Slide 1General InfoOp-Amps – How Good Are They Exactly?Example: BatteriesMeasuring the Quality of a SourceSource Quality ExampleThevenin Equivalents of Op-Amp circuitsThevenin of Inverting AmplifierBut if you really want to…What’s wrong?Resistive Op-Amp modelOutput Resistance of Inverting Op-AmpInput ResistanceInput Resistance of Inverting AmplifierWhy are these quantities useful?Why are these quantities useful?Why are these quantities useful?Bad Amplifier (Small Rs)Good AmplifierOp-Amp SaturationOp-Amp Saturation ExamplePositive FeedbackThat’s all forOp-Ampsks1EE40 Summer 2010HugEE40Lecture 6Josh Hug7/2/20102EE40 Summer 2010HugGeneral Info•HW2 due today at 5PM•HW3 out, due TUESDAY at 2PM•There will be an optional pre-midterm HW available Tuesday•No lecture Monday•Labs as usual on Tuesday•No lab Wednesday•Midterm next Friday in class–12:10-1:30 [be on time!]–No electronic devices–One 8.5”x11” (or A4) sheet of paper•Handwritten anything you want, both sides3EE40 Summer 2010HugOp-Amps – How Good Are They Exactly?•We’ve been studying ideal op-amps•Of course, real Op-Amps aren’t perfect–For example, you can’t drive every device in the universe from a real op-amp•How do we precisely state the quality of a voltage source?–Look at its Thevenin equivalent–Lower Thevenin resistance is better4EE40 Summer 2010HugExample: Batteries•Real voltage sources, like batteries, have a limit to how much current they can draw–Called “internal resistance”–This internal resistance often varies with charge status, load attached, temperature, and more–Just like Thevenin resistance–+VTHRTHVout+–e.g., a car battery supplies 12 Volts, and can supply at most 200 amps, what is its internal resistance?12V/200A=0.06Ω5EE40 Summer 2010HugMeasuring 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:• –+VTHRTHRLVout+–So basically, for loads which are more than 99 times the Thevenin resistance, you get >99% of the Thevenin voltageLower RTH is better, can handle smaller loads6EE40 Summer 2010HugSource Quality Example•Everyone’s favorite resistive power supply again, vo=vi/1000• VinVoutRL–+1/1000V2/3ΩabRL=99*2/3Ω=66Ω 66Ω load gets 99% of VTH7EE40 Summer 2010HugThevenin Equivalents of Op-Amp circuits•Can find Thevenin equivalent of an op-amp circuit at its output terminals:•Just like finding Thevenin equivalent of a simple resistor based voltage attenuator at its output terminals:–+1/1000V2/3Ωa–+VTHRTHvo8EE40 Summer 2010HugThevenin of Inverting Amplifier•Assuming that the op-amp here is IDEAL, what’s the best way to find the Thevenin equivalent circuit?–We’ve already derived that it’s a perfect voltage source!–+VTHRTHvo−������9EE40 Summer 2010HugBut if you really want to…���=−����������=����0=∞���=���∞=0Technically you should take limits here but we are lazy…10EE40 Summer 2010HugWhat’s wrong?•Our op-amp model is missing something–That’s why it’s the “ideal” op-amp model–We’ll now introduce the “resistive” op-amp modelIdealResistive Op-Amp Model11EE40 Summer 2010HugResistive Op-Amp model•Takes in to account the fact that–Some current flows into the input terminals–The op-amp cannot source all device in the universe (output resistance is non-zero)12EE40 Summer 2010HugOutput Resistance of Inverting Op-Amp•On board (using resistive model of op-amp)•Output Resistance–Tells us how small our load can be before we start losing signal fidelity����≅�������+ ��13EE40 Summer 2010HugInput Resistance•Resistance at the input terminals of a device•Tells us how much current will be generated for a fixed input voltage–Useful, for example, to find power needed to power a device (at that input)���=��14EE40 Summer 2010HugInput Resistance of Inverting Amplifier•What is the input resistance of an inverting amplifier using ideal op-amp model? ���=��•What is the input resistance of an inverting amplifier using resistive op-amp model? ���≅ ��(See sec 15.42 in book)15EE40 Summer 2010HugWhy are these quantities useful?���≅ ������≅�������+ ��•Input resistance tells us how much current (power) our input signal needs to provide•Output resistance says how small of a load we can drive16EE40 Summer 2010HugWhy are these quantities useful?•An iPod provides roughly 1V signal output with 20Ω internal resistance•Speakers might be 4Ω resistance•Connect iPod directly to such speakers–Internal resistance dominates��������=420+4×1 � =0.17 ���������=0.172/ 4 Ω=0. 0072�����17EE40 Summer 2010HugWhy are these quantities useful?���≅ ������≅�������+ ��–+1V20ΩiPodRs–+−����� + ��4Ω�������+ ��Speakers18EE40 Summer 2010HugBad Amplifier (Small Rs)•Very small Rs–iPod must supply 50mW–Output resistance is large (can’t drive speakers)–+1V20ΩiPodRs–+−����� + ��4Ω�������+ ��Speakers19EE40 Summer 2010HugGood Amplifier•Rs=1000, Rf=3000, A=106, Rt=1000–+1V20ΩiPodRs–+−����� + ��4Ω�������+ ��SpeakersMust provide 1 mW2.93V0.00133Ω20EE40 Summer 2010HugOp-Amp Saturation•Remember those power ports we’ve been ignoring?•They specify the maximum and minimum voltage that our op-amp can deliver–If •Op-Amp output is –If ,•Op-Amp output is –If ,•Op-Amp output is 21EE40 Summer 2010HugOp-Amp Saturation Example•, •If A=3:• VinVo-5 V -12V-1V -3V2V 6V1,512,312V 12V12V-12V4V-4V22EE40 Summer 2010HugPositive FeedbackOn the board23EE40 Summer 2010HugThat’s all forOp-Ampsks•No class Monday•Enjoy weekend (doing op-amp
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