Chapter 10 Operational Amplifier Theory and Performance  Modeling an Operational Amplifier  Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance  Frequency Response o Stability o The Gain-Bandwidth Product  Slew Rate

Chapter 10 Operational Amplifier Theory and Performance  Modeling an Operational Amplifier  Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance  Frequency Response o Stability o The Gain-Bandwidth Product  Slew Rate

FIGURE 10-1 A simple operational amplifier model with three components: differential input resistance, differential gain, and output resistance Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Modeling an Operational Amplifier

Chapter 10 Operational Amplifier Theory and Performance  Modeling an Operational Amplifier  Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance  Frequency Response o Stability o The Gain-Bandwidth Product  Slew Rate

FIGURE 10-2 The noninverting amplifier using the simplified op-amp model Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Noninverting amplifier model FIGURE 10-3 A block diagram representation of the noninverting amplifier

FIGURE 10-4 (Example 10-1) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example 10-1 Find the closed-loop gain of the amplifier when (1) a = (2) A = 10 6, and (3) A = 10 3.

FIGURE 10-5 Obtaining the closed-loop input resistance in a noninverting amplifier Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. r i = v i /i i i i = (v i – βv o )/r id = (v i – βAi i r id )/r id r i = v i /i i = r id (1+A β)

FIGURE 10-6 An external source v o driving the output to obtain the closed-loop output resistance Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

Chapter 10 Operational Amplifier Theory and Performance  Modeling an Operational Amplifier  Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance  Frequency Response o Stability o The Gain-Bandwidth Product  Slew Rate

FIGURE Frequency response of the open-loop gain of an operational amplifier; A 0 = dc gain, f 0 = cutoff frequency, f u = unit- gain frequency Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. f u = A 0 f 0 also called gain-bandwidth product or GBP

 Closed-loop bandwidth BW CL BW CL = f u β = A 0 f 0 β = βGBP Where β is the feedback ratio  Any point along the sloped portion of the open-loop gain plot satisfies the relationship gain x frequency = GBP  Only minimum guaranteed A 0 is given  f 0 is not known, but GBP is always given

FIGURE (Example 10-5) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example 10-5 Each of the op-amp has an open-loop GBP equal to 1 x 10 6 Hz. Find the cutoff frequencies in the closed-loop configurations shown. BW CL = f u β = A 0 f 0 β = βGBP

FIGURE Closed-loop gain vs. frequency for noninverting and inverting amplifiers Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. where A CLO = 1 + R f /R 1 (noninverting) or A CLO = R f /R 1 (inverting) and f c = β GBP

FIGURE Open-loop frequency response for the op-amp in Example 10-6 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example 10-6 With reference to the op-amp whose open-loop frequency response is shown in the following figure, find 1.The unity-gain frequency, 2.The open-loop 3-dB frequency, 3.The BW when the feedback ration is 0.02, and 4.The closed-loop gain at 0.4 MHz when the feedback ration is 0.04

Chapter 10 Operational Amplifier Theory and Performance  Modeling an Operational Amplifier  Feedback Theory o Feedback in the Noninverting Amplifier o Noninverting Input/Output Resistance  Frequency Response o Stability o The Gain-Bandwidth Product  Slew Rate

FIGURE The rate of change of a linear, or ramp, signal is the change in voltage divided by the change in time Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. The maximum possible rate at which an amplifier’s output voltage can change, in volts per second, is called its slew rate.

FIGURE (Example 10-7) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example 10-7 The op-amp has a slew-rate specification of 0.5 V/µs. If the input is the ramp waveform shown, what is the maximum closed-loop gain that the amplifier can have without exceeding its slew rate?

Conclusion The maximum frequency at which an amplifier can be operated depends on both bandwidth and the slew rate The rate change of v o (t) = V p sin ωt is (V p ω) volts/second so V p ω S or 2πf V p S where S is the specified slew rate of an amplifier f s (max) S/(2πV p ) and f (max) BW CL

FIGURE (Example 10-8) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example The op-amp has a slew rate of 0.5 V/µs. The amp must be capable of amplifying the following input signals: v 1 = 0.01 sin (10 6 t), v 2 = 0.05 sin (350 x 10 3 t), v 3 = 0.1 sin (200 x 10 3 t), and v 4 = 0.2 sin (50 x 10 3 t). 1.Determine whether the output will be distorted due to slew-rate limitations on any input. 2.If so, find a remedy (other than changing the input signals).

FIGURE (Example 10-9) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Example 10-9 The op-amp has a unity-gain frequency of 1 MHz (f u ) and a slew rate of 1 V/µs. Find the maximum frequency of a 0.1-V- peak sine-wave input that can be amplified without slew-rate distortion.