Operational Amplifiers

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Operational AmplifiersA Linear IC circuitOperational Amplifier (op-amp) An op-amp is a high-gain amplifier that has highinput impedance and low output impedance. An ideal op-amp has infinite gain and inputimpedance and zero output impedance. An integrated circuit (IC) contains a number ofcomponents on a single piece of semiconductor. Most op-amps are IC chips.1

The 741 Operational AmplifierOp-Amp Input/Output We consider the op-amp as a singlecomponent with inputand outputcharacteristics. Two signal inputs: Inverting Non-inverting Two dc power supplyleads ( and ) One output lead2

Op-Amp PackagesThe Operation of Op-amps The input stage of an op-amp is adifferential amplifier. The op-amp amplifies the differencebetween the two input terminal voltages.Vdiff V2 V1V1 V2 3

Op-Amp Output The output of the amplifier is determined by The gain of the amplifier.The polarity relationship between V1 and V2.The values of the supply voltages, V and -V.The load resistanceOp-Amp Gain The maximum possible gain of an op-ampis called the open-loop gain AOL. Generally AOL is greater than 10,000. Typical values are on the order of 200,000. An ideal op-amp would have infinite gain.4

Input/Output Polarity The output polarity follows the sign of Vdiff. If V2 – V1 0 the output polarity will be positive. If V2 – V1 0 the output polarity will be negative.V1 V2 Supply Voltages The supply voltages determine the limits of outputvoltage swing. No matter what the gain and inputvoltages the output value can not exceed V or–V. In practice the maximum output voltage is slightlyless than the supply voltages. For resistive loads 10kΩ the output voltages areabout 1V “less” than the supply voltages. For resistive loads 2kΩ the output voltages are about2V “less” than the supply voltages.5

Open Loop Op-amp Use As the open loop gain of most op-amps isextremely large the output of an open-loop circuitis either the maximum positive or negativevoltage. 15 VV1 V2 # 14 VVout "! 14 VV2 V1V2 V1-15 VFeedback Circuits6

Feedback Most op-amp circuits are designed to usefeedback. Feedback is defined as taking a portion of theoutput of a circuit and coupling or feeding it backinto the input. If the output fed back is in phase with the inputthen the circuit has positive feedback. If the output fed back is out of phase with theinput then the circuit has negative feedback.Negative Feedback Most amplifiers use negative feedback. Disadvantages: decreased gain. Advantages: increased circuit stability, increased input impedance, decreased output impedance, increased frequency bandwidth at constantgain.7

Negative Voltage Feedback A fraction B 1 of the output voltage is subtracted from theinput voltage.v" vin ! Bvoutv′ΣvinAOLvout-BNegative Voltage Feedback The closed loop gain, Av, is defined as The closed loop gain can be calculated from two equationsv′vinAOLΣvout-B8

Negative Voltage Feedback Solving for Av gives Usually the open-loop gain is so large that we can approximate:v′vinAOLΣvout-BNegative Feedback The gain of the amplifier circuitdepends only on B, the fractionof output voltage fed back. B can be made very constant sothat the amplifier has great gainstabilization. Example: B could be determinedby two resistors in a voltagedivider relationship.voutR1BvoutR29

Negative Feedback Impedance The input and output impedance is alsochanged by the feedback.Op-Amp Circuits With NegativeFeedback10

Non-Inverting Amplifier Using Kirchoff’s rule, Ohm’s Law, and our knowledge ofop-amps we can derive a closed loop-voltage gain for thenon-inverting amplifier circuit shown below.i2R2i1i R1vinv1voutv2Non-Inverting Amplifier As the input resistance of the op-amp is very large we canneglect i . The output voltage is given by the voltage difference andthe open-loop gain.i2R2i1i R1vinv1voutv211

Non-Inverting Amplifier Combining the previous equations we find:Av v outAOL (R1 R2 ) v in (AOL 1)R1 R2 If the open-loop gain is very large:!i2R2i1i R1v1vinvoutv2Inverting Amplifier Using Kirchoff’s rule, Ohm’s Law, and our knowledge ofop-amps we can derive a closed loop-voltage gain for theinverting amplifier circuit shown belowi2R2i1R1vini v1voutv212

Inverting Amplifier The output voltage is related to the voltage difference. Neglecting i and combining the equations givesi2R2i1R1vini v1voutv2Inverting Amplifier For a very large open-loop gainbecomesi2R2i1R1vini v1voutv213

The Two Golden Rules ofOp-Amp Circuits Notice in both derivations two approximations were made: (1)the input current i flowing into the op-amp was neglectedcompared to other currents; and (2) the open-loop op amp gainAOL was assumed to be very large compared to the gain withfeedback. These two approximations can be extended to form two “goldenrules” for analyzing an op-amp circuits with negative feedback. Op-Amp Current Rule (OACR): The current into or out of eachop-amp input terminal is approximately zero. Op-Amp Voltage Rule (OAVR): The voltage difference betweenthe two op-amp input terminals is approximately zero.Op-Amp Current Rule The OACR basically says that the inputimpedance of the op-amp is much higherthan the external input impedance from theinput terminal to ground. For BJT op-amps input impedance is on theorder of 10MΩ. For FET op-amps input impedance is on theorder of 1012 Ω.14

Op-Amp Voltage Rule The OAVR is the equivalent of saying that the open-loopgain is infinite. The output of the op-amp can never be greater than thesupply voltage ( 15V) which means that (v2-v1 ) must beless that 150 µV for a typical AOL or the output will besaturated. Therefore if the op-amp is not saturated then thedifference between the input terminals must be nearly zero. The rule says that in an actual op amp circuit the negativefeedback plus the high gain of the op-amp effectively zerosthe difference between the two inputs.Non-inverting Amp OACR: i1 i2OAVR: v1 v2 vini2R2i1R1vinv1voutv215

Inverting Amp OACR: i1 i2OAVR: v1 v2 0i2R2i1R1vinv1voutv2Instrumentation Amplifier16

Peak Detection AmplifierPositive Feedback17

Positive Feedback Circuits Rather than placing a portion of the outputback into the inverting input a portion of theoutput is sent back to the non-invertingterminal to produce positive feedback.Positive Feedback Circuits Oscillators18

Positive Feedback Circuits Oscillators19

7 Feedback Most op-amp circuits are designed to use feedback. Feedback is defined as taking a portion of the output of a circuit and coupling or feeding it back into the input. If the output fed back is in phase with the input then the circuit has positive feedback. If the output fed back is out of phase with the input then the circuit has negative feedback.

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