Operational Amplifier Noise

Techniques and Tips for Analyzing and Reducing Noise

Art Kay

• Publisher: Newnes
• Year: 2012
• eBook ISBN: 9780080942438
• Topic: Design
• Subtopic: Industrial Design

Arthur Kay's exciting new publication is a must have for practicing, professional electrical engineers. This comprehensive guide shows engineers how to design amplifiers and associated electronics to minimize noise, providing tricks, rules-of-thumb, and analysis to create successful low noise circuits. Forget the classical textbook traps of equations, virtual grounds, and a lot of double-speak, the novel but educational presentation used here uses definition-by -example and straight-forward analysis. This is the ultimate reference book for engineers who don't have the time to read, since the concepts are presented in detailed pictures and then repeated in the text for those who like both.Operational amplifiers play a vital role in modern electronics design. Today, op amps serve as the interfaces between the digital world of microprocessors, microcontrollers, and other digital circuits and the analog "real world". If an analog signal must be amplified, conditioned, filtered, or converted to be used by a digital system, an op amp is almost always involved. Noise is an unwanted signal that will corrupt or distort the desired signal, and veteran engineers as well as new college graduates are often faced with a lack of experience in noise analysis for operational amplifiers. The author has created a publication that is packed with essential information, while still being accessible to all readers.- Clear, definition-by-example presentation allows for immediate use of techniques introduced- Tricks and rules-of-thumb, derived from author's decades of experience- Extreme use of figures for rapid absorption of concepts- Concise text explains the key points in all figures- Accessible to all types of readers- Analysis and design of low-noise circuits using op amps, including design tradeoffs for low-noise- Desktop reference for designing low-noise op amp circuits for novice to experienced engineers- Accurate measurement and prediction of intrinsic noise levels, using analysis by hand and SPICE simulation

Chapter 1

Introduction and Review of Statistics

Noise analysis can be done in the time domain, in the frequency domain, or by using statistical analysis. This chapter introduces these three analysis methods. These methods will be utilized throughout this book.

1.1 Time Domain View of Noise

Noise is most commonly viewed in the time domain. A typical plot of time domain noise is shown in Figure 1.1. In the time domain, noise voltage is on the y-axis and time is on the x-axis. Noise can be viewed in the time domain using an oscilloscope. Figure 1.1 also shows that if you look at this random signal statistically, it can be represented as a Gaussian distribution. The distribution is drawn sideways to help show its relationship with the time domain signal. In Section 1.2, the statistical view is discussed in detail.

Figure 1.1 Thermal noise shown in the time domain and statistically

Figure 1.1 shows thermal noise in the time domain. Thermal noise is generated by the random motion of electrons in a conductor. Because this motion increases with temperature, the magnitude of thermal noise increases with temperature. Thermal noise can be viewed as a random variation in the voltage present across a component (e.g., resistor). Figure 1.2 gives the equation for finding the root mean square (RMS) thermal noise given resistance temperature and bandwidth.

Figure 1.2 Thermal noise voltage equation

The important thing to know about the thermal noise equation is that it allows you to find an RMS noise voltage. In many cases, engineers want to know the peak-to-peak noise voltage. In Section 1.2, we will learn some statistical methods that can be used to estimate peak-to-peak noise voltage given the RMS noise value. Section 1.2 also covers other basic statistical methods that are used in noise analysis.

1.2 Statistical View of Noise

Most forms of intrinsic noise have a Gaussian distribution and can be analyzed using statistical methods. For example, statistical methods must be used to calculate the sum of two noise signals or estimate peak-to-peak amplitude. This section gives a short review of some basic statistical methods required to carry out noise analysis.

1.2.1 Probability Density Function

The mathematical equation that forms the normal distribution function is called the “probability density function” (see Figure 1.3). Plotting a histogram of noise voltage measured over a time interval will approximate the shape of this function. Figure 1.4 illustrates a measured noise histogram with the probability distribution function superimposed on it.

Figure 1.3 Probability density function for a Gaussian distribution

Figure 1.4 Measured distribution with superimposed probability density function

1.2.2 Probability Distribution Function

The probability distribution function is the integral of the probability density function. This function is very useful because it tells us about the probability of an event that will occur in a given interval (see Figures 1.5 and 1.6. For example, assume that Figure 1.6 is a noise probability distribution function. The function tells us that there is a 30% chance that you will measure a noise voltage between −1 V and +1 V [i.e., the interval (−1, 1)] at any instant in time.

Figure 1.5 Probability distribution function

Figure 1.6 Probability density function and probability distribution function

This probability distribution function is instrumental in helping us translate RMS to peak-to-peak voltage or current noise. Note that the tails of the Gaussian distribution are infinite. This implies that any noise voltage is possible. While this is theoretically true, in practical terms the probability that extremely large instantaneous noise voltages are generated is very small. For example, the probability that we measure a noise voltage between −3σ and +3σ is 99.7%. In other words, there is only a 0.3% chance of measuring a voltage outside of this interval. For this reason, ±3σ (i.e., 6σ) is often used to estimate the peak-to-peak value for a noise signal. Note that some engineers use 6.6σ to estimate the peak-to-peak value of noise. There is no agreed-upon standard for this estimation. Figure 1.7 graphically shows how 2σ will catch 68% of the noise. Table 1.1 summarizes the relationship between standard deviation and probability of measuring a noise voltage.

Figure 1.7 Illustrates how standard deviation relates to peak-to-peak

Table 1.1. Number of Standard Deviations and Chance of Measuring Voltage

Number of Standard Deviations	Chance of Measuring Voltage (%)
2σ (same as ±σ)	68.3
3σ (same as ±1.5σ)	86.6
4σ (same as ±2σ)	95.4
5σ (same as ±2.5σ)	98.8
6σ (same as ±3σ)	99.7
6.6σ (same as ±3.3σ)	99.9

Thus, we have a relationship that allows us to estimate peak-to-peak noise given the standard deviation. In general, however, we want to convert RMS to peak-to-peak amplitude. Often, people assume that the RMS and standard deviation are the same. This is not always the case. The two values are equal only when there is no DC component (the DC component is the average value μ). In the case of thermal noise, there is no DC component, so the standa...

Table of contents

• Cover Image
• Content
• Title
• Copyright
• Preface
• Acknowledgments
• Chapter 1. Introduction and Review of Statistics
• Chapter 2. Introduction to Op-Amp Noise
• Chapter 3. Op-Amp Noise Example Calculations
• Chapter 4. Introduction to Spice Noise Analysis
• Chapter 5. Introduction to Noise Measurement
• Chapter 6. Noise Inside the Amplifier
• Chapter 7. Popcorn Noise
• Chapter 8. 1/f Noise and Zero-Drift Amplifiers
• Chapter 9. Instrumentation Amplifier Noise
• Chapter 10. Photodiode Amplifier Noise
• Chapter 11. Photodiode Noise Amplifier Example Results
• Glossary
• Answers to Questions
• Index