L23-24 Opamps 1- may 5 - ‫٣‐٥‐

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Unformatted text preview: ‫٣‐٥‐ ﺗﻘﻮﻳﺖﻛﻨﻨﺪﻩﻫﺎﻱ ﻋﻤﻠﻴﺎﺗﻲ )‪(Operational Amplifiers‬‬ ‫• ‪ OP-Amp‬ﻫﺎ ﺍﺯ ﺗﻌﺪﺍﺩ ﺯﻳﺎﺩﻱ ﺗﺮﺍﻧﺰﻳﺴﺘﻮﺭ. ﻣﻘﺎﻭﻣﺖ ﻭ ﺩﺭ ﻣﻮﺍﺭﺩﻱ ﺧﺎﺯﻥ ﺗﺸﻜﻴﻞ ﺷﺪﻩﺍﻧﺪ ﻛﻪ ﺑﻄﻮﺭ‬ ‫ﭘﻴﭽﻴﺪﻩﺍﻱ ﺑﻪ ﻳﻜﺪﻳﮕﺮ ﻣﺘﺼﻞ ﮔﺸﺘﻪﺍﻧﺪ. ﺑﻄﻮﺭ ﻣﺸﺨﺺ ﻳﻚ ‪ Op-Amp‬ﺩﺍﺭﺍﻱ ﺣﺪﺍﻗﻞ ٥ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻲﺑﺎﺷﺪ.‬ ‫ﺗﺮﻣﻴﻨﺎﻝﻫﺎﻱ‬ ‫ﺳﻴﮕﻨﺎﻝ‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ١ : ‪) inverting input‬ﻭﺭﻭﺩﻱ ﻣﻌﻜﻮﺱ ﻛﻨﻨﺪﻩ(‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ٢ : ‪) non-inverting input‬ﻭﺭﻭﺩﻱ ﻏﻴﺮﻣﻌﻜﻮﺱ ﻛﻨﻨﺪﻩ(‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ٣ : ‪) output‬ﺧﺮﻭﺟﻲ(‬ ‫ﺗﺮﻣﻴﻨﺎﻝﻫﺎﻱ‬ ‫ﻣﻨﺒﻊ ﺗﻐﺬﻳﻪ‬ ‫‪+ VCC‬‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ٤ : ‪Positive Supply‬‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ٥ : ‪Negative supply‬‬ ‫‪− VCC‬‬ ‫3‬ ‫‪4I‬‬ ‫‪L‬‬ ‫−‬ ‫+‬ ‫‪5 − VCC‬‬ ‫• ﻛﻠﻴﻪ ﺳﻴﮕﻨﺎﻟﻬﺎ ﺩﺭ ‪ op-amp‬ﻧﺴﺒﺖ ﺑﻪ ﺯﻣﻴﻦ )ﻳﺎ ﭘـﺎﻳﺎﻧﻪ ﻣﺸﺘﺮﻙ ﺩﻭ ﻣﻨﺒﻊ ﺗﻐﺬﻳﻪ( ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﻣﻲﺷﻮﻧﺪ. ﺍﻣﺎ‬ ‫ﻋﻤﻮﻣﺎ ﻫﻴﭽﻴﻚ ﺍﺯ ﭘﺎﻳﺎﻧﻪﻫﺎﻱ ﻣﺤﻔﻈﻪ ‪ op-amp‬ﺑﻄﻮﺭ ﻓﻴﺰﻳﻜﻲ ﺑﻪ ﺯﻣﻴﻦ ﻣﺘﺼﻞ ﻧﻤﻲﺷﻮﻧﺪ. ﻋﻼﻭﻩ ﺑﺮ ٥ ﺗﺮﻣﻴﻨﺎﻝ‬ ‫ﹶ‬ ‫ﻣﺰﺑﻮﺭ، ﻳﻚ ‪ op-amp‬ﻣﻤﻜﻦ ﺍﺳﺖ ﺩﺍﺭﺍﻱ ﺗﺮﻣﻴﻨﺎﻝﻫـــﺎﻱ ﺩﻳﮕﺮﻱ ﺑﺮﺍﻱ ﺍﻫﺪﺍﻑ ﺧﺎﺻﻲ ﺑﺎﺷﺪ )ﻣﺜﻼ ﺑﺮﺍﻱ ﺣﺬﻑ‬ ‫ﹶ‬ ‫ﻭﻟﺘﺎﮊﻫﺎﻱ ﺍﻓﺴﺖ ﻭ ﺟﺒﺮﺍﻥ ﻓﺮﻛﺎﻧﺲ، ... (‬ ‫1‬ ‫2‬ ‫• ﺟﻬﺖ ﺗﺤﻠﻴﻞ ﻭ ﻃﺮﺍﺣﻲ ﻣﺪﺍﺭﻫﺎﻱ ‪ op-amp‬ﻣﻌﻤﻮﻻ ﺍﺯ ﻣﺪﻝ ‪ op-amp‬ﺍﻳﺪﻩ ﺁﻝ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﺷﻮﺩ،‬ ‫ﹶ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺍﻳﺪﻩﺍﻝ ﺿﻤﻦ ﺗﺴﻬﻴﻞ ﺗﺤﻠﻴﻞ ﻭ ﻃﺮﺍﺣﻲ، ﺑﻪ ﻧﺘﺎﻳﺠﻲ ﻧﺰﺩﻳﻚ ﺑﻪ ﻭﺍﻗﻌﻴﺖ ﺩﺭ‬ ‫ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﭘﺎﻳﻴﻦ ﻣﻨﺠﺮ ﻣﻲﺷﻮﺩ.‬ ‫٣‐٥‐١‐ ﻣﺪﻝ ‪ op-Amp‬ﺍﻳﺪﻩﺁﻝ‬ ‫ﻣﺸﺨﺼﻪﻫﺎﻱ ﺍﻭﻟﻴﻪ ﻳﻚ ‪ op-Amp‬ﺍﻳﺪﻩﺁﻝ ﺑﺸﺮﺡ ﺯﻳﺮ ﺍﺳﺖ :‬ ‫١‐ ﺑﻬﺮﻩ ﻭﻟﺘﺎﮊ ﺑﻴﻨﻬﺎﻳﺖ ﺍﺳﺖ :‬ ‫‪Vo‬‬ ‫∞=‬ ‫)1‪( V2 − V‬‬ ‫٢‐ ﺍﻣﭙﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ﺑﻴﻨﻬﺎﻳﺖ ﺍﺳﺖ :‬ ‫‪Vo‬‬ ‫−‬ ‫+‬ ‫2‪V‬‬ ‫∞ = ‪Zi‬‬ ‫٣‐ ﺍﻣﭙﺪﺍﻧﺲ ﺧﺮﻭﺟﻲ ﺻﻔﺮ ﺍﺳﺖ :‬ ‫= ‪AV‬‬ ‫1‪V‬‬ ‫٠ = ‪Zo‬‬ ‫٤‐ ﻭﻟﺘــﺎﮊ ﺍﻧﺤﺮﺍﻑ ﺍﺯ ﻣﻴﺰﺍﻥ ﻭﺭﻭﺩﻱ ﺁﻥ ﺻﻔﺮ ﺍﺳﺖ )ﺍﮔﺮ 0=1‪ V2-V‬ﻭﻟﺘﺎﮊ ﺧﺮﻭﺟﻲ 0=‪ Vo‬ﺧﻮﺍﻫﺪ ﺑﻮﺩ(‬ ‫٥‐ ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻳﻚ ‪ op-Amp‬ﺍﻳﺪﻩﺁﻝ ∞ ﺍﺳﺖ.‬ ‫ﻋﻼﻭﻩ ﺑﺮ ﻣﺸﺨﺼﻪﻫﺎﻱ ﻓﻮﻕ ﻫﻤﻮﺍﺭﻩ ﻓﺮﺽ ﻣﻲﺷﻮﺩ ﻛﻪ ﺩﺭ ﻳﻚ ‪ op-Amp‬ﺍﻳﺪﻩﺁﻝ‬ ‫٦‐ ﺍﮔﺮ 0>)1‪ (V2-V‬ﺁﻧﮕﺎﻩ ‪Vo=+Vsat‬‬ ‫٧‐ ﺍﮔﺮ 0<)1‪ (V2-V‬ﺁﻧﮕﺎﻩ ‪Vo=-Vsat‬‬ ‫٨‐ ﺍﮔﺮ 0=)1‪ (V2-V‬ﺁﻧﮕﺎﻩ ‪-Vsat<Vo<+Vsat‬‬ ‫1‪I‬‬ ‫‪Vo‬‬ ‫−‬ ‫+‬ ‫)ﻣﻌﻤﻮﻻ ‪ Vsat‬ﻳﻚ ﻳﺎ ﺩﻭ ﻭﻟﺖ ﺍﺯ ‪ Vcc‬ﻛﻤﺘﺮ ﺍﺳﺖ(‬ ‫ﹶ‬ ‫1‪V‬‬ ‫2‪V‬‬ ‫2‪I‬‬ ‫ﻧﺎﺣﻴﻪ ‪ -Vsat<Vo<+Vsat‬ﻧﺎﺣﻴﻪ ﺧﻄﻲ ﻛﺎ ‪ op-Amp‬ﻣﻲﺑﺎﺷﺪ.‬ ‫• ﺩﺭ ﻧﺎﺣﻴﻪ ﺧﻄﻲ ﻋﻤﻠﻜﺮﺩ ‪ ، op-Amp‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺸﺨﺼﻪ ٨ ﻫﻤﻮﺍﺭﻩ ﻣﻲﺗﻮﺍﻥ ﻓﺮﺽ ﻧﻤﻮﺩ ﻛﻪ 1‪V2=V‬‬ ‫• ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻣﭙﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ∞ =‪ Zi‬ﻫﻤﻮﺍﺭﻩ ﻣﻲﺗﻮﺍﻥ ﻓﺮﺽ ﻧﻤﻮﺩ ﻛﻪ 0=2‪I1=I‬‬ ‫٣‐٥‐٢‐ ﻣﺪﺍﺭﺍﺕ ﻭ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ‪op-Amp‬‬ ‫1‪i2 = i‬‬ ‫• ﻣﺒﻨﺎﻱ ﻛﻠﻲ ﺑﺴﻴــﺎﺭﻱ ﺍﺯ ﻣﺪﺍﺭﻫﺎﻱ ‪ op-amp‬ﺑﺎ ﻣﺪﺍﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ‬ ‫ﻗﺎﺑﻞ ﺗﻮﺟﻴﻪ ﺍﺳﺖ.‬ ‫2‪Z‬‬ ‫ﺟﻬﺖ ﺗﺤﻠﻴﻞ ﻣﺪﺍﺭ ﺍﺯ ﻓﺮﺽ ﻫﺎﻱ ﺳﺎﺩﻩﻛﻨﻨﺪﻩ ﻓﻮﻕ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﺷﻮﺩ:‬ ‫•‬ ‫ﺟﺮﻳﺎﻥ ﻭﺭﻭﺩﻱ ﺑﻪ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻨﻔﻲ ﺻﻔﺮ ﺍﺳﺖ.‬ ‫•‬ ‫ﻭﻟﺘﺎﮊ ﺩﻭ ﺗﺮﻣﻴﻨﺎﻝ ﻭﺭﻭﺩﻱ ‪ op-amp‬ﺑﺎ ﻫﻢ ﺑﺮﺍﺑﺮ ﺍﺳﺖ‬ ‫‪V‬‬ ‫1‬ ‫−‬ ‫‪Vo‬‬ ‫+‬ ‫‪i =o‬‬ ‫‪Vi‬‬ ‫1‪Z‬‬ ‫1‪i‬‬ ‫0‬ ‫1‪⎧Vi = Z1 i‬‬ ‫⎨‬ ‫1‪⎩Vo = − Z 2 i‬‬ ‫1‪⎧(Vi − V1 ) = Z1 i‬‬ ‫⎨‬ ‫1‪⎩(V1 − Vo ) = Z 2 i 2 = Z 2 i‬‬ ‫0‬ ‫) ‪Vo ( s‬‬ ‫)‪Z (s‬‬ ‫2 −=‬ ‫) ‪Vi ( s‬‬ ‫) ‪Z1 ( s‬‬ ‫‪Vo‬‬ ‫2‪Z‬‬ ‫1‪i2 = i‬‬ ‫‪V1 = o‬‬ ‫1‪Z‬‬ ‫1‪i‬‬ ‫‪Vi‬‬ ‫1‪i 2 = i‬‬ ‫• ﻣﺪﺍﺭ ﺩﻳﮕﺮ ﻣﻔﻴﺪ ﻣﻄﺎﺑﻖ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﻣﻲﺑﺎﺷﺪ.‬ ‫2‪Z‬‬ ‫ﻣﺠﺪﺩﹶﺍ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻨﻜﻪ‬ ‫• ﻭﻟﺘــﺎﮊ ﺩﻭ ﺗﺮﻣﻴﻨﺎﻝ ﻭﺭﻭﺩﻱ ‪ op-amp‬ﺑﺎ ﻫﻢ ﺑﺮﺍﺑﺮ ﺍﺳﺖ‬ ‫*‬ ‫1‪⎧(0 − Vi ) = Z1 i‬‬ ‫⎨‬ ‫1‪⎩(Vi − Vo ) = Z 2 i 2 = Z 2 i‬‬ ‫**‬ ‫ﺑﺎ ﺣﺬﻑ 1‪ i‬ﺍﺯ ﺩﻭ ﺭﺍﺑﻄﻪ * ﻭ ** ﻣﻲﺗﻮﺍﻥ ﻧﻮﺷﺖ:‬ ‫) ‪Vo (s‬‬ ‫) ‪Z (s‬‬ ‫2 +1 =‬ ‫) ‪Vi (s‬‬ ‫) ‪Z1(s‬‬ ‫−‬ ‫1‪V‬‬ ‫+‬ ‫‪Vo‬‬ ‫• ﺟﺮﻳﺎﻥ ﻭﺭﻭﺩﻱ ﺑﻪ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻨﻔﻲ ‪ op-amp‬ﺻﻔﺮ ﺍﺳﺖ‬ ‫1‪i‬‬ ‫2‪Z‬‬ ‫‪V1 = Vi‬‬ ‫‪Vo‬‬ ‫‪Vi‬‬ ‫1‪i‬‬ ‫1‪i 2 = i‬‬ ‫‪Vo‬‬ ‫1‪Z‬‬ ‫1‪Z‬‬ ‫‪Vi‬‬ ‫+‬ ‫−‬ ‫2‪Z‬‬ ‫1‪Z‬‬ ‫ﺷﻜﻞ‬ ‫ﻣﻌﺎﺩﻝ‬ ‫2‪Z‬‬ ‫• ﻣﺪﺍﺭ ﺯﻳﺮ ﺑﺎ ﻋﻤﻠﻜﺮﺩﻱ ﻣﺸﺎﺑﻪ ﻣﺪﺍﺭﻫﺎﻱ ﻓﻮﻕ ﺍﻣﺎ ﺑﺼﻮﺭﺕ ﺗﻔﺎﺿﻠﻲ‬ ‫)‪ (Differential‬ﻋﻤﻞ ﻣﻲﻧﻤﺎﻳﺪ.‬ ‫‪Vo‬‬ ‫ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺳﺎﺩﻩ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺩﺭ ﺷﻜﻞ ﺯﻳﺮ ﻣﻲﺗﻮﺍﻥ‬ ‫ﺭﻭﺍﺑﻂ ﺯﻳﺮ ﺭﺍ ﻧﻮﺷﺖ‬ ‫1 ‪⎧ ( V1 − Vc ) = Z1 i‬‬ ‫⎨‬ ‫1 ‪⎩ ( V c − Vo ) = Z 2 i‬‬ ‫2 ‪⎧ ( V2 − Vc ) = Z 1 i‬‬ ‫⎨‬ ‫2 ‪⎩ Vc = Z 2 i‬‬ ‫−‬ ‫+‬ ‫1‪Z‬‬ ‫1‪Z‬‬ ‫2‪Z‬‬ ‫2‪Z‬‬ ‫‪Vo‬‬ ‫1‪i‬‬ ‫1‪i‬‬ ‫‪Vc‬‬ ‫2‪Z‬‬ ‫‪Vc‬‬ ‫1‪Z‬‬ ‫2‪i‬‬ ‫2‪i‬‬ ‫ﺑﺎ ﺣﺬﻑ 1‪ i2 ، i‬ﻭ ‪ VC‬ﺍﺯ ٤ ﺭﺍﺑﻄﻪ ﻓﻮﻕ ﺑﻪ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺩﺳﺖ ﻣﻲﻳﺎﺑﻴﻢ.‬ ‫)‪Z 2 (s‬‬ ‫) 1‪(V2 − V‬‬ ‫) ‪Z 1( s‬‬ ‫= ‪Vo‬‬ ‫1‪Z‬‬ ‫2‪V‬‬ ‫1‪V‬‬ ‫1‪V‬‬ ‫2‪V‬‬ ‫2‪Z‬‬ ‫−‬ ‫+‬ ‫‪Vo‬‬ ‫1‪Z‬‬ ‫1‪Z‬‬ ‫1‪V‬‬ ‫) ‪= Z2 ( s‬‬ ‫) ‪Z1(s‬‬ ‫+‬ ‫−‬ ‫2‪V‬‬ ‫2‪Z‬‬ ‫‪Vo‬‬ ‫‪Vo‬‬ ‫)1‪( V2 − V‬‬ ‫‪Vi‬‬ ‫2‪Z‬‬ ‫2‪Z‬‬ ‫−‬ ‫1‪Z‬‬ ‫‪Vo‬‬ ‫) ‪Z (s‬‬ ‫2 +1 =‬ ‫) ‪Z1(s‬‬ ‫‪Vi‬‬ ‫‪Vo‬‬ ‫1‪Z‬‬ ‫+‬ ‫‪Vo‬‬ ‫) ‪Z (s‬‬ ‫2 −=‬ ‫) ‪Z1(s‬‬ ‫‪Vi‬‬ ‫ﻛﺎﺭﺑﺮﺩ ﻣﺪﺍﺭﻫﺎﻱ ﻓﻮﻕ ﺩﺭ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﻧﻮﺍﻉ ﻛﻨﺘﺮﻟﺮﻫﺎﻱ .… ‪PID , PD , PI , Lead , Lag‬‬ ‫ﺩﺭ ﺟﺪﻭﻝ ﺻﻔﺤﻪ ﺑﻌﺪ ﺍﺭﺍﺋﻪ ﮔﺮﺩﻳﺪﻩ ﺍﺳﺖ.‬ ‫‪Vi‬‬ ‫ﺩﺭ ﺍﻳﻨﺠﺎ ﭼﻨﺪﻳﻦ ﻣﺪﺍﺭ ﻣﻔﻴﺪ ﺩﻳﮕﺮ ﺗﺸﺮﻳﺢ ﻣﻲﮔﺮﺩﻧﺪ.‬ ‫• ﻣﺪﺍﺭ ﺑﺎﻓﺮ ‪ Buffer‬ﻳﺎ )‪(Voltage follower‬‬ ‫−‬ ‫+‬ ‫‪Vo‬‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻨﻜﻪ ﻭﻟﺘﺎﮊ ﺩﻭ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻨﻔﻲ ﻭ ﻣﺜﺒﺖ ﺩﺭ‬ ‫‪ op-amp‬ﺑﺎ ﻫﻢ ﺑﺮﺍﺑﺮ ﻣﻲﺑﺎﺷﻨﺪ ﺩﺍﺭﻳﻢ : ‪Vo=Vi‬‬ ‫ﺍﺯ ﺁﻧﺠﺎﺋﻴﻜﻪ ﺟﺮﻳـــﺎﻥ ﻭﺭﻭﺩﻱ 0=‪ ii‬ﻣﻲﺑﺎﺷﺪ،‬ ‫ﻣﺪﺍﺭ ﻓﻮﻕ ﺩﺍﺭﺍﻱ ﺍﻣﭙــﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ﺑﺴﻴــﺎﺭ‬ ‫ﺑﺎﻻ ﺑﻮﺩﻩ )ﺩﺭ ﺣﺎﻟﺖ ﺍﻳﺪﻩﺁﻝ ∞ =‪ (Zi‬ﺩﺭ‬ ‫ﺣﺎﻟﻴﻜﻪ ﺍﻣﭙﺪﺍﻧﺲ ﺧﺮﻭﺟﻲ ﺁﻥ ﺑﺴﻴﺎﺭ ﭘﺎﻳﻴﻦ )ﺩﺭ‬ ‫ﺣﺎﻟﺖ ﺍﻳﺪﻩﺁﻝ 0=‪ (Zo‬ﺍﺳﺖ. ﻣــﺪﺍﺭ ﻓﻮﻕ ﺍﻏﻠﺐ‬ ‫ﺟﻬﺖ ﻣﻤـــﺎﻧﻌﺖ ﺍﺯ ﺑﺎﺭﮔــــﺬﺍﺭﻱ ﻳﻚ ﻣﺪﺍﺭ‬ ‫)ﻛــﻪ ﺑﻪ ‪ Vo‬ﻣﺘﺼـﻞ ﻣﻲﺷﻮﺩ( ﺑﺮ ﺭﻭﻱ ﻣﺪﺍﺭ‬ ‫ﺩﻳﮕﺮ )ﻛﻪ ﺧﺮﻭﺟﻲ ﺁﻥ ﺑﻪ ‪Vi‬ﻣﺘﺼﻞ ﻣﻲﺷﻮﺩ(‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﺷﻮﺩ. ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ:‬ ‫0=‪ii‬‬ ‫2‪R‬‬ ‫2‪Z‬‬ ‫‪Vo‬‬ ‫‪Vi‬‬ ‫−‬ ‫+‬ ‫1‪R‬‬ ‫1‪Z‬‬ ‫1‪R‬‬ ‫1‪Z‬‬ ‫+‬ ‫−‬ ‫−‬ ‫+‬ ‫2 ‪Z2 R‬‬ ‫ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﺎﻓﺮﻫﺎ ﺩﺭ ﻭﺭﻭﺩﻱ ﺗﻘﻮﻳﺖ ﻛﻨﺪﻩ ﺗﻔﺎﺿﻠﻲ، ﺍﻣﭙﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ﺗﻘﻮﻳﺖﻛﻨﻨﺪﻩ ﺗﻔﺎﺿﻠﻲ ﺍﺯ )2‪(Z1+Z‬‬ ‫ﺑﻪ ∞ ﺍﻓﺰﺍﻳﺶ ﻣﻲﺑﺎﺑﺪ.‬ ‫1‪V‬‬ ‫2‪V‬‬ ‫• ﻣﻘﺎﻳﺴﻪ ﻛﻨﻨﺪﻩ )‪(Comparator‬‬ ‫‪Vo‬‬ ‫‪Vsat‬‬ ‫‪Vin‬‬ ‫‪Vref‬‬ ‫‪Vin‬‬ ‫+‬ ‫−‬ ‫‪Vo‬‬ ‫‪Vref‬‬ ‫‪− Vsat‬‬ ‫ﺍﺯ ﺟﻤﻠﻪ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﻣﻘﺎﻳﺴﻪﮔﺮ‬ ‫‪t‬‬ ‫‪Vi‬‬ ‫‪Vo‬‬ ‫‪Vo , Vi‬‬ ‫‪t‬‬ ‫ﻣﺪﺍﺭ ﺷﻜﺎﺭ ﺳﺎﺯ ﻋﺒﻮﺭ ﺍﺯ ﺳﻄﺢ ﺻﻔﺮ‬ ‫‪Vo‬‬ ‫‪Vi‬‬ ‫‪Vo , Vi‬‬ ‫‪Vsat‬‬ ‫‪− Vsat‬‬ ‫ﺗﺒﺪﻳﻞ ﻣﻮﺝ ﺳﻴﻨﻮﺳﻲ ﺑﻪ ﻣﺮﺑﻌﻲ‬ ‫‪Vo‬‬ ‫+‬ ‫−‬ ‫‪Vi‬‬ (‫• ﺟﻤﻊ ﻛﻨﻨﺪﻩ )ﺑﺎ ﺑﻬﺮﻩ ﻣﻨﻔﻲ‬ R R V1 V2 V3 R1 R2 i − + R3 Vo V1 ‫ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ‬ V2 V3 n R2 i1 i2 R3 V=0 Vo ‫ﺯﻣﻴﻦ ﻣﺠﺎﺯﻱ‬ i3 n Vk i = ∑ ik = ∑ k =1 k =1 R k n ( 0 − V o ) = Ri ⇒ V o = − R i + − Rn Rf nR Vk Vo = − R ∑ = −∑ Vk k =1 R k k =1 R k n Vo = − ∑ Vk Rp V1 R1 V2 R 2 i R1 ‫ ﺁﻧﮕﺎﻩ‬Rk = R ∀ k ‫ﺍﮔﺮ‬ k =1 Vo (‫• ﺟﻤﻊ ﻛﻨﻨﺪﻩ )ﺑﺎ ﺑﻬﺮﻩ ﻣﺜﺒﺖ‬ Vj RF n )∑ Vo = R P (1 + R n j=1R p + R j n ‫ﻣﻲﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﻛﻪ‬ Vo = ∑ Vj ‫ ﺑﺎﺷﺪ ﺁﻧﮕﺎﻩ‬Rn = Rf = Rp = R j ∀j ‫ﻭ ﺩﺭ ﺻﻮﺭﺗﻴﻜﻪ‬ j=1 ‫• ﻣﻨﺎﺑﻊ ﺟﺮﻳﺎﻥ ﻭ ﻣﺒﺪﻝﻫﺎﻱ ﻭﻟﺘﮊ ﺑﻪ ﺟﺮﻳﺎﻥ‬ ‫ﺍﻟﻒ‐ ﺳﺎﺩﻩﺗﺮﻳﻦ ﻣﻨﺒﻊ ﺟﺮﻳﺎﻥ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ‬ ‫ﺷﺪﻩ ﺍﺳﺖ. ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺁﻥ ﻣﻄﺎﺑﻖ ﺷﻜﻞ ﺭﻭﺑﺮﻭ ﻣﻲﺑﺎﺷﺪ :‬ ‫+‬ ‫−‬ ‫‪Vout‬‬ ‫‪Load‬‬ ‫‪IL‬‬ ‫‪ Op-amp‬ﺧﺮﻭﺟﻲ ﺧﻮﺩ ﺭﺍ ﺁﻧﭽﻨﺎﻥ ﺗﻐﻴﻴﺮ ﻣﻲﺩﻫﺪ ﻛﻪ‬ ‫ﻭﻟﺘﺎﮊ ﺩﻭ ﻭﺭﻭﺩﻱ ﻣﻌﻜﻮﺱ ﻛﻨﻨﺪﻩ ﻭ ﻏﻴﺮﻣﻌﻜﻮﺱ ﻛﻨﻨﺪﻩ ﺑﺎ‬ ‫ﻫﻢ ﺑﺮﺍﺑﺮ ﺷﻮﺩ . ﻟﺬﺍ‬ ‫‪V‬‬ ‫‪I L = in‬‬ ‫‪R‬‬ ‫‪Vout‬‬ ‫‪Load‬‬ ‫‪IL‬‬ ‫ﺩﺭ ﻣﺪﺍﺭ ﻓﻮﻕ ﻫﻴﭽﻴﻚ ﺍﺯ ﺩﻭ ﺳﺮ ‪ Load‬ﺑﻪ ﺯﻣﻴﻦ ﻣﺘﺼﻞ ﻧﻴﺴﺖ. ﺩﺭ ﻣﻮﺍﺭﺩﻱ ﻛﻪ ﻣﻠﺰﻡ ﺑﻪ ﺍﺗﺼﺎﻝ‬ ‫ﻳﻜﺴﺮ ‪ Load‬ﺑﻪ ﺯﻣﻴﻦ ﺑﺎﺷﻴﻢ ﻣﻲﺗﻮﺍﻥ ﺍﺯ ﻣﺪﺍﺭﻫﺎﻱ ﺯﻳﺮ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ.‬ ‫‪Vin‬‬ ‫‪R‬‬ ‫‪Vin‬‬ ‫‪R‬‬ ‫‪Vcc‬‬ ‫ﺏ‐ ﺩﺭ ﻣﺪﺍﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ، ﺑﺎ ﺗﻮﺟـﻪ ﺑﻪ ﭘﺴﺨﻮﺭﺍﻧﺪ ﺍﺯ ﻧﻘﻄﻪ‬ ‫‪ op-amp ، A‬ﺧﺮﻭﺟــﻲ ﺧﻮﺩ ﺭﺍ ﺁﻧﭽﻨﺎﻥ ﺗﻐﻴﻴﺮ ﻣﻲﺩﻫﺪ‬ ‫ﻛﻪ ‪ VA=Vin‬ﮔﺮﺩﺩ.‬ ‫‪IE‬‬ ‫‪R‬‬ ‫‪I=o‬‬ ‫−‬ ‫+‬ ‫‪VA = Vin‬‬ ‫ﺩﺭ ﺍﻳﻨﺼﻮﺭﺕ :‬ ‫‪IL‬‬ ‫‪Vin‬‬ ‫‪Load‬‬ ‫‪V − Vin‬‬ ‫‪I L = I E = cc‬‬ ‫‪R‬‬ ‫ﺩﺭ ﻣﺪﺍﺭ ﻓﻮﻕ ﻓﺮﺽ ﮔﺮﺩﻳﺪﻩ ﻛﻪ ﺩﺭ ﺗﺮﺍﻧﺰﻳﺴﺘﻮﺭ ‪) IC‬ﻳﺎ ‪ (IL‬ﺑﺎ ‪ IE‬ﺑﺮﺍﺑﺮ ﻣﻲﺑﺎﺷﺪ ﺣﺎﻝ ﺁﻧﻜﻪ‪IC=αdcIE+ICBO‬‬ ‫. ﺑﺪﻳﻦ ﻣﻨﻈـــﻮﺭ ﻣﻲﺗﻮﺍﻥ ﺑﺠﺎﻱ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺮﺍﻧﺰﻳﺴﺘﻮﺭ ﻣﻌﻤﻮﻟﻲ ﺍﺯ ﻳﻚ ﺩﺍﺭ ﻟﻴﻨﮕﺘﻮﻥ )ﺑﺎ ١‬ ‫≈‪dc‬‬ ‫‪ (α‬ﻳﺎ ﻳﻚ‬ ‫‪ FET‬ﺍﺳﺘﻔـﺎﺩﻩ ﻧﻤﻮﺩ )ﻛﻪ ﺩﺭ ﺁﻧﻬﺎ ‪(ID=IS‬‬ ‫‪diL‬‬ ‫ﻳﻜﻲ ﺍﺯ ﻣﺸﻜﻼﺕ ﻣﺪﺍﺭ ﻓﻮﻕ ﺁﻧﺴﺘﻜﻪ ‪ IL‬ﺑﺎ ﺍﻓﺖ ﻭﻟﺘﺎﮊ ﻧﺴﺒﺖ ﺑﻪ ‪ VCC‬ﻣﺘﻨﺎﺳﺐ ﺍﺳﺖ ﻭ ﻧﻪ ﺑﺎ ‪< 0) Vin‬‬ ‫‪dvin‬‬ ‫ﺩﺭ ﺻﻮﺭﺗﻴﻜﻪ ﺑﺨﻮﺍﻫﻴﻢ ‪ IL= kVin‬ﺑﺎﺷﺪ ﻣﺪﺍﺭ ﺻﻔﺤﻪ ﺑﻌﺪ ﺗﻮﺻﻴﻪ ﻣﻲﺷﻮﺩ.‬ ‫(‬ ‫ﺝ – ﺩﺭ ﻣﺪﺍﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ، ﻣﺮﺣﻠﺔ ﻧﻬﺎﻳﻲ ﻣﺸﺎﺑﻪ‬ ‫ﻣﺪﺍﺭ ﺷﻜﻞ ﺻﻔﺤﻪ ﻗﺒﻞ ﺑﻮﺩﻩ ﻭ ﻟﺬﺍ :‬ ‫)*(‬ ‫ﺍﺯ ﻃﺮﻓﻲ ‪ VC=Vin‬ﻭ ﻟﺬﺍ‬ ‫‪Vcc − VB‬‬ ‫3‪R‬‬ ‫3‪R‬‬ ‫3‪I‬‬ ‫2‪R‬‬ ‫‪A‬‬ ‫2‪I‬‬ ‫= 3‪I L ≈ I‬‬ ‫ﺑﺎ ﺟﺎﻳﮕﺰﻳﻨﻲ ** ﺩﺭ * ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ :‬ ‫2‪R‬‬ ‫‪V in‬‬ ‫1‪R 3 R‬‬ ‫−‬ ‫+‬ ‫‪IL‬‬ ‫‪B‬‬ ‫‪Load‬‬ ‫‪Vc Vin‬‬ ‫=‬ ‫1‪R1 R‬‬ ‫‪V‬‬ ‫) ‪VB = Vcc − R2 I 2 = Vcc − R2 ( in‬‬ ‫1‪R‬‬ ‫= 2 ‪I1 ≈ I‬‬ ‫)**(‬ ‫‪Vcc‬‬ ‫‪Vcc‬‬ ‫+‬ ‫_‬ ‫1‪Q‬‬ ‫‪C‬‬ ‫1‪I‬‬ ‫1‪R‬‬ ‫≈ ‪IL‬‬ ‫4‪R‬‬ ‫1‪R‬‬ ‫‪A‬‬ ‫ﺩ‐ ﻣﺪﺍﺭ ﺩﻳﮕﺮ ﻣﺒﺪﻝ ﻭﻟﺘﺎﮊ ﺑﻪ ﺟﺮﻳﺎﻥ ﺩﺭ ﺷﻜﻞ ﻣﻘﺎﺑﻞ ﻧﺸﺎﻥ‬ ‫ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ. ﻣﻲﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﻛﻪ‬ ‫ﺍﮔﺮ‬ ‫4‪R3 R‬‬ ‫=‬ ‫1‪R2 R‬‬ ‫ﺁﻧﮕﺎﻩ‬ ‫‪Vin‬‬ ‫2‪R‬‬ ‫‪Vin‬‬ ‫− = ‪IL‬‬ ‫+‬ ‫‪B‬‬ ‫3‪R‬‬ ‫‪Load‬‬ ‫ﻣﺸﻜﻞ ﺍﻳﻦ ﻣﺪﺍﺭ ﺗﻀﻤﻴﻦ ﻧﺴﺒﺖ ﺻﺤﻴﺢ ﻣﻘﺎﻭﻣﺖﻫﺎ ﻣﻲﺑﺎﺷﺪ.‬ ‫‪Vout‬‬ ‫−‬ ‫2‪R‬‬ ‫‪Vin‬‬ ‫• ﺗﻘﻮﻳﺖ ﻭﻟﺘﺎﮊ ﺑﺎ ﺟﺮﻳﺎﻧﻬﺎﻱ ﺑﺎﻻ )‪(Current Boosters for Voltage Amplifiers‬‬ ‫ﻣﺪﺍﺭﻫـﺎﻱ “ﺏ“ ﻭ ”ﺝ“ ﺿﻤﻦ ﺍﻳﻨﻜﻪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺮﺍﻧﺰﻳﺴﺘﻮﺭ ﺍﻣﻜﺎﻥ ﺗﺎﻣﻴﻦ ﺟﺮﻳﺎﻧﻬﺎﻱ ﺑﺎﻻﺗﺮﻱ ﺭﺍ ﺑﻪ‬ ‫ﺑﺎﺭ ﻓﺮﺍﻫﻢ ﻣﻲﺳــﺎﺯﻧﺪ، ﺍﻣﺎ ﺟﺮﻳﺎﻥ ﻓﻘﻂ ﺩﺭ ﻳﻚ ﺟﻬﺖ ﻗﺎﺑﻞ ﺗﺎﻣﻴﻦ ﺍﺳﺖ. ﺩﺭ ﻣﺪﺍﺭ ﺷﻜﻞ ﺯﻳﺮ ﺑﺎ‬ ‫ﺍﺳﺘﻔــﺎﺩﻩ ﺍﺯ ﺗﺮﺍﻧﺰﻳﺴﺘﻮﺭﻫﺎﻱ ‪ Push-pull‬ﺍﻣﻜﺎﻥ ﺗﺎﻣﻴﻦ ﺟﺮﻳﺎﻥ ﺩﺭ ﻫﺮ ﺩﻭ ﺟﻬﺖ ﻓﺮﺍﻫﻢ ﻣﻲﮔﺮﺩﺩ.‬ ‫‪Rf‬‬ ‫‪+ Vcc‬‬ ‫‪+ Vcc‬‬ ‫‪Vin‬‬ ‫‪Rf‬‬ ‫‪Rs‬‬ ‫_‬ ‫− = ‪Vout‬‬ ‫+‬ ‫‪A‬‬ ‫‪Load‬‬ ‫‪− Vcc‬‬ ‫‪− Vcc‬‬ ‫‪Rs‬‬ ‫‪Vin‬‬ ‫• ﻣﺒﺪﻝ ﺟﺮﻳﺎﻥ ﺑﻪ ﻭﻟﺘﺎﮊ‬ ‫ﺩﺭ ﺑﺴﻴـﺎﺭﻱ ﺍﺯ ﺳﻨﺴﻮﺭﻫـﺎ ﺟﻬﺖ ﺍﻧﺘﻘﺎﻝ‬ ‫ﺳﻴﮕﻨـﺎﻝ ﺩﺭ ﻓﻮﺍﺻـﻞ ﻃﻮﻻﻧﻲ، ﺍﺯ ﺧﺮﻭﺟﻲﻫـﺎﻱ‬ ‫ﺟﺮﻳﺎﻥ ﺍﺳﺘﻔــﺎﺩﻩ ﻣﻲﺷﻮﺩ )ﺑﻌﻠﺖ ﻋﺪﻡ‬ ‫ﺣﺴــﺎﺳﻴﺖ ﺩﺭ ﺑﺮﺍﺑﺮ ﻧﻮﻳﺰ( . ﻟﺬﺍ ﺩﺭ ﺍﻧﺘﻬـﺎ ﺑﺎﻳﺪ‬ ‫ﺳﻴﮕﻨــﺎﻝ ﻣﺠﺪﺩﹶﺍ ﺑﻪ ﻭﻟﺘﺎﮊﻱ ﻣﺘﻨـﺎﺳﺐ ﺗﺒﺪﻳﻞ‬ ‫ﮔﺮﺩﺩ. ﺍﻳﻦ ﻳﻜـﻲ ﺍﺯ ﻛﺎﺭﺑﺮﺩﻫــﺎﻱ ﻣﺒﺪﻝﻫـﺎﻱ‬ ‫ﺟﺮﻳﺎﻥ ﺑﻪ ﻭﻟﺘﺎﮊ ﺍﺳﺖ. ﺑﻌﻀﻲ ﺍﺯ ﺳﻨﺴﻮﺭﻫــﺎ‬ ‫)ﻣﺎﻧﻨــﺪ ﻓﺘﻮﺗﺮﺍﻧﺰﻳﺴﺘـﻮﺭ( ﺟﺮﻳﺎﻧﻲ ﻣﺘﻨﺎﺳﺐ ﺑﺎ‬ ‫ﻛﻤﻴﺖ ﻓﻴﺰﻳﻜﻲ ﻣﻮﺭﺩﻧﻈﺮ ﺗﻮﻟﻴﺪ ﻣﻲﻧﻤﺎﻳﻨﺪ ﻭ ﺍﺯ‬ ‫ﺍﻳﻦ ﺭﻭ ﻣﺠﺪﺩﹶﺍ ﺑﻪ ﻳﻚ ﻣﺒﺪﻝ ﺟﺮﻳﺎﻥ ﺑﻪ ﻭﻟﺘﺎﮊ ﻧﻴﺎﺯ‬ ‫ﻣﻲﺑﺎﺷﺪ. ﺩﺭ ﻣﺪﺍﺭ ﻓﻮﻕ‬ ‫‪V out = R I s‬‬ ‫ﻭ ﻭﻟﺘﺎﮊ ﺧﺮﻭﺟﻲ ﻣﺘﻨﺎﺳﺐ ﺑﺎ ﺟﺮﻳﺎﻥ ﻭﺭﻭﺩﻱ ‪ IS‬ﻣﻲﺑﺎﺷﺪ.‬ ‫‪R‬‬ ‫‪Is‬‬ ‫‪Vout‬‬ ‫−‬ ‫+‬ ‫‪I=o‬‬ ‫‪Is‬‬ ‫‪Rf = R‬‬ ‫• ﻣﺒﺪﻝ ﺩﻳﺠﻴﺘﺎﻝ ﺑﻪ ﺁﻧﺎﻟﻮﮒ‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻧﺘﺎﻳﺞ ﻣﺮﺑﻮﻁ ﺑﻪ ﺟﻤﻊﻛﻨﻨﺪﻩﻫﺎ ﻣﻲﺗﻮﺍﻥ‬ ‫ﻧﺘﻴﺠﻪ ﮔﺮﻓﺘﻪ ﻛﻪ ﺩﺭ ﻣﺪﺍﺭ ﻣﻘﺎﺑﻞ‬ ‫‪R‬‬ ‫−‬ ‫+‬ ‫‪Vout‬‬ ‫‪2R‬‬ ‫‪4R‬‬ ‫) 1‪Vout = −( B4 + 0.5 B3 + 0.25 B2 + 0.125 B‬‬ ‫‪8R‬‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻨﻜﻪ 1‪ ... ، B2 ، B‬ﻭ 4‪ B‬ﻛﻤﻴﺖﻫﺎﻱ ﺩﻳﺠﻴﺘﺎﻟﻲ ﻫﺴﺘﻨﺪ )0 ﻳﺎ ‪ (5V‬ﻟﺬﺍ‬ ‫ﻣﻲﺗﻮﺍﻥ ﺟﺪﻭﻝ ﺯﻳﺮ ﺭﺍ ﺗﺸﻜﻴﻞ ﺩﺍﺩ :‬ ‫‪BBB‬‬ ‫‪V‬‬ ‫4‪B‬‬ ‫0=0‬ ‫0‬ ‫0‬ ‫0‬ ‫0‬ ‫526.0=5)521.0(‬ ‫1‬ ‫0‬ ‫0‬ ‫0‬ ‫‪ ٤ A/D‬ﺑﻴﺘﻲ ﺑﺎ‬ ‫52.1=5)52.0(‬ ‫0‬ ‫1‬ ‫0‬ ‫0‬ ‫ﺭﺯﻭﻟﻮﺷﻦ526.0 ﻭﻟﺘﻲ :‬ ‫52.2=5)573.0(‬ ‫1‬ ‫1‬ ‫0‬ ‫0‬ ‫52.2=5)5.0(‬ ‫0‬ ‫0‬ ‫1‬ ‫1‬ ‫521.3=5)526.0(‬ ‫1‬ ‫0‬ ‫1‬ ‫0‬ ‫573.9=5)578.1(‬ ‫1‬ ‫1‬ ‫1‬ ‫1‬ ‫‪out‬‬ ‫)1 − ‪Vout max = Re solution * (2n‬‬ ‫1‬ ‫2‬ ‫3‬ ‫4‪B‬‬ ‫3‪B‬‬ ‫2‪B‬‬ ‫1‪B‬‬ ‫٣‐٥٤‐ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪﻩﻫﺎﻱ ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ )‪(Instrumentation Amplifiers‬‬ ‫• ‪ IA‬ﻫﺎ ﻣﻌﻤﻮﻻ ﺑﺼﻮﺭﺕ ‪ IC‬ﻫﺎﻱ ﻣﺴﺘﻘﻠﻲ ﻫﺴﺘﻨﺪ ﻛﻪ ﺩﺍﺭﺍﻱ ﻣﺸﺨﺼﻪﻫﺎﻱ ﻛﻠﻲ ﺯﻳﺮ ﻣﻲﺑﺎﺷﻨﺪ.‬ ‫ﹶ‬ ‫ ﺍﻣﭙﺪﺍﻧﺲ ﻭﺭﻭﺩﻱ ﺑﺴﻴﺎﺭ ﺑﺎﻻ )ﺑﺮﺍﻱ ﺗﻘﻮﻳﺖ ﺳﻴﮕﻨﺎﻝﻫﺎﻱ ﺑﺴﻴﺎﺭ ﺿﻌﻴﻒ(‬‫ ‪ CMRR‬ﺑﺴﻴﺎﺭ ﺑﺎﻻ )ﺑﺮﺍﻱ ﺗﻘﻮﻳﺖ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﻭﻟﺘﺎﮊ ﭘﺎﻳﻴﻦ ﻫﻤﺮﺍﻩ ﺑﺎ ﻧﻮﻳﺰ(‬‫ ﻗﺎﺑﻠﻴﺖ ﺗﻨﻈﻴﻢ ﺑﻬﺮﻩ ﺗﻮﺳﻂ ﻳﻚ ﻣﻘﺎﻭﻣﺖ ﺧﺮﻭﺟﻲ‬‫• ‪ IA‬ﻫﺎ ﻣﻌﻤﻮﻻ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪﻩﻫﺎﻱ ٢ ﻣﺮﺣﻠﻪﺍﻱ ﻫﺴﺘﻨﺪ. ﺳﺎﺧﺘﻤﺎﻥ ﻣﺮﺣﻠﻪ ﺍﻭﻝ ﻣﻄﺎﺑﻖ ﺷﻜﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ‬ ‫ﹶ‬ ‫ﺷﺪﻩ ﻣﻲﺑﺎﺷﺪ. ﻭﻟﺘﺎﮊ ﺩﻭ ﺳﺮ ‪ Rg‬ﻭ ﺟﺮﻳﺎﻥ ﺩﺭﻭﻥ ‪ Rg‬ﺑﺮﺍﺑﺮﻧﺪ ﺑﺎ :‬ ‫1‪e2 − e‬‬ ‫= ‪VRg = e2 − e1 ⇒ I Rg‬‬ ‫‪Rg‬‬ ‫ﺟﺮﻳﺎﻥ ‪ IRg‬ﺑﺎﻳﺪ ﺍﺯ ﻫﺮ ﺳﻪ ﻣﻘﺎﻭﻣﺖ ﻋﺒﻮﺭ ﻧﻤﺎﻳﺪ ﻟﺬﺍ‬ ‫‪e −e‬‬ ‫) ‪= I Rg ´ (2R + Rg ) = 2 1 (2R + Rg‬‬ ‫‪Vo‬‬ ‫‪Rg‬‬ ‫+‬ ‫− ‪I1 = o‬‬ ‫−‬ ‫‪Vo‬‬ ‫+‬ ‫‪R‬‬ ‫‪R‬‬ ‫‪I Rg‬‬ ‫1‪e‬‬ ‫1‪e‬‬ ‫‪Rg‬‬ ‫−‬ ‫+ ‪I2 = o‬‬ ‫2‪e‬‬ ‫‪2R‬‬ ‫)‬ ‫‪Rg‬‬ ‫ﹶ‬ ‫ﻣﻌﻤﻮﻻ ‪ Rg‬ﻳﻚ ﻣﻘﺎﻭﻣﺖ ﺧﺎﺭﺟﻲ ﻗﺎﺑﻞ ﺗﻐﻴﻴﺮ ﺑﻮﺩﻩ ﻭ ﺑﺪﻳﻦ ﻭﺳﻴﻠﻪ ﺑﻬﺮﻩ ﻣﺮﺟﻠﻪ ﺍﻭﻝ ﻗﺎﺑﻞ ﺗﻨﻈﻴﻢ ﺍﺳﺖ.‬ ‫+1()1‪Vo = (e2 − e‬‬ ‫2‪e‬‬ ‫• ﻣﺮﺣﻠﻪ ﺩﻭﻡ ﻣﻌﻤﻮﻻ ﻳﻚ ﺗﻘﻮﻳﺖﻛﻨﻨﺪﻩ ﺗﻔﺎﺿﻠﻲ ﺑﺎ ﺑﻬﺮﻩ ﭘﺎﻳﻴﻦ )ﻣﻌﻤﻮﻻ ﺑﻬﺮﻩ ١( ﻣﻲﺑﺎﺷﺪ.‬ ‫ﹶ‬ ‫ﹶ‬ ‫2‪R‬‬ ‫‪Sense‬‬ ‫1‪e‬‬ ‫+‬ ‫−‬ ‫‪R wire‬‬ ‫‪Output‬‬ ‫1‪R‬‬ ‫−‬ ‫+‬ ‫‪R‬‬ ‫‪R‬‬ ‫1‪R‬‬ ‫−‬ ‫+‬ ‫‪Load‬‬ ‫‪refrence‬‬ ‫‪Rg‬‬ ‫2‪R‬‬ ‫ﺑﻬﺮﻩ ﻣﺮﺣﻠﻪ ﺩﻭﻡ: 2 ‪R‬‬ ‫1‪R‬‬ ‫2‪e‬‬ ‫• ﻣﻌﻤﻮﻻ ﺳﻪ ﺗﺮﻣﻴﻨﺎﻝ ”‪ “output” ، “Sense‬ﻭ ”‪ “refrence‬ﺑﻪ ﺑﻴﺮﻭﻥ ﺁﻭﺭﺩﻩ ﻣﻲﺷﻮﻧﺪ. ﺑﻴﺮﻭﻥ ﺁﻭﺭﺩﻥ ﺳﻪ‬ ‫ﹶ‬ ‫ﻧﺮﻣﻴﻨﺎﻝ ﻣﺰﺑﻮﺭ ﻣﻮﺟﺐ ﺍﻓﺰﺍﻳﺶ ﺍﻧﻌﻄﺎﻑﭘﺬﻳﺮﻱ ‪ IA‬ﺟﻬﺖ ﺑﻜﺎﺭﮔﻴﺮﻱ ﺁﻥ ﺩﺭ ﻣﺼﺎﺭﻑ ﮔﻮﻧﺎﮔﻮﻥ ﻣﻲﮔﺮﺩﺩ ؛‬ ‫‐ ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺷﻜﻞ ﺻﻔﺤﻪ ﻗﺒﻞ ، ﺍﮔﺮ ‪ Load‬ﺩﺭ ﻓﺎﺻﻠﻪ ﺯﻳﺎﺩﻱ ﺍﺯ ‪ IA‬ﻗﺮﺍﺭ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ، ﻣﻘﺎﻭﻣﺖ ﺳﻴﻢ‬ ‫)‪ (Rwire‬ﻣﻮﺟﺐ ﺍﻓﺖ ﻭﻟﺘـــﺎﮊ ﺩﺭ ﺳﻴﻢ ﮔﺸﺘﻪ ﻭ ﺍﺯ ﺩﻗﺖ ﻭﻟﺘﺎﮊ ﺧﺮﻭﺟﻲ )ﻛﻪ ﺑﻪ ‪ Load‬ﺍﻋﻤﺎﻝ ﻣﻲﺷﻮﺩ( ﻣﻲﻛﺎﻫﺪ.‬ ‫ﺑﺮﺍﻱ ﺣﻞ ﺍﻳﻦ ﻣﺴﺌﻠﻪ ﻣــﺪﺍﺭ ﺯﻳﺮ ﺗﻮﺻﻴﻪ ﻣﻲﺷﻮﺩ. ﻣﻲﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﻛﻪ ﺍﻓﺖ ﻭﻟﺘـــﺎﮊ ﺑﻴﻦ ﺗﺮﻣﻴﻨــــﺎﻝ ﺧﺮﻭﺟﻲ‬ ‫”‪ “output‬ﻭ ”‪ “Load‬ﺩﻗﻴﻘﺎ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ﺑﻬﺮﻩ ﻣﺮﺣﻠﻪ ﺩﻭﻡ ﺣﻨﺜﻲ ﻣﻲﺷﻮﺩ )202 ‪(Jacob page‬‬ ‫ﹶ‬ ‫‪R wire‬‬ ‫‪Sense‬‬ ‫2‪R‬‬ ‫1‪e‬‬ ‫+‬ ‫−‬ ‫‪R wire‬‬ ‫‪Load‬‬ ‫‪R wire‬‬ ‫‪Output‬ ‫‪refrence‬‬ ‫1‪R‬‬ ‫−‬ ‫+‬ ‫‪R‬‬ ‫‪R‬‬ ‫‪Rg‬‬ ‫1‪R‬‬ ‫−‬ ‫+‬ ‫2‪R‬‬ ‫ﺑﻬﺮﻩ ﻣﺮﺣﻠﻪ ﺩﻭﻡ:‬ ‫2‪R‬‬ ‫1‪R‬‬ ‫2‪e‬‬ ‫‐ ﺍﺯ ﻃﺮﻓﻲ ﺍﮔﺮ ﺟﺮﻳﺎﻥ ﺗﺎﻣﻴﻦ ﺷﺪﻩ ﺗﻮﺳﻂ ‪ Op-Amp‬ﺑﺮﺍﻱ ﺗﻐﺬﻳﻪ ﺑﺎﺭ ﻣﻮﺭﺩﻧﻈﺮ ﻛﺎﻓﻲ ﻧﺒﺎﺷﺪ ﻣﻲﺗﻮﺍﻥ ﺍﺯ‬ ‫ﻣﺪﺍﺭ ﺯﻳﺮ ﺑﺮﺍﻱ ﺗﻘﻮﻳﺖ ﺟﺮﻳﺎﻥ ﺧﺮﻭﺟﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ )302 ‪(Jacob page‬‬ ‫‪R 2 Sense‬‬ ‫‪+V‬‬ ‫+‬ ‫‪Output‬‬ ‫2‪R‬‬ ‫−‬ ‫+‬ ‫1‪R‬‬ ‫−‬ ‫‪Rg‬‬ ‫2‪R‬‬ ‫1‪R‬‬ ‫−‬ ‫+‬ ‫‪− V Load‬‬ ‫‪R 2 refrence‬‬ ‫1‪e‬‬ ‫2‪e‬‬ (‫ ﻫﺎ )ﺑﺎ ﺫﻛﺮ ﻣﺮﺍﺟﻊ‬op-Amp ‫ﺳﺎﻳﺮ ﻣﻮﺍﺭﺩ ﻛﺎﺭﺑﺮﺩ‬ (‫( )ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﺍﻟﻜﺘﺮﻭﻧﻴﻜﻲ: ﺍﻣﻴﺮﺣﺴﻴﻦ ﺭﺿﺎﺋﻲ‬Jacob :Ch. 3) ‫• ﭘﺮﺩﺍﺯﺵ ﺳﻴﮕﻨﺎﻝ ﺑﺮﺍﻱ ﺍﻧﻮﺍﻉ ﻣﺨﺘﻠﻒ ﺳﻨﺴﻮﺭﻫﺎ‬ (Franco:Ch. 3-4 ; Horowitz :Ch. 5 ; Price :Ch.14) (active filters) ‫• ﻓﻴﻠﺘﺮﻫﺎﻱ ﻓﻌﺎﻝ‬ (Pass Band ) ‫( ;ﻣﻴﺎﻥ ﮔﺬﺭ‬High pass ) ‫( ;ﺑﺎﻻ ﮔﺬﺭ‬Low pass) ‫ﭘﺎﻳﻴﻦ ﮔﺬﺭ‬ (Jacob :Ch. 4) ‫• ﻣﺒﺪﻟﻬﺎﻱ ﻭﻟﺘﺎﮊ ﺑﻪ ﻓﺮﻛﺎﻧﺲ ﻭ ﻓﺮﻛﺎﻧﺲ ﺑﻪ ﻭﻟﺘﺎﮊ‬ (‫( )ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﺍﻟﻜﺘﺮﻭﻧﻴﻜﻲ‬Jacob :Ch. 6) Sample/Hold ‫ ﻭ ﻣﺪﺍﺭﻫﺎﻱ‬A/D ، D/A ‫• ﺍﻧﻮﺍﻉ ﻣﺒﺪﻟﻬﺎﻱ‬ (Jacob :Ch. 5) ‫• ﺍﻧﻮﺍﻉ ﻛﻨﺘﺮﻟﻬﺎﻱ ﺁﻧﺎﻟﻮﮒ‬ - Sergio Franco, Design with Operational Amplifiers & Analog Integrated Circuits, Mc Graw Hill, 1998. - T.E.Price, Analog Electronics an integrated pspice approach, Prentice Hall, 1997 - J.M. Jacob, Industrial Control Electronics : Application & Design, Prentice Hall, 1989. - P. Horowits, W.F.Hill, The Art of Electronics, Cambridge press. ‫‐ ﺩﻛﺘﺮ ﺍﻣﻴﺮﺣﺴﻴﻦ ﺭﺿﺎﺋﻲ، ﻣﻬﻨﺪﺱ ﻣﺤﻤﺪﺭﺿﺎ ﺫﻫﺎﺑﻲ، ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﺍﻟﻜﺘﺮﻭﻧﻴﻜﻲ، ﺍﻧﺘﺸﺎﺭﺍﺕ ﺩﺍﻧﺸﮕﺎﻩ ﺍﻣﻴﺮﻛﺒﻴﺮ‬ ...
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