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אאאאאא ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] אאאא א א א א ٢٤١ ٢٤١
א ٢٤١ א א W ،،אא،א אאאאאאאאאא א א ،א אאאאאא ،אאאאאא א א א א א K אא א אאאאאאא א،אאא א، א،אאאא אאאאאאאאאאאאא אא،א אא،אא אאאאאא K ? אאאאאא ? ? א ? אא א K אאאאאאא ،א،אאאא אאאאא K ،אאאא K א אאאא
٢٤١ א א אאא אאאאאאא אאאאאא אאא אאאאאא אאאאאא אאאאאאאא א K אאאא אאא א א K אאא אא אא K K אאא אא אאאאאאא אאאאא אאאאא אאאא א K א א K אאאא אא W א ٤ W W אא אא אאאאאאא אאאאאאא אאאאאאא א K W W אא אא אאאא אאאא אאאאא K אאאא W W אא אא
٢٤١ א א אאאא אאאאאא אאאאאא אא K W W אאא אאא אאא אאאאאא אאאאאא אאאאא K אאא
אאאאאא ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] אאאא א א א א א ١
אא א א א א ٢٤١ W אא W אאאאא א • א א • אא א אאא • • א אאא • א • W W אא א אא Diode o אאא אאאא MOSFET BJT o IGBT o א o Thyristor o Triac o Diac o K אא UJT o אאא אאאא אאאאא אא،א W K אא Thyristor W אא ١٩٥٧ א א א אא semiconductors א General Electrics ١ - -
אא א א א א ٢٤١ ، אא א W א א אא K אא א Anode (A) KE J ١ F ١ Gate (G) Cathode (K) Gate ﺔﺑاﻮﺒﻟا (G) G Cathode دﻮﺛﺎﻜﻟا (K) Anode دﻮﻧﻷا (A) K A P N P N J١ J٢ J٣ א WE J ١ F ١ א K א Silicon Controlled Rectifier (SCR) אאאאאאא אאאאא K אא א K ON state W W א Reverse biased state א States of a thyristor אא אאא אאאאא אא W Forward biased state K א KE א F K W W אאא אא א אא Static Characteristic of a thyristor אאא א אא א א K א א אא E אא F א J١ • K אאא J٢ J٣ ٢ - -
אא א א א א ٢٤١ אאאאא אאאא Forward Blocking (off) state F OA ، K א Forward leakage current א אאא KEE J ٢ F ١ א אאאאאא א אאאא אאא אאאאא אאאאא אא אאא אאאאא א، אא J٢ Forward Breakdown Voltage אא א א KEE J ٢ F ١ א א On State F J٢ BC K אא אאאא K ‘IH’ Holding K current א אא אאאא אא אאא E F א א א א אא א • K J٣ J١ J٢ א א א Reverse leakage current א KEE J ٢ F ١ F OD אאאא Avalanche • אאאא א KEE J ٢ F ١ א F DE ٣ - -
אא א א א א ٢٤١ +IA C IG١>IG٠ IG٢>IG١ IG٠=٠ B IH A VRB -VAK +VAK O VFB D -IA E אאא WE J ٢ F ١ א W W אאא אאא Ideal characteristic of a thyristor א אא E אאאא אא OA א F KEE J ٣ F ١ א F א אא K אא א אא א K אאא OC א EE J ٣ F ١ א F KEE J ٣ F ١ א F א OB ٤ - -
אא א א א א ٢٤١ IA A VAK O B C אאא WE J ٣ F ١ א W W א א Methods of triggering a thyristor א،אאא אאאאא K אא W אאא Thermal and light triggering אאא K א Light Activated Silicon Controlled Rectifier א אא אאאא אא אאא K K (LASCR) ٥ - -
אא א א א א ٢٤١ W אא אא High voltage triggering אאאא אאא אאאא K אאא א K dv W אאא אאא triggering dt אא K dv א אאאאאא אאאאאאאא אא dt אאא K ،אאא K ٢٠٠ ٢٠ א W אא אא Gate triggering אא E אאאא F אא ٥٠ ٠{١ אא אא K א W W אא אא Firing circuits of a thyristor אאא אאא ،א אאאאאא אאאאאא W ،א א • • K • W א אאא אא • • ٦ - -
אא א א א א ٢٤١ אא אא • W E אאא א אא אאא F ١ Rg א Rg K DC firing circuits אאא אאא אאאא אאאאאאא אאאא אאאאא אא ، J ٤ D K Eg אא SW א אא אאא K K א K א K אאאא אאא אאא WE J ٤ F ١ א W אאא אאא AC firing circuits אאאאאא F ١ אאאאאא אאא אאא אאאאאאאאא אאאאא א D אא א E J ٥ א K אאא א R٢ R١ K אא אאא R٢ K Rg R٢ ٩٠ K K ٧ - -
אא א א א א ٢٤١ אאא WE J ٥ F ١ א אא א א W Pulse triggering circuits אאאאאא אא،אא Pulse transformers K אאא אאא אאא K א א א E J ٦ F ١ א R١ R١ אא אאאא אאא א א C Q١ K א Vp K א Q٢ R٢ ٨ - -
אא א א א א ٢٤١ אא WE J ٦ F ١ א א אא א W W Thyristor protection אאאאאא אאאא אאאאא J ٧ K א א א אא אאא E F ١ א K אא W א • אאא אא K אאאא אאא،א Fuse K אא אאאאאאאא אא • K אא Snubber circuit אא K אאאא אאאאא • א ٩ - -
אא א א א א ٢٤١ אא WE J ٧ F ١ א W א Triac א אא אא אאא אאאאא G KE J ٨ F ١ T٢ T١ Terminal (T١) فﺮﻄﻟا ) أ ( Gate ﺔﺑاﻮﺒﻟا (G) G N N P G١ N A١ K١ P N T٢ T١ G٢ Terminal (T٢) فﺮﻄﻟا K٢ A٢ ج ( ) ( ب ) אאא E F א E F א F E א WE J ٨ F ١ א ١٠ - -
אא א א א א ٢٤١ א א K אאאאא א • אא א אא W א א א T٢ K א T١ K א G T٢ T١ T٢ T١ א T٢ א א א • T١ T٢ T١ G א אאאאא א K א K אאא א אאאאא אא KE J ٩ F ١ א I IG١>IG٠ IG٢>IG١ IG٠=٠ IH -VB V VB O אא WE J ٩ F ١ א ١١ - -
אא א א א א ٢٤١ W א Diac W אאאאא א א א א א א ١٠ א • T٢ T١ T٢ T١ א א א א • T١ T٢ T١ T٢ K א אאא K א E J F ١ א T٢ T١ ) أ ( N Terminal Terminal N P P (T٢) فﺮﻄﻟا (T١) فﺮﻄﻟا N ( ب ) א E F א F E א WE ١٠ J F ١ א אא אאאא E ١١ אאאא א אאא J F ١ K אא IG K ١٢ - -
אא א א א א ٢٤١ I IBR V O VB٠ אא WE ١١ J F ١ א ١٣ - -
אא א א א א ٢٤١ W ؟א J ١ J ٢ J ٣ J ٤ J ٥ J ٦ J ٧ J ٨ J ٩ ١٠ ١١ ١٢ ١٣ ١ ١ ١ ١ ١ ١ ١ ١ ١ ١ ١ ١ ١ ؟אאא ؟אאא ؟אאא ؟אאא ؟אא אאאאאא אאא אאאא ؟ אאא ؟ ؟א ؟ א T٢ T١ J J J J ؟ א T٢ T١ ١٤ - -
אאאאאא ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] אאאא א א אאאאא אאאאא אאאאא ٢
אא א א ٢٤١ אאאאא א W אא אאאאאאא אא אאאא אאא W • • אאאא • W אאאאאאאא אא (R-L) K אאא א אא אא K אא Vm (R) א K אאאאא Vm אאא אאא א WE F אאא אאא אא (Thyristor) E F (SCR) W אאאאא אאאאא ١ K K א אא א א א אא א א א ٢ K ٢π אא E J ١ F ٢ א ٢π K אא - ١٥ -
אא א א ٢٤١ אאאאא א Ig Ig ωt ωt α ٢π+α α ٢π+α E F F E א E FW אאא אא WE J ١ F ٢ א K E F אא אאאא Single-Phase Half-Wave Controlled Rectifiers with a resistive load א אאאאאא אאא אאא א א K E J ٢ F ٢ א R E F אאאאא א א אא E F א to E Vo F E J ٣ F ٢ א א אא R E F E F to K אא אאאאאאא אאאאא אאאאא אאאאאא א E Z F π א to 'R' אא 'R' אא אא K א א E J ٣ F ٢ Z ٢π to - ١٦ -
אא א א ٢٤١ אאאאא א אאא אאאאא ⎧ = ω , 0 אאאאא אאאאא א E א F א 'io' 'vo' W 'vT' < < / t t 0 V , 0 t 0 ⎪⎨ < < π ω / V t t sin , m 0 0 ⎪⎩ π < < π 2 ω w t / אא ٠ to א אא אא α ωto to γ K אא א π ωto 'R' K א WE J ٢ F ٢ א - ١٧ -
אא א א ٢٤١ אאאאא א KE J ٢ F ٢ אאאא WE J ٣ F ٢ א אאא אאא W W Average load voltage and current W E J ٢ F ٢ J ١ E אאאאאאאא V F ٢ ،אאאאא אאאא F ٢ א =V + α m .( 1 cos ) π o avg ( ) 2 K אא α Vm W V J ٢ E J ١ avg ( 0 ) I = o avg J ٢ ( ) R J F ٢ א E F ٢ E F ٢ א WE ٢ V J ٣ E אאאאאא F ٢ F ٢ I = + α m .( 1 cos ) π o avg ( ) R 2 W 'Im' =I J ٤ E I + α m .( 1 cos ) π o avg ( ) 2 - ١٨ -
אא א א ٢٤١ אאאאא א K א אא Vm/R Im אאא אאא R.M.S. value of the load voltage and current E J ٢ F ٢ אאאאאאאא W =V α+ α sin 2 J ٥ E אאאאאא I F ٢ אאאאאא E F ٢ V − m . 1 ( ) π π o rms ( ) 2 2 W =I α+ α sin 2 J ٦ E − m . 1 ( ) π π o rms ( ) 2 2 א F אא א E E F א אא α α K F α א אא א V אאא (Vdo) W E J ١ F ٢ E F ٠ Z α Vdo V J ٧ E F ٢ do= m π אא א Vo אאאא K אאא אא אא (Power Factor) אא א F ٢ אאאאאאא אא אאא א 'PF' W 'S' 'P' P J ٨ E PF = S R P I rms V I s rms J ٩ E ١٠ F ٢ F ٢ 2 = E J S = - ١٩ -
אא א א ٢٤١ אאאאא א E ١٠ J F ٢ E J ٩ F ٢ אא אאאא I PF = W E J ٨ F ٢ א rmsR E ١١ J F ٢ V s אאאאא א F ٢ J W E ١١ J ٢ F E J ٦ F ٢ א 1 π 'R' α+ α sin 2 E ١٢ = − PF .( 1 ) π 2 2 J ١ W J ١ W ٢ ٢ אא אאא ١٢٠ ، אאא אאא K ١٠Ω 'Vo' V W א F E ٩٠o E 'PL' α = ٠o α = ١٣٥o F E F E α = ٤٥o α = E F F α = ١٨٠o W W א א W =V V m א אאאא 7 . 169 2 120 = = V אא 'Vm' 2 s J F ٢ E J ١ F ٢ אא 'PL' 'Vo(avg)' W E ٩ =V V α + m .( 1 cos ) π o avg ( ) P 2 = 2 I R α = ٠o L rms אא V V I rms o P L W אא = V F E 169 7 . π sin = + o .( 1 cos 0 ) 54 o avg ( ) 2 α α 2 169 7 . A = − + = − = m . 1 ( ) 1 0 . 8 485 π 2 π . 8 ( ) R 2 2 = 20 10 W I = = 2 R 485 . 720 o rms ( ) - ٢٠ -
אא א א ٢٤١ אאאאא א W + א = א V E F α = ٤٥o 169 7 . π V = o .( 1 cos 45 ) 46 1 . o avg ( ) 2 . π 0 169 7 . 45 1 π = W + sin 90 π A I = − + = . 1 . . 8 09 o rms ( ) 20 ∴PL 180 . 09 7 . π 2 55 W אא = V = 2 . 8 10 654 α = ٩٠o . E F 169 V = o .( 1 cos 90 ) 27 o avg ( ) 2 . π 0 169 7 . 90 1 π 360 = :α = ١٣٥o sin 180 π A I = − + = . 1 . 6 o rms ( ) 20 ∴PL 180 10 . 62 + 2 W = אא = V F E 169 7 . π V = o .( 1 cos 135 ) . 7 91 o avg ( ) 2 . π 0 169 7 . 135 1 π sin 270 π W אא = V A I = − + = . 1 . . 2 56 o rms ( ) 20 180 56 . 2 2 ∴PL = = 2 . 10 α = ١٨٠o W + 65 4 . E F 169 7 . π V = o .( 1 cos 180 ) 0 o avg ( ) 2 . π 0 169 7 . 180 1 π W sin 360 π A I = − + = . 1 . 0 o rms ( ) 20 180 2 ∴PL = 0 א א אאאאא אא א 'α' W ٤٥o ٤٦{١ ٦٥٤{٦ ٩٠o ٢٧ ٣٦٠ ١٣٥o ٧{٩١ ٦٥{٤ ١٨٠o ٠ ٠ ٠ ٥٤ ٧٢٠ α Vo(avg) V PL W - ٢١ -
אא א א ٢٤١ אאאאא א J ٢ W J ٢ W ٢ ٢ אא אאא ١٢٠ ‘α’ אאא K ١٠Ω V W ، J J א J ٦٠o K אאאאא אאא 'PL' K 'PF' W W א W 120 אאא 'Im' V 2 A I = = = m 16 97 . m R 10 W אא R J 2 P I = L rms =I α+ α sin 2 I − m . 1 ( ) Q π π o rms ( ) 2 2 2 I α α π 2 sin 2 16 . 97 60 π sin 120 π m W PL ∴ = − + = − + = R . .( 1 ) . 10 .( 1 . 579 π π J 4 2 4 180 ' PF' 2 W E ١٢ F ٢ אא 1 π sin 180 א J α+ α sin 2 = − PF .( 1 ) Q π 2 2 π 1 60 π 120 π Lag. ∴ = − + = PF .( 1 . ) . 634 2 2 J ٣ W J ٣ W ٢ ٢ ١٥٠ V אא אאא W ، אאא אאא אאא אאא אאא 'γ' K K J J J J J J ٣٠o ١٠Ω 'Im' K 'Vo(avg)' K 'Io(rms)' K 'PL' K ٦٠ Hz 'α' K 'Io(avg)' אא - ٢٢ -
אא א א ٢٤١ אאאאא א א אא K J J 'fo' K 'PF' W W א א 2 אאא V אאא J 'Vm' V =V = = 2 150 212 m s J ‘Im’ V 212= A I = = m 21 2 . m R 10 אאא J ‘Vo(avg)’ V 212 π V V = + = + = α 0 m .( 1 cos ) .( 1 cos 30 ) 63 π o avg ( ) 2 2 אאא J ‘Io(avg)’ V 63 A o avg I ( ) = = = 3 . 6 o avg ( ) R 10 אאא J ‘Io(rms)' I α α π o 30 π אאא 1092 W o o o 150 30 180 = − א אא 60 = = f f s o Hz 'PF' sin 2 21 2 . sin 60 π A I = − + = − + = m . 1 ( ) . 1 . 10 . 45 Q π π o rms ( ) 2 2 2 180 2 J 'PL' 2 P I = = = 2 R α 10 45 . 10 . L rms אא J 'R' = 'γ' γ = − o 180 אאאא אא E F א J ٣ W KE F ٢ 'fo' אא J α+ α 1 sin 2 = − PF .( 1 ) Q π π 2 2 π 1 30 π sin 60 π Lag. ∴ = − + = PF .( 1 . ) 7 . 0 2 180 2 - ٢٣ -
אא א א ٢٤١ אאאאא א אאאא Single-Phase Half-Wave Controlled Rectifiers with an Inductive Load 'R-L' א אא E J ٤ א א F ٢ א E J ٥ F ٢ 'vo' 'vs' ‘R-L’ א K אאאא 'vT' 'io' א WE J ٤ F ٢ א K 'R-L' W W אא אא W E J ٥ F ٢ אא אאא אאאאא אאא אא ⎠ ⎝ ⎠ ⎝ R אאאאא אאא אא אאאאאא אאאאאא E F 'vs' א ’α’ ωt = α א א אא ⎛ ⎞ ⎛ ⎞ ωL − 'α' ⎜⎜ ⎟⎟ = 1 ⎜ ⎟ Φ tan אא אא K (Extinction angle) 'β' ١٨٠o - ٢٤ -
אא א א ٢٤١ אאאאא א אאאאאא אאא אאאא א אאא אא א אאא אאא אא א א π < ωt < β K α < ωt <β J ٥ 'R' ١٨٠o 'β' 'vT' E F ٢ K J ٤ E F ٢ אאאא WE J ٥ F ٢ א W W אאא אאא אאאאאאאא W E J ٤ F ٢ =V E ١٣ J F ٢ V α − β m .(cos cos ) π o avg ( ) 2 W אאאא - ٢٥ -
אא א א ٢٤١ אאאאא א V V E ١٤ J F ٢ o avg ( ) I = = α − β m .(cos cos ) π o avg ( ) R אא R 2 W אא ' β' α tan − β ) ( φ β − α = α − φ e sin( ) sin( ). W אא α ⎛ ⎞ ω ⎛ ⎞ L K אאאא Φ − ⎜⎜ ⎝ Φ = ⎟⎟ ⎠ 1 ⎜ ⎝ ⎟ ⎠ tan R א א א א E J ٦ F ٢ א אא אא אא אא אאא אאא ' β' J F ٢ Φ = ٩٠o 'γ' K א α Φ β 'Φ' 'α' K E (β = γ + α) β ٦ Φ = ٠o 'R' K (L) W W W א אא א אא אא K א אאאאא אאאאאא אאאאא אאאאאאא 'α' W • W אא אא • 'β' K אא אאאאא W W אא א אא K • 'γ' - ٢٦ -
אא א א ٢٤١ אאאאא א אא א אא 'Φ' E J ٦ F ٢ א 'β' 'α' א אאאאא Single-Phase Half-Wave Controlled Rectifiers with an Inductive Load and a Free- Wheeling Diode אאאאאא אאאא אאא (Free-wheeling diode) K א אאא א אאא אאאאאאאאאאא E J ٧ א F ٢ א א אאאא ‘R-L’ - ٢٧ -
אא א א ٢٤١ אאאאא א אאאאאאאא א אא (Short-circuit) KE J ٧ F ٢ K א א א E J ٧ F ٢ א 'R-L' W W אא אא אאא אא אאאאא 'α' אאא F ٢ אאאא אאא אאא אא α < ωt < π אא אאאא א אאאאא אא E J ٧ F ٢ אאא K E J ٨ F ٢ אא אא אאא KE J ٨ א ٠ < ωt < α א אא ωt = α 'α' K אאא π < ωt < β אאאאא א α α < ωt < β 'β' אאא ، <ωt < π אא 'R-L' 'vs' vo = vs 'vs' 'vo' E J ٨ F ٢ א K א א ωt = π - ٢٨ -
אא א א ٢٤١ אאאאא א אאאאאא אאא אאאא אאאאאאאאא אא א F E אא π < ωt < β אא אאא אאא אא K אאאאא אאאא J ٧ E F ٢ אאאא WE J ٨ F ٢ א - ٢٩ -
אא א א ٢٤١ אאאאא א W W אאאא אאאא אאאאא א אאאא אאאאאא W אא אא 'vo' K א א K א ، J ١ E F ٢ אאאאאא W E J ٣ F ٢ =V V V + α m .( 1 cos ) π o avg ( ) 2 I = + α m .( 1 cos ) π o avg ( ) R 2 J ٤ W J ٤ W ٢ ٢ א א אא، ١٥٠ V א א א אאא אא K א ١٠Ω K א ١٠Ω ٦٠ Hz 'ωL' 'R' א ٣٠o K W W א א W אאאא V o א =V + α m .( 1 cos ) π avg ( ) 2 V I = + α m .( 1 cos ) π o avg ( ) R 2 אא 150 2 V V = + = o .( 1 cos 30 ) 63 π o avg ( ) 2 63 A I = = 3 . 6 o avg ( ) 10 - ٣٠ -
אא א א ٢٤١ אאאאא א א א Single Phase Full-Wave Controlled Rectifier אא א אא Resistive Load אא،אא R ’ . אא E J ٩ F ٢ ٤ ‘ א ’ א ’ Vs J ٩ KE F ٢ א אא WE J ٩ F ٢ א K 'R' W אאאאא אאאאא ‘ אא אאאאאא אאאאאא א π≤ωt ≤٢π א Pulse Transformer ’ אאא ‘ ’ T١, T٢ ‘ אאא אאא ’ T٣,T٤ K ٠≤ωt ≤π T٣ אאא T٢ T٤ T١ א ‘ Opto-Coupler ’ K - ٣١ -
אא א א ٢٤١ אאאאא א W אא אאא א ‘ אא א אאאאאא Vo אא אא אא אאא אא אאא א אאאא ‘ א אא א א ‘ ’ א א א אאאאאא ‘ ’ אא אאאאאאא א אא ‘ ’ אאאאא ‘ אאאאא א אאא E J ٩ T١ ٠≤ωt ≤π ’ F ٢ א KE ١٠ J F ٢ α ’ T٤ אא T١,T٤ vs א אא ‘ ’ ’ אאא אאאא א אא א אא ‘ T٤ R T١ K E F R T٢,T٣ α + π א ١٨٠o T٣ R T٢ אא אא T٢,T٣ T٤,T١ א vAK is ’ T٢ אא א T٤ T١ T٣ אא K א ‘ io ’ π K א - ٣٢ -
אא א א ٢٤١ אאאאא א אאאא WE ١٠ J F ٢ א K 'R' W אאא אא J ٢ אאאאאא אאאאא אאאאא V avg o אאאאא E J ٩ F ٢ E F ٢ W =V E ١٥ J F ٢ + α m .( 1 cos ) π ( ) W - ٣٣ -
אא א א ٢٤١ אאאאא א V V E ١٦ J F ٢ I o avg ( ) α = = + m .( 1 cos ) π ١٦ =I o avg ( ) R R W E J F ٢ א E ١٧ J F ٢ I + α m .( 1 cos ) π o avg ( ) W אאאאא אאאאא אאאא V I m Vm Vs W אא F ٢ Im Im V 2 E ١٨ J = = m s R R W אאא אאאאאאאא W E J ٩ F ٢ =V α+ α sin 2 E ١٩ J F ٢ V − m . 1 ( ) π π o rms ( ) 2 2 W אאאאאא I rms o =I α+ α sin 2 E ٢٠ J F ٢ − m . 1 ( ) π π ( ) 2 2 J ٥ W J ٥ W ٢ ٢ א ‘ ’ א אא K אא א ١٠Ω ٦٠ Hz ، ١٥٠V R W ٣٠o K אאא אאא אא ‘ אאא אאא א אא J J J J J J J ‘Vo(avg)’ K ‘Io(avg)’ ’ K 'Io(rms)' K 'PL' Im K K 'fo' K 'PF' - ٣٤ -
אא א א ٢٤١ אאאאא א W W א א W אאאא =V V avg o J + α m .( 1 cos ) π ( ) 150 2 V V ∴ = + = o .( 1 cos 30 ) 126 π o avg ( ) אאא 126 ) ( ) ( R I אאא 2 150 = = = R I אאא 2 . 21 ) 2 2 π π אאא 10 . 77 . 14 = = = R I P orms L אאאא 60 .( 2 2 = = ∴ f fo אא I orms PF = W J V A o avg = = = 12 6 . o avg 10 W J V A m 21 2 . m 10 W J I α α π o sin 2 30 π sin 60 π A I = − + = − + = m . 1 ( . 1 . 14 77 . o rms ( ) 180 2 2 W J W 2 2 2182 J Hz = ) 120 אאא J ’ ‘ Io(rms) I = אאא ‘ Is ’ 2 R R orms V 14 V I 77 . orms .( s s 10 ) Lag. ∴PF = = . 0 98 150 אא א R-L ’ ‘ אאאא E ١١ J F ٢ K (R-L) - ٣٥ -
אא א א ٢٤١ אאאאא א אא WE ١١ J F ٢ א K 'R-L' W אא אא אאאא ωt = α + π א אא אאאא אא אא אאאאא א אאא ‘ ’ ‘ L ’ א א אא ’ א T٢,T٣ אאאאאא א אא ’ אאאאא אאאאא T١,T٤ אא אא ωt = α F ٢ E ١٢ J אאא K α ‘ vs T١,T٤ אאא ωt = π T٤ T١ א א vo R א vs א אא ‘ β ’ T١, T٤ π < ωt <β אא vo אא J אאא א אא אאאא א ωt = π + α T٢, T٣ אא אא א E ١٢ F ٢ K א vs א ‘ T٢ - ٣٦ -
אא א א ٢٤١ אאאאא א אאא אאא אאא אאאאא אאאאאאא אאאא אא אאא ‘ א ‘ β ’ אאא אא T٣ אא ωt = π + β אאא ‘ ’ ωL אאאא K E ١٣ J F ٢ ، E E ١٢ ١٢ J J F ٢ F ٢ ١٨٠o א is ’ אא E ١٣ J F ٢ ٣٦٠o π + α K אאאא K WE ١٢ J F ٢ א 'R-L' - ٣٧ -
אא א א ٢٤١ אאאאא א א אאא א WE ١٣ J F ٢ א K W אאא אא אאאאאא אאא V avg o אאאאאאאא א W E אאא =V F E ١١ J F ٢ E ٢١ J F ٢ α − β m .(cos cos ) π ( ) א E אאא F אאא אא 2 ) ( V V m avg o אאא E ١١ J F ٢ W E ٢٢ J F ٢ = α . cos π Vo(avg)/R I o avg ( ) - ٣٨ -
אא א א ٢٤١ אאאאא א אאאא J אאאאאאא אאא אאא א אא אאא אאאא אאא אאאאאאאאא אא אאא אאא V I avg o W E E אאא F E ١١ J F ٢ א ٢٣ F ٢ = α − β m .(cos cos ) π ( ) R W ٢٤ J E אאא F E α ١١ J F ٢ א 2 R E F ٢ V ٢٢ I = . cos π E אא o avg ( ) m J F ٢ א א א א ٠ ٩٠o ٩٠o ١٨٠o (rectifier) (inverter) אאאא אא א (٢-Quadrant) K א W אאא VAK א א E F א T٢ א אאא א אאאאאא אאאאא V אא אא T٢ T١ אא T١ א W T٢ T١ vs E ٢٥ J F ٢ V V = + T s T 2 1 א V V T١ K אא vs T٢ T= 2 s - ٣٩ -
אא א א ٢٤١ אאאאא א J ٦ W J ٦ W ٢ ٢ א אא אאא א אא א ٢٠٠ V K ωL >> R ’ ٦٠ Hz ٢٣٠V ‘ .٠{٥Ω אא W א א א אאאאא ٢٢ ωL >> R W E J F ٢ 2 V V = α . cos π o avg m ( ) 2 ∴ 200 = α .( 230 2 ). cos π α α ∴ = ∴ = o cos . 0 966 15 J ٧ W J ٧ W ٢ ٢ א א ٣٠o ، א אא .١٠Ω אאא ωL >> R’ ٦٠ Hz ١٢٠V א J J J J J J J א J W א אאא אאא אאא ‘ אאא אאא אאא אא ‘ ’ K ’Vo(avg)’ K ’ K K 'Io(avg)’ Im 'Io(rms)' ’ K ‘ IoTh K 'PL' ’ K PF W W א אאאאא ‘ 170 2 120 2 = = s V אאא Vm ’ =V V m E א F J - ٤٠ -
אא א א ٢٤١ אאאאא א 2 π 2 π V V V = α = = o . cos 170 . . cos 30 94 o avg m ( ) אאא J V 94 A o avg I ( ) = = = 6 . 9 o avg ( ) R 10 אאאאאא J W א A I =I = 4 . 9 m o avg ( ) אאאאאא =I I orms ١٨٠o ’ אא א 1 = I I oTh W J A = 4 . 9 avg אא 4 . 9 ) A אאא 3 . 883 10 . 4 . 9 = W o ( ‘ ) J = = 7 . 4 o avg ( 2 2 J 2 P I = = 2 R L orms אאאאאא אאא 2 = I V orms s J W R I I R 94 Lag. = = = orms orms PF . 0 78 V 120 s W W א א אאא אאא אאא א אאאאאא אאאאא K אאאאא אאא אא אאאא אאאאא E ١١ J F ٢ E א F K א א E ١٤ J F ٢ א - ٤١ -
אא א א ٢٤١ אאאאא א אא א WE ١٤ J F ٢ א K א אא אא אאא אאא אאאא אא אאאאאאא אאאא אא אאא אאאא אאאאא אאא אא אאאא ‘ אאאאאא ‘ ’ אאא E ١٤ J F ٢ אאא E ١٥ ωL >> R ’ J א ‘ F ٢ W T١,T٤ א ‘ vs אאא T١ ωt = α אאא אא ωt = π א T٤ א אאא אא (α≤ωt ≤π) K ωt = π א אא א אא אא ωt+π אאאאא אא א אא (π≤ωt ≤π +α) אאאאאאאא is ’ T٢,T٣ - ٤٢ -
אא א א ٢٤١ אאאאא א vo = - vs ’ אא א אאא ‘ אאא אאאאא אאאא אאאאא F ٢ אאא אאאאאא אאא אאא T٣ T٢ אא אאאא אאא ωt = ٢π + α ωt = ٢π א א E ١٥ J א K א T١,T٤ K א א אא אאאא אא WE ١٥ J F ٢ א K א - ٤٣ -
אא א א ٢٤١ אאאאא א אאא א W W אאא אאאאא אאא אאא E ١٥ J F ٢ ، E ١٠ J F ٢ א F ٢ W EE ٢{١٥ F F =V E ٢٦ J V α + m .( 1 cos ) π o avg ( ) V V E ٢٧ J F ٢ o avg I ( ) α = = + m .( 1 cos ) π o avg ( ) R R אאאא אא אאא אא אא אאאא א א אא אא E ١٥ אא J F ٢ א אא א ٢π אא אאא α W אאא α π R I V α E ٢٨ J F ٢ I = = + α m . .( 1 cos ) π 2 D avg o avg ( ) ( ) J ٨ W J ٨ W ٢ ٢ א אא אאא א אא א ωL >> R ’ ، J J J J J J ٦٠ Hz ١٢٠V K א א ‘ ١٠Ω W ٣٠o אאא אאא אאא ‘ אאא אאאא אאא K 'Vo' 'Io(avg)' ’ K 'Iorms' K Im ’ K אא ‘ ID(avg) ’ K ‘ IoTh - ٤٤ -
