Slide 1General InfoThe Need for Dependent SourcesOperational AmplifiersMost Obvious Op-Amp CircuitOne ProblemSimple Op-Amp Circuit with Negative FeedbackNegative Feedback Op-Amp CircuitOp-Amp CircuitWait, so whoa, how did that happen?The Voodoo of Analog Circuit DesignThe Voodoo of Analog Circuit DesignConsequence of Negative FeedbackApproach to Op-Amp CircuitsApproach to Op-Amp CircuitsNegative Feedback AmplifiersIf you’re a little lostExample using the Summing-Point ConstraintSumming-Point ConstraintOp-Amp CircuitsBoard Problems TimeAnd then we were done…Op-Amps – How Good Are They Exactly?Measuring the Quality of a SourceSource Quality ExampleThevenin Equivalents of Op-Amp circuits1EE40 Summer 2010HugEE40Lecture 5Josh Hug6/30/20102EE40 Summer 2010HugGeneral 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 homework3EE40 Summer 2010HugThe Need for Dependent Sources•Suppose you build a circuit such that vo=vi/1000, to be used as a power supply–E.g. R1=332.667Ω, R2=R3=R4=1Ω•Consider what happens when you attach a load to the power supply, for example, a resistor• VinVoutRL4EE40 Summer 2010HugOperational 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 hard5EE40 Summer 2010HugMost Obvious Op-Amp Circuit��= ���e.g.A=1/1000We’ll ignore power supply ports for now6EE40 Summer 2010HugOne 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��= ���7EE40 Summer 2010HugSimple Op-Amp Circuit with Negative FeedbackOntheboard:b8EE40 Summer 2010HugNegative Feedback Op-Amp CircuitAssuming A is very big… ��=�����2�1+�2��=���2�1+�29EE40 Summer 2010HugOp-Amp Circuit•Output voltage is independent of load!•One op-amp fits all, just tweak your resistors!•Output is independent of A! 10EE40 Summer 2010HugWait, so whoa, how did that happen?•Let’s consider what happened to :• �−=� ��1+ ��2�1+�2×�2�1+�2+¿� �2�1+�2+ � �2�−=�¿andforlargeA…+¿(1− �)�−=�¿Whereεrepresentssometinynumberb11EE40 Summer 2010HugThe Voodoo of Analog Circuit Design+¿(1− �)�−=�¿ForlargeA:•The “negative feedback” forces to be extremely close to •This very tiny difference between and gives us vo•12EE40 Summer 2010HugThe Voodoo of Analog Circuit Design+¿(1− �)�−=�¿ForlargeA:•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 • For this circuit:13EE40 Summer 2010HugConsequence of Negative Feedback•This input forcing property generalizes to all circuits with “negative feedback”•Specifically, in any circuit where vo 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. •14EE40 Summer 2010HugApproach to Op-Amp Circuits•An op-amp connected in a negative-feedback configuration does the following:–Forces –Can approximate by • +¿�¿�−+¿�¿�−•Our prior approach was to replace the op-amp by dependent source and solve•This opens up a new approach15EE40 Summer 2010HugApproach to Op-Amp Circuits•If there’s only negative feedback:–Assume –Assume and •If there’s no feedback or positive feedback, replace the op-amp with equivalent dependent source and solve • +¿�¿�−+¿�¿�−“Summing-point constraint”16EE40 Summer 2010HugNegative Feedback Amplifiers+¿�¿�−+¿�¿�−+¿=�−�¿•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 itand17EE40 Summer 2010HugIf 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•18EE40 Summer 2010HugExample using the Summing-Point Constraint+¿=���−=�¿��2=�−�2=���2��=��+��1�1¿��+���1/ �2¿���1+�2�2+¿=0�−=0, �¿b19EE40 Summer 2010HugSumming-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 first20EE40 Summer 2010HugOp-Amp Circuits•There are a bunch of archetypical circuits, the one we’ve studied so far is the “non-inverting amplifier”��=−��������=��VoltagefollowerInvertingamplifier21EE40 Summer 2010HugBoard Problems Time•Let’s go through some problems on the board22EE40 Summer 2010HugAnd then we were done…•We did some op-amp problems in class and then called it a day here, next slides will appear on Friday23EE40 Summer 2010HugOp-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 better24EE40 Summer 2010HugMeasuring the Quality of a Source•If you attach a resistive load, then the output voltage
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