10.12071901

Progress In Electromagnetics Research B, Vol. 44, 223239, 2012

ANALYTICAL METHOD FOR COUPLING CALCULA-TIONS OF ROTATED IRIS COUPLED RESONATORCAVITY

R. Kumar1, *, P. Singh1, M. S. Bhatia2, and G. Kumar3

1Ion Accelerator Development Division, Bhabha Atomic ResearchCentre, Mumbai-400085, India2Laser and Plasma Technology Division, Bhabha Atomic ResearchCentre, Mumbai-400085, India3Department of Electrical Engineering, IIT Bombay, Mumbai-400076,India

AbstractIris type waveguide to cavity couplers are used to couplepower to particle accelerator cavities. Waveguide to cavity couplingfor arbitrarily oriented rectangular iris is analyzed using Bethes smallhole coupling theory. Magnetic moment of rotated iris is obtained bydefining its dyadic magnetic polarizability. Power radiated by magneticmoment into the incoming waveguide is used for coupling calculationsat arbitrary angle. A close agreement is found between the proposedtheory, simulations and microwave measurements.

1. INTRODUCTION

Theory of coupling and radiation by small apertures in an infiniteconducting wall has been studied by H. Bethe [1]. Further, forapertures of arbitrary shapes, Cohn has obtained electric and magneticpolarizibility values by measurements in a chemical cell [2]. Bethestheory has been used to obtain analytical expressions for waveguide tocavity coupling by Gao [3]. Gao has further extended the analysisfrom end coupled waveguide [3] to side coupled waveguide-cavitysystem [4]. For practical apertures of finite thickness, Gao has includedattenuation coefficient to evaluate coupling coefficient of a waveguide-cavity coupled system.

Recently, first author has reported a novel way of changing thecoupling coefficient by iris rotation in RF couplers for accelerator

Received 19 July 2012, Accepted 19 September 2012, Scheduled 26 September 2012* Corresponding author: Rajesh Kumar (rkthakur [email protected]).

224 Kumar et al.

cavities [5]. Concept of iris rotation is demonstrated in [5] using fullwave simulations on commercial EM solver CST Microwave Studio(CST-MWS). In [5], a pill box cavity resonating at 350MHz is studiedfor rotated rectangular and square iris coupling using simulations only.The work reported in present paper is distinct from [5] in mainly threeways. First, analytical expressions for rotated irises are derived fromfirst principles using Bethes theory. Second, other iris shapes likecircular and elliptical are also analyzed apart from rectangular andsquare irises. Third, prototyping and microwave measurements are alsocarried out to verify the proposed analytical results. Considering theease of fabrication, smaller coupler-cavity system at S band is analyzedhere as compared to 350MHz system in [5]. Iris rotation basedtechnique is expected to be useful alternative to existing techniquesbased upon post fabrication machining for coupling adjustments inparticle accelerator cavities [6]. Hence, a detailed analytical study ofsuch coupling structures will be important.

In the context of accelerator cavities, Pascal has proposed anuseful technique for calculating external Q numerically with lessersolver runs [7]. An equivalent circuit based approach for external Qcalculations is reported in [8] but it doesnt consider rotated iris.

Though, iris at an angle has been used in waveguide directionalcouplers as a means to get different power divisions [911], thetechniques used to obtain coupling values are either purely numericalor studied in the context of waveguide to waveguide coupling. Thereare many numerical studies on rotated iris coupling in the context offilters, e.g., [12] and EMC applications [13]. Bethes theory has alsobeen used recently to evaluate coupling in rectangular coaxial lines [14].

Bethes original theory is modified by Collins by including reactionterms [15]. The modified theory is useful for waveguide-waveguide andwaveguide-cavity coupling calculations in-order to obtain physicallyrealizable equivalent circuits. The Collins approach has been usedfor analytical studies on open resonator coupling [16] and cavity tocavity coupling [17]. However, in particle accelerator resonator cavities,information of external quality factor and coupling coefficient is goodenough for describing their behavior at resonance because of singlefrequency operation. Hence, description of reaction terms for obtainingthe physically realizable equivalent circuit may not be needed. Asdescribed in [3, 4], by using Bethes original theory, coupling coefficientfor iris coupled waveguide to cavity system can be obtained withreasonable accuracy.

We also use Bethes original theory in this paper and arriveat analytical expressions for external Q and coupling of an iris atarbitrary orientation. We have chosen rectangular iris because of

Progress In Electromagnetics Research B, Vol. 44, 2012 225

its simplicity and regular use in practical waveguide-cavity coupledsystems in accelerators. This is because of the fact that rectangulariris is easier to machine as compared to elliptical one. As shown inSection 3.1, rectangular iris also provides more coupling than circularand square iris. It also provides wider range of coupling variation withiris rotation as compared to square and circular iris shapes as discussedin Section 3.1.

Though, analytical expressions are not available for rectangulariris as opposed to elliptical iris, polynomial based methods areavailable [1820]. We calculate the magnetic polarizability (i.e.,longitudinal and transverse magnetic polarizability) of rectangular irisfrom these polynomial methods. These values are used to definedyadic magnetic ploarizability of rectangular iris for arbitrary irisorientation in the plane of incoming waveguide. Attenuation basedterm is included to account for finite iris length [3, 21].

We evaluate external quality factor explicitly because it isthe characteristic of coupler-cavity geometry and size only. It isindependent of cavity material and its surface qualities. The externalQ values for arbitrary iris angle are used to obtain coupling coefficientof the given system for a known intrinsic quality factor.

2. THEORY OF EXTERNAL Q AND COUPLINGCALCULATIONS

We consider a WR340 waveguide and rotatable rectangular iris forcoupling power to a cylindrical pill box cavity. End coupled waveguideto cavity coupling is used in this study. The schematic of waveguide-cavity system along with rotatable iris cylinder is shown in Figure 1.

The incoming waveguide and cylindrical cavity operate in TE10and TM010 mode respectively. The dimensions of waveguide, cavityand iris are also shown in Figure 1. The rectangular iris is cut insidea solid metallic cylinder. For the chosen dimensions, cavitys resonantfrequency from analytical calculations comes out to be 2.373GHz.

Iris length (major axis) is denoted by l and width (minor axis) asw. Incoming waveguide length is a and width is b. Cavity lengthis denoted by L and diameter as D.

2.1. Magnetic Polarizability of Oriented Rectangular Iris

Iris oriented at angle in the plane of incoming waveguide is shownin Figure 2. The incoming waveguide cross-section is shown in x-y co-ordinates whereas rotated iris is shown in u-v co-ordinate system. Itcan be observed that u-v co-ordinate system can be obtained by simple

226 Kumar et al.

Rotatable iris cylinder

WR340a

b

d

L

DPill box cavity

l

w

a = 86.36, b = 43.2 d = 41.5 l = 36, w = 10 L= 73.5 D = 96.8All dimensions in mm

Figure 1. Schematic of iriscoupled waveguide-cavity system.

x

yuv

a

blw

E H

Figure 2. Cross-section of in-coming waveguide and rotated iris(in x-y and u-v coordinate sys-tem respectively) coupling powerto TM010 mode of cavity.

transformation of x-y system. Iris depth is not shown in Figure 2. Irisis shown in u-v coordinate system which is rotated by an angle w.r.tthe x-y plane of incoming waveguide. Electric and magnetic fields ofpill-box cavitys TM010 mode are shown as E and H respectively.

As there is no electric field perpendicular to iris plane, we willconsider magnetic polarizability only. Magnetic polarizability Pm1 ofrectangular iris at zero angle (also called longitudinal polarizability) isgiven by a polynomial expression as [19]:

Pm1 = f1l3 (1a)

f1 =0.132

ln(1 + 0.660(w/l)

) (1b)Here, l is iris length and w is iris width. Magnetic field orientationfor longitudinal polarizability is shown in Figure 3(a). The irisorientation for transverse polarizability is shown in Figure 3(b).

Similarly, transverse magnetic polarizability of rectangular iris isgiven as [20]:

Pm2 = f2l3 (2a)

f2 =pi

16

(wl

)2 (1.0 + 0.3221

w

l

)(2b)

Magnetic polarizability at an arbitrary angle can be defined by dyadicrepresentation as [15]:

Pm = Pm1auau +Pm2avav (3)


w

l

H

w

H

l w

(a) (b)

Figure 3. (a) Magnetic field and iris orientation for longitudinalpolarizability. (b) Magnetic field and iris orientation for transversepolarizability.

The vectors au and av are unit vectors in u-v plane. The au isunit vector for u axis and av is unit vector for v axis.

We will use this dyadic magnetic polarizability for external Q andcoupling calculations using Bethes original theory.

2.2. Analytical Expressions for External Q and CouplingCalculations

The normalized fields for TE10 mode of rectangular waveguide aregiven as [15]

E+10 = e10ejz (4a)

H+10 = (h10 + hz10) ejz (4b)

E10 = e10ejz (4c)

H10 = (h10 + hz10) ejz (4d)Here,

e10 = jkoZoN sin (pix/a)ay (5a)h10 = j10N sin (pix/a)ax (5b)hz10 =

Npi

acos (pix/a)az (5c)

N = (2/ (abkoZo10))1/2 (5d)Here, Zo is the intrinsic impedance of free space, ko the free spacepropagation constant, and 10 the waveguide propagation constant.

228 Kumar et al.

For all field equations discussed here, time dependence is not explicitlyshown.

Let us assume that cavitys magnetic field at aperture locationis H. It is also assumed that cavity field is aligned with x-axis on theaperture surface. Magnetic moment (M) produced by dyadic magneticpolarizabilty can be written as [15]:

M = Pm H (6a)After replacing polarizability value from Equation (3) into Equa-tion (6a), we get

M = (Pm1auau + Pm2avav)Hax (6b)

After simplification, (6b) becomes

M = (Pm1 cos()au + Pm2 sin()av)H (6c)

This means that cavity field is effectively splitting to two orthogonalpolarizations in the rotated iris. In u-v coordinate system, upolarization couples to cavity field magnitude of H cos() whereas vpolarization to field magnitude of H sin().

This magnetic dipole will radiate into the incoming waveguide.The induced magnetic field (Ho) in the incoming waveguides cross-section can be written as [15, 16]

Ho =(joH+10 M

)H10 ax (7a)

The above expression reduces to:

Ho =(joh210

)M ax (7b)

After substituting Equation (5b) into above equation, it reduces to

Ho =2j10M ax

ab(7c)

After replacing magnetic moments value from Equation (6c) intoEquation (7c), we obtain

Ho =2j10 (Pm1 cos()au ax + Pm2 sin()av ax)H

ab(8)

The Ho is x component of waveguides maximum magnetic field.After simplification, Equation (8) reduces to

Hx =2j10

(Pm1 cos2() + Pm2 sin2()

)H

ab(9)

Corresponding maximum electric field Ey at the center of waveguidecan be obtained from waveguide impedance (ZTE) given below [22]

ZTE =EyHx

=koZo10

(10)


With the information obtained so far, the average power radiated intothe waveguide can be calculated as [22]

Prad =EyHxab

4(11a)

Power radiated into the waveguide can also be written as

Prad =H2xabZTE

4(11b)

From Equations (9), (10) and (11b), we get

Prad =10koZo


)2H2

ab(11c)

External quality factor (Qext) can be written as

Qext =oU

Prad(12a)

Here, o is resonant frequency and U is energy stored in cavity.After placing Equation (11c) into Equation (12a), we obtain

Qext =oUab

10koZoH2(Pm1 cos ()

2 + Pm2 sin()2)2 (12b)

This expression is obtained for zero iris thickness. For iris of thicknessd, an attenuation term is included for the magnetic field [3, 21]. If is attenuation coefficient of dominant TE10 mode of rectangular iris,Equation (12b) can be written for iris of finite thickness as

Qext =oUab

10koZoH2 exp(2d) (Pm1 cos()2 + Pm2 sin()2)2 (12c)

Intrinsic quality factor (Qo) of the resonator can be written as [22]

Qo =oU

Po(13)

Here, Po is energy dissipated on the cavity walls. Coupling coefficient can be calculated as [22]

=QoQext

(14a)

After using Equations (12c), (13) and (14a), we get

=10koZo exp(2d)


)2H2

abPo(14b)

230 Kumar et al.

After simplification, (14b) can be written as

=(

1 cos2() +2 sin2()

)2(14c)

Here,

1 =210koZo exp(2d) (Pm1)2H2

abPo(14d)

2 =210koZo exp(2d) (Pm2)2H2

abPo(14e)

From Equation (14c), we can observe that the coupling contributionsfrom longitudinal and transverse polarizabilities get combined toproduce the overall coupling. The contribution from longitudinalcoupling is given in Equation (14d) whereas the contribution fromtransverse coupling is shown in Equation (14e).

2.3. Special Cases

2.3.1. Elliptical Iris

Magnetic polarizability of elliptical iris with magnetic field parallel tolonger dimension (i.e., longitudinal polarizability) is given as [15]

Pm1 =pil31e

2o

3 (K (eo)E (eo)) (15)

Here, l1 is semi-major axis of ellipse and l2 is semi-minor axis. K(eo)and E(eo) are elliptic integrals of first and second order respectively.Also, eccentricity eo is given as

eo =

1 l

22

l21(16)

As a special case, for zero degree iris orientation, Equation (12c)reduces to

Qext1 =oUab

10koZo exp(2d)H2P 2m1(17)

From (14a), (15) and (17), we get

1 =10koZopi2 exp2d l6e4oH2

9ab (K(eo)E(eo))2 Po(18)

This equation is the same as that reported in [4]. Transverse couplingvalue can be obtained by same procedure. This is a validation ofproposed expressions.


2.3.2. Circular Iris

Coupling for circular iris with radius r can be obtained by similarprocedure. The magnetic polarizability of circular iris is given as

Pm1 =4r3

3(19)

As circle is azimuthally symmetrical, it is interesting to note thatcoupling for zero and 90 degrees is same. Due to this fact,Equation (14c) can be written as

=(

1(cos2() + sin2()

))2(20a)

After simplification, Equation (23) reduces to:

=(

1

)2= 1 (20b)

This implies that coupling for circular iris remains constant with irisrotation in the plane of incoming wave-guide cross-section. This resultis quite logical and thus validates the proposed theoretical procedure.

2.3.3. Square Iris

For a square iris also, the coupling for zero and 90 degrees irisorientation will be the same. This happens because the longitudinaland transverse polarizability values are same owing to equal armlengths [19, 20]. Hence, we will get the same result as that ofEquation (20b). This implies that coupling for square iris shouldremain constant with iris rotation.

However, as reported in [5], there is about + 10% variationin the beginning and end of rotation range for square iris. This isattributed to the fact that square iris simulated in [5] is conformal tothe cavity surface. Because of curved nature of cavity surface, effectiveiris thickness changes during its rotation range. Other factor causingthe small variation in coupling of square iris can be field non-uniformityat waveguide end. For large apertures, the non-uniform nature ofwaveguides TE10 fields leads to errors as proposed theory assumesuniform field.

2.3.4. Rectangular Iris with Low Aspect Ratio (w/L 1)For rectangular iris with small aspect ratio, it is noticed that transversecoupling is several orders of magnitude lower than longitudinalcoupling (2 1). This happens because of lower polarizability(Pm2 Pm1) and higher attenuation in transverse slot. Hence, after

232 Kumar et al.

neglecting the contribution of transverse term, Equation (12c) andEquation (14c) can be written as:

Qext =oUab

10koZo exp(2d)H2P 2m1 cos4()(21)

() =(

1 cos2())2

= 1 cos4() (22)

2.4. Calculation of External Q and Coupling Coefficient

As the resonant frequency of the structure is known analytically, weneed the value of maximum magnetic field H on cavity surface. Themaximum magnetic field on cavity surface for 1 J of energy storedcan also be obtained analytically for a pill box cavity. All otherparameters required for Qext calculations from Equation (12c) areknown analytically.

As practical structures are complex, one may need at least oneEM modal solver run to get the value of H for 1 J of energy stored.For example, in our case, this value is obtained from one CST Modalsolver run and is found to be 65000A/m. From this H value, we couldobtain Qext for any iris orientation from Equation (12c).

Further, if intrinsic quality factor is known, coupling coefficientcan be obtained by simply dividing it with Qext. By using H, o andPo values from one modal solver run, we could calculate Qext and for any arbitrary iris orientation.

We used the Qext values obtained from Equation (12c) and values from (14) and compared them with measurements and simulatedvalues. The comparison is discussed in next section.

3. FULL WAVE SIMULATIONS AND EXPERIMENTALRESULTS

3.1. Full Wave Simulations

Considering the ease of fabrication, it is decided to demonstrate theconcept experimentally on a small cavity operating in S band.

A cylindrical cavity is modeled using commercial EM solverCST-MWS. The analytical value of resonant frequency for the cavitydimensions given in Figure 1 comes out to be 2.373GHz. The simulatedvalue of resonant frequency for TM010 mode is 2.360GHz. Slightdecrease in simulation values ( from analytically calculated value of2.373GHz) is because the RF port, iris and incoming waveguide arealso included in the simulation.


Figure 4. Cut-view of simulation model.

(a) (b)Figure 5. (a) Simulated arrow plots of E field in the rotated iris.(b) Magnetic field arrow plots in the rotated iris.

The coupler-cavity simulation model is shown in Figure 4. Foreach Eigen Mode solver run of CST MWS, iris is rotated in theplane of incoming WR340 waveguide. Conducting boundary with = 5.8e7 S/m is used. Intrinsic quality factor of approx. 22,000 isobtained during simulations for the entire rotation range. ExternalQ value is obtained from the CST-MWS Modal Solver for every 15degrees iris rotation by defining a matched boundary at waveguideport.

In order to have a better view of fields in the rotated iris, arrowplots of simulated E and H fields are shown in Figure 5(a) andFigure 5(b), respectively.

Full wave simulations are performed for rectangular, elliptical,square and circular iris shapes. As shown in Figure 1, rectangulariris of length 36mm and with 10mm is chosen. To keep the sizescomparable, elliptical iris with major axis of 36mm and minor axisof length 10mm is considered. Similarly, diagonal of square iris anddiameter of circular iris are chosen to be 36mm.

The plots for variation of external Q with iris rotation are givenin Figure 6(a). It should be noted that external Q is plotted on logscale because of several orders of variation over the rotation range.

234 Kumar et al.

Also, coupling coefficient variation with rotation angle is shown inFigure 6(b). It is important to observe that rectangular iris is plottedon the left scale whereas other iris shapes are plotted on the right scalebecause of orders of magnitude difference in coupling values.

We can observe from these plots that square and circular irisesgive very low coupling as compared to rectangular and elliptical irises.Moreover, square and circular irises are not useful for rotatable irisbased coupling variation schemes as there is practically no couplingvariation over the entire rotation range. The rectangular iris givesmore coupling than elliptical iris for chosen dimensions. Hence, wechose rectangular iris for validation with measurements as it providesmore coupling, wide range and is easier to fabricate.

5.00E+05

5.00E+06

5.00E+07

5.00E+08

5.00E+09

5.00E+10

5.00E+11

5.00E+12

Exte

rnal

Qua

lity fa

ctor

CST MWS simulations for rectanguar irisSimulations for elliptical iris

Simulations for square iris

Simulations for circular iris

0 15 30 45 60 75 90Angle of iris rotation (degree)

(a)

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02CST MWS simulations for rectanguar irisSimulations for elliptical iris

Simulations for square iris

Simulations for circular iris

Angle of iris rotation (degree)0 15 30 45 60 75 90

Coup

ling

Coef

ficie

nt

(b)Figure 6. (a) External Q simulation results for different iris shapes.(b) Coupling coefficient simulation results for different iris shapes.

(a) (b)Figure 7. (a) Iris cylinder with rectangular iris. (b) Cavity connectedto VNA through WR340-N Type adapter and auxiliary port fortransmission measurements.


3.2. Measurements for External Q and Coupling Coefficient

The coupler parts and fabricated cavity are shown in Figure 7(a) andFigure 7(b) respectively. The incoming waveguide port from WR340to N Type adapter is blocked with a stainless steel (SS) flange. TheSS flange has a provision for mounting the iris at the center. The irispart can be rotated with respect to the waveguide cross-section. TheSS flange is also provided with holes so that it can be mounted on tothe cavity port. Cavity port diameter is 40mm. The Cavity, ports andiris are made with SS and plated with Cu.

In order to measure the coupling with transmission method [23],a small port of 10mm diameter is provided on the cavity. A small loopmade of an N Type connector is mounted on this auxiliary port. Inorder to feed the microwave power to WR340 waveguide, a WR 340to N Type adapter is used. Measurements are performed with VectorNetwork Analyzer (VNA) of R&S ZVB4 series.

The coupling coefficient of auxiliary loop coupled cavity can bewritten as [22]:

a =R

Zo(23)

Here, R is the impedance of cavity at resonance, and Zo is 50Ohms.Also, the reflection coefficient of coupled cavity at resonance is givenas:

S11 =RZo 1

RZo

+ 1(24)

A reflection measurement (S11) at auxiliary port is used to calculatethe coupling coefficient from Equations (23) and (24).

Hence, coupling of auxiliary loop (a) is found to be 0.7 frommeasured S11 of 15 dB. The relevant equations for Qo and Qextcalculations from measurements are given as [23]:

Qo = QL (1 + a + ext) (25)

Qext =4aQL1 + a

10|S21 dB|/10 (26)

Loaded quality factor QL is obtained from transmissionmeasurements using 3 dB method. Qo of fabricated cavity is calculatedfrom Equation (25) and it came out to be 7219. As found fromreflection measurements, coupling coefficient of iris coupled waveguideto cavity system (ext) is very low and hence neglected for calculatingQo from Equation (25). For each measurement, iris coupler is rotatedand corresponding transmission magnitude is noted. Finally, unknown

236 Kumar et al.

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09CST MWS simulations

M icrowave measurements Proposed theory

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02CST MWS simulations

Microwave measurements

Proposed Theory

0 15 30 45 60 75 90Angle of iris rotation (degree)

(a)Angle of iris rotation (degree)

0 15 30 45 60 75 90

(b)

Exte

rnal

Qua

lity fa

ctor

Coup

ling

Coef

ficie

ntFigure 8. (a) External Q variation of simulated, measured, andproposed analytical results for different rotation angle of rectangulariris. (b) Coupling variation of simulated, measured, and proposedanalytical results for different rotation angle of rectangular iris.

Qext and coupling coefficient are calculated from Equation (26) andEquation (14a) respectively.

The external Q and coupling coefficient values are obtainedfrom measurements and compared with simulations and theoreticallycalculated values. For coupling coefficient calculations, measured valueof Qo is used for comparative analysis.

The plots for external Q and coupling coefficient variation with irisrotation are shown in Figure 8(a) and Figure 8(b) respectively. A closeagreement is found between simulations, measurements and proposedtheory. Maximum mismatch between theoretical and measured valuesas compared to simulations is found to be less than 10%.

Hence, proposed theory shows good agreement with simulationsand measurements in terms of trend and absolute values.

It will be important to discuss the possible sources of measurementerrors and uncertainties. The external Q measurements are verysensitive to S21 magnitude especially at higher angles (because ofvery weak coupling). This error is found to be around 34% athigher angles with + 1 dB change in S21 magnitude. The angleof iris rotation was adjusted within accuracy of + 1 degree duringmeasurements. The dimensional accuracy of fabricated componentswas within + 100 microns. The coupling is highly sensitive to irislength and can result in around 1.52% change of coupling for saidtolerances. The cavity surface is not exactly planar at iris interface asassumed in proposed theory. All of these factors may be responsiblefor difference in theoretical, simulated and measured results.


4. CONCLUSIONS

Analytical expressions are derived for waveguide to cavity couplingwith rotated rectangular iris. From proposed generalized expressionsfor arbitrary iris orientation, analytically known results for non-rotatedelliptical iris could be obtained as a special case. Other iris shapeslike square and circular are also analyzed with proposed theory andsimulations. The results are validated with full wave simulations andmeasurements. These expressions will be useful in reducing the designtime of RF couplers for accelerator cavities and other novel devicesbased upon rotated iris coupling. Proposed theoretical results willalso be useful in establishing the coupling scaling laws for an iris atarbitrary angle.

ACKNOWLEDGMENT

The authors are thankful to Dr. S. Kailas for his keen interest andencouragement for development of novel coupling schemes at IonAccelerator Development Division (IADD), BARC. First author wouldalso like to thank Dr. J. Gao, IHEP, China for useful discussionson waveguide to cavity coupling. We also acknowledge the usefuldiscussions with Dr. S. R. Jain, NPD, BARC.

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