# HW_12 - ‫ﺻﻔﺤﻪ ۱‬ ‫ﺩﻭﻗﻄﺒﯽ...

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Unformatted text preview: ‫ﺻﻔﺤﻪ ۱‬ ‫ﺩﻭﻗﻄﺒﯽ ﻫﺎ‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻳﺎﺯﺩﻫﻢ‬ ‫١ ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Z‬ﺩﻭ ﻗﻄﺒﻲﻫﺎﻱ ﺷﻜﻞ ﺍﻟﻒ ﺗﺎ ﺕ ﺯﻳﺮ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ. ﺩﺭ ﭼﻪ ﺻﻮﺭﺗﻲ ﺩﻭﻗﻄﺒﻲ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Z‬ﻧﺪﺍﺭﺩ؟ )ﭘﺎﺳﺦ ﻛﻠﻲ‬ ‫ﺑﮕﻮﺋﻴﺪ(.‬ ‫‪1H‬‬ ‫1‪I‬‬ ‫‪2H‬‬ ‫+‬ ‫1‪V‬‬ ‫−‬ ‫‪3Ω‬‬ ‫2‪I‬‬ ‫‪3Ω‬‬ ‫‪1F‬‬ ‫+‬ ‫1‬ ‫‪F‬‬ ‫2‪V‬‬ ‫2‬ ‫−‬ ‫‪3Ω‬‬ ‫‪2F‬‬ ‫‪1Ω‬‬ ‫ﺏ‬ ‫ﺍﻟﻒ‬ ‫1‪2v‬‬ ‫1‪i‬‬ ‫2‪2i‬‬ ‫‪2H‬‬ ‫2‪i‬‬ ‫1‪3i‬‬ ‫+‬ ‫1‪v‬‬ ‫−‬ ‫‪i‬‬ ‫‪2Ω‬‬ ‫‪1Ω‬‬ ‫‪2i‬‬ ‫ﺕ‬ ‫ﭖ‬ ‫٢‐ ﺍﻟﻒ‐ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ‪Y‬ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺯﻳﺮﻳﻦ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ. ﺩﺭ ﭼﻪ ﺻﻮﺭﺗﻲ ﻳﻚ ﺩﻭﻗﻄﺒﻲ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Y‬ﻧﺪﺍﺭﺩ؟ )ﭘﺎﺳﺦ ﻛﻠﻲ ﺑﮕﻮﺋﻴﺪ(.‬ ‫ﺏ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Y‬ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﻣﺴﺌﻠﻪ ١ ﻭ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Z‬ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺯﻳﺮ ﺭﺍ ﻫﻢ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫1‪3v‬‬ ‫+‬ ‫1‪v‬‬ ‫−‬ ‫−‬ ‫‪1Ω‬‬ ‫‪1Ω‬‬ ‫‪1F‬‬ ‫‪1Ω‬‬ ‫‪1H‬‬ ‫‪1Ω‬‬ ‫‪i‬‬ ‫‪2i‬‬ ‫‪1Ω‬‬ ‫‪1H‬‬ ‫ﭖ‬ ‫1‪i‬‬ ‫‪1Ω‬‬ ‫‪1H‬‬ ‫1‪3i‬‬ ‫‪1Ω‬‬ ‫ﺏ‬ ‫‪3Ω‬‬ ‫‪2H‬‬ ‫‪3Ω‬‬ ‫‪3Ω‬‬ ‫1‬ ‫‪F‬‬ ‫2‬ ‫ﺍﻟﻒ‬ ‫‪2Ω‬‬ ‫ﺙ‬ ‫1‪I‬‬ ‫−‬ ‫‪Za‬‬ ‫‪Zb‬‬ ‫‪Zc‬‬ ‫2‪I‬‬ ‫2‪(z12 − z21)I‬‬ ‫ﺕ‬ ‫٣‐ ﺍﻟﻒ‐ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﻳﻚ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ‪ T‬ﺑﺮﺍﻱ ﺩﻭﻗﻄﺒﻲ ﻣﺸﺨﺺ ﺷﺪﻩ ﺍﺳﺖ‬ ‫)ﺍﻣﭙﺪﺍﻧﺲﻫﺎﻱ ‪ Z c , Z b , Z a‬ﺭﺍ ﺑﺮ ﺣﺴﺐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ 11‪z 22 , z 21, z12 , z‬‬ ‫ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫ﺻﻔﺤﻪ ۲‬ ‫1‪I‬‬ ‫+‬ ‫1‪V‬‬ ‫−‬ ‫ﺩﻭﻗﻄﺒﯽ ﻫﺎ‬ ‫2‪I‬‬ ‫‪YB‬‬ ‫‪YC‬‬ ‫‪YA‬‬ ‫+‬ ‫2‪V‬‬ ‫−‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻳﺎﺯﺩﻫﻢ‬ ‫ﺏ‐ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﻳﻚ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ‪ π‬ﺑﺮﺍﻱ ﺩﻭﻗﻄﺒﻲ ﻣﺸﺨﺺ ﺷﺪﻩ ﺍﺳﺖ.‬ ‫ﺍﺩﻣﻴﺘﺎﻧﺲﻫﺎﻱ ‪ YC , YB , YA‬ﺭﺍ ﺑﺮ ﺣﺴﺐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ 11‪Y22 , Y21, Y12 , Y‬‬ ‫ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫2‪(Y12 − Y21)V‬‬ ‫ﭖ‐ ﺩﺭ ﺻﻮﺭﺗﻴﻜﻪ ﺩﻭﻗﻄﺒﻲﻫﺎ ‪ N R‬ﺑﺎﺷﻨﺪ، ﺭﺍﺑﻄﻪ ﺍﻣﭙﺪﺍﻧﺲﻫﺎﻱ ‪ Z c , Z b , Za‬ﻭ ﺍﺩﻣﻴﺘﺎﻧﺲﻫﺎﻱ ‪ YC , YB , YA‬ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ‬ ‫)ﺍﻳﻦ ﺭﻭﺍﺑﻂ ﺑﻪ ﺗﺒﺪﻳﻞﻫﺎﻱ ﺳﺘﺎﺭﻩ – ﻣﺜﻠﺚ ﻣﻌﺮﻭﻑ ﻫﺴﺘﻨﺪ(.‬ ‫٤‐ ﺍﻟﻒ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ H‬ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺏ ﻣﺴﺌﻠﻪ ١ ﻭ ﺍﻟﻒ ﻣﺴﺌﻠﻪ ٢ ﺭﺍ ﻣﺸﺨﺺ ﻛﻨﻴﺪ.‬ ‫ﺏ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ H‬ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺯﻳﺮ ﺭﺍ ﻣﺸﺨﺺ ﻛﻨﻴﺪ. ﺁﻳﺎ ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﻓﺎﻗﺪ ﻣﻨﺎﺑﻊ ﻭﺍﺑﺴﺘﻪ ﻫﻤﻴﺸﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ H‬ﺩﺍﺭﻧﺪ؟‬ ‫)ﺍﺳﺘﺪﻻﻝ ﻧﻤﺎﺋﻴﺪ(. ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺷﺎﻣﻞ ﻣﻨﺎﺑﻊ ﻭﺍﺑﺴﺘﻪ ﭼﻄﻮﺭ؟ ﺍﺳﺘﺪﻻﻝ ﺧﻮﺩ ﺭﺍ ﺑﻴﺎﻥ ﻧﻤﺎﺋﻴﺪ.‬ ‫‪αI‬ ‫1‪1 I‬‬ ‫1‬ ‫2 2‪I‬‬ ‫‪1 I1 2Ω‬‬ ‫−‬ ‫‪1Ω‬‬ ‫'1‬ ‫2 ‪βI‬‬ ‫2‪3V‬‬ ‫1‪4I‬‬ ‫'2‬ ‫2‬ ‫+‬ ‫1‬ ‫‪3Ω‬‬ ‫2‬ ‫‪1F‬‬ ‫‪1Ω‬‬ ‫2‪V‬‬ ‫−‬ ‫‪1Ω‬‬ ‫'1‬ ‫‪2H‬‬ ‫1‬ ‫ﭖ‬ ‫+‬ ‫‪V 1Ω‬‬ ‫−‬ ‫‪αI‬‬ ‫‪1Ω‬‬ ‫‪I‬‬ ‫'1‬ ‫'2‬ ‫'2‬ ‫2‬ ‫ﺏ‬ ‫1‬ ‫1‪I‬‬ ‫2‬ ‫+‬ ‫2‪2V‬‬ ‫1‪3 I‬‬ ‫‪1Ω‬‬ ‫‪1F‬‬ ‫ﺍﻟﻒ‬ ‫‪µV‬‬ ‫'1‬ ‫2‪V‬‬ ‫−‬ ‫'2‬ ‫'1‬ ‫‪2H‬‬ ‫'2‬ ‫ﺕ‬ ‫٥ ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ﺩﻭﻗﻄﺒﻲﻫﺎﻱ ﺍﻟﻒ ﺗﺎ ﺙ ﺑﺎﻻ )ﻣﺴﺌﻠﻪ ٤( ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫ﭼﻪ ﺭﺍﺑﻄﻪﺍﻱ ﺑﻴﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ‪ D,C,B,A‬ﺑﺮﻗﺮﺍﺭ ﺑﺎﺷﺪ ﺗﺎ ﺩﻭﻗﻄﺒﻲ ﻣﺘﻘﺎﺑﻞ ﺑﺎﺷﺪ؟ ﺩﺭ ﺷﻜﻞ ﺙ ﺭﺍﺑﻄﻪ ﺑﻴﻦ ‪ α‬ﻭ ‪ μ‬ﺑﺮﺍﻱ ‪NR‬‬ ‫ﺑﻮﺩﻥ ﭼﻴﺴﺖ؟‬ ‫٦‐ ﺩﻭﻗﻄﺒﻲﻫﺎﻱ 1‪ N2, N‬ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﺑﺎ ﺭﻭﺍﺑﻂ ﺯﻳﺮ ﺩﺭ ﺳﺮﻫﺎ‬ ‫1: ‪n‬‬ ‫ﻣﺸﺨﺺ ﻣﻲﺷﻮﻧﺪ:‬ ‫‪N‬‬ ‫1‬ ‫1‬ ‫⎧‬ ‫⎧‬ ‫2‪N‬‬ ‫‪N‬‬ ‫2‪V1 = −3 I 2 − V‬‬ ‫2‪I 2 = − I 1 − V‬‬ ‫2‬ ‫1‬ ‫‪N‬‬ ‫ﺙ‬ ‫⎪‬ ‫⎪‬ ‫⎪‬ ‫⎪‬ ‫2‬ ‫2‬ ‫⎨ : 1‪N‬‬ ‫⎨ : 2‪N‬‬ ‫‪⎪V = 1 I − 4 I‬‬ ‫‪⎪V = 3 I − I‬‬ ‫23 12 2⎪‬ ‫2 1 2 2⎪‬ ‫⎩‬ ‫⎩‬ ‫ﺍﻟﻒ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ﺩﻭﻗﻄﺒﻲ ‪ N‬ﺑﺎ ﻗﻄﺒﻬﺎﻱ )′1,1( ,)′2 ,2(‬ ‫ﭼﻴﺴﺖ ؟‬ ‫ﺻﻔﺤﻪ ۳‬ ‫ﺩﻭﻗﻄﺒﯽ ﻫﺎ‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻳﺎﺯﺩﻫﻢ‬ ‫ﺏ‐ ﺍﻣﭙﺪﺍﻧﺲ ﺑﺎﺭ ‪ Z L‬ﺭﺍ ﺑﻪ ﺳﺮ ﻫﺎﯼ )′2 ,2( ﺩﻭ ﻗﻄﺒﯽ ‪ N‬ﻭﺻﻞ ﻣﯽ ﮐﻨﻴﻢ . ﻧﺴﺒﺖ ﺗﺒﺪﻳﻞ ‪ n‬ﺭﺍ ﻃﻮﺭﻱ ﺗﻌﻴﻴﻦ ﻛﻨﻴﺪ ﻛﻪ ﺍﻣﭙﺪﺍﻧﺲ‬ ‫‪ Zin‬ﺩﺭ ﺳﺮﻫﺎﻱ )′1,1( ﺑﺮﺍﺑﺮ ‪ -ZL‬ﺷﻮﺩ. )ﺑﻪ ﺩﻭﻗﻄﺒﻲ ‪ N‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻳﻚ ﻣﺒﺪﻝ ﺍﻣﭙﺪﺍﻧﺲ ﻣﻨﻔﻲ ﻳﺎ ‪ NIC‬ﮔﻔﺘﻪ ﻣﻲﺷﻮﺩ.(‬ ‫‪αV‬‬ ‫1‪I‬‬ ‫‪2Ω V‬‬ ‫1‬ ‫‪F‬‬ ‫2‬ ‫+ ‪2H‬‬ ‫‪Vo‬‬ ‫− ‪4Ω‬‬ ‫٧‐ﺍﻟﻒ‐ ﻣﺎﺗﺮﻳﺲ ﺍﻧﺘﻘﺎﻝ ‪) T‬ﺑﺎ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ (D,C,B,A‬ﺩﻭﻗﻄﺒﻲ ﻣﻘﺎﺑﻞ ﺭﺍ ﻣﺸﺨﺺ‬ ‫ﻧﻤﺎﺋﻴﺪ.‬ ‫= )‪ Z T ( s‬ﻣﺴﺘﻘﻞ ﺍﺯ ﻓﺮﻛﺎﻧﺲ‬ ‫) ‪Vo ( s‬‬ ‫ﺏ‐ ‪ α‬ﭼﻘﺪﺭ ﺑﺎﺷﺪ ﺗﺎ ﺗﺎﺑﻊ ﺷﺒﻜﻪ ﺍﻧﺘﻘﺎﻟﻲ‬ ‫)‪I1 ( s‬‬ ‫ﻣﻲﺑﺎﺷﺪ؟‬ ‫‪2H‬‬ ‫‪2Ω‬‬ ‫1‬ ‫‪F‬‬ ‫2‬ ‫‪1H‬‬ ‫2 :1‬ ‫‪2F‬‬ ‫‪2Ω‬‬ ‫٨‐ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﻬﻢ ﭘﻴﻮﺳﺘﻦ ﺳﺮﻱ ﺩﻭﻗﻄﺒﻲﻫﺎ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Z‬ﺩﻭﻗﻄﺒﻲ ﺷﻜﻞ‬ ‫ﻣﻘﺎﺑﻞ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫1: 3‬ ‫1‬ ‫‪F‬‬ ‫4‬ ‫٩‐ ﺩﻭﻗﻄﺒﻲ ‪ N‬ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﺑﺎ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ h‬ﺗﻮﺻﻴﻒ ﺷﺪﻩ ﺍﺳﺖ.‬ ‫‪2Ω‬‬ ‫+‬ ‫−‬ ‫‪Vin‬‬ ‫2⎡‬ ‫⎢= ‪H‬‬ ‫4 −⎢‬ ‫⎣‬ ‫⎤1‬ ‫⎥1‬ ‫⎥2‬ ‫⎦‬ ‫1‬ ‫‪F‬‬ ‫2‬ ‫+‬ ‫‪Vo‬‬ ‫−‬ ‫= )‪ H V ( s‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﺋﻴﺪ‬ ‫‪Vo‬‬ ‫ﺗﺎﺑﻊ ﺍﻧﺘﻘﺎﻝ ﻭﻟﺘﺎﮊ‬ ‫‪Vin‬‬ ‫٠١‐ﺍﻟﻒ – ﺳﻪ ﺩﻭﻗﻄﺒﻲ 1‪ N3, N2, N‬ﺑﺎ ﻣﺎﺗﺮﻳﺲﻫﺎﻱ ﻫﺎﻳﺒﺮﻳﺪ 1‪ H3, H2, H‬ﺭﺍ ﭼﮕﻮﻧﻪ ﺑﻬﻢ ﻭﺻﻞ ﻛﻨﻴﻢ ﺗﺎ ﺩﻭﻗﻄﺒﻲ ﺣﺎﺻﻞ ﺍﺯ ﺍﺗﺼﺎﻝ‬ ‫1− ) 3 ‪ H = H1−1 + (H 2 + H‬ﺑﺸﻮﺩ؟‬ ‫‪⎛z‬‬ ‫⎞‪z‬‬ ‫[‬ ‫]‬ ‫1−‬ ‫ﺁﻧﻬﺎ ﺩﺍﺭﺍﻱ ﻣﺎﺗﺮﻳﺲ ‪ H‬ﺑﺮﺍﺑﺮ:‬ ‫ﺏ‐ ﺳﻪ ﺩﻭ ﻗﻄﺒﻲ ﻳﻜﺴﺎﻥ ‪ ، N‬ﻛﻪ ﻣﺎﺗﺮﻳﺲ ﺍﻣﭙﺪﺍﻧﺲ ﻫﺮ ﻳﻚ ﺍﺯ ﺁﻧﻬﺎ ⎟ 21 11 ⎜ = ‪ Z‬ﻭ ﻣﺎﺗﺮﻳﺲ ﻫﺎﻳﺒﺮﻳﺪ ﻫﺮ ﻛﺪﺍﻡ‬ ‫‪⎜z‬‬ ‫⎟‬ ‫⎠ 22‪⎝ 21 z‬‬ ‫11‬ ‫21‬ ‫⎜ = ‪ T‬ﺍﺳﺖ ﺭﺍﺑﺼﻮﺭﺕ ﺳﺮﻱ ﺑﻬﻢ ﻭﺻﻞ ﻣﻲﻧﻤﺎﺋﻴﻢ.ﻣﺎﺗﺮﻳﺲ ﺍﻣﭙﺪﺍﻧﺲ‬ ‫⎟ ‪ H = ⎜ h h‬ﻭ ﻣﺎﺗﺮﻳﺲ ﺍﻧﺘﻘﺎﻝ ﻫﺮ ﻛﺪﺍﻡ ⎟ ‪⎜ C D‬‬ ‫⎟‬ ‫⎜‬ ‫⎟‬ ‫⎝‬ ‫⎠‬ ‫⎠ 22 12 ⎝‬ ‫ﺩﻭﻗﻄﺒﻲ ﺣﺎﺻﻞ، ′‪ ، Z‬ﺭﺍ ﺑﺮﺣﺴﺐ ‪ Z‬ﻭﻣﺎﺗﺮﻳﺲ ﻫﺎﻳﺒﺮﻳﺪ ﺩﻭﻗﻄﺒﻲ ﺣﺎﺻﻞ، ′‪ ، H‬ﺭﺍﺑﺮﺣﺴﺐ ﺩﺭﺍﻳﻪﻫﺎﻱ ﻣﺎﺗﺮﻳﺲ ‪ H‬ﻭ ﻫﻤﭽﻨﻴﻦ‬ ‫ﻣﺎﺗﺮﻳﺲ ﺍﻧﺘﻘﺎﻝ ′‪ T‬ﺩﻭﻗﻄﺒﻲ ﺣﺎﺻﻞ ﺭﺍ ﺑﺮﺣﺴﺐ ﺩﺭﺍﻳﻪﻫﺎﻱ ﻣﺎﺗﺮﻳﺲ ﺍﻧﺘﻘﺎﻝ ‪ ،T‬ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫‪⎛A‬‬ ‫⎞‪B‬‬ ‫‪⎛h‬‬ ‫⎞‪h‬‬ ‫ﺻﻔﺤﻪ ۴‬ ‫1‬ ‫‪I‬‬ ‫2‬ ‫‪I‬‬ ‫‪1Ω‬‬ ‫ﺩﻭﻗﻄﺒﯽ ﻫﺎ‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻳﺎﺯﺩﻫﻢ‬ ‫‪a‬‬ ‫−‬ ‫1: 2‬ ‫‪1Ω‬‬ ‫‪b‬‬ ‫'‪a‬‬ ‫‪1 2Ω‬‬ ‫'1‬ ‫ﺍﻟﻒ‬ ‫‪N‬‬ ‫‪N‬‬ ‫ﺏ‬ ‫‪1F‬‬ ‫2‬ ‫'2‬ ‫١١‐ ﺍﻟﻒ – ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ﺩﻭﻗﻄﺒﻲ ‪ N‬ﺩﺭ ﺷﻜﻞ ﺍﻟﻒ ﻣﻘﺎﺑﻞ ﺭﺍ ﺑﻴﺎﺑﻴﺪ.‬ ‫ﺏ‐ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ Z‬ﺩﻭﻗﻄﺒﻲ ﺷﻜﻞ ﺏ ﻣﻘﺎﺑﻞ ﺭﺍ ﺑﻴﺎﺑﻴﺪ )‪ N‬ﺩﻭﻗﻄﺒﻲ ﺷﻜﻞ ﺍﻟﻒ ﺍﺳﺖ(.‬ ‫ﭖ‐ ﺧﺎﺯﻥ ﻳﻚ ﻓﺎﺭﺍﺩﻱ ﺭﺍ ﺑﻪ ﺳﺮﻫﺎﻱ )′2,2( ﺩﺭ ﺷﻜﻞ ﺏ ﻭﺻﻞ ﻣﻲﻛﻨﻴﻢ. ﺍﻣﭙﺪﺍﻧﺲ‬ ‫ﻭ ﺍﺩﻣﻴﺘﺎﻧﺲ ﻭﺭﻭﺩﻱ ﺩﺭ ﺳﺮﻫﺎﻱ )′1,1( ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﺋﻴﺪ.‬ ‫'‪b‬‬ ‫ﺕ‐ ﺳﻠﻒ ﻳﻚ ﻫﺎﻧﺮﯼ ﺭﺍ ﺑﻪ ﺗﻨﻬﺎﺋﻲ ﺑﻪ ﺳﺮﻫﺎﻱ )′2,2( ﺩﺭ ﺷﻜﻞ ﺏ ﻭﺻﻞ‬ ‫ﻣﻲﻛﻨﻴﻢ ﻭ ﻣﻨﺒﻊ ﻧﺎﺑﺴﺘﻪ ‪ Vs‬ﺭﺍ ﺑﻪ ﺳﺮﻫﺎﻱ )′1,1( ﻣﻲﺑﻨﺪﻳﻢ. ﻓﺮﻛﺎﻧﺲ ﻃﺒﻴﻌﻲ‬ ‫ﻣﺪﺍﺭ ﺣﺎﺻﻞ ﭼﻴﺴﺖ؟‬ ‫1:1‬ ‫1‪1 I‬‬ ‫+‬ ‫1‪V‬‬ ‫−‬ ‫'1‬ ‫‪N‬‬ ‫1:1‬ ‫⎞1 1 ⎛‬ ‫⎜ = ‪HN‬‬ ‫٢۱‐ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﺩﻭ ﻗﻄﺒﻲﻫﺎﻱ ‪ N‬ﺩﺍﺭﺍﻱ ﻣﺎﺗﺮﻳﺲ ﻫﺎﻳﺒﺮﻳﺪ ⎟ 2 1⎜‬ ‫⎟‬ ‫⎝‬ ‫⎠‬ ‫ﻣﻲﺑﺎﺷﻨﺪ . ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﺩﻣﻴﺘﺎﻧﺲ ‪ Y‬ﺩﻭ ﻗﻄﺒﻲ ﺑﺰﺭﮒ ﺷﻜﻞ ﺑﺎ ﻗﻄﺐ ﻫﺎﻱ 2 2 ‪I‬‬ ‫+‬ ‫)′1,1( ﻭ )′2,2( ﺭﺍ ﺑﻪ ﻫﺮ ﺭﻭﺷﻲ ﻛﻪ ﻣﻲﺩﺍﻧﻴﺪ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﺋﻴﺪ . ﭼﻨﺎﻧﭽﻪ‬ ‫ﻣﻘﺎﻭﻣﺖ ﻳﻚ ﺍﻫﻤﻲ ﺭﺍ ﺑﻪ ﺳﺮﻫﺎﻱ )′2 ,2( ﻭﺻﻞ ﻛﻨﻴﻢ، ﺍﻣﭙﺪﺍﻧﺲ ﺩﻳﺪﻩ ﺷﺪﻩ 2‪V‬‬ ‫ﺩﺭ ﺳﺮﻫﺎﻱ )′1,1( ﺑﻴﺎﺑﻴﺪ.‬ ‫−+‬ ‫'2‬ ‫‪N‬‬ ‫‪1Ω‬‬ ‫‪1F‬‬ ‫‪Vs 1Ω‬‬ ‫+‬ ‫−‬ ‫‪1Ω‬‬ ‫+‬ 2‪V‬‬ ‫−‬ ‫٣١‐ﻣﺎﺗﺮﻳﺲ ﺍﻧﺘﻘﺎﻝ ‪ T‬ﻳﺎ )‪ (A,B,C,D‬ﻫﺮ ﻳﻚ ﺍﺯ ﺩﻭﻗﻄﺒﻲﻫﺎ ‪ N‬ﺩﺭﺷﻜﻞ ﻣﻘﺎﺑﻞ‬ ‫‪N‬‬ ‫‪N‬‬ ‫= )‪ H ( s‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﺋﻴﺪ.‬ ‫⎞1 2 ⎛‬ ‫) ‪V2 ( s‬‬ ‫⎟ ⎜ = ‪ T‬ﻣﻲﺑﺎﺷﺪ. ﺗﺎﺑﻊ ﺷﺒﻜﻪ‬ ‫⎟1 1 ⎜‬ ‫) ‪Vs ( s‬‬ ‫⎝‬ ‫⎠‬ ‫‪3F‬‬ ‫+‬ ‫1‪V‬‬ ‫−‬ ‫‪N‬‬ ‫1‬ ‫+‬ ‫2‪V‬‬ ‫−‬ ‫‪2F‬‬ ‫٤١‐ﺍﻟﻒ – ﺩﺭ ﻣﺪﺍﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ 1‪ N‬ﺍﺯ ﻋﻨﺎﺻﺮ ﺧﻄﻲ ﻭ ﺗﻐﻴﻴﺮﻧﺎﭘﺬﻳﺮ ﺑﺎ ﺯﻣﺎﻥ ﻭ ﻣﻨﺎﺑﻊ‬ ‫ﻭﺍﺑﺴﺘﻪ ﺧﻄﻲ ﺗﺸﻜﻴﻞ ﻳﺎﻓﺘﻪ ﺍﺳﺖ ، ﻭ ﻣﻌﺎﺩﻻﺕ ﺣﺎﻟﺖ ﻣﺪﺍﺭ ﺑﻪ ﺻﻮﺭﺕ‬ ‫⎞ 1‪⎛ dv‬‬ ‫⎜‬ ‫⎞ ‪⎟ ⎛ 2 3⎞ ⎛ v‬‬ ‫⎟ 1 ⎜⎟‬ ‫⎜ = ⎟ ‪ ⎜ dt‬ﻣﻲﺑﺎﺷﺪ. ﻣﺎﺗﺮﻳﺲ ﺍﺩﻣﻴﺘﺎﻧﺲ ‪ Y‬ﺩﻭﻗﻄﺒﻲ 1‪ N‬ﺭﺍﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ.‬ ‫⎟ 2‪dv2 ⎟ ⎜ 3 5 ⎟ ⎜ v‬‬ ‫⎜‬ ‫⎠ ⎝⎠‬ ‫⎜‬ ‫⎝⎟‬ ‫⎠ ‪⎝ dt‬‬ ‫ﺏ‐ ﺧﺎﺯﻧﻬﺎ ﺭﺍ ﺑﻪ ﺳﻠﻔﻬﺎﺋﻲ ﺑﺎ ﻫﻤﺎﻥ ﻣﻘﺎﺩﻳﺮ )ﺑﻪ ﻫﺎﻧﺮﻱ( ﺗﺒﺪﻳﻞ ﻧﻤﺎﺋﻴﺪ ﻭ ﻣﻌﺎﺩﻻﺕ ﺣﺎﻟﺖ ﻣﺪﺍﺭ ﺟﺪﻳﺪ ﺭﺍ ﺑﻨﻮﻳﺴﻴﺪ.‬ ‫ﺻﻔﺤﻪ ۵‬ ‫ﺩﻭﻗﻄﺒﯽ ﻫﺎ‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻳﺎﺯﺩﻫﻢ‬ ‫٥١‐ ﺳﻪ ﻗﻄﺒﻲ ﻣﻘﺎﻭﻣﺘﻲ ‪ N‬ﺑﺎ ﻣﺎﺗﺮﻳﺲ ﻫﺎﻳﺒﺮﻳﺪ ‪ H‬ﺑﺎ ﺭﺍﺑﻄﺔ ‪ (v1 , i2 , i3 ) T = H .(i1 , v 2 , v3 ) T‬ﻣﺸﺨﺺ ﻣﻲﺷﻮﺩ:‬ ‫1‬ ‫+‬ ‫1‪v‬‬ ‫−‬ ‫'1‬ ‫1‪i‬‬ ‫2‪i‬‬ ‫2‬ ‫+‬ ‫ﺍﻟﻒ‐ ﺩﺭ ﻣﻮﺭﺩ ﻋﻼﻣﺖ )ﻣﺜﺒﺖ ﻳﺎ ﻣﻨﻔﻲ ﺑﻮﺩﻥ( ﻭ ﺭﻭﺍﺑﻂ ﺑﻴﻦ ﺩﺭﺍﻳﻪﻫﺎﻱ 31‪v2 h23, h32, h31, h‬‬ ‫'2 −‬ ‫11‪ h22, h21, h12, h‬ﻭ 33‪ h‬ﭼﻪ ﻣﻲﺩﺍﻧﻴﺪ؟ )ﺍﺯﭘﺴﻴﻮ ﺑﻮﺩﻥ ﻣﻘﺎﻭﻣﺖﻫﺎﻭﻗﻀﻴﻪ ﻫﻢ ﭘﺎﺳﺨﻲ‬ ‫‪N‬‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﺎﺋﻴﺪ(‬ ‫ﺏ‐ ﺳﻠﻒ ‪ L1=2H‬ﻭ ﺧﺎﺯﻧﻬﺎﻱ ‪ C2 = C 3 = 3 F‬ﺭﺍ ﺑﺘﺮﺗﻴﺐ ﺑﻪ ﻗﻄﺒﻬﺎﻱ )′1,1( ﻭ )′2 ,2( ﻭ‬ ‫3‪i‬‬ ‫)′3 ,3( ﻭﺻﻞ ﻣﻲﻧﻤﺎﺋﻴﻢ. ﻣﺎﺗﺮﻳﺲ ﺣﺎﻟﺖ ‪ A‬ﻣﺪﺍﺭ ﺣﺎﺻﻞ ﺭﺍ ﺑﺮﺣﺴﺐ ﺩﺭﺍﻳﻪﻫﺎﻱ‬ ‫'‬ ‫3 + 3‪− v‬‬ ‫3‬ ‫11‪ h‬ﺗﺎ 33‪ h‬ﺑﻨﻮﻳﺴﻴﺪ.‬ ‫ﭖ‐ ﺣﺎﻝ ﺧﺎﺯﻥ ‪ C1=2F‬ﻭ ﺳﻠﻔﻬﺎﻱ ‪ L2=L3=4H‬ﺭﺍ ﺑﻪ ﻗﻄﺒﻬﺎ ﻭﺻﻞ ﻣﻲﻧﻤﺎﺋﻴﻢ ﺑﺎﺭ ﺩﻳﮕﺮ ‪ A‬ﺭﺍ ﺑﻴﺎﺑﻴﺪ.‬ ‫٦١‐ ﺩﺭ ﺳﻪ ﻗﻄﺒﻲ ﻣﺴﺌﻠﻪ ﻗﺒﻞ ﺳﻪ ﺳﻠﻒ ‪ H‬ﺭﺍ ﺑﻪ ﻗﻄﺒﻬﺎ ﻭﺻﻞ ﻣﻲﻧﻤﺎﺋﻴﻢ ﭼﻨﺎﻧﭽﻪ ﻣﺎﺗﺮﻳﺲ ‪ Z‬ﺳﻪ ﻗﻄﺒﻲ ﺑﺎ ﺩﺭﺍﻳﻪﻫﺎﻱ 3 = 11‪ z‬ﻭ‬ ‫23 ‪ z 23 = z‬ﺑﺎﺷﻨﺪ، ﺣﺎﺻﻞ ﺿﺮﺏ ﻓﺮﻛﺎﻧﺲﻫﺎﻱ ﻃﺒﻴﻌﻲ ﺭﺍ‬ ‫ﺑﻴﺎﺑﻴﺪ.‬ ‫1‬ ‫1‪C‬‬ ‫'1‬ ‫2‬ ‫1‬ ‫2‬ ‫4 = 22 ‪ z‬ﻭ 2 = 33 ‪ z‬ﻭ 1 = 12 ‪ z12 = z‬ﻭ 2− = 13 ‪ z13 = z‬ﻭ 1− =‬ ‫‪N‬‬ ‫2‪C‬‬ ‫'2‬ ‫٧١‐ ﺍﻟﻒ – ‪ N‬ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﺍﺯ ﻣﻘﺎﻭﻣﺖﻫﺎﻱ ﺍﻫﻤﻲ ﻣﺜﺒﺖ ﺗﺸﻜﻴﻞ ﻳﺎﻓﺘﻪ , ﺛﺎﺑﺖ ﻛﻨﻴﺪ‬ ‫ﻓﺮﻛﺎﻧﺲ ﻫﺎﻱ ﻃﺒﻴﻌﻲ ﺑﺎ ﻫﺮ ﻣﻘﺪﺍﺭ 0 > 2‪ , C1, C‬ﺍﻋﺪﺍﺩ ﺣﻘﻴﻘﻲ ﻣﻨﻔﻲ‬ ‫ﻫﺴﺘﻨﺪ.‬ ‫ﺏ‐ ﻗﺴﻤﺖ ﺍﻟﻒ ﺭﺍ ﺑﺮﺍﻱ ﻳ ‪ n‬ﻗﻄﺒﻲ ﺑﺎ ﺧﺎﺯﻧﻬﺎ 1‪ C‬ﺗﺎ ‪ Cn‬ﻣﺜﺒﺖ ﺩﺭ ﻗﻄﺒﻬﺎﻱ‬ ‫۱ﺗﺎ ‪ n‬ﺗﻌﻤﻴﻢ ﺩﻫﻴﺪ ﻭ ﺛﺎﺑﺖ ﻛﻨﻴﺪ ﻫﻤﻪ ﻓﺮﻛﺎﻧﺲﻫﺎ ﺍﻋﺪﺍﺩ ﺣﻘﻴﻘﻲ ﻣﻨﻔﻲ ﻫﺴﺘﻨﺪ.‬ ...
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## This note was uploaded on 02/06/2011 for the course ECE 423 taught by Professor Dolatabadi during the Spring '11 term at Amirkabir University of Technology.

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