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EE101: Op Amp circuits (Part 6) M. B. Patil [email protected] www.ee.iitb.ac.in/~sequel DepartmentofElectricalEngineering IndianInstituteofTechnologyBombay M.B.Patil,IITBombay xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) →A ≡ xo = A . f xi 1−Aβ SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. M.B.Patil,IITBombay →A ≡ xo = A . f xi 1−Aβ SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) M.B.Patil,IITBombay SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) →A ≡ xo = A . f xi 1−Aβ M.B.Patil,IITBombay AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) →A ≡ xo = A . f xi 1−Aβ SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) M.B.Patil,IITBombay Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) →A ≡ xo = A . f xi 1−Aβ SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. M.B.Patil,IITBombay Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network Consideranamplifierwithfeedback. xo =Axi(cid:48)=A(xi+xf)=A(xi+βxo) →A ≡ xo = A . f xi 1−Aβ SinceAandβ willgenerallyvarywithω,were-writeA as, f A(jω) →A (jω)= . f 1−A(jω)β(jω) AsA(jω)β(jω)→1,Af(jω)→∞,andwegetafinitexo evenifxi =0. Inotherwords,wecanremovexi andstillgetanon-zeroxo. Thisisthebasic principlebehindsinusoidaloscillators. M.B.Patil,IITBombay * Thecondition,A(jω)β(jω)=1,foracircuittooscillatespontaneously(i.e., withoutanyinput),isknownastheBarkhausencriterion. * Forthecircuittooscillateatω=ω0,theβ networkisdesignedsuchthatthe Barkhausencriterionissatisfiedonlyforω0,i.e.,allcomponentsexceptω0 get attenuatedtozero. * Theoutputxo willthereforehaveafrequencyω0 (ω0/2π inHz),butwhatabout theamplitude? Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network M.B.Patil,IITBombay * Forthecircuittooscillateatω=ω0,theβ networkisdesignedsuchthatthe Barkhausencriterionissatisfiedonlyforω0,i.e.,allcomponentsexceptω0 get attenuatedtozero. * Theoutputxo willthereforehaveafrequencyω0 (ω0/2π inHz),butwhatabout theamplitude? Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network * Thecondition,A(jω)β(jω)=1,foracircuittooscillatespontaneously(i.e., withoutanyinput),isknownastheBarkhausencriterion. M.B.Patil,IITBombay * Theoutputxo willthereforehaveafrequencyω0 (ω0/2π inHz),butwhatabout theamplitude? Sinusoidal oscillators xi xx′i Amplifier Ax′i xo f Frequency−sensitive βxo network * Thecondition,A(jω)β(jω)=1,foracircuittooscillatespontaneously(i.e., withoutanyinput),isknownastheBarkhausencriterion. * Forthecircuittooscillateatω=ω0,theβ networkisdesignedsuchthatthe Barkhausencriterionissatisfiedonlyforω0,i.e.,allcomponentsexceptω0 get attenuatedtozero. M.B.Patil,IITBombay

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Sinusoidal oscillators. Amplifier principle behind sinusoidal oscillators. The gain of the 741 Op Amp starts falling at rather low frequencies, with fc ≃ 10 Hz!

EE101: Op Amp circuits (Part 6) - Electrical Engineering - IIT Bombay PDF

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Sinusoidal oscillators. Amplifier principle behind sinusoidal oscillators. The gain of the 741 Op Amp starts falling at rather low frequencies, with fc ≃ 10 Hz!

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