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**OPERATIONAL AMPLIFIERS**

Operational Amplifiers(Op-Amp) Ideal characteristics Practical Op Amp Inverting Non inverting Applications Adder Subtractor summing difference Instrumentation amplifiers

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**OPERATIONAL AMPLIFIER**

Operational Amplifiers are represented both schematically and realistically below: Active component!

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**Originally invented in early 1940s using vacuum tube technology**

Initial purpose was to execute math operations in analog electronic calculating machines Shrunk in size with invention of transistor Most now made on integrated circuit (IC) Only most demanding applications use discrete components Huge variety of applications, low cost, and ease of mass production make them extremely popular Single-ended Amplifier Differential Amplifier Amplifies difference between inputs

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Output gain high A ~= 106 Tiny difference in the input voltages result in a very large output voltage Output limited by supply voltages Comparator If V+>V-, Vout = HVS If V+<V-, Vout = LVS If V+=V-, Vout = 0V

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3-stage Op-Amp

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**Why are they useful? Negative feedback leads to stable equilibrium**

Sensor signals are often too weak or too noisy Op Amps ideally increase the signal amplitude without affecting its other properties Negative feedback leads to stable equilibrium Voltage follower (direct feedback) If Vout = V- , then Vout ~ V+ Closed Loop Transfer Function H(s) = A / (1 + AF) When AF >> 1… H(s) = 1 / F Where: A = Op Amp Open Loop Gain F = Feedback Loop Gain

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**Attenuates and phases at high frequencies (depends on slew rate)**

Ideal Op Amp Zin is infinite; ; Zout is zero; Amplification (Gain) Vout / Vin = ∞; Unlimited bandwidth; Vout = 0 when Voltage inputs = 0 Ideal Op-Amp Typical Op-Amp Input Resistance infinity 106 (bipolar) 109 (FET) Input Current 10-12 – 10-8 A Output Resistance 100 – 1000 Operational Gain Common Mode Gain 10-5 Bandwidth Attenuates and phases at high frequencies (depends on slew rate) Temperature independent Bandwidth and gain

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Inverting Op-Amp

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Non-inverting Op-Amp

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Summation

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Difference If all resistors are equal:

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Integrating Op-Amp

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**Differentiating Op-Amp**

(where Vin and Vout are functions of time)

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