• Aucun résultat trouvé

A Nonlinear Order-Reducing Behavioral Modeling Approach for Microwave Oscillators

N/A
N/A
Protected

Academic year: 2021

Partager "A Nonlinear Order-Reducing Behavioral Modeling Approach for Microwave Oscillators"

Copied!
17
0
0

Texte intégral

(1)A Nonlinear Order-Reducing Behavioral Modeling Approach for Microwave Oscillators Michael Kraemer, Daniela Dragomirescu, Robert Plana. To cite this version: Michael Kraemer, Daniela Dragomirescu, Robert Plana. A Nonlinear Order-Reducing Behavioral Modeling Approach for Microwave Oscillators. IEEE Transactions on Microwave Theory and Techniques, Institute of Electrical and Electronics Engineers, 2009, 57 (4), pp. 991 - 1006. �hal-00420342�. HAL Id: hal-00420342 https://hal.archives-ouvertes.fr/hal-00420342 Submitted on 28 Sep 2009. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2)      

(3)        

(4)       . .  

(5)             .     .   

(6) .

(7)  

(8)     

(9)        

(10) .     

(11)                    

(12)                  !" # 

(13)         

(14)     .                    "          

(15)  

(16)     $    "                                           "             

(17)   "           $ .       

(18)      %      .     "    &              

(19)          '" # .           &               ½  ¾  (    " )    !         .       .  "  

(20)                

(21)  $  '   *+,-" 

(22)     

(23)       ! ./     . . . )-+ ).+  )/+ &

(24)     

(25)

(26)        0   

(27)        1 %   "             "     $%&            

(28)   $%&!#'(       

(29)           "           0                   "    !       "     

(30) 

(31)    2 3    

(32)     

(33)  "                   

(34)   )4+ )5+  %                                   

(35)                

(36)  6       7         " "  0        

(37) 

(38)        !      $  !0  2 %                   0  7&3.  " . 

(39)            

(40)     

(41)

(42)           )8+ #      

(43)              . .     "          " .   

(44)          .         

(45)      "  .        

(46)         .          

(47)  

(48)     .       

(49)            .  "            

(50)   . 

(51)         

(52)      .       

(53)     "   $.                .  !0  . 

(54)      

(55)   

(56)       .                   !.  !           .     0     

(57)     . " 

(58)  " "       

(59)  .      

(60)

(61)            . #    

(62)       

(63)     ". "   "        

(64)       6 .       $%&!#'( )*+.            .  

(65)   ".        

(66) "    , $%&!#'(. )9+            "   .  "  "     "      !.         ):+      7&3  .     

(67)       .  "    )*;+.           "     . %       .  

(68)  .     

(69)        "   

(70)

(71)  .             

(72)

(73)   .          "      

(74) .                .      "   

(75)    

(76) .

(77)   

(78) 

(79)         !

(80)   "# $ % $  &   $  #  

(81)   '   (  ) *+,-./  0 1    1 

(82)   2&.  3$  ( 4( 5 

(83)  

(84)  & &  $ %,.55 

(85) &

(86)  %     6  

(87) &

(88)  2(  (  2 (7 4( %,.55 

(89) &

(90)  %  ,1 &8 1! 19&. :  & 9&. : &. 9&. : 8 .-+;-5<.. . .     

(91)  

(92)       

(93)

(94) 

(95) 

(96)  

(97)  

(98) 

(99)   "    < "   

(100)   "    6 !   7&3       

(101)       0    

(102)   "    6      #      )9+.      !

(103)   " ".    

(104) "  

(105)          .

(106)      

(107)        

(108)       . .             .                <.   .  

(109)  

(110)        #

(111)    .     0    

(112) 

(113)    .         "       .   2 =           .  

(114)   .         "        .   

(115)  

(116)          .      "  "  !    .    "        "   !.  

(117)  &

(118)             .    

(119)  7&3        !  .      

(120)

(121)       !  .  

(122)   $%&!#'(     

(123)   .      

(124)    

(125)

(126)   " 

(127)    .   

(128)  

(129)            .   "         

(130)  ".       1     "  "

(131)  .       

(132)  

(133)   #   .   @   

(134)    @     .      >          .             

(135)   .           

(136)

(137)  "  .   <        .   . ¼. $!# .   

(138)      

(139)    

(140) "            

(141)     6 "                  $?7   

(142)                 6           @     6   

(143)            "    

(144)

(145)  6     

(146) 

(147)       2 ( .   .            

(148)  

(149)           

(150)  

(151)        !  ( .        

(152)    .   0 "           

(153)     @                      

(154)       "             . > 

(155)         

(156)      (  $.        

(157) "     .

(158)        #         $. .                 @  

(159) 

(160)          

(161)    "             

(162) 

(163)    

(164)     !      

(165)              

(166)   "         @     0       . .   &             7&3.   @    

(167)       

(168)  

(169)   @          "       0  "  2  6       "  

(170)    . . . .    " "   0   . .     .            &   "     

(171)                        @     !

(172)   

(173)     .     

(174)   . .              

(175)    . #      !          ". . .    0  "           .   .   . .    

(176)    

(177)     " 

(178)  .          * . =774 =0> .

(179)     .  

(180)     "      @  

(181)

(182)  . .  "           

(183)    .  . *.    1        . Ü. .  .                                              "      >      7              .  

(184)  0 .       

(185)     .   "  "              7&3  " 

(186)      " .          . Ý.      .   1    . Ü. .  .       

(187)         .  . -.   < 

(188)  .        

(189) .      !     

(190)    .  . . 6     <       .    "       

(191) "          =.  .  "    .             "   "   0  "   A    "            

(192) 

(193)      

(194)    

(195)           . $!& .    " 

(196)    

(197)

(198)          

(199)                           )**+)*-+.                   

(200)      .  .   .    

(201) "      

(202)    <       

(203)            

(204)    6  "   

(205)  0      

(206)     A  

(207) !

(208)          

(209)  6  >   

(210) .       .                  0 

(211) 

(212)  " $   )8+   "              .  .  . . . . . . . . . .  . . ..

(213)      

(214)        

(215)       . 9. 2.5. x 10. .    A        

(216)                        . 2.         . velocity vectors. 1.5. %            

(217)               >  . 1.  

(218)       "   

(219)  6             . x2(t). 0.5. 

(220)        

(221)  " "  .    

(222) "          . 0.  . −0.5.       $  !0   . −1. !?.     @        "  ". singular point.  !      

(223)     "   ". −1.5.       

(224)       

(225)          "          . limit cycle. −2.              . −2.5 −2.5. −2. −1.5. −1. −0.5. 0. 0.5. 1. 1.5. 2. 2.5. x1(t). %  2&  : $  ' # : ?  2 &, &&   1

(226) &   ?=4,  ( ( 

(227) &     Ü   ¼ :  Ü   ¼.         "      " 

(228)

(229)   6           " )9+           0  "  

(230) 

(231)     "             

(232)                  . = 6      $  !  . . 0  .. .  . .  . .  . .  . . . . . . . . . . . /.  "          . . . . . . .  .      . . . . .   . . . 4. =   

(233)   0     6    "     

(234)  0           . 5. . . 

(235)    

(236)   

(237)   " "               .  . .  . .   .       "

(238)  " #                 

(239)            "            $  ! 0   %        

(240)                 " 6       " 

(241)

(242)     

(243)  0    

(244)     6       6               "  

(245)   "  

(246)  ". .   . !5        "  <. .    0 %   

(247) 

(248)      . .  .     

(249) "      "              .  . .      .     

(250)        . .      0  "     $  !      @        "   

(251)  $%&!#'(    6   *. .    "             2.  . .  . . .  .  . .  . .  .  . .  . .  . 8.            " "     ! <     

(252) 

(253)           .    .     $  !       !.       "   

(254)      

(255)                6   -.   0   "  

(256)    

(257)

(258)    . "  $?7   

(259)      

(260) 

(261)  .   <               <. '        "   

(262) @ . 

(263)          

(264)       ".     <  @            .              >  .  

(265)    !     

(266)    "  .     

(267)         

(268)    .  =  

(269) @      

(270) " .       .       

(271)          .  

(272)   

(273)  

(274)         !. "             .   " "        

(275)     !.  6       

(276)      .  < "             .   

(277)         @     " .  

(278)              .     .          "  "   

(279)   .       

(280)     6   *     . ?           

(281)     .   .     

(282)         "      .        .    @        .  .    " .

(283)      

(284)        

(285)       . . 11. VDD. 8. Ibias. 6. L. L. x 10. 4 2. vx(t). x2(t). in(t) vy(t). −2. Cvar. Cvar. 0. −4. vcontrol(t). −6 −8 −2 C. −1. 0 x1(t). C. 1. 2. % .  ' # : - >=A ::  &  & &&    $ 3 , 1  &     @   )5/ %  (1&@ $1  : # &     , :,$,  ?. 6   *            !                 "         @   "          .   . .  . .  . . .  .  .  . . . .  . .  .   9. 3  "            "  "  !      

(286)      .                 ".    @  "    6  

(287)

(288)    .                 ". 

(289)     

(290)              .      

(291)  .    

(292)   ! 

(293)      $  !.       .   <

(294)         

(295)

(296)            

(297)      . !# . 0   6  . 

(298) 

(299)     

(300) . "                  .  

(301)  0          

(302)  . 

(303)                .       < 

(304)       .          

(305)           . 

(306)     

(307)   . 

(308)   .                 . :.  < 

(309)            " "   

(310)    "   .  .  !   "#. =     6  

(311)           

(312) 

(313)   

(314) 

(315)  .        $?7       6   -   .   6      #. .    "   

(316)   "        9.               

(317)     .   .   . . .  . . .  .  . . *;.   "    <.  :         " >. $%  

(318)   &. # #      . "   "         .                .    "  

(319)           " .   $  !  .  

(320)       

(321) "  

(322)  

(323)   !. # 

(324)     @  "         .    

(325) .          #&(   6   . . #     6        " 

(326)  .          ?

(327)  $?7    

(328)  6.

(329)       

(330) !

(331)  

(332)

(333)       .    6   -       .   

(334)  

(335)   '.       8    #&( 

(336)   .         . . )*.+.  .    

(337)

(338)       .    0   *.    

(339)         > "   .      " 9.      2.  '<

(340)           

(341)  .        

(342)  

(343)  .         $      

(344) . ( +  #$ + "# &  $ & .  .   - .              

(345)

(346)   7            

(347)   

(348)               

(349)      .

(350)      

(351)        

(352)       . ib(1).                 . jb(1).          

(353)     

(354)  . jw(1,1) iw(1,1). 1. 1. . lw(1,1). 1. …. …. Ib(k). jb(k). lb(1).  .              .   '          "   

(355)

(356)           

(357)   . 1.     

(358)     

(359)    

(360)

(361)      

(362)            )*.+. …. …. …. k. lb(Nout). …. …. Nin. …. k. …. ib(Nh).       

(363) "           %   6     

(364)  

(365)    "             . "         " 

(366)

(367)   . jb(Nm). Nout.  !6 "     "    '           . iw(Nin, Nh). Nh. jw(Nh, Nm). 1st hidden layer. input layer. Nm.  

(368)

(369)      . lw(Nm, Nout). 2nd hidden layer.       

(370)   7     

(371)   .         . output layer.     

(372)  '                   

(373)      "       6           

(374)     

(375)    . % ; ($1  : 1

(376) &,& #  3$ 3 $ & # .     

(377)           

(378) 2   

(379)   "        . 

(380)      

(381)                  

(382) 

(383)      '   )*.+2                                .          0    '(3. .       "  

(384)         

(385)

(386)       0  6        "  0    .   '     "            "    "    "!

(387) 

(388)         . . !  #     . 

(389)  "    

(390)    "          . .   #   0   

(391)   . '   "   1                    1 

(392)  

(393)                  "                    3         " 

(394)       "    

(395) . )   * +

(396).  #* .           "       6

(397) " )*.+2 &  

(398)       "    #   @     "  # 

(399)      

(400) !

(401)  

(402)

(403)   

(404)   "         9  #       .

(405) !

(406) 

(407)   

(408)     #   

(409) 

(410)      

(411)

(412)    

(413)

(414)  

(415) !

(416) 

(417)    #       1        " "  

(418)

(419)  

(420)     

(421)    

(422)

(423) 

(424)  

(425) .        

(426)  

(427)       . #

(428) 

(429)       '    "!

(430) 

(431)    .         /       .           2     .         ". 

(432)           . .  . 

(433) . .    .  

(434)   .   . .  .   "  

(435)        .     1 "      

(436)    ' **.  

(437)  "  

(438) 

(439)             "  

(440)             

(441)     .   

(442)   "       

(443)   .     "            .           "      . "         " !  " "  . 

(444)                   .               > . "   B       "       .  

(445)            =. 

(446)

(447)  "    1    

(448)    1.             

(449)      .  '.

(450) 

(451)   "                       #  >  . '%  "#  (    )  &.      "            .  

(452)

(453)     "            6  . @       "!

(454) 

(455)   

(456)  .    '          

(457)   . 

(458)            '(3 "    " . "      6          .    "    "         .      

(459)

(460)          

(461) !.              )*.+. 

(462)  

(463)

(464) )*/+ 

(465)

(466)    ' %     .               

(467)  .

(468)      

(469)        

(470)       .    

(471)   '    

(472)

(473)    .    1  "        "    $  . . n1(t) [=in(t)]. Neural Network f( ). vcontrol(t).       

(474)       A       

(475)     '       

(476)    

(477)       . inputs. out.     

(478) 

(479)          

(480)     $%&!#'(    

(481)       "      "              '"     ". .  ". x1(t). ³ dt. 

(482)      '    " !' 0 . •. x2(t). x2(t). ³ dt. "!

(483) 

(484)       in 1 , "+#. in 2. Neural Network ȥ( ) out 1.            

(485)     !. vcontrol(t). in 3. out 2.      

(486)   6    

(487)      

(488)

(489)        "       "  . n2y(t). n2x(t).  2  6           

(490)         "   

(491) 2                " 

(492)   =           '(3 

(493)    

(494)                    '(3           < "  . vy(t). vx(t). 

(495)

(496)    "           . % + B& !   1 : $ &&   1 & :  $   : ::  &

(497) 

(498)            &  

(499)     B& ! 3$  $ 1     3$ >

(500)        .                  .    1 "                

(501)    (         0     

(502)  

(503)         

(504)  "     "         

(505)         

(506)   

(507)

(508)       

(509)       "      (        0    

(510)

(511)               "  "  .  . =7  ?74 ' 74 > !# 22=. =      "  

(512)   

(513)  !      "       

(514)    

(515)

(516)  "        ?!       "  

(517)    

(518)       6         

(519) 

(520)     "   

(521)     !      !!!  $?72           

(522)              

(523)                

(524)          "  

(525)    #  !

(526)  ?

(527)         1" " 

(528)          

(529)  .  

(530)           

(531)       '7(3  $?7      "       0     5; C%1           

(532)

(533)    

(534)   .          

(535)     .   .  . != .    

(536)                     #&(  ( ?3.  .    

(537)  "   

(538)  " 

(539)  "     D             

(540)     "              "   "          .  .      

(541) 

(542)   

(543)   6   4         

(544)        $?7       6   -   0    9.  

(545)  . "  

(546)

(547) 

(548)       2  

(549)    #   "  

(550)      "  "            0        

(551)   

(552)   

(553)                      .         "  #   

(554)  

(555)   " 

(556)  .  . .  

(557)  

(558)

(559) . . .  . *-. 

(560)   

(561)           

(562)

(563)     .         @  .  

(564)             " 

(565) ".  !               .  

(566)    >           .

(567) 

(568) 2               .     0  "     

(569) 

(570)    .        "       .        

(571)      

(572)   . "    "     @     .     

(573)    

(574)  "   

(575)   .   .

(576)  "  

(577)   

(578)       "     .    . . $       

(579)       @  . & " 5   #$ <;,5 "# $ $ !.  .     %   " 

(580)   "     

(581)    "     7     .

(582)      

(583)        

(584)       .  

(585)       

(586)         . . 0  

(587)     .         

(588)   "  . 

(589). 

(590)      

(591)       6      

(592)

(593)        .  $%&!#'(   . . .

(594)

(595). .   . . . *..   

(596)  

(597)        

(598)  .

(599)    #        "   . #     

(600)          .      C            .   

(601)      

(602)      .       .     

(603)  

(604)

(605)  9.   1 "         "      

(606)       "2       .  . .    

(607)  

(608)

(609)    

(610)      .               

(611)     

(612)             

(613)   "   

(614)            

(615)     ".             # 

(616)        . .   . 

(617)     >   .        

(618) @     0    

(619) . . .  . . .  .  .  . . ¼. . */.      .   .  "      6   4     .   

(620)      0        .             C    .         .                   

(621) .           0      .          >   . " 

(622)

(623)   ". != . . .  "      0  A   .                 " " .   .       2       "            "           "    !     

(624)  6    "2 7    

(625)  

(626)                  .   . . *4.           

(627)    #     !0  

(628)               @    . 

(629).    "  "       

(630)             $  !           ". .    

(631)   . . .

(632)

(633) .

(634)   . . *5. &   0

(635)             . .  

(636)     

(637)

(638)   

(639)    = 

(640).     . 

(641) 

(642)         

(643)      " .  . 

(644)     

(645)   

(646)      

(647)     "

(648)         

(649)    

(650)    "          .              

(651)     

(652)     "  )*4+ ' 

(653)    > . 

(654)         "    

(655)    

(656)   

(657)   "          .

(658)     >       #                 "      .             

(659)       

(660)   

(661)  

(662)          "   

(663)      E       

(664)             1      "         

(665)             

(666)    

(667)                 

(668)                

(669)    

(670)   "                 6   

(671)       

(672)    1      =       

(673)   

(674)     "    

(675)   1.        "     .    .   >          

(676)  "  6    ?!  )*5+.           

(677)

(678)      ".               "  .  "   1            

(679)

(680)     6 

(681)      

(682)   

(683)   .         6    6       .   # $%&!#'( 

(684)        "         "    "     )*8+   .  .  !   

(685)   " $%&!#'( .            "    "            "        >     

(686)    

(687)     "               .              

(688)    =  

(689)      

(690)           

(691)   @           

(692)  "    

(693)         6   4  0

(694)                      

(695)   

(696)   .  @       

(697)  

(698)     .         

(699)

(700)   

(701)               6   -.       .  !0  

(702)     

(703)

(704)       

(705)                     

(706)    !.   * )".   >

(707)              

(708)        " "!     

(709)  

(710)       .

(711)      

(712)        

(713)       . Circuit level simulation: ADS/ SPECTRE. training data. Generation and training g of neural network: Matlab. . "

(714)       <

(715)  

(716)     . g , weights, biases. VHDL-AMS simulation: i l ti SMASH.  

(717)  

(718)        < "                         

(719)  

(720)                        <  @  =                 . adjust ı1 and ı2 for phase noise emulation.  

(721)    

(722)      

(723)   

(724)   

(725)    

(726)          . parameters: - tolerances - solver type - time step - initial conditions. Phase noise measurements.       ; $  * $            "    

(727)       <  

(728)    

(729)          "     . % - &  C 38 : 1 

(730)  && 1

(731) &   "$   & 1 &.   "         C    

(732)       "    6       " 

(733)  

(734) .      6     "       .    6   

(735)   "     2 =.     6          .        

(736)      

(737)     .      

(738)         6   5. "      >    

(739)      .    "     "  

(740)    .      

(741)    

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to