EE40 Lecture 5 Josh Hug 6 30 2010 EE40 Summer 2010 Hug 1 General Info Lab 2 today HW1 grades up on bspace Make up lab next week Date TBA Discussions going back to 2 hours HW2 still due Friday at 5 PM It is long you should be half done Get started tonight if you haven t started yet Don t forget about the discussion board Don t forget there are other human beings who are also working on this homework EE40 Summer 2010 Hug 2 The Need for Dependent Sources Suppose you build a circuit such that v o vi 1000 to be used as a power supply Vout Vin RL E g R1 332 667 R2 R3 R4 1 Consider what happens when you attach a load to the power supply for example a resistor EE40 Summer 2010 Hug 3 Operational Amplifiers Dependent Sources are handy Allows for decoupling Only one problem They don t exist The Operational Amplifier approximates an ideal voltage dependent voltage source Very very cool circuits Analog IC design is hard EE40 Summer 2010 Hug 4 Most Obvious Op Amp Circuit We ll ignore power supply ports for now e g A 1 1000 EE40 Summer 2010 Hug 5 One Problem The open loop gain A is Hard to reliably control during manufacturing Typically very large A 1 000 000 Fixed for a single device Negative feedback helps us overcome these issues EE40 Summer 2010 Hug 6 Simple Op Amp Circuit with Negative Feedback On the board EE40 Summer 2010 Hug 7b Negative Feedback Op Amp Circuit Assuming A is very big 2 1 2 2 1 2 EE40 Summer 2010 Hug 8 Op Amp Circuit Output voltage is independent of load One op amp fits all just tweak your resistors Output is independent of A EE40 Summer 2010 Hug 9 Wait so whoa how did that happen Let s consider what happened to 2 2 1 2 1 1 2 2 1 2 2 1 EE40 Summer 2010 and for large A Where represents some tiny number Hug 10b The Voodoo of Analog Circuit Design For large A 1 The negative feedback forces to be extremely close to This very tiny difference between and gives us v o EE40 Summer 2010 Hug 11 The Voodoo of Analog Circuit Design For large A For this circuit 1 No longer focus on how op amp drives the output but instead on how it drives its own input The gain A disappears since if it s really big the op amp just forces EE40 Summer 2010 Hug 12 Consequence of Negative Feedback This input forcing property generalizes to all circuits with negative feedback Specifically in any circuit where v o is connected back to and not to we have the property that We ll approximate this by assuming that Not actually equal otherwise the op amp would not do anything However with A 1 000 000 this approximation is incredibly accurate Less error from this approximation than component variation temperature variation etc EE40 Summer 2010 Hug 13 Approach to Op Amp Circuits An op amp connected in a negativefeedback configuration does the following Forces Can approximate by Our prior approach was to replace the opamp by dependent source and solve This opens up a new approach EE40 Summer 2010 Hug 14 Approach to Op Amp Circuits If there s only negative feedback Assume Assume and Summing point constraint If there s no feedback or positive feedback replace the op amp with equivalent dependent source and solve EE40 Summer 2010 Hug 15 Negative Feedback Amplifiers and Concept was invented on a ferry to Manhattan by Harold Stephan Black during his morning commute to Bell Labs in Manhattan in 1927 originally sketched out on a blank spot of his New York Times The idea is bizarre but really epic Completely revolutionized electronics 9 years before patent office believed it EE40 Summer 2010 Hug 16 If you re a little lost Don t fret the idea is weird At first just keep in mind the important thing An op amp with negative feedback has the properties that and Later if you want to show that this really works do an op amp circuit from scratch by replacing the op amp with a voltage source and you ll get the same answer EE40 Summer 2010 Hug 17 Example using the Summing Point Constraint 0 0 2 2 2 1 1 2 1 1 2 2 EE40 Summer 2010 Hug 18b Summing Point Constraint You don t have to use the summing point constraint However it is much faster albeit less familiar and thus a little tricky at first EE40 Summer 2010 Hug 19 Op Amp Circuits There are a bunch of archetypical circuits the one we ve studied so far is the noninverting amplifier Inverting amplifier Voltage follower EE40 Summer 2010 Hug 20 Board Problems Time Let s go through some problems on the board EE40 Summer 2010 Hug 21 And then we were done We did some op amp problems in class and then called it a day here next slides will appear on Friday EE40 Summer 2010 Hug 22 Op Amps How Good Are They Exactly Of course Op Amps aren t perfect You can t drive every device in the universe from one op amp How do we measure how good a voltage source is Looking at its Thevenin equivalent Lower Thevenin resistance is better EE40 Summer 2010 Hug 23 Measuring the Quality of a Source If you attach a resistive load then the output voltage is If you want Vout to be 99 of VTH then RTH VTH EE40 Summer 2010 RL Vout So basically for loads which are more than 99 times the Thevenin resistance you get 99 of the Thevenin voltage Lower RTH is better can handle smaller loads 24 Hug Source Quality Example Suppose you build a circuit such that vo vi 1000 to be used as a power supply Vout Vin 2 3 RL a 1 1000V EE40 Summer 2010 b RL 99 2 3 66 66 load gets 99 of VTH25 Hug Thevenin Equivalents of Op Amp circuits Can look at Thevenin equivalent of an opamp circuit at its output terminals RTH VTH vo Just like converting a simple resistor based voltage attenuator 2 3 a 1 1000V EE40 Summer 2010 Hug 26
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