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Operational Amplifiers. A brief introduction. Op-Amp Introduction. Need exists for a circuit element that can perform: Add, subtract, multiply, divide, differentiate, integrate Evolved from Analog Computers Op-Amp properties

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## Operational Amplifiers

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**Operational Amplifiers**A brief introduction BAE 5413**Op-Amp Introduction**• Need exists for a circuit element that can perform: • Add, subtract, multiply, divide, differentiate, integrate • Evolved from Analog Computers • Op-Amp properties • Single building block which can be assembled into above functions by adding passive components (R,L,C) • Inexpensive (used in high volume) • Compact • Op-Amp analysis • Use assumptions of “Ideal Op-Amp” to allow low frequency performance to be approximated • Typically have near ideal characteristics but frequency response of an integrator (G(s) = 1/ts). (Otherwise, the high bandwidth would be impossibly difficult to manage.) BAE 5413**Ideal Op-Amp Assumptions**• Differential function • Vout = A•DV • Infinite • Intrinsic gain: A = • Input impedance: Zin = • Bandwidth: Vout f(w) • Zero • Input offset voltage: Vio= 0 for Vout+ Vio= A•DV • Input impedance: Zout = 0 BAE 5413**Inverting Amplifier**• Consider the circuit configuration to the right • Assuming intrinsic gain of the op-amp is very large for the frequency of interest: • Voutis finite and typically within +15 to -15 V implying DV is very small • Assuming ib is very small given the intrinsic input impedance is very large, Vb must be very small BAE 5413**Inverting Amplifier**• Amplifier performance is a function of external components only for ideal assumptions • Input and output impedances of the amplifier can be calculated as approximately: BAE 5413**Non-Inverting Amplifier**BAE 5413**Non-Inverting Amplifier**• Input and output impedances can be calculated as approximately: BAE 5413

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