Embedded Systems Operational AmplifiersOpAmpsSlide 3Slide 4Slide 5OpAmps - Negative FeedbackOpAmps - Stable Inverting AmplifierOpAmps - Stable Non-Inverting AmplifierOpAmps - Unity Gain FollowerOpAmps - Current-to-Voltage ConverterOpAmps - Summing AmplifierOpAmps - Bipolar Power AmplifierLaboratory for Perceptual Robotics – Department of Computer ScienceEmbedded SystemsOperational AmplifiersLaboratory for Perceptual Robotics – Department of Computer ScienceOpAmps…very high gain dc-coupled differential amplifierswith single-ended outputs…-15Vnon-invertinvertoffset nullNC+15Voutoffset nullabout $0.60 a piece24 transistors11 resistors 1 capacitoramplifier gains ~ 105-106Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmpsoutput ~ K (V+ - V-)K ~ 106V+V-+15V-15V1. output swings dramatically and via feedback, makes difference between the inputs go to zero2. inputs draw no current (10-9A)a few millivolts difference betweeninputs will cause the output to swingfull rangeLaboratory for Perceptual Robotics – Department of Computer ScienceOpAmpsVout= K (V+ - V-)V+V-What does it mean to say the op amp is stable?stable or unstable?Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmpsWhat does it mean to say the op amp is stable?Vout= K (V+ - V-)V+V-stable or unstable?Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Negative Feedbackfeedback - comparing the output of a system to the desired output in order to make a signed corrective actionCYBERNETICSnegative 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 negativefeedback in 1928 was “…treated in the same manner as one for a perpetual motion machine.”Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Stable Inverting Amplifierassume V+=V-=GNDI2I1I1+I2 = 0note: low input and output impedance, R1+R2Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Stable Non-Inverting Amplifierassume V+=V-=GNDlarge input impedanceZin ~ 108 WLaboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Unity Gain FollowerLaboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Current-to-Voltage ConverterLaboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Summing Amplifierweighted sum?digital to analog converter?Laboratory for Perceptual Robotics – Department of Computer ScienceOpAmps - Bipolar Power