Magnetic field tunable 75–110 GHz dielectricphase shifter

M.A. Popov, I.V. Zavislyak and G. Srinivasan

A magnetic field tunable W-band phase shifter based on dielectricresonance in barium hexaferrite has been designed and characterised.A phase shift of 608 with low losses is demonstrated at low bias mag-netic field.

Introduction: Tunable phase shifters are among the crucial componentsin phased array radars for beam formation and steering, as well as inwireless and satellite communication systems [1]. Phase shifters forthe frequency range 75–110 GHz are of interest for use in phasedarray transmitters and receivers for automobile radars [2]. Among theavailable options, ferrite phase shifters have the advantages of low inser-tion loss and high power handling capability. Traditional ferrite phaseshifters exploit the fast variation of magnetic permeability near ferro-magnetic resonance (FMR) frequency; hence their operating frequencyis defined by the FMR frequency range of a ferrite material. Spinel fer-rites or garnets are not suitable for millimetre-wave phase shifters owingto the large external magnetic field necessary to operate at highfrequencies.

Pure or Sc-doped barium, or strontium hexagonal ferrites with M-typestructures, have high uniaxial anisotropy fields and are appropriatematerials for phase shifters in the Ka- and V-bands [3]. However,devices at higher frequencies, such as W-band, would still require avery large bias magnetic field.

One possible solution for phase shifters in the W-band is the use of Al-substituted M-type hexaferrites [4], which have a much larger uniaxialmagnetocrystalline anisotropy field than BaFe12O19 (BaM), but substi-tution of Al for Fe increases losses. An alternative to FMR baseddevices is the utilisation of dielectric resonances BaM. Such resonancesoccur at a much higher frequency than FMR in gyrotropic resonatorswith rotational symmetry and could be tuned with an external bias fieldH to achieve a differential phase shift. Magnetic field dependence ofdielectric resonance frequency is well understood in garnets and spinelferrites [1, 5, 6], but has not been studied in any detail in hexaferrites.

075

80

reso

nanc

e fr

eque

ncy,

f r, G

Hz

85

90

95

100

105

110

100 200

S=0.35 mm

d2

d1S

D

BaM

S

N

polyethilene

S=0.28 mm

S=0.2 mm

E11δ

300d1, μm

ϕ ϕ+Δϕ(H)

400 500

Fig. 1 Zero-field frequency of E11d dielectric resonance against dielectriclayer thickness

Transmitted wave has magnetic field dependent phase shift relative to incidentwaveInset: Schematics of phase shifter cross-section with magnetic system

Design: A waveguide phase shifter, as in Fig. 1, is proposed. A singlecrystal BaM with a uniaxial anisotropy field of 16.8 kOe was used. A diskwith diameter D ¼ 1.24 mm and thickness S ¼ 0.28 mm was chosensince rotational symmetry for the sample is a key requirement. The abovedimensions ensure the lowest-frequency of dielectric resonances to be inthe W-band. The sample was mounted in a WR-10 waveguide flange andsandwiched between a 30 mm-thick dielectric polyethylene layer and afoam slab. The dielectric layer serves two purposes; by moving the BaMdisk away from metal surface one decreases the high frequency losses andslightly increases the frequency of the main E11d dielectric mode.

For H ¼ 0, the frequencies f of E-type dielectric modes are derived to be

tan(bzS) = (tanh(b1zd1) + tanh(b1zd2))/(

bz

b1z1⊥− b1z1⊥

bz

tanh(b1zd1) tanh(b1zd2))

(1)

ELECTRONICS LETTERS 15th April 2010 Vol. 46

Here

bz =

����������������������2pf

c

( )2

1⊥ − 1⊥1||

b2

√,b1z =

����������������b2 − 2pf

c

( )2√

and 1⊥ and 1|| are the transverse and longitudinal dielectric per-meability, respectively, c is the speed of light, d1 and d2 arethickness of air space between the resonator and metal planes aboveand below, b = 2Anm/D,Anm is an mth root of Bessel functionsJ ′

n(x) = 0.Owing to the nonreciprocity of a magnetised ferrite medium with

respect to two rotation directions the degeneracy is removed for H =

0 and their frequencies become magnetic field dependent [1, 5, 6].When the resonator centre point is placed at a quarter-width from thewaveguide sidewall, the polarisation of waveguide H10 wave acrossthe resonator is predominantly circular (left or right, depending on thedirection of propagation). Hence, the direct wave at a given frequencyexcites the counterclockwise rotation mode, e.g. the reverse wavecannot excite either the counterclockwise mode (owing to unfavourablepolarisation) or the clockwise mode (polarisation is appropriate but thefrequency is different). Therefore, such an arrangement ensures oper-ation with only one of the split modes and the phase shifter becomesnonreciprocal [7].

Calculations of zero-field E11d resonance frequency against d1 using(1) with 1⊥ = 1|| = 16 for a series of thicknesses S are shown inFig. 1. Here we assumed that the sample lies in a WR-10 waveguidewith dimensions a ¼ 2.54 mm and b ¼ 1.27 mm so that d2 ¼ b-S-d1.As can be seen from Fig. 1, one can easily control the zero-fieldfrequency of the E11d mode; hence the phase shifter operating point inthe whole W-band by just varying d1.

76

0

50

100

150

200

250

300

–30

–25

–20

–15

–10

–5

0

78 80 82f, GHz

phas

e sh

ift, d

eg.

inse

rtio

n lo

sses

, dB

84 86 88

76 78 80 82 84 86 88

H=3200

H=1600H=800

H=0

Fig. 2 Dielectric resonance absorption profiles and differential phaseshift of BaM gyromagnetic resonator at different values of applied magneticfield

Results: Microwave measurements were carried out using a 75–110 GHz Agilent vector network analyser with the standard calibrationprocedure performed before measurements. A swept input signal wasapplied to the sample mounted flange that was inserted between tworeference planes of WR-10 waveguides. This ensured that only contri-butions from the phase shifter were measured. The bias magnetic fieldH was aligned parallel to the disk axis. Profiles of S21 amplitude anddifferential phase shift against f, for a series of H, are shown in Fig. 2.High-frequency split mode E211d was chosen because it provideslarger phase shift compared with low frequency E+11d. The operatingfrequency of 80 GHz is a compromise between insertion losses andphase shift. Data on the differential phase shift Dw ¼ w( f, H) 2

w( f, H ¼ 0) against H is shown in Fig. 3. A maximum Dw of 608 forH ¼ 3200 Oe and an insertion loss of 1.5–4 dB are obtained. Thisphase shifter is indeed nonreciprocal with Dw up to 22508 in thereverse direction, while the losses are 10 dB. Note that on the contraryto the work in [3] where ferrite needs to be saturated, our resonator isbased on dielectric resonance, hence it can operate in the unsaturatedregime.

No. 8

0

0

10

diffe

rent

ial p

hase

shi

ft, d

eg.

inse

rtio

n lo

sses

, dB

20

30

40

50

60

70

80

500 1000 1500 2000H, Oe

theory

experiment

2500 3000 3500–20

–18

–16

–14

–12

–10

–8

–6

–4

–2

0

Fig. 3 Direct phase shift and insertion losses of phase shifter at 80 GHz

If we consider the resonator as a pure dielectric with quality factor Qand resonant frequency fr, the transmission coefficient T is given by [8]:

T ( f ) = 1 + ij

1 + K + ij, j = Q

f

fr− fr

f

( ),

S21 = −20 log(|T |)(2)

Here K is the coupling coefficient defined by K = (1 − Tr)/Tr, whereTr-is the transmission coefficient at resonance. From (2) one can findthe phase

w( f ,H) = arctan j(H) 1 − Tr

1 + Trj2(H)

( )(3)

In (3) j(H) stands for Q(f /fr(H) − fr(H)/f ). By estimating values of Q,Tr and fr (H ) obtained from data and used in (3), we obtained theoreticalDw against H shown in Fig. 3, which is smaller than the measured valuesby a factor of 3, which is probably owing to the gyrotropic nature of theresonator and the presence of split modes.

Conclusion: A magnetic field tunable W-band ferrite phase shifter uti-lising dielectric resonances in barium ferrite has been demonstrated. Itwas shown that the magnetic field dependence of dielectric resonancefrequencies creates possibilities for using high-quality hexaferritematerials at frequencies much higher than for traditional FMR devices.

ELECTR

Acknowledgments: This work was supported by grants from the ArmyResearch Office and the Office of Naval Research.

# The Institution of Engineering and Technology 20106 November 2009doi: 10.1049/el.2010.3124One or more of the Figures in this Letter are available in colour online.

M.A. Popov and I.V. Zavislyak (Radiophysics Department, ShevchenkoNational University, Kyiv 01033, Ukraine)

G. Srinivasan (Physics Department, Oakland University, Rochester,Michigan 48309-4401, USA)

E-mail: srinivas@oakland.edu

References

1 How, H., and Vittoria, C.: ‘Microwave phase shifter utilizingnonreciprocal wave propagation’, IEEE Trans Microw. Theory Tech.,2004, 52, p. 1813

2 Natarajan, A., Komijani, A., Guan, X., Babakhani, A., and Hajimiri, A.:‘A 77-GHz phased-array transceiver with on-chip antennas in silicon:transmitter and local LO-path phase shifting’, IEEE J. Solid-StateCircuits, 2006, 41, p. 2807

3 Zuo, X., Shi, P., Oliver, S.A., and Vittoria, C.: ‘Single crystal hexaferritephase shifter at Ka band’, J. Appl. Phys., 2002, 91, p. 7622

4 Popov, M.A., Zavislyak, I.V., Tatarenko, A.S., Srinivasan, G., andBalbashov, A.M.: ‘Magnetic and dielectric excitations in the W-bandin aluminum substituted barium and strontium hexaferrites’, IEEETrans. Magn., 2009, 45, p. 2053

5 Schloemann, E.F.: ‘Circulators for microwave and millimeter-waveintegrated circuits’, Proc. IEEE, 1988, 76, p. 188

6 Gibson, A.A.P., Dillon, B.M., and Sheikh, S.I.: ‘Applied field/frequencyresponse of planar gyromagnetic disks’, Int. J. Electron., 1994, 76,p. 1073

7 Pozar, D.M.: ‘Microwave engineering’ (John Wiley & Sons Inc, 1998,2nd edn.)

8 Ilchenko, M.E., and Kudinov, E.V.: ‘Ferritovye i dielectricheckyeresonatory SVCh’ (Izdatelstvo Kievskogo universiteta, 1973), (inRussian)

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