2 Ideal OP AmpCircuit modelTwo golden rules to perform calculations on op amps with negative feedback:iin=0, no current flow into op amp.V+=V-Typically one end of op amp is connected to ground, therefore, V+=V-= 0V, virtual ground. Often V+ is connected to ground to avoid stability problem.
3 Applications: building block for analog systems AmplifiersAdders and SubstractorsIntegrators & DifferentiatorsClock generatorsFiltersDigital-to-analog converters
6 When A is very large Suppose A=106, R1=9R, R2=R Gain: determined by resistance ratioinsensitive to A, temperature, fab variation
7 Why did this happen? Negative feedback e.g. vIN=5VSuppose I perturb the circuit (e.g. force v0 momentarily to 12V somehowStable point is when v+v-Key: negative feedback portion of output fed to –ve input.e.g. Car antilock brakes small corrections
8 How to control a high-strung device Antilock brakes
9 More op amp insights: Observe, under negative feedback, We also know Yield an easier analysis method (under negative feedback)
10 Insightful analysis method: under negative feedback
11 Voltage follower Why is this circuit useful? has minimum effects on previous and next circuit.
12 Inverting AmplifierFeedback resistor, always to negative input
13 Summing Amplifier: Add Circuit If RS1=RS2=…=RSN=RS
14 Non-innverting Amplifier Feedback resistor, always to negative input
15 Differential Amplifier: Substractor Very useful if both signals are corrupted with noise: Electrocardiogram (EKG)