# Operational Amplifiers

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

2 The 741 Operational Amplifier Op-Amp Input/Output We consider the opamp as a single component with input and output characteristics. Two signal inputs: Inverting Non-inverting Two dc power supply leads (+ and ) One output lead 2

3 Op-Amp Packages The Operation of Op-amps The input stage of an op-amp is a differential amplifier. The op-amp amplifies the difference between the two input terminal voltages. V diff =V 2 V 1 V 1 V 2 + 3

4 Op-Amp Output The output of the amplifier is determined by The gain of the amplifier. The polarity relationship between V 1 and V 2. The values of the supply voltages, +V and -V. The load resistance Op-Amp Gain The maximum possible gain of an op-amp is called the open-loop gain A OL. Generally A OL is greater than 10,000. Typical values are on the order of 200,000. An ideal op-amp would have infinite gain. 4

5 Input/Output Polarity The output polarity follows the sign of V diff. If V 2 V 1 > 0 the output polarity will be positive. If V 2 V 1 < 0 the output polarity will be negative. V 1 V 2 + Supply Voltages The supply voltages determine the limits of output voltage swing. No matter what the gain and input voltages the output value can not exceed +V or V. In practice the maximum output voltage is slightly less than the supply voltages. For resistive loads > 10kΩ the output voltages are about 1V less than the supply voltages. For resistive loads > 2kΩ the output voltages are about 2V less than the supply voltages. 5

6 Open Loop Op-amp Use As the open loop gain of most op-amps is extremely large the output of an open-loop circuit is either the maximum positive or negative voltage. +15 V V 1 V 2 + # + 14 V V > V 2 V out = " \$ 14 V V2 <! V V Feedback Circuits 6

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. Negative Feedback Most amplifiers use negative feedback. Disadvantages: decreased gain. Advantages: increased circuit stability, increased input impedance, decreased output impedance, increased frequency bandwidth at constant gain. 7

8 Negative Voltage Feedback A fraction B < 1 of the output voltage is subtracted from the input voltage. v " =! Bv out Σ v A OL v out -B Negative Voltage Feedback The closed loop gain, A v, is defined as The closed loop gain can be calculated from two equations Σ v A OL v out -B 8

9 Negative Voltage Feedback Solving for A v gives Usually the open-loop gain is so large that we can approximate: Σ v A OL v out -B Negative Feedback The gain of the amplifier circuit depends only on B, the fraction of output voltage fed back. B can be made very constant so that the amplifier has great gain stabilization. Bv out R 1 v out Example: B could be determined by two resistors in a voltage divider relationship. R 2 9

10 Negative Feedback Impedance The input and output impedance is also changed by the feedback. Op-Amp Circuits With Negative Feedback 10

11 Non-Inverting Amplifier Using Kirchoff s rule, Ohm s Law, and our knowledge of op-amps we can derive a closed loop-voltage gain for the non-inverting amplifier circuit shown below. i 2 i 1 R 2 R 1 i v 1 v 2 v out Non-Inverting Amplifier As the input resistance of the op-amp is very large we can neglect i. The output voltage is given by the voltage difference and the open-loop gain. i 2 i 1 R 2 R 1 i v 1 v 2 v out 11

12 Non-Inverting Amplifier Combining the previous equations we find: A v = v out = A OL (R 1 + R 2 ) (A OL +1)R 1 + R 2 If the open-loop gain is very large: i 2 i 1 R 2 R 1 i v 1 v 2 v out Inverting Amplifier Using Kirchoff s rule, Ohm s Law, and our knowledge of op-amps we can derive a closed loop-voltage gain for the inverting amplifier circuit shown below i 2 i 1 R 2 R 1 i v 1 v 2 vout 12

13 Inverting Amplifier The output voltage is related to the voltage difference. Neglecting i and combining the equations gives i 2 i 1 R 2 R 1 i v 1 v 2 vout Inverting Amplifier For a very large open-loop gain becomes i 2 i 1 R 2 R 1 i v 1 v 2 vout 13

14 The Two Golden Rules of Op-Amp Circuits Notice in both derivations two approximations were made: (1) the input current i flowing into the op-amp was neglected compared to other currents; and (2) the open-loop op amp gain A OL was assumed to be very large compared to the gain with feedback. These two approximations can be extended to form two golden rules for analyzing an op-amp circuits with negative feedback. Op-Amp Current Rule (OACR): The current into or out of each op-amp input terminal is approximately zero. Op-Amp Voltage Rule (OAVR): The voltage difference between the two op-amp input terminals is approximately zero. Op-Amp Current Rule The OACR basically says that the input impedance of the op-amp is much higher than the external input impedance from the input terminal to ground. For BJT op-amps input impedance is on the order of 10MΩ. For FET op-amps input impedance is on the order of Ω. 14

15 Op-Amp Voltage Rule The OAVR is the equivalent of saying that the open-loop gain is infinite. The output of the op-amp can never be greater than the supply voltage (~15V) which means that (v 2 -v 1 ) must be less that 150 µv for a typical A OL or the output will be saturated. Therefore if the op-amp is not saturated then the difference between the input terminals must be nearly zero. The rule says that in an actual op amp circuit the negative feedback plus the high gain of the op-amp effectively zeros the difference between the two inputs. Non-inverting Amp OACR: i 1 = i 2 OAVR: v 1 = v 2 = i 2 i R 1 2 R 1 v 1 v 2 v out 15

16 Inverting Amp OACR: i 1 = i 2 OAVR: v 1 = v 2 = 0 i 2 i R 1 2 R 1 v 1 v 2 vout Instrumentation Amplifier 16

17 Peak Detection Amplifier Positive Feedback 17

18 Positive Feedback Circuits Rather than placing a portion of the output back into the inverting input a portion of the output is sent back to the non-inverting terminal to produce positive feedback. Positive Feedback Circuits Oscillators 18

19 Positive Feedback Circuits Oscillators 19

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