Operational AmplifiersOperational Amplifier PinsClassic 741 SchematicEquivalent Circuit Model (hard)Example CalculationVoltage Gain of CircuitDifferential rather than Difference AmplifierOp-Amp Feedback SystemDynamic Range of AmplifierEE 42/100Lecture 8: Op-AmpsELECTRONICSRev C 2/8/2012 (9:54 AM)Prof. Ali M. NiknejadUniversity of California, BerkeleyCopyrightc 2012 by Ali M. NiknejadA. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 1/23 – p. 1/23Operational AmplifiersVS+VS−VoutV+V−•Invented in 1941by Bell Labs engineer Karl D. Swartzel Jr. using vacuum tubes. Itfound wide application in WW-II.•First monolithic IC op-amp was designed by Bob Widlar at FairchildSemiconductor.•The 741 op-amp is perhaps the best known op-amp in the world. Many otherop-amps use the same pin configuration as the 741.•The output voltage is usually millions of times larger than the voltage presented atthe inputs.•Op-amps are ubiquitous low cost components used in countless applications foranalog signal processing (gain, filtering, signal conditioning).A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 2/23 – p. 2/23Operational Amplifier PinsVS+VS−VoutV+V−•The op-amp has 6 pins. There are the supply pins, where we connect a positiveand negate voltage, and three signal pins, the two inputs, and an output. There isalso a ground pin (not shown).•The signal pins are usually AC voltages whereas the supply voltages are DCvoltages.•Some op-amps work with a single supply, in which case the negative rail is ground.•Commonly known as the op-amp, is a high gain amplifier with a differential input.vo= A · (v+− v−)A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 3/23 – p. 3/23Classic 741 SchematicA. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 4/23 – p. 4/23Equivalent Circuit Model (hard)vin voutRoutRinVS− VS+Gvin v+v−•We model the complex op-amp by using the simple equivalent circuit shownabove. The most salient features are the high gain A (tyipcally a million or more),very high input resistance Rin, and low output resistance Rout.•Because of the large gain, only a few microvolts of input signal is required tosaturate the op-amp output. Thus the amplifier is very impractical if used withoutfeedback. In fact, the gain of the op-amp is a very poorly controlled parameter,often varying wildly with temperature or from part-to-part. How do you design withsuch an imperfect component? Feedback.A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 5/23 – p. 5/23Example Calculation+R1R2A(v+− v−)v+v−vsvoRin•The above example shows a typical op-amp configuration where the output signalis fed-back to the negative input terminals. This is called negative feedback.•This seems strange at first because we are subtracting the output from the input,but as we shall see, this is a self-regulation mechanism that results in a veryprecise amplifier.•Write KCL at the input node of the amplifier(v−− vo)G2+ v−Gin+ (v−− vs)G1= 0A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 6/23 – p. 6/23Voltage Gain of Circuit•But the output voltage in this case is simply given by vo= −Av−, where A is verylarge, which means that v−= −vo/A is a very small voltage(−voA− vo)G2+−voAGin+ (−voA− vs)G1= 0•which allows us to write the complete expression for gainvovs=−AG1G2(A + 1) + Gin+ G1•Assuming that the op-amp has a very large gain, the above equation simplifiesvovs≈−AG1G2(A + 1)≈−G1G2=−R2R1A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 7/23 – p. 7/23Differential rather than Difference Amplifier•Why do we call an op-amp a differential amplifier rather than a difference amplifier?•In the inverting amplifier configuration, we can calculate the effective input voltageby(v+− v−) =voA=−R2R1vsA≈ 0•A difference amplifier is perhaps a better name, but somewhat misleading since aswe see the input voltage must be small for the op-amp to operate correctly (hencea “differential” voltage).•We will build a true difference amplifier with op-amps later.A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 8/23 – p. 8/23Op-Amp Feedback Systemsi(s)so(s)+−a(s)f(s)•In the derivation we have a nice result that the voltage gain of the overall circuit isjust set by the ratio of two resistors, which can be made very precise and can tracktemperature.•The internal gain of the amplifier A does not appear in the final expression, whichmeans if it varies due to temperature or from part to part, it plays a negligible rolein setting the gain.•So we sacrificed gain to arrive at a solution that is much more robust. This is theconcept of negative feedback and it is used widely in electronic systems(biological, chemical, and mechanical systems use it too).•The idea is to sample a fraction of the output and compare it to the input. Byforcing equality between the sample and the fraction of the output, the gain isdetermined by the fraction rather than by the raw gain of the amplifier.•Note that positive feedback is not used, since it has a saturating (rather thanregulating) characteristic.A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 9/23 – p. 9/23Dynamic Range of Amplifier•So what did we gain when we designed an op-amp with such a high value of gain?For one, it’s an extremely versatile device that can be reconfigured to have anygain range by simply selecting the feedback components (R1and R2).•Subtle Point: Unlike a non-feedback (“open loop”) amplifier, the input linear rangecan be made larger since regardless of the input voltage source magnitude, thedifferential input of the op-amp is always small (v+− v−) = vo/A ≈ 0.A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 10/23 –
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