Lecture 10. Op Amps I• What is an Op Amp?• Ideal Op Amps•ApplicationsApplications• Examples1What is an Op Amp?What is an Op Amp?•Op Amp is short for operational amplifier.pp p p• An operational amplifier is modeled as a voltage controlled voltage source.•An operational amplifier has a very high input impedance and a very high gain.•It has usually differential inputs and a single output•It has usually differential inputs and a single output. 2Use of Op Ampspp•Op amps can be configured in many different ways using pp g y y gresistors and other components. • Amplifiers provide gains in voltage or current.• Op amps can convert current to voltage.• Op amps can provide a buffer between two circuits.Op amps can be used to implement integrators and•Op amps can be used to implement integrators and differentiators.• Lowpass and bandpass filters.pp3Applications of Op Ampspp p p•Amplifiers provide gains in voltage or current.pp g g• Op amps can convert current to voltage.• Op amps can provide a buffer between two circuits.• Op amps can be used to implement integrators and differentiators.4The Op Amp SymbolppyHigh SupplyHigh Supply+Non-inverting inputItiitOutput-Inverting inputGroundGroundLow Supply5The Op Amp Model–Voltage DependentThe Op Amp Model –Voltage Dependent Sourcev+Non-inverting inputRv++vo-Inverting inputRinv-+-A(v+-v)gpA(v+ v-)6Typical Op Ampyp p p• The input resistance Rinis very large (practically infinite).• The voltage gain Ais very large (practically infinite).+Non-inverting inputv+voInverting inputRinv-+-A()o-Inverting inputA(v+ -v-)7“Ideal” Op Amppp• The input resistance is infinite.p• The gain is infinite.• The op amp is in a negative feedback configuration. • Infinite input resistance means the current into the inverting input is zero:i=0i-= 0• Infinite gain means the difference between v+and v-is zero:v+- v-= 08The Basic Inverting AmplifiergpRR2-+V++R1+Vin--Vout9Solving the Amplifier CircuitgpNodal Analysis:yR2R1i2i1+ i2+ i-=0-i1i-1 2 10Solving the Amplifier Circuit0=−igp111RvRvviinin=−=−11RR2vvvioutout=−=−222RR0=+RvRvoutini1 + i2 + i-=01121RRSolving the Amplifier CircuitRSolve for voutgpinoutvRRv21−=outAmplifier gain:2RRvGout−==1Rvin12How to solve Op Amp Circuit? pp•Nodal analysis or other methods to solve for the•Nodal analysis or other methods to solve for the output voltage in terms of the input(s). •Keep in mind that the ideal op amp model leadsKeep in mind that the ideal op amp model leads to the following conditions:i=0i- 0v+= v-13Where is the Feedback?RR2-+V++R1+Vin--Vout14The Non-Inverting Amplifiergp+-+vin+-voutoutR1R2-15Nodal Analysis: Finding the nodesyg+-+vin+-vouti-iioutR1R2i1i2-16Nodal Analysis: Apply KCL0Nodal Analysis: Apply KCL0=−ivvi−−111RvRviin==−222RvvRvviinoutout−=−=−17Nodal Analysis: Solve for Voutyout021=−+−RvvRvinoutin⎞⎜⎜⎛+=21Rvv⎠⎜⎜⎝+=11Rvvinout18A Mixer CircuitRRfR1+-+++R2v1-+v2--vout19Nodal Analysis: Finding the nodesygRRfR1+i1if-+++R2v1-i2i-+v2--vout20Nodal Analysis: Apply KCLyppy11vvvi=−=−111RRi==22222RvRvvi =−=−0=−ioutoutfRvRvvi =−=−21fffRRNodal Analysis: Solve for Voutyout02211=++foutRvRvRvfvRvRvff−−=2211vRvRvout−−=22Class Examplesp• Seeing atoms with STM1 nA23Class Examplesp• Solar cell1 nAA circuit constructed for measuring current from the solar cell. The first Op Amp is the current-to-voltage converter and the second op Amp inverts the voltage. 24pp
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