L. Landau and E. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z Sowjetunion, vol.8, pp.153-169, 1935.
DOI : 10.1016/B978-0-08-036364-6.50008-9

T. L. Gilbert, A Lagrangian Formulation of the Gyromagnetic Equation of the Magnetization Field, Phys. Rev, vol.100, issue.4, pp.1243-1255, 1955.

D. Polder and J. Smit, Resonance Phenomena in Ferrites, Reviews of Modern Physics, vol.25, issue.1, pp.89-90, 1953.
DOI : 10.1103/RevModPhys.25.89

R. F. Soohoo, Microwave ferrite materials and devices, Microwave Ferrite Materials and Devices, pp.118-133, 1968.
DOI : 10.1109/TMAG.1968.1066207

M. E. Hines, Reciprocal and Nonreciprocal Modes of Propagation in Ferrite Stripline and Microstrip Devices, MTT-19, pp.442-451, 1971.
DOI : 10.1109/TMTT.1971.1127545

T. Hasegawa, Low Loss Two-Port Lumped Element Isolator using Improved Gyrator Circuit, IEEE MTT-S International Microwave Symposium Digest, 2005., pp.339-342, 2005.
DOI : 10.1109/MWSYM.2005.1516596

S. Takeda, Lumped-Element Isolator With Lower Symmetrical Configuration of Three Windings, IEEE Transactions on Microwave Theory and Techniques, vol.52, issue.12, pp.2697-2703, 2004.
DOI : 10.1109/TMTT.2004.838304

Y. Konishi, Lumped-Element Y-Circulator, MTT- 13, pp.852-864, 1965.
DOI : 10.1109/tmtt.1965.1126116

Y. Konishi, New Theorical Concept for Wide Band Gyromagnetic Devices, IEEE Trans. on Magnetics, pp.505-508, 1972.

. Konishi, Lumped-Element Circulators, IEEE Trans. on Magnetics, pp.1262-1266, 1975.
DOI : 10.1109/tmag.1975.1058838

[. Miura, M. Kobayashi, and Y. Konishi, Optimization of a lumped element circulator based on eigenvalue evaluation and structural improvement, IEEE Transactions on Microwave Theory and Techniques, vol.44, issue.12, pp.2648-2654, 1996.
DOI : 10.1109/22.554616

T. Miura, M. Hasegawa, H. Oh-'hata, and T. Kurahashi, Temperature stabilization of a lumped element circulator without an apparent compensating element, 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282), pp.1161-1164, 1999.
DOI : 10.1109/MWSYM.1999.779593

[. H. Knerr, A Thin Film Lumped Element Circulator, 1969 G-MTT International Microwave Symposium, pp.1152-1154, 1969.
DOI : 10.1109/GMTT.1969.1122669

R. H. Knerr, An Improved Equivalent Circuit for the Thin-Film Lumped-Element Circulator, IEEE Transactions on Microwave Theory and Techniques, vol.20, issue.7, pp.446-452, 1972.
DOI : 10.1109/TMTT.1972.1127784

[. G. Schuchinsky, Lumped element circulator (LEC) with variable couplings, 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282), pp.1165-1168, 1999.
DOI : 10.1109/MWSYM.1999.779594

[. Perron, Etude théorique et expérimentale de circulateurs ultraminiatures en technologie uniplanaire, 1998.

N. Ch and . Kouam, Contribution à la Modélisation des Circulateurs Ultraminiatures : Etudes des Limitations en Fréquence, 1995.

S. A. Oliver, P. M. Zavracky, N. E. Mcgruer, and R. Schmidt, A monolithic single-crystal yttrium iron garnet/silicon X-band circulator, IEEE Microwave and Guided Wave Letters, vol.7, issue.8, pp.239-241, 1997.
DOI : 10.1109/75.605490

H. How, S. A. Oliver, S. W. Mcknight, P. M. Zavracky, N. E. Mcgruer et al., Theory and experiment of thin-film junction circulator, IEEE Transactions on Microwave Theory and Techniques, vol.46, issue.11, pp.1645-1653, 1998.
DOI : 10.1109/22.734547

H. How, S. A. Oliver, S. W. Mcknight, P. M. Zavracky, N. E. Mcgruer et al., Influence of non-uniform magnetic field on a ferrite junction circulators, IEEE Trans. Microwave Theory & Tech, vol.47, issue.10, pp.419-431, 1999.

[. Bènevent, Influence de l'Epaisseur de Ferrite sur les Performances d'un Circulateur 40 GHz, 9èmes Journées de Caractérisation Micro-ondes et Matéraiux (JCMM)-St-Etienne-C5, pp.29-31, 2006.

M. Vérité, Etude de Dépôts de Ferrite pour Dispositifs Intégrés Micro-ondes Non-réciproques, thèse de Doctorat, 2002.

K. Oshiro, Fabrication of circulator with coplanar wave guide structure, IEEE Transactions on Magnetics, vol.41, issue.10, pp.3550-3552, 2005.
DOI : 10.1109/TMAG.2005.854729

P. Shi, H. How, X. Zuo, S. A. Oliver, N. E. Mcgruer et al., Application of Single-Crystal Scandium Substitued Barium Hexaferrite for Monolithic Millimeter-Wavelength Circulators, IEEE Trans. Microwave Theory & Tech, vol.37, issue.6, pp.3941-3946, 2001.

[. S. Chen and E. K. Yung, Analysis of microstrip circulator with a ferrite sphere, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313), pp.384-387, 2002.
DOI : 10.1109/APS.2002.1016328

[. Yang, H. C. Wu, and W. B. Dou, Analysis of Millimeter Wave Microstrip Circulator, 2005 Asia-Pacific Microwave Conference Proceedings, 2005.
DOI : 10.1109/APMC.2005.1606434

. Iii-1-]-h and . Bosma, On the principle of Stripline Circulation, Proc. IEEE, pp.137-146, 1962.

D. Polder, On the theory of ferromagnetic resonance, Physica, vol.15, issue.1-2, p.99, 1949.
DOI : 10.1016/0031-8914(49)90051-8

C. M. Krowne and R. E. Neidert, Theory and numerical calculations for radially inhomogeneous circular ferrite circulators, IEEE Transactions on Microwave Theory and Techniques, vol.44, issue.3, pp.419-431, 1996.
DOI : 10.1109/22.486151

C. M. Newman and . Krowne, Analysis of Ferrite Circulators by 2D Finite Element and Recursive Green's Function Techniques, IEEE Trans. Microwave Theory & Tech, 1998.

S. A. Oliver, P. M. Zavracky, N. E. Mcgruer, and R. Schmidt, A monolithic single-crystal yttrium iron garnet/silicon X-band circulator, IEEE Microwave and Guided Wave Letters, vol.7, issue.8, pp.239-241, 1997.
DOI : 10.1109/75.605490

H. How, S. A. Oliver, S. W. Mcknight, P. M. Zavracky, N. E. Mcgruer et al., Theory and experiment of thin-film junction circulator, IEEE Transactions on Microwave Theory and Techniques, vol.46, issue.11, pp.1645-1653, 1998.
DOI : 10.1109/22.734547

H. How, S. A. Oliver, S. W. Mcknight, P. M. Zavracky, N. E. Mcgruer et al., Influence of non-uniform magnetic field on a ferrite junction circulators, IEEE Trans. Microwave Theory & Tech, vol.47, issue.10, pp.419-431, 1999.

K. Berthou-pichavant, New Consistent Model for Ferrite Permeability tensor with Arbitrary Magnetization state": Applications aux ferrites non-saturés, IEEE Trans. Microwave Theory & Tech, vol.45, pp.1185-1192, 1997.

. Iii-10-]-p, P. Gelin, F. L. Quéffélec, and . Pennec, Effect of Domain and Grain Shapes on the Dynamic Behavior of Polycrystalline Ferrites. Application to the Initial Permeability, JAP, vol.28, p.53906, 2005.

]. D. Iii-11, J. Polder, and . Smit, Resonance phenomena in ferrites, Rev. Mod. Phys, vol.25, issue.1, pp.89-90, 1953.

J. L. Gilbert and . Kelley, Permeability tensor of magnetized ferrites at microwaves frequencies: a comparison between theory and experimentAnomalous rotational damping in ferromagnetic sheets, Proc.1 st Conf. Magn. Mater, pp.7471-7473, 1955.

. C. Iii-14-]-e, E. P. Stoner, and . Wohlfarth, A mechanism of magnetic hysteresis in heterogeneous alloys, IEEE Trans. Magnetic, vol.27, issue.7, p.3475, 1948.

S. Mallegol, Caractérisation et Application de Matéraiux composites Nanostructures à la réalisation de dispositifs hyperfréquences Non-réciproques, thèse de Doctorat, 2003.

S. Mallegol, Theoretical and experimental determination of the permeability tensor components of magnetized ferrites at microwave frequencies, IEEE Transactions on Magnetics, vol.39, issue.4, 2003.
DOI : 10.1109/TMAG.2003.812709

H. How, Influence of non-uniform magnetic field on a ferrite junction circulators, IEEE Trans. Microwave Theory & Tech, vol.47, issue.10, pp.419-431, 1999.

G. Riblet, Techniques for broad-branding above resonance circulator junctions without the use of external matching networks, MTT-28, pp.125-129, 1980.

H. How, Design of six-port stripline ferrite junction circulators, IEEE Transactions on Microwave Theory and Techniques, vol.42, issue.7, pp.1272-1275, 1994.
DOI : 10.1109/22.299767

K. Gaukel, El badawy El sharawyAnalysis of six-port disk circulator subdivided by ports, IEEE Trans. Microwave Theory & Tech, 2000.

J. Lenge, D. Schulz, R. I. Joseph, and E. Schloemann, Three-dimensional FDTD Modeling and Analysis of Microwave Circulators" [IV-6] informations disponibles sur le site http://www.temex-ceramics.com/site/fichiers/dielectricDemagnetizing field in nonellipsoidal bodies, J. Appl. Phys, vol.36, issue.148, pp.1579-1593, 0192.

E. Tremolet-de-lacheisserie, Magnétisme I-Fondements, EDP Sciences, 2001.

H. Bosma, On the principle of stripline circulation, Proc. IEEE, pp.137-146, 1962.
DOI : 10.1049/pi-b-2.1962.0027

E. C. Stoner and E. P. Wohlfarth, A mechanism of magnetic hysteresis in heterogeneous alloys, IEEE Transactions on Magnetics, vol.27, issue.4, p.3475, 1948.
DOI : 10.1109/TMAG.1991.1183750

K. Berthou-pichavant, Contribution à la modélisation des matériaux magnétiques hétérogènes : Applications aux ferrites non-saturés, thèse de Doctorat, 1996.

P. Gelin, P. Quéffélec, and F. L. Pennec, Effect of domain and grain shapes on the dynamic behavior of polycrystalline ferrites. Application to the initial permeability, J. Appl. Phys, vol.28, p.53906, 2005.

D. Polder, On the theory of ferromagnetic resonance, Physica, vol.15, issue.1-2, p.99, 1949.
DOI : 10.1016/0031-8914(49)90051-8

P. Shi, H. How, X. Zuo, S. D. Yoon, S. A. Oliver et al., MMIC Circulators Using Hexaferrites, IEEE Trans. Microwave Theory & Tech, vol.37, issue.4, pp.2389-2391, 2001.

X. Zuo, H. How, S. Somu, and C. Vittoria, Self-biased circulator/isolator at millimeter wavelengths using magnetically oriented polycrystalline strontium M-type hexaferrite, IEEE Transactions on Magnetics, vol.39, issue.5, pp.3160-3162, 2003.
DOI : 10.1109/TMAG.2003.816043

]. R. Joseph and E. Schloemann, Demagnetizing Field in Nonellipsoidal Bodies, Journal of Applied Physics, vol.36, issue.5, pp.1579-1593, 1965.
DOI : 10.1063/1.1703091

G. Riblet, P. Guennou, P. Queffelec, J. L. Gelin, and . Mattei, Techniques for broad-branding above resonnace circulator junctions without the use of external matching networks Valorisation du travail de recherche Publications internationales : ASelf-biased Y-junction circulators using polycrystalline hexaferrite: An accurate electromagnetic analysis, MTT-28, pp.125-129, 1980.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Coupled Magnetostatic / Electromagnetic Studies of Nonuniformly Biased Y-Junction Circulator: Application to Transmission Bandwidth Increase, IEEE Trans. Magnetics, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01301593

A. Guennou, B. Della, P. Queffelec, P. Gelin, and J. L. Mattei, Influence of the Magnetic Field Nonuniformity on an X-Band Microstrip Y-Junction Circulator Bandwidth: Theory/Experiment Comparison, IEEE Transactions on Magnetics, vol.43, issue.6, pp.2642-2644, 2007.
DOI : 10.1109/TMAG.2007.893785

URL : https://hal.archives-ouvertes.fr/hal-00172026

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Electromagnetic Study of Self-Biased Y-Junction Circulators using Polycrystalline Hexaferrite, 50th international Conference on Magnetism and Magnetic Materials (MMM), 2005.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Experimental demonstration of the influence of the magnetic field non-uniformity on the X-band Y-junction circulator bandwidth, 10th Joint MMM/Intermag Conference, pp.7-12, 2007.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Etude de l'influence de la variation spatiale du champ de polarisation sur les performances des circulateurs à jonction Y, 8èmes Journées de Caractérisation Microondes et Matériaux (JCMM), pp.31-33, 2004.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Optimisation de la réponse d'un circulateur à jonction Y polarisé non uniformément' 14èmes journées nationales microondes (JNM), pp.11-13, 2005.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Etude des circulateurs à jonction-Y à base d'hexaferrite polycristallins utilisés à la rémanence' 14èmes journées nationales microondes (JNM), pp.11-13, 2005.

A. Guennou, P. Queffelec, P. Gelin, and J. L. Mattei, Etude électromagnétique d'un circulateur à jonction-Y à base d'hexaferrite polycristallin autopolarisé, 9èmes Journées de Caractérisation Microondes et Matériaux (JCMM), Saint-Etienne, pp.29-31, 0192.

A. Guennou, B. Della, P. Queffelec, P. Gelin, and J. L. Mattei, Conception et réalisation de circulateurs à jonction-Y en technologie microruban : influence de la nonuniformité du champ de polarisation, 15 èmes Journées Nationales Microondes (JNM), pp.23-25, 2007.