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E E 2415. Lecture 05 - Introduction to Operational Amplifiers. Operational Amplifiers. Ideal operational amplifiers are easily analyzed Assumptions for ideal operation are realistic Inexpensive commercial Op-Amps available as integrated circuits
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E E2415 Lecture 05 - Introduction to Operational Amplifiers
Operational Amplifiers • Ideal operational amplifiers are easily analyzed • Assumptions for ideal operation are realistic • Inexpensive commercial Op-Amps available as integrated circuits • Practical applications for instrumentation, signal processing and control circuits
Assumptions for Ideal Op Amp • Open loop Gain, A vp - vn 0 • Then vp - vn 0 Ri • Ri ip 0 and in 0 • Gain is linear up to the saturation voltage • Saturation voltage equals power supply voltage
Inverting Amplifier Vn = 0 and in = 0. Then KCL at node n yields: and
Saturated Mode • Inverting Amplifier with +Vcc = 5 V and Vcc = -5V. • Rf = 10 k and Rg = 1 k
Non-Inverting Amplifier vn = vp = vg KCL at node n:
Difference Amplifier (1/3) KCL @ n:
Difference Amplifier (2/3) Voltage Divider @ p:
Difference Amplifier (3/3) Substitute: into: and simplify: If: Then: