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“Op-Amp” Operational Amplifier Non Inverting Amplifier Inverting Amplifier Adder –(and Subtractor using an Inverter) Differential Amplifier Integrator Differentiator Op-Amp name derives from early usage of these elements in performing mathematical operations in analog computers.

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Three Ways to Examine Op-Amp Behavior Consider as an Ideal Op-Amp Component Consider as a Feedback Model and Examine Behavior Perform Conventional Circuit Analysis

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V E = V IN+ - V IN- V OUT = a * V E V IN+ V IN-

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Ideal Op-Amp Model V E = V IN+ - V IN- V OUT = a * V E

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Behavior of Feedback Model

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of Non Inverting Amplifier

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Behavior of Feedback Model

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Summary

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Circuit Analysis Approach

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“Op-Amp” Operational Amplifier Non Inverting Amplifier Inverting Amplifier Adder –(and Subtractor using an Inverter) Differential Amplifier Integrator Differentiator Op-Amp name derives from early usage of these elements in performing mathematical operations in analog computers.

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Differential Amplifier Circuit Analysis a (V + - V - )

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Differential Amplifier Circuit Analysis a (V + - V - )

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Differential Amplifier Circuit Analysis a (V + - V - )

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Differential Amplifier Circuit Analysis a (V + - V - )

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Differential Amplifier Circuit Analysis a (V + - V - ) Z F / Z G

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Common Mode Rejection Ratio v icm v2v2 v1v1 vi1vi1 vi2vi2 v id / 2 v2v2 v1v1 Original Inputs Model of inputs with common- mode and differential-mode components

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where A is the differential mode gain and A cm is the common mode gain Ideally: CMRR Typically: 60 dB CMRR 120 dB Common Mode Rejection Ratio CMRR

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Assumes R 2 = R 4 and R 1 = R 3

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Differential Amplifier Circuit Analysis with Component Imbalance

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Differential Amplifier Circuit Analysis with Component Imbalance

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Differential Amplifier Circuit Analysis with Component Imbalance

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Differential Amplifier Circuit Analysis with Component Imbalance

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Differential Amplifier Circuit Analysis with Component Imbalance

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The Maximum Power Transfer Theorem simply states, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power.

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To create the Thevenin Equivalent Circuit we need: 1.Value of the Thevenin Voltage Source 2. Value of the Thevenin Resistance

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Input and Output Impedances of Noninverting Op-amp Configuration The unity gain buffer input impedance is much higher than the op-amp input impedance R d. The amplifier output impedance is much smaller than the op-amp output impedance R o. + RdRd i RoRo RLRL CLCL ioio Av d vdvd vovo vivi +

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Instrumentation Amplifier v out R3R3 v1v1 R2R2 R3R3 v2v2 R1R1 R2R2 R4R4 R4R4 v ref

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Instrumentation Amplifier Example Burr-Brown INA118 Parameters: Gain:

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Instrumentation Amp (cont.) A feedback network may also be included with the instrumentation amplifier. v out R3R3 v1v1 R2R2 R3R3 v diff = v 2 - v 1 2R 1 R2R2 R4R4 R4R4 R C v2v2

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