V. Dyke, The electric network equivalent of piezoeletric resonator, Phys. Rev, vol.25, p.895, 1925.

W. G. Cady, The piezoelectric resonator, Phys. Rev, vol.17, p.531, 1921.

R. Brendel, Bruit interne des oscillateurs à quartz Thèse de doctorat, p.55, 1975.

R. J. Matthys, Crystal oscillator circuits, 1983.

R. Brendel, G. Marianneau, T. Blin, and M. Brunet, Computer aided design of quartz crystal oscillators, Proc. IEEE IFCS, pp.559-566, 1994.

R. Bechman, Frequency temperature angle characteristics of AT?Type resonators mode of natural and synthetic quartz, Proc. IRE, pp.1600-1607, 1956.

M. E. Frerking, Crystal oscillator design and temperature compensation, 1978.
DOI : 10.1007/978-94-011-6056-8

G. Théobald, G. Marianneau, R. Prétot, and J. J. Gagnepain, Dynamic Thermal Behavior of Quartz Resonators, 33rd Annual Symposium on Frequency Control, pp.239-246, 1979.
DOI : 10.1109/FREQ.1979.200324

J. J. Gagnepain, Mécanismes non linéaires dans les résonateurs à quartz : Théories, expériences et applications métrologiques, Thèse de doctorat, 1972.

J. R. Vig, Military applications of high accuracy frequency standards and clocks, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.40, issue.5, pp.522-527, 1993.
DOI : 10.1109/58.238104

J. A. Kusters, The SC Cut Crystal - An Overview, 1981 Ultrasonics Symposium, pp.402-409, 1981.
DOI : 10.1109/ULTSYM.1981.197652

P. Bressy, Modélisation des régimes transitoires des oscillateurs à quartz, Thèse de doctorat, 1977.

H. Barkhausen, Lehrbuch der Elektronen?Rohre, 3, Band, 1935.

J. R. Vig, Quartz crystal resonators and oscillators, for frequency control and timing applications, Army Communications-Electronics Command. Attn: AMSEL?RD?C2? PT; Fort Monmouth, NJ 07703, 2001.

S. Withtsoonthorn, Photodiode UTC et oscillateur différentiel commandé en tension à base de TBdH InP pour récupération d'horloge dans un réseau de transmission optique à très haute débit, Thèse de doctorat, 2004.

S. Finocchiaro, G. Palmisano, R. Salerno, and C. Sclafani, Design of bipolar RF ring oscillators, ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357), pp.5-8, 1999.
DOI : 10.1109/ICECS.1999.812210

B. Parzen and A. Ballato, Design of crystal and other harmonic oscillators, 1983.

D. Göhring and J. Haffelder, Simulation of pierce oscillators with digital inverters using the negative resistance mode, Proc. 12 th EFTF, pp.374-378, 1999.

J. D. Holmbeck, Frequency tolerance limitations with logic gate clock oscillator, Proc. 31 st IEEE AFCS, pp.390-395, 1977.

V. Komine, S. Galliou, and A. , A parametric quartz crystal oscillator, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.12, pp.1656-1661, 2003.
DOI : 10.1109/TUFFC.2003.1256305

URL : https://hal.archives-ouvertes.fr/hal-00776506

F. L. Walls and J. J. Gagnepain, Environmental sensitivities of quartz oscillators, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.39, issue.2, pp.241-249, 1992.
DOI : 10.1109/58.139120

J. R. Vig and F. L. Walls, Fundamental limits on the frequency instabilities of quartz, Proc. 48 th IEEE AFCS, pp.506-523, 1994.

E. P. Ernisse, Quartz resonator freqency shifts arising from electrode stress, Proc. 29 th IEEE AFCS, pp.1-4, 1975.

R. Besson, A New Piezoelectric Resonator Design, 30th Annual Symposium on Frequency Control, pp.78-83, 1976.
DOI : 10.1109/FREQ.1976.201299

R. Besson and U. R. Peier, Further Advances on B.V.A. Quartz Resonators, 34th Annual Symposium on Frequency Control, pp.175-182, 1980.
DOI : 10.1109/FREQ.1980.200399

R. Besson, J. J. Boy, and M. M. Mourey, Acceleration sensitivity of B.V.A Resonators, Proc. 49 th IEEE AFCS, pp.457-463, 1995.

R. L. Filler, The acceleration sensitivity of quartz crystal oscillators: a review, IEEE Trans. Ultrason., Ferroelect., Freq. Contr, vol.50, pp.235-305, 1988.

J. M. Przyjemski, Improvement in System Performance Using a Crystal Oscillator Compensated for Acceleration Sensitivity, 32nd Annual Symposium on Frequency Control, pp.426-431, 1978.
DOI : 10.1109/FREQ.1978.200270

J. R. Vig, C. Audoin, L. S. Cutler, M. M. Driscoll, E. P. Eernisse et al., Acceleration, vibration and shock effects-IEEE standards Project P1193, Proceedings of the 1992 IEEE Frequency Control Symposium, pp.763-781, 1992.
DOI : 10.1109/FREQ.1992.269960

R. Brendel and J. J. Gagnepain, Electroelastic Effects and Impurity Relaxation in Quartz Resonators, 36th Annual Symposium on Frequency Control, pp.97-107, 1982.
DOI : 10.1109/FREQ.1982.200558

R. Brendel, Influence of a magnetic field on quartz crystal resonators, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.43, issue.5, pp.818-831, 1996.
DOI : 10.1109/58.535482

R. Chévralis, Effets des rayonnements ionisants sur les résonateurs à quartz " Rapport technique no 32/7132 PN; ONRA, 1986.

M. Brunet, Etude expérimentale sur la dérive des OUS spatiaux soumis aux irradiations, Rapport CNES, 1990.

P. Y. Bourjois, Référence secondaire de fréquence à résonateur saphir cryogénique, Thèse de doctorat, 2004.

R. Nardin and J. Ho, Computer Design and Analysis for High Precision Oscillators, 28th Annual Symposium on Frequency Control, pp.237-242, 1974.
DOI : 10.1109/FREQ.1974.200026

Y. Ohata, New Approach to the Design of Crystal Oscillators, 28th Annual Symposium on Frequency Control, pp.221-231, 1974.
DOI : 10.1109/FREQ.1974.200024

B. Parzen and A. Ballato, Design of crystal and other harmonic oscillators, 1983.

T. Adachi, M. Hirose, and Y. Tsuzuki, Computer Analysis of Colpitts Crystal Oscillator, 39th Annual Symposium on Frequency Control, pp.176-182, 1985.
DOI : 10.1109/FREQ.1985.200841

A. Benjaminson, The design and analysis of VHF/UHF crystal oscillators, Proc. 41 th IEEE AFSC, pp.452-459, 1987.

J. Goldberg, A simple way of characterizing high Q oscillators, Proceedings of the 42nd Annual Frequency Control Symposium, 1988., pp.304-326, 1988.
DOI : 10.1109/FREQ.1988.27619

T. M. Hall, Computer Aided Design and Assembly of Oscillators, 36th Annual Symposium on Frequency Control, 1982.
DOI : 10.1109/FREQ.1982.200616

T. Blin, Méthodologie de modélisation des oscillateurs à quartz : application aux oscillateurs pour applications spatiales " Thèse de doctorat, 1995.

R. Brendel, G. Marianneau, T. Blin, and M. Brunet, Computer aided design of quartz crystal oscillators, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.42, issue.4, pp.700-708, 1995.
DOI : 10.1109/58.393112

L. Couteleau, Modélisation automatique du comportement et du bruit des oscillateurs à quartz, Thèse de doctorat. Université de Franche?Comté, 1998.

R. Brendel, N. Ratier, L. Couteleau, G. Marianneau, and P. Guillemot, Slowly varying function method applied to quartz crystal oscillator transient calculation, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.45, issue.2, pp.520-527, 1998.
DOI : 10.1109/58.660161

URL : https://hal.archives-ouvertes.fr/hal-00344032

R. Brendel, D. Gillet, N. Ratier, M. Addouche, and J. Delporte, Oscillator noise simulation by using non linear dipolar method, Proc. 15 th EFTF, pp.184-188, 2001.

M. Addouche, Modélisation non linéaire des oscillateurs à quartz, développement d'un logiciel de simulation, Thèse de doctorat, 2002.

M. Addouche, R. Brendel, D. Gillet, N. Ratier, F. Lardet et al., Modeling of quartz crystal oscillators by using nonlinear dipolar method, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.5, pp.520-527, 2003.
DOI : 10.1109/TUFFC.2003.1201461

URL : https://hal.archives-ouvertes.fr/hal-00077166

J. J. Gagnepain, Mécanismes non linéaires dans les résonateurs à quartz : Théories, expériences et applications métrologiques, Thèse de doctorat, 1972.

J. J. Gagnepain, Nonlineaire effects in piezoelectric quartz crystal, XI, W.P. Mason, Edition Academic, pp.245-288, 1975.

R. Brendel, Bruit interne des oscillateurs à quartz Thèse de doctorat, p.55, 1975.

J. Hagg, Sur certains systèmes différentiels à solutions périodique, Bulletin des sciences mathématiques, 1946.

R. J. Matthys, Crystal oscillator circuits, 1983.

M. E. Frerking, Crystal oscillator design and temperature compensation, 1978.
DOI : 10.1007/978-94-011-6056-8

R. Brendel, F. Chirouf, D. Gillet, N. Ratier, F. Lardet-vieudrin et al., Quartz crystal oscillator classification by dipolar analysis, IEEE International Frequency Control Sympposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 2003. Proceedings of the 2003, 2003.
DOI : 10.1109/FREQ.2003.1275157

URL : https://hal.archives-ouvertes.fr/hal-00135067

R. Brendel, F. Chirouf, D. Gillet, N. Ratier, F. Lardet-vieudrin et al., Quartz crystal oscillator characterization by dipolar analysis, Proc. 1 st IEEE Int. Conf on Advanced Optoelectronics and Lasers CAOL, pp.233-243, 2003.

R. Brendel, F. Chirouf, D. Gillet, N. Ratier, F. Lardet et al., Quartz crystal oscillator characterization by dipolar analysis, Proc. SPIE, pp.323-333, 2004.
DOI : 10.1109/caol.2003.1251320

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.678.1747

D. Göhring and J. Haffelder, Simulation of pierce oscillators with digital inverters using the negative resistance mode, Proc. 12 th EFTF, pp.374-378, 1998.

F. Chirouf, R. Brendel, M. Addouche, D. Gillet, N. Ratier et al., Using dipolar method for CMOS oscillator analysis, Proc. 2 nd IEEE Intr Conf on Electronic Sciences, Information Technology and Telecommunication?SETIT, p.211, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00077494

B. Du, C. Iii-]-l, and . Nagel, SPICE2: A computer program to simulate semiconductor circuits, Electron. Res. Lab, vol.520, issue.1, 1975.

T. Quarles, The SPICE 3 implementation guide, Electron. Res. Lab, vol.8944, 1989.

K. S. Kundert, The designer guide SPICE & SPECTRE, Boston: Kluwer Academic, 2003.

A. Vladimirescu, The SPICE book, 1994.

C. Hull and R. Meyer, A systematic approach to the analysis of noise in mixers, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.40, issue.12, pp.909-919, 1993.
DOI : 10.1109/81.269032

A. Hajimiri and T. Lee, A general theory of phase noise in electrical oscillators, IEEE Journal of Solid-State Circuits, vol.33, issue.2, pp.179-194, 1998.
DOI : 10.1109/4.658619

M. Addouche, R. Brendel, D. Gillet, N. Ratier, F. Lardet et al., Modeling of quartz crystal oscillators by using nonlinear dipolar method, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.5, pp.520-527, 2003.
DOI : 10.1109/TUFFC.2003.1201461

URL : https://hal.archives-ouvertes.fr/hal-00077166

A. Vladimirescu, SPICE-the fourth decade analog and mixed-signal simulation-a state of the art, CAS '99 Proceedings. 1999 International Semiconductor Conference (Cat. No.99TH8389), pp.39-44, 1999.
DOI : 10.1109/SMICND.1999.810383

K. Mayaram, D. C. Lee, S. Moinian, D. A. Rich, and J. Roychowdhury, Computer-aided circuit analysis tools for RFIC simulation: algorithms, features, and limitations, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.47, issue.4, pp.274-286, 2000.
DOI : 10.1109/82.839663

T. J. Aprille and T. Trick, Steady-state analysis of nonlinear circuits with periodic inputs, Proc. IEEE (Special Issue on Computers in Design), pp.108-114, 1972.
DOI : 10.1109/PROC.1972.8563

. Skelboe, Computation of the periodic steady-state response of nonlinear networks by extrapolation methods, IEEE Transactions on Circuits and Systems, vol.27, issue.3, pp.161-175, 1980.
DOI : 10.1109/TCS.1980.1084794

E. M. Baily, Steady state harmonic analysis of nonlinear networks, 1968.

J. C. Lindenlaub, An approach for finding the sinusoidal steady state response of nonlinear systems, Proc. 7 th Ann. Allerton Conf. Circuit and System Theory, 1969.

M. S. Nakhla and J. Vlach, A piecewise harmonic balance technique for determination of periodic response of nonlinear systems, CAS?23, pp.85-91, 1976.
DOI : 10.1109/TCS.1976.1084181

A. Ushida and L. O. Chua, Frequency-domain analysis of nonlinear circuits driven by multi-tone signals, CAS?31, pp.766-779, 1984.
DOI : 10.1109/TCS.1984.1085584

K. S. Kendert, A. Sangiovanni, and ?. Vincentelli, Simulation of Nonlinear Circuits in the Frequency Domain, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.5, issue.4, pp.521-535, 1986.
DOI : 10.1109/TCAD.1986.1270223

V. Rizzoli, C. Cecchetti, A. Lipparini, and F. Fastri, General-purpose harmonic balance analysis of nonlinear microwave circuits under multitone excitation, IEEE Transactions on Microwave Theory and Techniques, vol.36, issue.12, pp.361650-1660, 1988.
DOI : 10.1109/22.17396

C. R. Chang, M. B. Steer, S. Martin, and J. E. Reese, Computer-aided analysis of free-running microwave oscillators, IEEE Transactions on Microwave Theory and Techniques, vol.39, issue.10, pp.1735-1745, 1991.
DOI : 10.1109/22.88545

V. Rizzoli, A. Costanzo, and A. Neri, Harmonic-balance analysis of microwave oscillators with automatic suppression of degenerate solution, Electronics Letters, vol.28, issue.3, pp.256-257, 1992.
DOI : 10.1049/el:19920158

K. S. Kundert, J. K. White, A. Sangiovanni, and ?. Vincentelli, Steady?state Method for Simulating Analog and Microwave Circuits, 2003.
DOI : 10.1007/978-1-4757-2081-5

K. S. Kundert, A. Sangiovanni, and ?. Vincentelli, Finding the steady-state response of analog and microwave circuits, Proceedings of the IEEE 1988 Custom Integrated Circuits Conference, pp.6-7, 1988.
DOI : 10.1109/CICC.1988.20808

E. Ngoya, A. Suãrez, R. Sommet, and R. Quéré, Steady state analysis of free or forced oscillators by harmonic balance and stability investigation of periodic and quasi-periodic regimes, International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering, vol.41, issue.3, pp.210-233, 1995.
DOI : 10.1002/mmce.4570050308

M. Gayral, Contribution à la simulation des circuits non?linéaires micro?ondes par la méthode de l'équilibrage harmonique et spectrale " Thèse de doctorat, 1987.

E. Ngoya, Contribution à la création d'outils de C.A.O des circuits non?linéaires microondes, Thèse de doctorat, 1988.

E. Gad, R. Kkhazaka, M. S. Nakhla, and R. Griffith, A circuit reduction technique for finding the steady-state solution of nonlinear circuits, IEEE Transactions on Microwave Theory and Techniques, vol.48, issue.12, pp.2389-2396, 2000.
DOI : 10.1109/22.898988

K. S. Kundert, Introduction to RF simulation and its application, IEEE Journal of Solid-State Circuits, vol.34, issue.9, pp.1298-1319, 1999.
DOI : 10.1109/4.782091

R. Telichevesky, K. S. Kundert, I. Elfadel, and J. K. White, Efficient steady-state analysis based on matrix-free Krylov-subspace methods, Proceedings of the 32nd ACM/IEEE conference on Design automation conference , DAC '95, 1995.
DOI : 10.1145/217474.217574

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.9366

L. Fox, The Numerical Solution of Tow?point Boundary Value Problems in Ordinary Differential Equations, 1957.

H. B. Keller, Numerical Methods for Tow?point Boundary Value Problems, 1968.

H. B. Keller, Numerical Methods for Tow?point Boundary Value Problems, 1976.

G. Hall and J. M. Watt, Modern Numerical Methods for Ordinary Differential Equations, 1976.

B. Childs, M. Scott, J. W. Daniel, E. Denman, and P. Nelson, Codes for Boundary Value Problems in Ordinary Differential Equations, 1979.
DOI : 10.1007/3-540-09554-3

J. Soter and R. Bulirsch, Introduction to Numerical Analysis, 1980.

H. William, B. P. Press, S. A. Flannery, W. T. Teukolsky, and . Vetterling, Numerical Recipes : the Art of Scientific Computing, 1986.

L. O. Chua and A. Ushida, Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies, IEEE Transactions on Circuits and Systems, vol.28, issue.10, pp.953-971, 1981.
DOI : 10.1109/TCS.1981.1084921

K. S. Kundert, J. White, A. Sangiovanni, and ?. Vincentelli, A mixed frequency-time approach for distortion analysis of switching filter circuits, IEEE Journal of Solid-State Circuits, vol.24, issue.2, pp.443-451, 1989.
DOI : 10.1109/4.18606

H. Brachtendorf, G. Wesch, and R. Laur, A novel time-frequency method for the simulation of the steady state of circuits driven by multi-tone signals, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97, pp.1508-1511, 1997.
DOI : 10.1109/ISCAS.1997.621414

J. Roychowdhury, Efficient methods for simulating highly nonlinear multi?rate circuits, Proc. IEEE DAC, pp.269-274, 1997.

J. Roychowdhury, Analyzing circuits with widely separated time scales using numerical PDE methods, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.48, issue.5, 1999.
DOI : 10.1109/81.922460

K. S. Kundert, J. White, A. Sangiovanni, and ?. Vincentelli, An envelope-following method for the efficient transient simulation of switching power and filter circuits, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers, pp.446-449, 1988.
DOI : 10.1109/ICCAD.1988.122546

E. Ngoya and R. Larchevêque, Envelop transient analysis: a new method for the transient and steady state analysis of microwave communication circuits and systems, 1996 IEEE MTT-S International Microwave Symposium Digest, pp.1365-1368, 1988.
DOI : 10.1109/MWSYM.1996.512189

URL : https://hal.archives-ouvertes.fr/hal-00924487

E. Rizolli, A. Neri, and F. Mastri, A modulation-oriented piecewise harmonic-balance technique suitable for transient analysis and digitally modulated signals, 26th European Microwave Conference, 1996, pp.546-550, 1996.
DOI : 10.1109/EUMA.1996.337640

P. Feldmann and J. Roychowdhury, Computation of circuit waveform envelopes using an efficient, matrix-decomposed harmonic balance algorithm, Proceedings of International Conference on Computer Aided Design, pp.295-300, 1996.
DOI : 10.1109/ICCAD.1996.569712

M. Okumura, T. Suguwara, and H. Tanimoto, An efficient small signal frequency analysis method of nonlinear circuits with two frequency excitations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.9, issue.3, pp.225-235, 1990.
DOI : 10.1109/43.46798

R. Telichevesky, K. S. Kundert, and J. K. White, Efficient AC noise analysis of tow?tone RF circuits, Proc. IEEE DAC, pp.292-297, 1996.

R. Telichevesky, K. S. Kundert, I. Elfadel, and J. K. White, Fast simulation algorithms for RF circuits, Proceedings of Custom Integrated Circuits Conference, pp.437-444, 1996.
DOI : 10.1109/CICC.1996.510592

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.9014

R. Telichevesky, K. S. Kundert, I. Elfadel, and J. K. White, Efficient steady-state analysis based on matrix-free Krylov-subspace methods, Proceedings of the 32nd ACM/IEEE conference on Design automation conference , DAC '95, 1995.
DOI : 10.1145/217474.217574

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.9366

Y. Saad and M. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986.
DOI : 10.1137/0907058

M. Addouche, Modélisation non linéaire des oscillateurs à quartz, développement d'un logiciel de simulation, Thèse de doctorat, 2002.

M. Addouche, N. Ratier, D. Gillet, and F. Lardet-vieudrin, ADOQ: a quartz crystal oscillator simulation software, Proceedings of the 2001 IEEE International Frequncy Control Symposium and PDA Exhibition (Cat. No.01CH37218), pp.753-757, 2001.
DOI : 10.1109/FREQ.2001.956375

M. Addouche, N. Ratier, D. Gillet, R. Brendel, and J. Delporte, Experimental validation of the nonlinear dipolar method, Proc. 16 th EFTF, 2002.