of the guided wavelength. The equation as given in [8] is shown below 2πr = nλ g (2) where r is the mean radius of the ring equal to average of outer and inner radius of the ring, n is the number of modes and λ g is the guided wavelength. Various types of oupling tehniques used in ring resonators inlude loose oupling, enhaned oupling, diret oupling, side oupling and annular oupling [9]. As loose oupling suffer from high insertion losses in this paper enhaned oupling based ring resonator having both upper and lower arm as shown in Figure 1 was simulated sine maximum power will be oupled to the ring resonator from the feed lines. 2.2 Surfae aousti wave based delay line Surfae Aousti Waves (SAW) based devies are mainly used as filters and resonators in ommuniation systems and as variety of sensors in many other appliations [10]. SAW is generated by Inter-Digital Transduers (IDT) on a piezoeletri material substrate. The basi SAW Delay line is omposed of two IDT metalli array fingers on a piezoeletri substrate like Quartz, Lithium Tantalate and Lithium Niobate. The SAW delay line is the most ritial sub-omponent of a mirowave gyrosope that enhanes the sensitivity. The priniple of operation of SAW delay line is as follows; When the First IDT is exited by the sinusoidal eletrial signal, then the piezoeletri effet of the substrate generates the aousti waves. These waves propagate to the other IDT to generate an eletrial signal through the inverse piezoeletri effet. The aousti wave only penetrates the substrate up to a depth of the order of magnitude of the wavelength [11,12]. Elsevier Publiations

3 Sandeep Kommineni, Swarna Bai Arniker and Rambabu Kammili Figure 2. SAW delay line with spae between two IDT s. 3. Theoretial Bakground of Mirowave Gyrosope This setion presents theoretial bakground regarding the differene in frequeny of both beams in a ring resonator. Let irumferene of the ring be L, resonant frequeny is f. Then the resonant ondition is given by L = nλ (3) If the surfae aousti waves of phase ϕ( f ) and frequeny f 1 is added to mirowaves, then resonator will resonate at new ondition as given in equation (3) [13]. L * f 1 + ϕ( f 1) 2π = n. (4) The equation (4) holds well when the resonator is stationary. If the resonator is rotated, a path length hange is indued due to rotation. If hange in path length is δl and hange in resonant frequeny due to hange in path length is δ f then equation (4) is modified as equation (5) (L + δl) * ( f 1 + δ f ) + ϕ( f 1 + δ f ) 2π The phase term in equation (5) is expanded in terms of Taylor s series as below. ( f 1 )δ f 2 + 2δ f ( ( f 1 ) + By simplifying equation 6, one gets the below equation ( f 1 )δ f 2 + 2δ f = n (5) ) ( ) (L + δl) *2π (L + δl) *2πf ϕ( f 1 ) = 4πn (6) ( ( f 1 ) + ) (L + δl) *2π + 4π f 1δL = 0 (7) This equation (7) is a seond order quadrati equation and the roots are ( ) A ± A 2 ( f 1 ) 4π f1 δl δ f = ( f 1 ) (8) where (L + δl) *2π A = + ( f 1 ) (9) By approximating the equation (9), δf is rewritten as follows. 4π f 1 δl δ f =± * (10) ( f 1 ) From [14] we have ( f 1 ) = / δl (11) L 750 Elsevier Publiations 2013.

4 Simulation of Enhaned Ring Resonator with PZT for Mirowave Gyrosope Appliation Figure 3. Beat frequeny in mirowave gyrosope Versus Ring laser gyrosope. Figure 4. Beat frequeny of mirowave gyrosope with and without delay line. and δl = 2S (12) S is the total area enlosed by the path. So, the final form of equation for differene in frequeny of two opposite waves in a ring resonator is given by / 8π S δ f =±f 1 (13) ( f 1 ) As an example, we take the values as f 1 = 600 MHz, S = 1m 2, ϕ ( f 1 ) = *10 6 1/Hz, = 2*10 8 m/s. The omparison of the beat frequeny δ f for both mirowave gyrosope (solid line) and RLG (dashed line) is presented in figure 3 and the omparison of the beat frequeny for mirowave gyrosope with and without delay line is shown in figure 4 respetively. 4. Simulation Results A survey of various simulation tools for mirowave omponents was arried out to hek their suitability for simulating a mirowave gyrosope. It was found that there is no software to our knowledge that supports to simulate a integrated mirowave gyrosope Hene various software simulation tools like AWR 2009, Matlab 2009, CST Mirowave studio were explored in arrying out this simulation ativity. Primarily the ring resonator and IDT were simulated stand alone. Later Ring resonator with piezoeletri transduer was simulated as integrated approah Elsevier Publiations

5 Sandeep Kommineni, Swarna Bai Arniker and Rambabu Kammili Figure 5. Simulation of enhaned ring resonator. Figure 6. Insertion loss S Ring resonator Enhaned ring resonator was simulated using iruit shemati approah in AWR 2009 simulation software. Enhaned ring resonator was realised by taking feed line more lose to the ring and the urves on the orners of the ring are onneted to gap whih takes feed from the miro-strip tee. Dimensions of the ring inlude gap = 16 mil and feed lines are of 200 mil eah onneted to 50 port [15]. The simulation results of the enhaned ring resonator, its insertion loss and return loss are shown in figure 5 and 6 respetively. The resonant frequeny was obtained at 2.6 GHz with insertion loss of 21 db and the return loss for 2.6 GHz is about 102 db. 4.2 Inter-digital transduers (IDT) The IDT was simulated using Matlab 2009 and the equations for design of IDT along with its frequeny response, effetive finger width; number of finger pairs for one IDT [16,17] is given as follows ( ) N p π f f 0 ) f 0 H ( f ) =2k Sin C s f 0 N p ( N p π f f 0 f 0 ) exp ( ωj2π fnp W a = 1 1 4k 2 N p R in 2C s N p f 0 (4k 2 N p ) 2 + π 2 (15) ( ) 2 N p = round NBW f 0 (16) 2 f 0 (14) 752 Elsevier Publiations 2013.

6 Simulation of Enhaned Ring Resonator with PZT for Mirowave Gyrosope Appliation Figure 7. Return loss S 11. Figure 8. Frequeny response of the IDT. Figure 9. Enhaned ring resonator with piezoeletri transduer. where f o is entre frequeny, k is oupling oeffiient, C s is apaitane of the pair of finger per unit length, N p is number of finger pairs, W a is effetive finger width, NBW is frational frequeny. The simulation result of the frequeny response plot of the IDT for the lithium Niobate substrate for Z axis for the given values of aousti veloity ν = 3488 m/s, entre frequeny 52.6Mhz, k = , C s = 4.6pF/m, NBW = 1.5Mhz,W f = 100 μm isshowninfigure Integrated enhaned ring resonator with PZT The enhaned ring resonator was simulated on a RT Duroid Substrate with the radius of the ring mm, oupling gap mm, width = mm and with 50 ohm feed lines using CST mirowave studio as shown in figure 9. Elsevier Publiations

7 Sandeep Kommineni, Swarna Bai Arniker and Rambabu Kammili Figure 10. S 11 and S 21 of enhaned ring resonator with PZT. A piezoeletri transduer using quartz material is plaed on the top of the resonator with a gap. By varying the applied input eletri voltage on the PZT the resonant frequenies of the enhaned ring resonator is found to be 2.9 GHz to 4.1 GHz respetively as shown in figure 10. This simulation was arried out using CST Mirowave studio. 5. Conlusion An attempt was made to inrease the sensitivity of the ring resonator based gyrosope. This was ahieved by olleting the frequenies from the enhaned ring resonator using piezoeletri transduer. By hanging the applied input voltage to the PZT on the enhaned ring resonator the resonant frequeny of the ring resonator hanges aordingly and at a partiular applied voltage it produes two frequenies, whose beat frequeny may be used for measuring the applied rotation rate. Further studies inlude fabriation and testing of the ring resonator along with PZT for sensing rotation rate. Referenes [1] E. J. Post, Sagna Effet, Reviews of Modern Physis, Vol. 39(2), [2] Bernard G. Fidri Ring Laser Gyro Frame Design Resistant to Thermal Gradient Effets, US patent No , [3] Mark S. Grasso and Joseph P. Fialora, Ring Laser Gyrosope Having Redued Sensitivity to Effets, US patent No , [4] Smith David D. Ring Laser Gyrosope Using Dispersive Elements, US patent No , [5] Wah L. Lim, James P. Hauk, Jak W. Raquet, Pentagonal Ring laser Gyro design, US patent No , [6] Zhenfang Fan et al., Dynami Lok-in Compensation for Mehanially Dithered Ring Laser Gyros, Chinese Optis Letters, COL 10(6), , [7] G. G. Karapetyan, Mirowave Gyrosope Novel Rotation Sensor, Mirow. Opt. Tehnol. Lett. 27, pp , [8] Kai Chang and Lung-Hwa Hsieh, Mirowave Ring Ciruits and Related Strutures, John Wiley & Sons In., [9] G. K. Gopalakrishnan and K. Chang, Novel Exitation Shemes for the Mirostrip Ring Resonator with Lower Insertion Loss, Eletron. Lett., Vol. 30, No. 2, pp , [10] B. Drafts, Aousti Wave Tehnology Sensors, IEEE Transations on Mirowave Theory and Tehniques, Vol. 49(4), [11] Jared Kirshner, Surfae Aousti Wave Sensors (SAWS), Miromehanial Systems, [12] Aamir F. Malik, Asif Iqbal and Zainal A. Burhanudin, Design and Simulation of SAW Delay Line for Corrosion Detetion, Int. Conf. on Ele. Devies Systems and Appliations (ICEDSA), [13] Y. Yun and K. Chang, Piezoeletri-Transduer-Controlled Tunable Mirowave Ciruits, IEEE Trans. Mirowave Theory Teh., Vol. 50, No. 5, pp , [14] G. G. Karapetyan, The Possibility of Deteting Gravitational Waves from a Shift in the Resonane Frequeny of an Optial Resonator, Tehnial Physis, Vol. 46(10), pp , [15] Athanasios Vitas et al., Review of different ring resonator oupling methods, 9 th WSEAS Int. Conf on Teleommuniations and Informatis. [16] Joana C. Mendes et al., Simulation of Aousti Devies Using Matlab, Eletrial Review Teleommuniations Institute, Aveiro, Portugal, [17] W. C. Wilson and G. M. Atkinson, 1st Order Modelling of a SAW Delay Line using MathCAD, NASA Langley Researh Centre. 754 Elsevier Publiations 2013.