# HW_10 - ‫ﺻﻔﺤﻪ١‬ ‫ﻗﻀﺎﻳﺎﻱ...

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Unformatted text preview: ‫ﺻﻔﺤﻪ١‬ ‫ﻗﻀﺎﻳﺎﻱ ﺷﺒﮑﻪ‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻧﻬﻢ‬ ‫‪B‬‬ ‫‪B‬‬ ‫١‐ﺍﻟﻒ‐ ﭘﺎﺳﺦ )‪ i٢(t‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺵ ﺗﺤﻠﻴﻞ ﻣﺶ ﻭ ﺑﮑﻤﮏ ﺗﺒﺪﻳﻞ‬ ‫1‬ ‫‪Ω‬‬ ‫2‬ ‫‪vc‬‬ ‫‪1F‬‬ ‫1‬ ‫‪Ω‬‬ ‫2‬ ‫1‬ ‫‪iL‬‬ ‫2‬ ‫ﻻﭘﻼﺱ، ﻭﻗﺘﻴﮑﻪ ﺣﺎﻟﺖ ﺍﻭﻟﻴﻪ ﻣﺪﺍﺭ: ٠ = )‪ iL(o‬ﻭ‪ vc(o) = ٤v‬ﺍﺳﺖ،‬ ‫ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﻳﻴﺪ.‬ ‫‪P‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪iL‬‬ ‫1‬ ‫‪H‬‬ ‫2‬ ‫3‬ ‫‪Ω‬‬ ‫2‬ ‫ﺍﻫﻤﻲ ﺭﺍ ﺑﺎ ﭼﻪ ﻣﻨﺒﻊ ﻭﻟﺘﺎﮊﻱ ﺟﺎﻧﺸﻴﻦ ﻧﻤﺎﻳﻴﻢ ﺗﺎ ﻭﻟﺘﺎﮊ ﻭﺟﺮﻳﺎﻥ‬ ‫3‬ ‫ﺏ‐ ﻣﻘﺎﻭﻣﺖ‬ ‫2‬ ‫2‪i‬‬ ‫ﺷﺎﺧﻪ ﻫﺎﻱ ﻣﺪﺍﺭ ﺗﻐﻴﻴﺮ ﻧﮑﻨﻨﺪ.‬ ‫ﭖ‐ ﺧﺎﺯﻥ ﺭﺍ ﺑﺎ ﭼﻪ ﻣﻨﺒﻊ ﻭﻟﺘﺎﮊ ﻧﺎﺑﺴﺘﻪ ﺍﻱ ﺟﺎﻧﺸﻴﻦ ﮐﻨﻴﻢ ﮐﻪ ﺟﺮﻳﺎﻥ ﻭ ﻭﻟﺘﺎﮊ‬ ‫ﺷﺎﺧﻪ ﻫﺎﻱ ﺩﻳﮕﺮ ﺗﻐﻴﻴﺮ ﻧﮑﻨﺪ. ﺁﻳﺎ ﺑﺎ ﺍﻳﻦ ﮐﺎﺭ ﻓﺮﮐﺎﻧﺲ ﻫﺎﻱ ﻃﺒﻴﻌﻲ ﻣﺪﺍﺭ‬ ‫ﺗﻐﻴﻴﺮ ﻣﻴﮑﻨﺪ؟ ﻓﺮﮐﺎﻧﺲ ﻫﺎﻱ ﻃﺒﻴﻌﻲ ﻣﺪﺍﺭ ﺍﺻﻠﻲ ﺩﺭ ﺷﮑﻞ ﺑﺎﻻ ﺭﺍ ﺑﺎ‬ ‫ﻓﺮﮐﺎﻧﺲ ﻃﺒﻴﻌﻲ ﻣﺪﺍﺭ ﺟﺎﻧﺸﻴﻦ ﺷﺪﻩ ﻣﻘﺎﻳﺴﻪ ﮐﻨﻴﺪ ) ﺑﺎ ﻣﺤﺎﺳﺒﻪ‬ ‫ﻓﺮﮐﺎﻧﺲ ﻫﺎ ﺩﺭ ﺩﻭ ﻣﺪﺍﺭ(‬ ‫‪1Ω‬‬ ‫‪6V‬‬ ‫‪3Ω‬‬ ‫‪1Ω‬‬ ‫1‬ ‫‪Ω‬‬ ‫2‬ ‫‪3Ω‬‬ ‫‪3Ω‬‬ ‫‪1Ω‬‬ ‫٢‐ﺍﻟﻒ‐ ﻣﻘﺎﻭﻣﺖ ﻧﻴﻢ ﺍﻫﻤﻲ ﺭﺍ ﺑﺎ ﭼﻪ ﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﻧﺎﺑﺴﺘﻪ ﺍﻱ ﺟﺎﻳﮕﺰﻳﻦ ﮐﻨﻴﻢ ﺗﺎ‬ ‫ﺟﺮﻳﺎﻥ ﻭ ﻭﻟﺘﺎﮊ ﺷﺎﺧﻪ ﻫﺎﻱ ﻣﺪﺍﺭ ﺗﻐﻴﻴﺮ ﻧﮑﻨﺪ ؟‬ ‫ﺏ‐ ﻧﺸﺎﻥ ﺩﻫﻴﺪﮐﻪ ﺩﺭﺍﻳﻦ ﻣﺪﺍﺭﻧﻤﻲ ﺗﻮﺍﻧﻴﻢ ﻣﻘﺎﻭﻣﺖ ﻧﻴﻢ ﺍﻫﻤﻲ ﺭﺍ ﺑﺎ ﻳﮏ ﻣﻨﺒﻊ‬ ‫ﻭﻟﺘﺎﮊ ﻧﺎﺑﺴﺘﻪ ﺟﺎﻳﮕﺰﻳﻦ ﻧﻤﺎﻳﻴﻢ.‬ ‫٣‐ﺍﻟﻒ‐ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﺭ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ‪ B‬ﻣﺪﺍﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ ﺭﺍ ﻣﺸﺨﺺ‬ ‫‪4V‬‬ ‫‪1F‬‬ ‫1‪2v‬‬ ‫‪Α‬‬ ‫+‬ ‫ﻧﻤﺎﻳﻴﺪ. ﺩﺭ ﻣﺤﺎﺳﺒﻪ ‪ eoc‬ﺍﺯ ﺟﻤﻊ ﺁﺛﺎﺭ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﺎﻳﻴﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺏ‐ ﻳﮏ ﺳﻠﻒ ﻳﮏ ﻫﺎﻧﺮﻱ ﺑﻪ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ‪ B‬ﻭﺻﻞ ﻣﻲ ﻧﻤﺎﻳﻴﻢ، ﺟﺮﻳﺎﻥ‬ ‫ﮔﺬﺭﻧﺪﻩ ﺍﺯ ﺁﻥ ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﻳﻴﺪ.‬ ‫+‬ ‫‪cos t‬‬ ‫−‬ ‫1‪v‬‬ ‫−‬ ‫‪1Ω‬‬ ‫‪1A‬‬ ‫‪Β‬‬ ‫٤‐ ﺩﺭ ﻣﺪﺍﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ ﺣﺎﻟﺖ ﺍﻭﻟﻴﻪ ﻣﺪﺍﺭ ﺭﺍ ﺻﻔﺮﻓﺮﺽ ﻧﻤﺎﻳﻴﺪ ﻭ )‪ is٢ = δ(t‬ﻭ‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫)‪ is١ = ٢u(t‬ﺍﺳﺖ:‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫1‪2 v‬‬ ‫‪2H‬‬ ‫‪Α‬‬ ‫ﺍﻟﻒ‐ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﺭ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ‪ B‬ﺭﺍ ﺩﺭ ﺣﻮﺯﻩ ﻓﺮﮐﺎﻧﺲ ﻣﺸﺨﺺ‬ ‫ﻧﻤﺎﻳﻴﺪ. ﺩﺭ ﺗﻌﻴﻴﻦ ‪ eoc‬ﺍﺯ ﻗﻀﻴﻪ ﺟﻤﻊ ﺁﺛﺎﺭ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﺎﻳﻴﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫1‪i s‬‬ ‫‪1F‬‬ ‫+‬ ‫‪1Ω‬‬ ‫2‪i s‬‬ ‫‪1F‬‬ ‫‪Β‬‬ ‫ﺏ‐ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﺭﺍ ﺑﻬﻢ ﻭﺻﻞ ﻣﻲ ﮐﻨﻴﻢ )ﺑﺎﺭ ﺍﺗﺼﺎﻝ ﮐﻮﺗﺎﻩ( ﺟﺮﻳﺎﻥ‬ ‫ﮔﺬﺭﻧﺪﻩ ﺍﺯ ﺍﻳﻦ ﺑﺎﺭ ﺍﺗﺼﺎﻝ ﮐﻮﺗﺎﻩ )‪ Isc(s‬ﺭﺍ ﻣﺸﺨﺺ ﮐﻨﻴﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫1‪v‬‬ ‫−‬ ‫‪1Ω‬‬ ‫ﭖ‐ ﭼﻪ ﺑﺎﺭ‪ ZL‬ﺑﻪ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﻭﺻﻞ ﮐﻨﻴﻢ ﮐﻪ ﺟﺮﻳﺎﻥ ﮔﺬﺭﻧﺪﻩ ﺍﺯ ﺁﻥ‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺷﻮﺩ ؟ ﺟﻬﺖ ﺟﺮﻳﺎﻥ ﺭﺍ ﺍﺯ ﺑﺎﻻ ﺑﻪ ﭘﺎﻳﻴﻦ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ.‬ ‫1‬ ‫2‬ ‫ﺕ‐ ﭼﻪ ﻣﻨﺒﻊ ﻭﻟﺘﺎﮊﻧﺎﺑﺴﺘﻪ ﺍﻱ ﺑﻪ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﻭﺻﻞ ﮐﻨﻴﻢ ﮐﻪ ﺟﺮﻳﺎﻥ‬ ‫ﮔﺬﺭﻧﺪﻩ ﺍﺯ ﺁﻥ، ﺑﺎ ﺟﻬﺖ ﺍﺯ ﺑﺎﻻ ﺑﻪ ﭘﺎﻳﻴﻦ، ‪ Isc‬ﺑﺎﺷﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫1‬ ‫‪Isc‬‬ ‫3‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺻﻔﺤﻪ٢‬ ‫‪Α‬‬ ‫ﻗﻀﺎﻳﺎﻱ ﺷﺒﮑﻪ‬ ‫‪iL‬‬ ‫‪1Ω‬‬ ‫1‬ ‫‪H‬‬ ‫4‬ ‫+‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻧﻬﻢ‬ ‫٥‐ ﺍﻟﻒ‐ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﺭ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﻣﺪﺍﺭ ﻣﻘﺎﺑﻞ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫‪1Ω‬‬ ‫1‪3v‬‬ ‫‪Β‬‬ ‫1‬ ‫‪Ω‬‬ ‫3‬ ‫‪1F‬‬ ‫1‪v‬‬ ‫−‬ ‫ﺣﺎﻟﺖ ﺍﻭﻟﻴﻪ ﻣﺪﺍﺭ ﺭﺍ ﺻﻔﺮ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ. ﻭﺭﻭﺩﻱ)‪is(t) =٢ e-tu(t‬‬ ‫ﻣﻨﻈﻮﺭ ﺷﻮﺩ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫ﺏ‐ ﭼﻨﺎﻧﭽﻪ ‪ i (o) =٢A‬ﻣﻨﻈﻮﺭ ﺷﻮﺩ ﺑﺎﺭ ﺩﻳﮕﺮ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﻓﻮﻕ ﺭﺍ ﺗﺼﺤﻴﺢ ‪is‬‬ ‫‪L‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫1‬ ‫‪F‬‬ ‫2‬ ‫ﻧﻤﺎﻳﻴﺪ. ﺍﺯ ﮐﺪﺍﻣﻴﮏ ﺍﺯ ﺗﻮﺍﺑﻊ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ‪ Eoc‬ﻭ )‪ Zth(s‬ﻣﻲ ﺗﻮﺍﻥ‬ ‫ﻓﺮﮐﺎﻧﺲ ﻃﺒﻴﻌﻲ ﻣﺘﻐﻴﺮ )‪ iL(t‬ﺷﺒﮑﻪ ﺷﮑﻞ ﺑﺎﻻ ﺭﺍ ﻳﺎﻓﺖ ؟ ﭼﮕﻮﻧﻪ ؟‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫٦‐ ﺩﺭ ﻣﺪﺍﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ ﮊﻳﺮﺍﺗﻮﺭ ﺑﺎ ﻣﻌﺎﺩﻻﺕ ﺯﻳﺮ ﻣﺸﺨﺺ ﻣﻲ ﺷﻮﺩ:‬ ‫‪1Ω‬‬ ‫‪A‬‬ ‫1‪i‬‬ ‫) ‪2u (t‬‬ ‫+‬ ‫) ‪δ (t‬‬ ‫2‪i‬‬ ‫+‬ ‫1‪v‬‬ ‫_‬ ‫2‪v‬‬ ‫_‬ ‫‪2H‬‬ ‫‪B‬‬ ‫٢‪ V١=٢I‬ﻭ ١‪ V٢ = ‐٢I‬ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﺭ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪B‬‬ ‫ﭼﻴﺴﺖ؟ ﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﺭﺍ ﺍﺯ ﺷﮑﻞ ﺣﺬﻑ ﮐﻨﻴﺪ ﻭ ﻭﻟﺘﺎﮊ ﺍﻭﻟﻴﻪ ﻱ‬ ‫)‪ vc(o‬ﻣﺨﺎﻟﻒ ﺻﻔﺮ ﭼﻨﺎﻥ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ ﮐﻪ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ‬ ‫ﺟﺪﻳﺪ ﺑﺎ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﻗﺒﻠﻲ ﻳﮑﺴﺎﻥ ﺑﺎﺷﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫٧‐ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﺭ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﻳﮏ ﻗﻄﺒﻲ ‪ N‬ﺭﺍ ﺩﺭ ﺣﻮﺯﻩ ﻓﺮﮐﺎﻧﺲ‬ ‫ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ. ﻣﻘﺪﺍﺭﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﻧﺎﺑﺴﺘﻪ )‪ is(t) = ٢e-٢tu(t‬ﻓﺮﺽ‬ ‫ﺷﻮﺩ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪Α‬‬ ‫٨‐ ﺩﺭ ﻣﺪﺍﺭ ﻣﻘﺎﺑﻞ ‪ N‬ﻫﻤﺎﻥ ﻳﮏ ﻗﻄﺒﻲ ﺑﺎ ﺳﺮﻫﺎﻱ ‪ A‬ﻭ ‪ B‬ﻣﺪﺍﺭ ﻣﺴﺌﻠﻪ ٧ ﺍﺳﺖ‬ ‫+‬ ‫−‬ ‫‪N‬‬ ‫1‪i s‬‬ ‫‪vs‬‬ ‫‪Β‬‬ ‫‪N‬‬ ‫+‬ ‫0‬ ‫‪NR‬‬ ‫‪NR‬‬ ‫2‪v‬‬ ‫−‬ ‫ﻭ ٠‪ N‬ﻫﻤﺎﻥ ﻳﮏ ﻗﻄﺒﻲ ‪ N‬ﺑﺪﻭﻥ ﺗﺤﺮﻳﮏ ﺍﺳﺖ. ﻣﻲ ﺧﻮﺍﻫﻴﻢ ﻣﻨﺒﻊ‬ ‫ﻭﻟﺘﺎﮊ )‪ vs(t‬ﺭﺍ ﺑﺎ ﻳﮏ ﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﻧﺎﺑﺴﺘﻪ )‪ is(t‬ﺟﺎﻧﺸﻴﻦ ﮐﻨﻴﻢ. ﺷﮑﻞ‬ ‫ﻣﻮﺝ )‪ is(t‬ﺭﺍ ﭼﻨﺎﻥ ﻣﺸﺨﺺ ﺳﺎﺯﻳﺪ ﮐﻪ ﭘﺎﺳﺦ ﻫﺎﻱ ﺷﺒﮑﻪ ﻗﺒﻞ‬ ‫ﺍﺯﺟﺎﻧﺸﻴﻨﻲ ﻭ ﺑﻌﺪ ﺍﺯ ﺟﺎﻧﺸﻴﻨﻲ ﻳﮑﺴﺎﻥ ﺑﺎﺷﻨﺪ. ﺩﺭ ﺣﻞ ﺍﻳﻦ ﻣﺴﺌﻠﻪ ﺍﺯ‬ ‫ﻗﻀﻴﻪ ﺟﻤﻊ ﺁﺛﺎﺭ ﻫﻢ ﺑﻬﺮﻩ ﺑﮕﻴﺮﻳﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫∧‬ ‫+‬ ‫2‪is‬‬ ‫‪BA‬‬ ‫1‪v‬‬ ‫−‬ ‫٩‐ ﺑﺎﺗﻮﺟﻪ ﺑﻪ ﺍﻃﻼﻋﺎﺕ ﻣﺸﺨﺺ ﺷﺪﻩ ﺩﺭ ﺷﮑﻞ ﻫﺎﻱ ﻣﻘﺎﺑﻞ )‪ v١(t‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ‬ ‫‪EA‬‬ ‫‪B‬‬ ‫^‬ ‫ﻧﻤﺎﻳﻴﺪ.‬ ‫−+‬ ‫‪vs‬‬ ‫‪1Ω‬‬ ‫+‬ ‫+ ‪ is٢(t) = sin(t‬ﻭ )‪ v٢(t) = (e-t + e-٢t)u(t‬ﻭ‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪PB‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪π‬‬ ‫4‬ ‫)‪)u(t‬‬ ‫‪B‬‬ ‫1‪v‬‬ ‫−‬ ‫‪1F‬‬ ‫‪NR‬‬ ‫‪NR‬‬ ‫‪2F‬‬ ‫)‪is١(t)=δ(t‬‬ ‫‪is‬‬ ‫‪1F‬‬ ‫2‪i‬‬ ‫= )‪ H٢(s‬ﺩﺭ ﻣﺪﺍﺭﻫﺎﻱ‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪2F‬‬ ‫‪1Ω‬‬ ‫)‪V (s‬‬ ‫)‪I 2 ( s‬‬ ‫٠١‐ ﺍﺭﺗﺒﺎﻁ ﺩﻭ ﺗﺎﺑﻊ ﺷﺒﮑﻪ‬ ‫1 = )‪ H١(s‬ﻭ‬ ‫)‪I s ( s‬‬ ‫) ‪V2 ( s‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪ic‬‬ ‫ﻣﻘﺎﺑﻞ ﭼﻴﺴﺖ ؟ ﭼﻨﺎﻧﭽﻪ)‪ is(t) = u(t‬ﻭ)‪ vs(t) = δ(t‬ﻭ‬ ‫)‪ v١(t)=(e-t+e-٢t)u(t‬ﺑﺎﺷﺪ ﺟﺮﻳﺎﻥ )‪ ic(t‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﻳﻴﺪ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪PB‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫ﺻﻔﺤﻪ٣‬ ‫1+‬ ‫1‪v‬‬ ‫ﻗﻀﺎﻳﺎﻱ ﺷﺒﮑﻪ‬ ‫2 ‪2F‬‬ ‫ﻣﺴﺎﻳﻞ ﻓﺼﻞ ﻧﻬﻢ‬ ‫)‪V1 ( s‬‬ ‫1‬ ‫2=‬ ‫١١‐ ﺩﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ:‬ ‫) ‪V2 ( s‬‬ ‫‪s + 2αs + β‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﻣﻲ ﺑﺎﺷﺪ ﻭ ﭼﻨﺎﻧﭽﻪ‬ ‫^‬ ‫^‬ ‫'1 −‬ ‫‪NR‬‬ ‫1‬ ‫+‬ ‫−‪v 2 v‬‬ ‫2‬ ‫−‬ ‫'2‬ ‫2‬ ‫‪BA‬‬ ‫+‬ ‫)‪ v٢(t) = (١+sint)u(t‬ﺑﺎﺷﺪ، ﭘﺎﺳﺦ ﺣﺎﻟﺖ ﺩﺍﻳﻤﻲ ﺑﻪ ﺻﻮﺭﺕ‬ ‫‪ v١(t)=١ - cost‬ﺩﺭ ﻣﻲ ﺁﻳﺪ. ﭼﻨﺎﻧﭽﻪ )‪ i(t) =e-tu(t‬ﺑﺎﺷﺪ، )‪v٢(t‬‬ ‫‪EAB‬‬ ‫‪B‬‬ ‫‪A‬‬ ‫‪EA‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺭﺍ ﺑﺮﺍﻱ 0 > ‪ t‬ﺗﻌﻴﻴﻦ ﮐﻨﻴﺪ.‬ ‫‪B‬‬ ‫1‬ ‫2‬ ‫+‬ ‫1‪i‬‬ ‫‪NR‬‬ ‫'1‬ ‫2‪v‬‬ ‫^‬ ‫‪2F‬‬ ‫−‬ ‫'2‬ ‫٢١‐ ﺩﺭ ﺩﺍﺧﻞ ﺟﻌﺒﻪ ‪ N‬ﺷﮑﻞ ١ ﻣﻘﺎﺑﻞ، ﺗﻨﻬﺎ ﻣﻘﺎﻭﻣﺖ ﻫﺎ، ﺳﻠﻒ ﻫﺎ ﻭ‬ ‫ﺧﺎﺯﻧﻬﺎﻱ ﺧﻄﻲ ﻭ ﺗﻐﻴﻴﺮﻧﺎﭘﺬﻳﺮ ﺑﺎ ﺯﻣﺎﻥ ﻭ ﺗﺮﺍﻧﺲ ﺍﻳﺪﻩ ﺁﻝ ﻗﺮﺍﺭ ﺩﺍﺭﻧﺪ.‬ ‫ﺍﻣﭙﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ﻭﻗﺘﻴﮑﻪ ﺳﺮﻫﺎﻱ ) `٢ ﻭ٢ ( ﺍﺗﺼﺎﻝ ﮐﻮﺗﺎﻩ ﻫﺴﺘﻨﺪ:‬ ‫= ‪ Zin‬ﻣﻲ ﺑﺎﺷﺪ. ﺩﺭ ﺷﮑﻞ ٢ ﻣﻘﺎﺑﻞ، ﺷﮑﻞ ﻣﻮﺝ ﻫﺎﻱ ﻣﻨﺎﺑﻊ‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺷﮑﻞ 1‬ ‫1‬ ‫2‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪Z in‬‬ ‫1‬ ‫'1‬ ‫'2‬ ‫−‬ ‫1‪v s‬‬ ‫+‬ ‫−‬ ‫‪i‬‬ ‫'1‬ ‫2 ‪vs‬‬ ‫3‪vs‬‬ ‫+‬ ‫−‬ ‫ﻭﻟﺘﺎﮊ ﻧﺎﺑﺴﺘﻪ ﻭ ﺟﺮﻳﺎﻥ 0‪ i‬ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﻣﻌﻠﻮﻡ ﻣﻲ ﺑﺎﺷﻨﺪ:‬ ‫)‪ vs١ = e u(t) ، vs٢ =٢u(t) ، vs٣= δ(t) ، vs۴ = u(t‬ﻭ‬ ‫)‪.i٠(t)=δ(t) – e-tu(t‬‬ ‫ﺟﺮﻳﺎﻥ ﻣﺸﺨﺺ ﺷﺪﻩ )‪ i(t‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ‬ ‫4 ‪vs‬‬ ‫2‬ ‫ﻧﻤﺎﻳﻴﺪ.‬ ‫٢/‪-t‬‬ ‫‪P‬‬ ‫‪PB‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪P‬‬ ‫‪P‬‬ ‫‪B‬‬ ‫2 )1 + ‪( s‬‬ ‫1‬ ‫) + ‪s( s‬‬ ‫2‬ ‫+‬ ‫+‬ ‫0‪i‬‬ ‫'2‬ ‫٣١‐ ﺍﻟﻒ‐ ﻭﻟﺘﺎﮊ )‪ vab(s‬ﺭﺍ ﺑﮑﻤﮏ ﻗﻀﻴﻪ ﺟﻤﻊ‬ ‫‪B‬‬ ‫‪B‬‬ ‫ﺁﺛﺎﺭ ﺩﺭ ﻣﺪﺍﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﻳﻴﺪ )ﻭﻟﺘﺎﮊ ﺩﺭ ﺳﺮﻫﺎﻱ ﻣﺪﺍﺭ ﺑﺎﺯ(‬ ‫‪1F‬‬ ‫‪1H‬‬ ‫‪1F‬‬ ‫) ‪2δ (t‬‬ ‫‪a‬‬ ‫ﺏ‐ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ، ﺩﺭ ﺳﺮﻫﺎﻱ ‪ a‬ﻭ ‪ ،b‬ﻣﺪﺍﺭ ﺷﮑﻞ ﻣﻘﺎﺑﻞ ﺭﺍ ﺩﺭ‬ ‫ﺣﻮﺯﻩ ﻓﺮﮐﺎﻧﺲ ‪ s‬ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫ﭖ‐ ﭼﻪ ﺍﻣﭙﺪﺍﻧﺴﻲ ﺑﻪ ﺳﺮﻫﺎﻱ ‪ a‬ﻭ ‪ b‬ﻭﺻﻞ ﻧﻤﺎﻳﻴﻢ ﺗﺎ ﺩﺭ ﻣﺪﺍﺭ ﺟﺪﻳﺪ‬ ‫ﻭﻟﺘﺎﮊ )‪ vab(s‬ﺩﺭ ﺍﻳﻦ ﻣﺪﺍﺭ، ﻧﺼﻒ ﻭﻟﺘﺎﮊ )‪ vab(s‬ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺩﺭ‬ ‫ﻗﺴﻤﺖ ﺍﻟﻒ ﺑﺸﻮﺩ.‬ ‫ﻣﻨﺒﻊ ﻭﻟﺘﺎﮊ ﻧﺎﺑﺴﺘﻪ )‪ ٢δ(t‬ﻭ ﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﻧﺎﺑﺴﺘﻪ )‪ ٢u(t‬ﻣﻲ ﺑﺎﺷﺪ. ﺣﺎﻟﺖ‬ ‫ﺍﻭﻟﻴﻪ ﻣﺪﺍﺭ ﺻﻔﺮ ﻣﻨﻈﻮﺭ ﺷﻮﺩ.‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪B‬‬ ‫‪1Ω‬‬ ‫‪1Ω‬‬ ‫‪1Ω‬‬ ‫) ‪2u (t‬‬ ‫‪1F‬‬ ‫‪b‬‬ ...
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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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