Digi-sign Event Feedback Made Easy

Digi sign event feedback

Hello. And welcome to the TI Precision Lab, Discussing intrinsic Op Amp Noise, Part 1. Overall, this video series on noise will show how to predict op amp noise with calculation and simulation, as well show how to accurately measure noise. In part 1, we will define intrinsic noise, introduce the different types of noise, and discuss noise spectral density. Noise can be defined as an unwanted signal that combines with the desired signal to result in an error. In audio, for example, noise can be noticed as a hiss or a popping sound. In a sensor system, noise can be an error in the measured sensor output, such as pressure or temperature. Noise can be categorized into two basic groups, extrinsic and intrinsic. Extrinsic noise is noise produced from some external circuit or natural phenomena. For example, 60 hertz powerline noise and interference from mobile phones are common examples of extrinsic noise. Cosmic radiation is another example of a natural phenomenon that causes extrinsic noise. Intrinsic noise is caused by components within a circuit. Resistors and semiconductor devices, for example, generate noise. Intrinsic noise is very predictable. Whereas extrinsic noise is typically difficult to predict. In this noise video series we will focus on intrinsic noise. As we mentioned before, our discussion will focus on how to calculate, simulate and measure noise. We will also discuss techniques for reducing noise. This slide illustrates how an amplifier circuit can be translated into a noise equivalent circuit. Each resistor has a noise voltage source associated with it. The noise voltage source is denoted by a circle with an asterisk inside. The amplifier also has a noise voltage source, and a noise current source. The noise current source is denoted by a diamond with an asterisk inside. The magnitude of the noise sources inside the amplifier is given in the amplifier's data sheet. The magnitude of the noise associated with the resistor is dependent on the resistance value, and can be calculated. We will soon learn how to combine the effects of all the noise sources to determine the total output noise. But first, let's look at some general categories of noise. This slide shows the time domain waveform for white noise, also known as broadband noise. The time domain waveform is what you would see if you measured noise with an oscilloscope. Notice that the horizontal axis is 1 millisecond full scale. Taking the reciprocal of the full scale time gives the frequency of 1 kilohertz. In general, broadband noise is considered to be in the middle-to-high high frequency range. That is frequencies greater than 1 kilohertz. In the next slide we'll consider lower frequency noise sources. Also note the statistical distribution to the right-hand of the slide. The distribution is Gaussian, with a mean value of 0 volts, and the skirts of the distribution at approximately plus or minus 40 millivolts. The distribution indicates that the probability of measuring noise near 0 volts is high. Whereas the probability of measuring noise near the skirts of the distribution is relatively low. Later we will see how the distribution can be used to estimate the peak-to-peak value of the noise signal. Flicker noise, also known as 1 over f, or low frequency noise, is another category of noise. This slide shows the time domain waveform, as well as the statistical distribution for 1 over f noise. The time domain waveform is what you would see if you measured noise with an oscilloscope. Notice that the horizontal axis is 10 seconds full scale. Taking the reciprocal of the full scale time gives a frequency of 0.1 hertz. In general, 1 over f noise is considered to be in the low-frequency range. That is frequencies less than 1 kilohertz. Another category of noise is called burst or popcorn noise. Popcorn noise is a sudden change or step in voltage or current. It does not follow a Gaussian distribution. Instead it has a bimodal or multimodal distribution. The example above jumps between three discrete modes of operation. Popcorn noise is low frequency from 0.1 hertz to 1 kilohertz. Popcorn noise sounds like popping popcorn when played on a speaker or headphones. Popcorn noise is caused by defects in a device, and unfortunately it cannot be mathematically predicted. This presentation does not give further details on popcorn noise. As we have already seen, the various categories of noise have many synonyms. For example, broadband noise is also called white noise, Johnson noise, thermal noise, and resistor noise. It can become very confusing to engineers that are new to the subject, when literature and presentations switch between these different terms. A brief background in statistics is helpful with noise analysis, because most noise has a Gaussian distribution. The probability density function creates the outline of the Gaussian curve. The probability distribution is derived by integrating the probability density function. The probability distribution function gives the probability that an event will occur in a certain interval. For example, if the probability distribution function is equal to 0.3 for x in the range of minus 1 to plus 1, then there is a 30% chance that x will be between minus 1 and plus 1 at any instant in time. In the case of noise, we will use the probability distribution function to estimate peak-to-peak noise. The probability distribution function indicates that there is a 68% chance that a peak will occur between plus or minus 1 standard deviation or 2 sigma. For plus or minus 3 standard deviations, or 6 sigma, the probability increases to 99.7%. This is often used as an estimate of peak-to-peak noise. Keep in mind, however, that the tails of the Gaussian curve are infinite. So there's always a finite probability that noise can be measured outside of the interval of plus or minus 3 sigma. The table shown here relates the number of standard deviations to the probability that a measurement is bounded by this range. For example, there's a 68.3% chance that any instantaneous noise measurement will be in the range of 2 sigma, or plus or minus 1 standard deviation. 6 sigma and 6.6 sigma are common ways of estimating the peak-to-peak noise. In the case of 6 sigma, for example, there is a 99.7% percent chance that any instantaneous measurement will occur within that range. Thus the chance that a noise reading is outside this limit at any instant in time is only 0.3%. The 0.3% probability is considered to be negligible. So 6 sigma is often used as an approximation for peak-to-peak noise. If you are familiar with noise analysis you may have heard the term standard deviation and RMS used interchangeably. This leads one to wonder, is RMS equivalent to standard deviation? The answer is both yes and no. If the signal has no DC offset, the answer is yes. This is the case for most noise signals. Notice that the equation for RMS and standard deviation are the same, except that the standard deviation equation subtracts out the average or DC offset. In the case where a signal has a DC offset, RMS will not be equal to the standard deviation. Fortunately, op amp and resistor noise do not have a DC offset. So we can consider RMS to be equivalent to the standard deviation in these cases. Some extrinsic noise, such as digital switching noise, may not be symmetrical and thus will have a DC offset. It is important to note, however, that some instruments or simulation tools will report RMS noise, including the offset term, AC plus DC, and others will report RMS without the offset term, AC only. An important concept in noise analysis is adding noise values. Noise cannot be added algebraically, for example, 3 plus 5 equals 8. Noise must be added as a vector as shown here, where we take the square root of 3 millivolts RMS squared, plus 5 millivolts RMS squared for a result of 5.83 millivolts RMS. It is important to note that this relationship applies only to uncorrelated random noise. If the noise source is correlated, a different formula applies. Do you remember that white light is the combination of all colors? Well, white noise is the combination of all frequencies. This figure shows that when you add several signals of different frequencies together in the time domain, the result is a random-looking signal. In the frequency domain, each one of these signals looks like an impulse. Combining an infinite number of these signals across all frequencies, creates what is called a noise spectral density curve. Voltage noise spectral density is often a confusing parameter to engineers who are not familiar with noise analysis. Spectral density has units of nanovolts per square root hertz. Multiplying spectral density by the square root of the noise bandwidth gives the RMS noise, as shown in the equation on the top right. Looking at the units in the equation, you can see how the square root hertz cancels out. The spectral density curve is the main amplifier specification used to describe an amplifier's noise characteristics. In this video series we will use the spectral density curve extensively in noise calculations. At this point we have introduced many of the fundamentals needed to understand noise. This slide shows how to calculate the noise produced by a resistor. This noise is generated by the random motion of charges within the resistor. The equation shown above gives the total RMS noise generated by a resistor. Notice that the equation requires the temperature in Kelvin, the resistance, the bandwidth, and Boltzmann's constant. Dividing both sides of the equation by the square root of the bandwidth yields the voltage spectral density equation. Remember that amplifier's noise specifications are usually given in terms of spectral density. Determining the noise spectral density for a resistor is useful. Because it allows for easy comparison of the noise generated by resistors and the noise generated by amplifiers. This plot was generated using the equation given in the last slide. Note that the equation was divided by the square root of the bandwidth to give a spectral density, which is useful, because it provides a quick way of comparing resistor noise to op amp noise. Remember, most op amps specify noise in nanovolts per square root hertz. A very low noise amplifier may have intrinsic noise of only 1 nanovolt per root hertz. Comparing to this plot, 1 nanovolt per root hertz corresponds to a resistor value of approximately 70 ohms. Thus for this example, you should try to use resistors of 70 ohms or less with this op amp. For best performance it's recommended for the amplifier in a circuit to generate more noise than the resistors. Low noise amplifiers can be expensive. And you would not want to pay extra for an expensive low-noise amplifier, and have resistor noise dominate the circuit's noise performance. Neglecting resistor noise is a very common oversight of engineers who are new to noise analysis. For this reason, it is useful to have this chart available for quick reference. This slide shows the typical op amp noise model. In some cases, it is important to have two separate current noise sources, as shown in the upper left. In other cases, the simplified model with a single noise source between the inputs, is adequate. The noise sources represent the spectral density curves. In the following videos discussing noise, we will learn how to use the op amp noise model to predict the total peak-to-peak output noise for different amplifier configurations. That concludes this video. Thank you for watching. Please try the quiz to check your understanding of this video's content.