1. Laboratory for Perceptual Robotics – Department of Computer Science Embedded Systems Operational Amplifiers

2. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps …very high gain dc-coupled differential amplifiers with single-ended outputs… -15V non-invert invert offset null NC +15V out offset null about $0.60 a piece 24 transistors 11 resistors 1 capacitor amplifier gains ~ 10 5 -10 6

3. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps output ~ K (V + - V - ) K ~ 10 6 V+V+ V-V- +15V -15V 1.output swings dramatically and via feedback, makes difference between the inputs go to zero 2.inputs draw no current (10 -9 A) a few millivolts difference between inputs will cause the output to swing full range

4. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps V out = K (V + - V - ) V+V+ V-V- What does it mean to say the op amp is stable? stable or unstable?

5. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps What does it mean to say the op amp is stable? V out = K (V + - V - ) V+V+ V-V- stable or unstable?

6. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Negative Feedback feedback - comparing the output of a system to the desired output in order to make a signed corrective action CYBERNETICS negative feedback - connect the output back to the input in such a way as to cancel some of the input. Harold S. Black - patent application on negative feedback in 1928 was “…treated in the same manner as one for a perpetual motion machine.”

7. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Stable Inverting Amplifier assume V + =V - =GND I2I2 I1I1 I 1 +I 2 = 0 note: low input and output impedance, R 1 +R 2

8. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Stable Non-Inverting Amplifier assume V + =V - =GND large input impedance Z in ~ 10 8 W

9. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Unity Gain Follower

10. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Current-to-Voltage Converter

11. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Summing Amplifier weighted sum? digital to analog converter?

12. Laboratory for Perceptual Robotics – Department of Computer Science OpAmps - Bipolar Power Amplifier