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

74 Pages·2015·0.86 MB·English

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