三相直流無刷馬達之特性參數估測
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(3) The Parameter Estimation of the Three-phase DC Brushless Motor. .
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(12) The Parameter Estimation of the Three-phase DC Brushless Motor. º »¼ : . Student Advisor. º º. ½¾¿À< ÁÂÃÄÅÆ Ç È 89 A Thesis Submitted to Department of Electrical and Control Engineering National Chiao Tung University in partial Fulfillment of the Requirements for the Degree of Master in Electrical and Control Engineering June 2006 Hsinchu, Taiwan, Republic of China. ÉÊH½ ËÌÍ Î Ï. Tien-Wei Kao Dr. Shir-Kuan Lin.
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(18) The Parameter Estimation of the Three-phase DC Brushless Motor. Student : Tien-Wei Kao. Advisor : Dr. Shir-Kuan Lin. Department of Electrical and Control Engineering National Chiao Tung University. ABSTRACT There are eleven pins connecting to the motor driver in three-phase direct current brushless motor(DCBM). The proposed method in pin identification categorizes these eleven pins into three groups. The first group contains three pins of the three-phase coil . The second group contains two pins of the three-phase hall sensor source. The third group contains six pins of the three-phase hall sensor signal. A testing voltage can be supply to any one of the eleven pins. Because of the difference in the connection relationship of eleven pins, the eleven pins will be divided into two sets, three-phase coil and three-phase hall sensor. Next, any two of the eight pins of three-phase hall sensor are connecting to two testing voltages. The measured voltage signals of other pins are different according to distinctive testing condition, so two pins of the three-phase hall sensor source can be verified. Finally, the outputs of three-phase hall sensors can be verified from the signals of three-phase back electromotive forces when the DCBM rotates by manual. The torsion constant(or called the reaction EMF constant) in DCBM relates to value of the torque, rotational speed that can be operated, and the performance of the motor. Therefore, the motor designer or user concern about this constant very much. If this constant can be measured in advance, the motor designer can take it as reference when designing motors. The proposed method in measuring torsion constant uses driver IC(BA6849) and AD/DA card to measure the constant. By the characteristic of DCBM rotating in single-phase mode, the torsion constant can be measured correctly and efficiently.. ii.
(19) iii As the respect of manufacturing DCBM, measuring the values of resistance and inductance of three-phase coil is also an important test. After winding the coils on the iron of DCBM, the impedance of three-phase coil should match with each other. Hence, the linearity and controllability of DCBM will be better. The proposed method in measuring the impedance of three-phase coil use LCR METER to finish the test. Supplying a DC bias to the measuring AC current to the three-phase coil, then DCBM will be locked in the same position. As a result, measuring the impedance of threephase coil can be more accurate..
(20) . i. . ii. . iii. . vi. . x.
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(32) . . . . . . . . . . . . . . . . . . . . 5.15 ÕÖ¹ëÂg|iJ X6 . . . . . . . . . . . . . . 5.16 ÕÖ¹ëÒÆt . . . . . . . . . . . . . . . . . . . . . . . . 5.17 ÕÖ¹Áæ¹ë¯° . . . . . . . . . . . . . . . . . . 5.18 ÕÖÁûÁ ëÂgV . . . . . . . . . . . . . . . . . . . . . 5.19 ÕÖ LCR METER ëÞÙt . . . . . . . . . . . . . . . . . . 5.20 ÕÖÁûÁ ëÂg|iJ X6 . . . . . . . . . . . . 5.21 ÕÖÁûÁ ëÒÆt . . . . . . . . . . . . . . . . . . . . . . 5.22 >ÃÄ6t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.23 ÕÖ ÁÒë|iJ X6 . . . . . . . . . . . . . . . 5.1. viii 62 63 66 66 67 68 68 70 71 72 73 74 74 75 76 76 77 78 79 80 80 81 81 82 83.
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(63) Ø 2 Ù Í«È XY Í«@mº ÙXYÍ«@m 0ÈA¨BÄSdâº. 9. F =I ·L×B =N I ·L×B. (2.1). âC I SâÒaäåÁÒ L SâäåMÔO8 ì×'1> B SâOÀ> N SâÒ!D óÕÖÁÒm⺠F. T = F · r = N I · L × B · r = Kt I. (2.2). Sâ E K Sâ¹ OÀ> B θ Fθ ׺ r. t. r. s. B = B(θr , θs ) = Bmax sin[P (θr − θs )/2]. (2.3). âkM#$O7Oÿ θ âkM)SkÉv>Ê θ âSkMFØ)SkÉv>Ê Hmn 2.2oFmn 2.3o ÇÈÕÖ¹ K ?kÜ óªú+J P. r. s. t. Kt = N Bmax L r cos(P θr /2). (2.4).
(64) Ø 2 Ù Í«È XY 10 t 2.6 â;ÕÖ ^ ác
(65) a b c ÐSkaw A1: K ÁvÂuv+Jt tM K <þ01aJõt 2.4 0È Áv / Âuv = 6 ÁvG¸ 360 > ÂuvÁG¸ 60 > ;H% ÕÖÁ¸ 60 > t. t. 2.6: ) a*b*c + #$,- K ./ t. ÕÖÛÜ6mº ÕÖÛÜ6máâG9Ð:äåÀ6mýh áâÁæÛÜI ÁÒÛÜló¹ÁæÛÜ[m áâ lº 1 120 >6ÁæÛÜ Ð : ä å É ô À : Ø : â
(66) ± º À ac : ÁÒõ a :ÒA c : ^ b :â
(67) ^¹zâ K = K −K ≡ K t 2.7 â a b c Ð:SkäåôÀ:ÁÒ J K Áv+Jt t. ta. tc. t. t(a→c).
(68) Ø 2 Ù Í«È XY. 11. 2.7: 0(1! K ./ t. õmn 2.4oÈ (?ÕÖâ <ü K ßàK! < ü
(69) 120 >6ÁæÛÜ[m Æõt 2.7 ÇAÁÒ Ávaw± 2.1 2 2.1: 120 3. 456 789:;2 ÀÁÒ67 Áv Ø a→c [ 0, 60 ] b→c [ 60, 120 ] Ð b→a [ 120, 180 ] p c→a [ 180, 240 ] Í c→b [ 240, 300 ] Î a→b [ 300, 360 ] ÁÒ 0, 60, 120, 180, 240, 300, 360 t.
(70) Ø 2 Ù Í«È XY 12 HÕÖ
(71) Ávaw +L^ <ÀÁÒ67 ? Õ Ö < ± º Õ Ö a ö Á v [ 0, 60 ] | ø nθ = [ 0, 60 ]o ^+LÀÁÒâ a Ò:A c : ÕÖé < )9t 2.7 2.1 MÕÖ 360 Ávn60 >Âu vo{±t 2.8 r. 2.8:. 120. 3. 456<=.. 2 180 >6ÁæÛÜ Ð:äåÉ Ð:%âÀ ×l[mºÁÒõØ:äå Ò7´µ:äåè$%ÁÒõ´µ:äåÒ7NØ:ä å ± º Á Ò õ a : Ò 7 bFc : ^ ¹ z â K = K − (K + K ) ≡ K èóÁÒõ aFb :Ò7 c : ¹ zâ K = (K + K ) − K ≡ K t 2.9â a b c Ð:Skäå% ÀJ K Áv+Jt t. ta. tb. t. tc. t(a→b,c). ta. tb. t. tc. t(a,b→c).
(72) Ø 2 Ù Í«È XY. 13. 2.9: !>?1 K ./ t. hZ
(73) 180 >6ÁæÛÜ[m Æõt 2.9 ÇAÁÒ Ávaw± 2.2 2 2.2: 180 3. 456 789:;2 ÀÁÒ67 Áv Ø a → b,c [ -30, 30 ] a,b → c [ 30, 90 ] Ð b → a,c [ 90, 150 ] p b,c → a [ 150, 210 ] Í c → a,b [ 210, 270 ] Î a,c → b [ 270, 330 ] ÁÒ -30, 30, 90, 150, 210, 270, 330.
(74) Ø 2 Ù Í«È XY 14 HÕÖ
(75) Ávaw +L^ <ÀÁÒ67 ?ÕÖ < )9t 2.9 2.2 MÕÖ 360 Á vn60 >Âuvo{±t 2.10 . 2.10:. 180. 3. 456<=.. ÇÈÁÒ â¸
(76) O;^¡MÛÜ -.Õ ÖSkMéê ëÝÇÈO8+J )ëÕÖkSk:)a wéê ëÝéê'ì ëOÀ>|<þ0|¡:)ì+J |Áæü0È;kOPÜ^ )hØawóQ´ ì|OÀ>ß | +J éê ëÝawýh ´¡| ëñò¹| ß?|öRýh|:aÊ :aÊ
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(78) ^ßàT , 6Uéê ëÝñòÛÜÁ
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(80) öSéê ëÝñòÛÜ ñò|:)ÛÜÕÖ^ À¹°ÐÉéê ëÝ¡Ððéê ë Ýñò _`Ð:ñò:?.
(81) Ø 2 Ù Í«È XY 15 0ÈÐ:Áæñò:Êâ 120 >Áv )ÌÿkóQ Âuvâ 20 > ªV 120 >öG¼ 240 >nÂuv 40 >o F)Ìÿkó Q Ø Swéê ëÝ :øÂuv 20 >$ 40 >WåË"Ìÿ ÕÖ Ñ"XÂuvâ 40 > â,YSwéê ëÝö"Zø@â6 Fÿ éê ëÝ:øÂuv 40 > ë8 ~t 2.11 kSk xyawS SwÐÉéê ëÝ ÐÉéê ëÝ:)öÐ:Skäå ±t 2.11. 2.11: !@ABCD! !"#$ õMtfÇÐ:éêñò H FH . H ±t 2.12 z H ≡ H − H FH ≡ H − H ó H ≡ H − H õöÐÉéê ëÝ´awù :Ê 40 >Âuv FÐéêñòÿâ:Ê 120 >ÁÝvú ßéêñò[áâ HighFLow lÎa dÐ:éêñò H FL Îaz :)ö^+Jáczâ H1FH2 . H3 ÿM4ö t 2.12 É )9 2.1 i- H3 − H1FH1 − H2 . H2 − H3 ñò 120 >6Áæ ÛÜ^ a :Fb :. c :Îa^t:h FZ ÇA 120 >ÛÜ :ü± 2.3 o a. + a. − a. o b. + b. − b. o c. + c. − c. o b. o c. o a.
(82) Ø 2 Ù Í«È XY. 16. 2.12: @ABCDEF
(83) GH120 356 2 2.3: 120 3. 456E9!IJ2 Ð:Áæ éêñò ÀÁÒ67 a : b : c : H3 − H1 H1 − H2 H2 − H3 Ø a→c High Open Low H M L b→c Open High Low M H L Ð b→a Low High Open L H M p c→a Low Open High L M H Í c→b Open Low High M L H Î a→b High Low Open H L M Ð:éêñò:ÇA H − H FH − H . H − H ßÐ ñò[áâ HighFLow lÎa ´:)ö^+J H FL Îaz â H4FH5 . H6 ±t 2.13 o c. o a. o a. o b. o b. o c.
(84) Ø 2 Ù Í«È XY 17 )9 2.2 i- H4FH5 . H6 ñò 180 >6ÁæÛÜ^ a :F b :. c :Îa^t:h FZ ÇA 180 >ÛÜ:ü± 2.4. 2.13: @ABCDEF
(85) GH180 356 2 2.4: 180 3. 456E9!IJ2 Ð:Áæ éêñò ÀÁÒ67 a : b : c : H4 H5 H6 Ø a → b,c High Low Low H L L a,b → c High High Low H H L Ð b → a,c Low High Low L H L p b,c → a Low High High L H H Í c → a,b Low Low High L L H Î a,c → b High Low High H L H.
(86) Ø 2 Ù Í«È XY 18 HM 2.3 2.4 éêñò âÛÜÝGH ÕÖ
(87) 120 >$ 180 >ÛÜ[m ¦& 2.3 2.4\|: |ü]6)t 2.11 Ééê ëÝawóÇ Héê ëÝawý h N¾:ü;?ýh^öÁæ$ÁÒÛÜ ´Êè®
(88) öÛ ÜÁ
(89) 4 6m|ýh dý c.
(90) . 2.3. â¸
(91) Ù¨ÕÖ3ú C@DE
(92) \ÕÖ_ `6Æm ±m : . Vas Vbs Vcs. . . = . . . . . di R 0 0 ia Ls −M −M a dt di 2ωr Ke b + + −M 0 R 0 dt ib −M Ls P dic −M −M Ls ic 0 0 R dt. . cos(θr ) cos(θr − 2π ) 3 cos(θr + 2π 3) (2.5). mn 2.5oâÕÖÁ6Æm aõbcdeÁæSffó mÉ V V . V ácâÕÖ a b c Ð::Áæ R âÕÖ:Á û i i . i ácâÕÖ a b c Ð::ÁÒ L âÕÖ:b M âÕÖ:ø: ω âÕÖ ( Áv| ) K âÕÖÁæ¹ P âÕÖ#Oÿ θ âÕÖkvag ( Áv| ) ó÷:Á Òb:hÒ Éú s 67SâîÁÒ ( ',t 2.2)óÕÖÂu6 Æm±mz : as. a. bs. b. cs. c. p. r. e. r. √ Te = Kt [(ia − i2b − i2c ) cos(θr ) + 23 (ib − ic ) sin(θr )]. (2.6). dωr 2Bm = 2J P dt + P ωr + TL. mn 2.6oaõijkÜSffó mÉ K âÕÖ¹ T âÕÖ J âÕÖl B âÕÖûm T âïn
(93) m.k.s. Ä K = K t. e. m. e. t. L. .
(94) Ø 2 Ù Í«È XY 2.4. NI PCI-6052E AD/DA. . 19. «VW? PCI-6052E AD/DA / ( t 2.14 ) %õoI½²pÝqr ×s@t¡ AD/DA / î%Ø > 'u å_ PCI X6 ãC /ñ_` Visual C++ vmw`?#xy. 2.14: PCI-6052E AD/DA K _`ØKÙmÙä} Ùänt 2.15 o ß AD/DA /×ñòKÙAVW öVW^ëóÙ}M0×zt ß×ÀÞ\ ¨ÑÀÞ_ ? PCI-6052E. 2.15: PCI-6052E L MNL.
(95) Ø 2 Ù Í«È XY 20 ´z{±º ØFãC : 1. ãCè 2. ¡ |u AÖ 333kS/sè 3. dç> 16bitsè 4. }~ × -10V 10V 0V 10V ; bÁæMsè 5. û9º0.1 FãC : 1. ÌÎÀÞãC è 2. ¡ |u AÖ 333kS/sè 3. dç> 16bitsè 4. }~ × -10V 10V 0V 10Vè 5. û9º100G è 6. Ðli[m ÐFa : 1. Æmba h pF"^Ý : 1. ðM"^Ýè 2. qL_`ÍÎ|uº20MHz . 100kHzè 3. KL ÍÎ|uº20MHZ ÍFãCi : 1. dç>º12bitsè 2. ÃÄî $ï iè 3. |º700kHzè 4. û9º10K ÎFÇUhX6 : 1. h^ÃÄå ADDA / PCI-6052E _`¸ïå}Æm?#xy ;?àvm¼ ßàß nidaq.h nidaqex.h àPAÆm6 ±¨? PCI-6052E _`vmw XYÍ«¹Avmº.
(96) Ø 2 Ù Í«È XY ØFxy!S : ßàb AD/DA //òºdeviceNumber = 1. 21. FãC : AI Configureº !SãCÀÞFÿú.',Áæü AO VWriteº bì
(97) vmqL!SÁæü Áæüßà
(98) /}~q ÐFãC : AI Configureº !SãC ÀÞF [mFÁæü}~.ÿú ßà
(99) yã C |¼b© DAQ Rateº H/Í«|u !SãC |u Í«|u SCAN Setupº ãC Ü xyJ !S?ÀÞ ÀÞò ü SCAN Startº åÀÞãC xyJ H¼!S|u !Sç DAQ Checkº )ëåÀÞãC %:©ª ©ª éýìÜ SCAN Demuxº ß×G9|¼!SÀÞ G\ DAQ VScaleº E â a ?vmßâÑÙZ Áæü pFa :. º !SaÀÞ !Sâa[m DIG Prt Config.
(100) Ø 2 Ù Í«È XY DIG Out Prtº aÀÞ !S aü ÍF"^Ý :. 22. º ß"^ÝxyJ 0!S "^ÝØ$%"^Ý GPCTR Set Applicationº !S"^Ýë}~
(101) «9?É !SâëØ6=> GPCTR Change Parameterº !S"^ÝÍ«|u y"] îíi"ål[m GPCTR Watchº !Ã0P"] ÑA"© 0ß" ¯° M6\vm bì Visual C++ Æm à AD/DA /ÖA_ 9ÉVW%!"iJ X6 `?#ÑÙ
(102) Á M . GPCTR Control.
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(104) !" Ð:ÑÒÓÔÕÖç×ÌؤÙÚÛÜÝ:ÞÙ ± 3.1zº 1 2 3 4 5 6 7 8 9 10 11. 2 3.1: O# P2 a :äåhÁæÙÚ b :äåhÁæÙÚ c :äåhÁæÙÚ éê ëÝ H îñòÙÚ H éê ëÝ H ïñòÙÚ H éê ëÝ H îñòÙÚ H éê ëÝ H ïñòÙÚ H éê ëÝ H îñòÙÚ H éê ëÝ H ïñòÙÚ H éê ëÝî`ìÁí H éê ëÝï`ìÁí H a. + a. a. − a. b. + b. b. − b. c. + c. c. − c. + −. 23.
(105) Ø 3 Ù Z8f VW6( 24 ±Mz Ñ:äå%×Ø´:~)éê ëÝ ± a :ä å~)âéê ëÝ H ó H . H âéê ëÝîï`ìÁí ¤ÙÚ «9]
(106) ö)hÈÕÖÌؤÙÚS @m(df ÕÖÚabÜ c6( aõ AD/DA / Ákí < ëÌؤÙÚS /³Åá( +. a. −. «89ßÕÖÌؤÙÚáâ Ð㺠A Ð:äåÁæÙÚÐä B éê ëÝ`ìÁíîïä C Ð:éê ëÝîïñòÙÚçÎä ë8ÕÖ
(107)
(108) ÷ÙÚ|ø«890ÈÕÖ Á6Æm ±mn 2.5o ¡ÕÖ
(109)
(110) n^6o Ð: ìÁÜ|øÒ! aFbFc Ð: ìÁÜâ E FE FE
(111)
(112) ß i = i = i = 0 1 ÕÖÁ6ÆmFÇmn 3.1oº a. a. b. b. c. c. Vas = Va − ( Va + V3b + Vc ) ≡ Ea = 2ωPr Ke cos θr Vbs = Vb − ( Va + V3b + Vc ) ≡ Eb = 2ωPr Ke cos(θr − 2π 3). (3.1). Vcs = Vc − ( Va + V3b + Vc ) ≡ Ec = 2ωPr Ke cos(θr + 2π 3). ´É V + V + V = V + V + V − 3V = 0 V = (V + V + V )/3 é fmn 3.1o´zÕÖ÷: ìÁÜ
(113) ÕÖ
(114) ^ Ð:äå÷hÁæñòeí¢Ç(^ÕÖ ω âî ( ^667 ) dõmn 3.1o i- E âG¼ E 120 >Áv E â V E 120 >Áv ( ± 3.2) E r¿âÍÎ õöÐ:Áæñ òác:Ê 120 >Áv B«9S a :äå GH E
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(116) Ø 3 Ù Z8f VW6(. 25. 2 3.2: QRSTU!BV 6WE;XY . E :ÊÁv E = 0 ^Áæü a. a. Ea 0. Eb. > V E. Ea = 0. a. Ec. 120. Eb < 0. > G¼ E. a. 120. >. Ec > 0. ;ÕÖéê ëÝ`ìÁíÙÚ ÛÜÁæ Bâéê ëÝ îïÙÚñòîCök¤¥OÀ Féê ëÝ ìýhO8<þ? ×ýhéê ëÝîïñò ñéê ëÝîïñòÐ:Áæñòâ h|uúñòéê ëÝîïñò%NW
(117) ÑÒMæüØð¿ Òñò ´Ð:Skäå:)aw±t 2.11 ªØðéê ëÝ îïñòùâ: F éê ëÝîïñò ßØð éê ëÝþã«89ßhðéê ëÝîïñò: ÇAئéêñò§ â¸z6 «89/¨éêÉÑÒMæLá ;éê ë Ý ÛÜÁæ 0?ÕÖ ^6 ^ ßÐÉéê ëÝÐé êñòâmn 3.2o$mn 3.3oº 5π Hao ≡ Ha+ − Ha− = −vo cos(θr + π 6 ) = vo cos(θr − 6 ) π Hbo ≡ Hb+ − Hb− = −vo cos(θr − π 2 ) = vo cos(θr + 2 ). (3.2). π Hco ≡ Hc+ − Hc− = −vo cos(θr + 5π 6 ) = vo cos(θr − 6 ). 5π −Hao ≡ Ha− − Ha+ = vo cos(θr + π 6 ) = −vo cos(θr − 6 ) π −Hbo ≡ Hb− − Hb+ = vo cos(θr − π 2 ) = −vo cos(θr + 2 ) π −Hco ≡ Hc− − Hc+ = vo cos(θr + 5π 6 ) = −vo cos(θr − 6 ). (3.3).
(118) Ø 3 Ù Z8f VW6( 26 õmn 3.2o mn 3.1o«89 i- H V E 150 >Áv H G¼ E 90 >Áv H V E 30 >Áv ( ± 3.3)è−H G¼ E 30 > Áv −H V E 90 >Áv −H G¼ E 150 >Áv ( ± 3.4) «89 E õïAîr¿âÍÎ ¡Ðéêñò r¿ H º»Ðéêñò)ìAéê ëÝâ H FH $ H è0G9Ðéêñò
(119) «âr¿¼ Q î Séê ëÝñòîïh«89ßhðéê ëÝ ÙÚñò: SâØéêñò ± H ≡ H − H ó −H ≡ H − H À
(120) E õïAîr¿. Ðéêñò ý Ì% H n$ −H oFH n$ −H o$ H n$ −H o r¿aw0ý ?+ ( ± 3.3 . 3.4 )Ðéêñòr¿ßÐé êñòþãAÐéê ëÝ ¡éêñò
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(122) GH[ E !#N\]^_`XY a. Hao. Hbo. Hco. a. a. . E :ÊÁv V E 150 > G¼ E 90 > V E 30 > r¿ 6ØÐ 6Ø 6Ø© ñòQ õïAî õîAï õïAî a. a. 2 3.4: a!@AF
(123) GH[ E !#N\]^_`XY a. −Hao. −Hbo. −Hco. . E :ÊÁv G¼ E 30 > V E 90 > G¼ E 150 > r¿ 6ØÐ 6Ø 6Ø© ñòQ õîAï õïAî õîAï a. a. a. a. − a.
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(125) Õ ÖÛÜÝÅ Áæ}~q
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(127) Ø 3 Ù Z8f VW6( 28 Ø
(128) ²³ÂÕÖMéê ëÝåâ InSb ´4ª HW-108A â ( µJª4 ) ´ û9¶â 250 · 450Ω ´î¶¸éê ëÝ;<¹×:ºû9üèF)ª\~wéê ëÝóQ éê ë Ý`ìÁíh H H øû9¶â 750 · 1350Ω ´¤éê ëÝ îïÙÚøû9 ( ± H . H ) ¶â 250 · 450Ω)0\éê ëÝ óQ éê ëÝ`ìÁíh H H øû9¶â 83 · 150Ω ´¤ éê ëÝîïÙÚøû9 ( ± H . H ) ¶â 250 · 450Ω «9_bÜÚa c(dOö«M\²³ÂÕÖ ´éê ë Ýâ0~w(Ò!
(129) Z¹ ÐÉéê ëÝ»:h éê ë Ý H â«89N¾éê ëÝÁû[\±t 3.2 éê ëݤ ñòÙÚhÁûâ 2R èóéê ëÝÁí`ìîïh H H |øÁûâ 2R +. −. − a. + a. +. −. + a. − a. a. +. 2. −. 1. 3.2: @ABCDE cde â¸6«89ë8 0ÈÕÖâ ÕÖÙÚS⺠PIN1 · PIN3 âÐ:äåÁæÙÚ éê ëÝÙÚâ»
(130) Fý ë8Ð:äåÁæÙÚéê ëÝÙä~w
(131) ´£ ¤éêÙ ÚÉn¼½éê ëÝñòÙÚ `ìÁíÙÚo PIN4 PIN11 âé ê ëÝ`ìÁí H H èPIN5 PIN6FPIN7 PIN8FPIN9 PIN10 ácâÐðéê ëÝîïñòÙÚ BHt 3.1 É0~w( `Jât 3.3 ntÉòéâÙÚòo +. −.
(132) Ø 3 Ù Z8f VW6(. 29. 3.3: fge@ABCDb$E cde «89É×ÚaS »õÚaø::ÇA h(d SÙÚ ×ïåýhð «9®ßØlS6m@ H« 9_m 6( hSÕÖÚa 0\éê ëÝ~wâ Ùë8à ¤éêÙÚ G9Ù ÚøSýh ô¾ÙÚ|øÁû ß´áâ p㺠A éê ëÝ`ìÁíÙÚéê ëÝñòÙÚ ¤ÙÚ Ø¤âéê ëÝ`ìÁíÙÚî$ïnPIN4 $ PIN11 ´Éôؤo ؤâéê ëÝñòÙÚî$ïnPIN5 A PIN10 ´Éôؤo þãâhØl B hØðéê ëÝñòÙÚîï ¤ÙÚâhØðéê ëÝñòÙÚ çÐlºPIN5 . PIN6FPIN7 . PIN8FPIN9 . PIN10 þãâhØl C ýhðéê ëÝñòÙÚîï ¤ÙÚâýhðéê ëÝñòÙÚÐðéê ëÝñòÙ Ú ôýâhðéê ëݤ ±ºØ¤â PIN5 $ PIN6 ´ Éôؤ ؤâ PIN7 $ PIN8 ´Éôؤ D éê ëÝ`ìÁíÙÚîï ¤ÙÚâéê ëÝ`ìÁíÙÚîï PIN4 PIN11.
(133) Ø 3 Ù Z8f VW6( 30
(134) nAoãÉ PIN4 PIN5 |øÁûâ ß´Áû[\` Jât 3.4 õt 3.4 "í PIN4 PIN5 |ø'Áû R = R + 32 R õt 3.3 ÈnPIN4 $ PIN11 ´Éؤo nPIN5 A PIN10 ´ Éؤo|øÁû»:nR o 4−5. 2. 1. 4−5. 3.4:. PIN4. PIN5 E; c.
(135) nBoãÉ PIN5 PIN6 |øÁûâ ß´Áû[\`J ât 3.5 õt 3.5 "í PIN5 PIN6 |ø'Áû R = 2R õt 3.3 È´ PIN7 PIN8 PIN9 PIN10 |øÁû»:nR o 5−6. 2. 5−6. 3.5:. PIN5. PIN6 E; c.
(136) Ø 3 Ù Z8f VW6( 31
(137) nCoãÉ PIN5 PIN7 |øÁûâ ß´Áû[\`Jâ t 3.6 õt 3.6 "í PIN5 PIN7 |ø'Áû R = 2R +R õt 3.3 È PIN5n$ PIN6o PIN7n$ PIN8 $ PIN9 $ PIN10o|øÁ û»:nR oÿéýhðéê ëÝñòÙÚ ¾ÙÚ|øÁ û»â R 5−7. 2. 1. 5−7. 5−7. 3.6:. PIN5. PIN7 E; c.
(138) nDoãÉ PIN4 PIN11 |øÁûâ ß´Áû[\`Jâ t 3.7 õt 3.7 "í PIN4 PIN11 |ø'Áû R = 32 R 4−11. 3.7:. PIN4. PIN11 E; c. 1.
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(145) Ø 3 Ù Z8f VW6( 33 naoФÙÚÁæñò% 2V nbo ¤ÙÚÁæñò% 2V àlýh ß@ФÙÚ ´Áæ<þ´µ ¤Ù ÚÁæ<þýhBÐ:äåÁæÙÚ@ ßà¨%^ hßÐ:äåÁæÙÚî S Á%ßÐ:äåÁæÙÚ@ 6 ÙÚa c no@éê ëÝ`ìÁæÙÚ @¸Ð:äåÁæÙÚ| ÙH%@éê ëÝ`ìÁ æÙÚBâ@éê ëÝ`ìÁíÙÚ¨?éê ëÝî Ü ëkOÿî awBÃÐ:äåÁæÙÚФÙÚ ß ´£ ¤éêÙÚô¤ÙM 2V . GN D à ÁæÜ ¤ÙÚÁæñò HàÙÚÁæ<þýh î @é ê ëÝ`ìÁíÙÚýhÙÚÙÔAÁæ^ õöéê ëÝñ òÙÚ$%`ìÁæÙÚ|øÁûü<þIÏZýh à ¤Ù Ú AÁæ;×<þýh ¤ÙÚ )ýÈÞ´ÙÚS G9 3.1 ¨ t 3.3 z H 2V . GN D :Þ¤ÙÚýh ¤ÙÚÁæ áâ\pl Æ @éê ëÝ`ìÁæÙÚº A 2V GN D ÙAéê ëÝ`ìÁíÙÚéê ëÝñòÙÚ PIN4 . PIN5 â ªáâlJº 1 2V ÙAéê ëÝ`ìÁíÙÚnPIN4o GN D ÙAéê ëÝñòÙÚnPIN5o t 3.4 ß PIN4 ÙM 2V èPIN5 ÙM GN D ÇÈ\Áæ <þº V4 = 2V > V7 = V8 = V9 = V10 > V11 > V6 > V5 = GN D. (3.4). BøÁæñòâ 2V . GN D à¤ÙÚ K ´£Î¤Ù ÚÁæñò»<ö$ö V V = (2R )/(R + 2R3 ) 6. 6. 2. 2. 1.
(146) Ø 3 Ù Z8f VW6( 34 ^Áæñòâ 2V nV oÙÚnPIN4oâؤéê ëÝÛÜ ÁíÙÚèó@´£Î¤ÙÚÉØþÁænV oÙÚ é@ ؤéê ëÝ`ìÁíÙÚnPIN11o 2 GN D ÙAéê ëÝ`ìÁíÙÚnPIN4o 2V ÙAéê ëÝñòÙÚnPIN5o t 3.4 ß PIN4 ÙM GN DèPIN5 ÙM 2V ÇÈ\Áæ <þº 4. 11. V5 = 2V > V6 > V11 > V7 = V8 = V9 = V10 > V4 = GN D. (3.5). BøÁæñòâ 2V . GN D à¤ÙÚ K ´£Î¤Ù ÚÁæñò»þö$ö V V = ( 4R3 )/(R + 2R3 ) ^Áæñòâ GN DnV oÙÚnPIN4oâؤéê ëÝÛ ÜÁíÙÚèó@´£Î¤ÙÚÉØ<ÁænV oÙÚ é @ؤéê ëÝ`ìÁíÙÚnPIN11o ó´îÙÚ:hJ± 3.1 »Ä:hÁæ B hØðéê ëÝñòÙÚîï 2V . GN D ÙAhØðéê ëÝñòÙÚ PIN5 . PIN6 â PIN5 . PIN6 ؤ٠2V ؤ٠GN D t 3.5 ß PIN5 ÙM 2V èPIN6 ÙM GN D ÇÈ\Áæ<þ º 6. 6. 1. 2. 1. 4. 11. V5 = 2V > V4 = V7 = V8 = V9 = V10 = V11 > V6 = GN D. (3.6). BøÁæñòâ 2V . GN D à¤ÙÚ K ´£Î¤ÙÚ Áæñò»
(147) hØÎan1V o ^ÃÁæñòâ 2V GN D à ¤ÙÚ SÁæñòâ 2V GN D ¤ÙÚâhØðéê ëÝñòÙÚ ýâéê ëÝ`ìÁíÙÚ Ã¤ÙÚ )´£ÙÚÃë ÑA@Aî éê ëÝ`ìÁíÙÚ ;0a@A¸Ððéê ëÝñòÙÚ N¤ÙÚ éâé ê ëÝ`ìÁíÙÚ.
(148) Ø 3 Ù Z8f VW6( 35 C ýhðéê ëÝñòÙÚîï 2V . GN D ÙAýhðéê ëÝñòÙÚ PIN5 . PIN7 â PIN5 . PIN7 ؤ٠2V ؤ٠GN D t 3.6 ß PIN5 ÙM 2V èPIN7 ÙM GN D ÇÈ\Áæ<þ º V5 = 2V > V6 > V4 = V9 = V10 = V11 > V8 > V7 = GN D. MâZ¹ ¤ÙÚøÁæ<þm ÀVM ±t 3.8 R . R 0ý©¤: é R 0ýör ó%×ØÅþÁÒü 5ª A. B. A. 6= Rb 6= R1. (3.7). F I. 1. V5 = 2V > V6 > V4 > V9 = V10 > V11 > V8 > V7 = GN D. , I1 > 0. (3.8). V5 = 2V > V6 > V11 > V10 = V9 > V4 > V8 > V7 = GN D. , I1 < 0. (3.9). $. 3.8:. PIN5. PIN7 Lh 2V N GN D ijk R. àlJ @Áæñòâ 2V GN D ¤ÙÚ K ´£Î ¤ÙÚ;ÉØþÁæÙÚ é@ؤéê ëÝ`ìÁíÙÚ nPIN4 I < 0 $ PIN11 I > 0o 1. 1.
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