**Operational Amplifiers at Higher Frequencies
**

*
George Rutkowski, P.E.
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Course Outline**

This course includes a Review of Fundamentals and Glossary of Terms. It reviews and introduces many basic equations and terms related to applications of operational amplifiers (Op Amps). Manufacturers’ specifications (Specs) are included and are values applicable at low frequencies. At higher frequencies, these tend to change and affect how well Op Amp applications perform.

In this course, you will consider problems caused by the decrease (roll-off) of the open-loop gain *AVOL* at higher frequencies and how the gain vs. frequency curves of some Op Amps can be tailored by the circuit designer. With other Op Amp types, the gain versus frequency curves are set by the manufacturer. The universally accepted definition of the term bandwidth (BW) is described here. And you will learn the multiple ways that BW of amplifiers are determined. You will also become familiar with other notable frequency-related performances, such as output-voltage swing capabilities, slew rates (switching speeds), common-mode-rejection ratios and that Op Amps’ have internally-generated noise.

This course covers the following topics:

- Gain (amplification) and phase Shift vs. Frequency
- Bode Diagrams
- External Frequency Compensation
- Compensated Operational Amplifiers
- Slew Rates
- Output Swing Capability
- Harmonics in Nonsinusoidal Waveforms
- Inherently Generated Noise
- Equivalent Input Noise Model
- Review of Fundamentals and Glossary of Terms
- Appendix A – Specs of the 741 Op Amp
- Table E-1 – List of Typical Op Amps, their Parameters and Specs
- Appendix I – Derivation of equation 6-1
- Review of Fundamentals and Glossary of Terms

This course includes a multiple-choice quiz at the end, which is designed to
enhance the understanding of the course materials.

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Learning Objective

At the conclusion of this course, the student will:

- Become familiar with open-loop gain versus frequency characteristics of typical uncompensated operational amplifiers;
- See how a typical uncompensated Op Amp’s gain versus frequency characteristics can be approximated with a series of straight lines, which enables you to predict stability of the circuit;
- Be aware of Op Amp operating frequency limitations and be able to predict their performance at various input frequencies and waveforms;
- Learn the advantages and disadvantages of compensated and uncompensated Op Amps;
- Know precisely what a specified gain-bandwidth product means;
- Learn how an amplifier’s bandwidth (BW) is defined;
- Determine BW from the specified gain-bandwidth product and the selected closed-loop gain of the Op Amp circuit;
- Determine BW from an Op Amp’s observed output rise or fall time resulting from a step or square wave input;
- See how to determine an Op Amp’s output rise and fall times given its slew rate;
- Understand that repetitious nonsinusoidal waveforms contain a fundamental sine wave frequency and harmonics that are integer multiples of that fundamental;
- See that the more rapid (shorter) the rise and fall times of a square or rectangular wave, the greater the number of harmonics it contains. Understanding this is very useful in the modern world of digital systems in which Op Amps work; and
- Learn that while induced noise comes from external sources, operational amplifiers, and amplifiers in general, generate noise internally.

**Intended Audience**

Engineers, technologists and anyone familiar with Ohm’s and Kirchoff’s laws (basic electrical circuits) that are interested in becoming competent with this very flexible electronic component.

**Benefit for Attendee**

Operational Amplifiers have many useful characteristics; their ease of use, typically low cost, compact size, large range of applications and low power consumption to name a few. But they have limitations too. Here you will see some including limited bandwidth, reduced common-mode rejection and increased thermally generated noise with larger bandwidths. If you have to select, or replace, an Op Amp that must operated with a wider bandwidth, you’ll know what specified parameters to look for.

**Course Introduction**

This course includes a Review of Fundamentals and Glossary of Terms. It reviews and introduces many basic equations and terms related to applications of operational amplifiers (Op Amps). Manufacturers’ specifications (Specs) are included and are values applicable at low frequencies. At higher frequencies, these tend to change and affect how well Op Amp applications perform.

Course Content

The course content are in the following PDF files:

**Chapter 6 - Op Amp’s behavior at Higher Frequencies
Appendix A – Specs of the 741 Op Amp
Table E-1 – List of Typical Op Amps, their Parameters and Specs
Appendix I – Derivation of equation 6-1
Review of Fundamentals and Glossary of Terms**

Please click on the above underlined hypertext to view, download or print the document for your study. Because of the file size, we recommend that you first save the file to your computer by right-clicking the mouse and choosing "Save Target As ...", and then open the file in Adobe Acrobat Reader from your computer.

**Course
Summary**

Knowing how Operational Amplifiers behave at higher frequencies is important in our modern world of digital electronic systems in which operational amplifiers often work. In such environments manufacturers’ specified terms like bandwidth, rise-and-fall times, slew rates and gain-bandwidth products define how well Op Amps will work in existing or contemplated applications. These terms are explained in this lesson.

This course begins with a review of operational amplifiers including a glossary of terms and equations related to circuit applications of Op Amps. Some of these terms, that are defined here, are specifications provided in the manufacturers’ literature. The equations are for inverting amplifier gain, noninverting amplifier gain, common-mode gain, and *effective* input resistance & output resistances. These were described in more detail, and derivations provided, in previous courses.

You’ll see that at higher frequencies, the Op Amp circuit’s output signal phase shifts and can cause the circuit to be unstable. How unstable operation is avoided is discussed here. Depending on the frequency range to be amplified, the choice of using a compensated or uncompensated Op Amp is selected. You’ll learn how to determine the amplifier’s bandwidth (BW) from its gain vs. frequency curve, its specified Slew Rate, or its output waveform as observed on an oscilloscope. The causes of added harmonics and of reduction of harmonics are described. Included is a discussion of where noise, in addition to induced noise, comes from; how generated.

Included here are descriptions of how typical Op Amps behave at higher frequencies. Op Amps at low frequencies, and when wired to have negative feedback, have output signals that are 180 degrees out of phase with input signals at the inverting input. At higher frequencies, however, the output signal’s phase shifts away from 180°. The greater this shift, the more in-phase the output signal become with the input signal. An in-phase feedback is a positive feedback that makes the amplifier unstable; that is, it can assert random oscillations and unpredictable variations at the output regardless of the input waveforms.

Related Links

For additional technical information related to this subject, please visit the following websites:

Operational Amplifiers (Op Amps) Applications by National Semiconductor

http://www.national.com/analog/amplifiers/application_notes

http://en.wikipedia.com/wiki/Operational_amplifier_applications

http://www.tmworld.com/article/CA6582570.html

**Qu****iz**

**Once
you finish studying ****the
above course content,****
you need to
take a quiz
to obtain the PDH credits**.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.