E80 Spring 2012

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E80 Spring 2014Op Amps CircuitsE80 Lecture 4.1: Basic Electrical Measurements

Agenda: Operational AmplifierooooooooRecap: Non-inverting amplifier and unity gain bufferInverting amplifier (multiplication)Summing amplifier (add and subtract)Differentiator and integratorDifference amplifierInstrumentation amplifierTransimpedance amplifierActive filters2E80 Lecture 4.2: Basic Electrical Measurements

Recap: Opamp ModelV V-V V-(2) 𝑖 0, 𝑖 0E80 Lecture 4.3: Basic Electrical Measurements31 v v

Recap: Non-inverting Amplifier Non-inverting amplifier is designed to produce positivevoltage gain𝑅𝑓𝑣0 (1 )𝑣𝑖𝑅1E80 Lecture 4.4: Basic Electrical Measurements4Special case:R1 , Rf 0Unity-gain buffer

Inverting amplifier Inverting amplifier reverses the polarity of the inputsignal while amplifying (or attenuating) itE80 Lecture 4.5: Basic Electrical MeasurementsR1vi5vo Rf

Summing amplifier Summing Amplifier is an op amp circuit that combinesseveral inputs and produces an output that is theweighted sum of the inputs.RfRf Rfvo v1 v2 v3 R2R3 R1E80 Lecture 4.6: Basic Electrical Measurements6Q: Is it possible to construct a non-inverting summing amp?

Opamp Circuit With CapacitorInverting amplifierE80 Lecture 4.7: Basic Electrical Measurements7What does this circuit do?How is Vo related to Vi?

Opamp Circuit With CapacitorIntegrator circuitt1vo (t ) vi ( )d vC (0) RC 0E80 Lecture 4.8: Basic Electrical Measurements8What does this circuit do?How is Vo related to Vi?

ExampleE80 Lecture 4.9: Basic Electrical Measurements9What does the output waveform look like?

Solving Differential Equation UsingOpamp Circuit𝑣0 3𝑣0 2𝑣0 4cos(10𝑑)E80 Lecture 4.10: Basic Electrical Measurements10RC 1 sec

Difference Amplifier Difference amplifier is a device that amplifies thedifference between two inputs but rejects any signalscommon to the two inputs.1 𝑅2 /𝑅1𝑅2𝑣0 𝑣 𝑣1 𝑅3 /𝑅4 2 𝑅1 1E80 Lecture 4.11: Basic Electrical Measurements𝑅1 𝑅2 π‘Žπ‘›π‘‘ 𝑅3 𝑅4𝑣0 𝑣2 𝑣111Special case:

Instrumentation AmplifierE80 Lecture 4.12: Basic Electrical Measurements

Instrumentation Amplifier Application(1) Only amplify difference(2) Infinite Input resistance zero Output resistanceE80 Lecture 4.13: Basic Electrical Measurements

Transimpedance amplifier forphotodiodeRphotonVbiasDivo𝑣0 𝑖 𝑅 Much easier to measure voltage than current Provide large amplificationE80 Lecture 4.14: Basic Electrical Measurements

Active filterE80 Lecture 4.15: Basic Electrical Measurements15 RC and OpAmp ( 1MHz, bulky inductorin RLC filters) 1st order filters– Low pass– High pass– Inverting– Non-inverting 2nd order low pass filter

Active Filter Example𝑅𝑓 /𝑅𝑖𝐻 π‘—πœ” 1 π‘—πœ”π‘…π‘“ 𝐢𝑓Say Rf RiLow pass filterSketch Bode PlotE80 Lecture 4.16: Basic Electrical Measurements

Active Filter Example1 𝑅2 /𝑅3𝐻 π‘—πœ” 1 π‘—πœ”π‘…1 𝐢1E80 Lecture 4.17: Basic Electrical Measurements17Non-inverting 1st order low pass active filter

Active Filter ExampleSay Rf Riπ‘—πœ”π‘…π‘“ 𝐢𝑖𝐻 π‘—πœ” 1 π‘—πœ”π‘…π‘– 𝐢𝑖Sketch Bode PlotE80 Lecture 4.18: Basic Electrical Measurements18High pass filter

Active Filter Example𝐻 π‘—πœ” 𝑅2)𝑅31 π‘—πœ”π‘…1 𝐢1π‘—πœ”π‘…1 𝐢1 (1 E80 Lecture 4.19: Basic Electrical Measurements19Non-inverting 1st order high pass active filter

Active Filter ExampleSay R2 R1 π‘—πœ”π‘…2 𝐢1𝐻 π‘—πœ” (1 π‘—πœ”π‘…1 𝐢1 )(1 π‘—πœ”π‘…2 𝐢2 )Bandpass filterE80 Lecture 4.20: Basic Electrical Measurements20Sketch Bode Plot

2nd order Active FilterSallen-Key Low Pass FilterFind frequency response function of unity-gain Sallen KeyTopologyE80 Lecture 4.21: Basic Electrical Measurements211𝐻 π‘—πœ” 1 π‘—πœ”(𝑅1 𝑅2 )𝐢1 πœ” 2 𝑅1 𝑅2 𝐢1 𝐢2

E80 Lecture 4.2: Basic Electrical Measurements Agenda: Operational Amplifier o Recap: Non-inverting amplifier and unity gain buffer o Inverting amplifier (multiplication) o Summing amplifier (add and subtract) o Differentiator and integrator o Difference amplifier o Instrumentation amplifier o Transimpedance amplifier o Active filters 2

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