Spectral density — Transcript

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1. 0:00Hello.
2. 0:01And welcome to the TI Precision Lab,
3. 0:03Discussing intrinsic Op Amp Noise, Part 1.
4. 0:07Overall, this video series on noise
5. 0:09will show how to predict op amp noise with calculation
6. 0:12and simulation, as well show how to accurately measure noise.
7. 0:16In part 1, we will define intrinsic noise,
8. 0:19introduce the different types of noise,
9. 0:21and discuss noise spectral density.
10. 0:26Noise can be defined as an unwanted signal that
11. 0:29combines with the desired signal to result in an error.
12. 0:33In audio, for example, noise can be noticed
13. 0:36as a hiss or a popping sound.
14. 0:38In a sensor system, noise can be an error in the measured sensor
15. 0:42output, such as pressure or temperature.
16. 0:46Noise can be categorized into two basic groups,
17. 0:49extrinsic and intrinsic.
18. 0:52Extrinsic noise is noise produced
19. 0:55from some external circuit or natural phenomena.
20. 0:59For example, 60 hertz powerline noise and interference
21. 1:03from mobile phones are common examples of extrinsic noise.
22. 1:08Cosmic radiation is another example of a natural phenomenon
23. 1:12that causes extrinsic noise.
24. 1:14Intrinsic noise is caused by components within a circuit.
25. 1:19Resistors and semiconductor devices, for example,
26. 1:22generate noise.
27. 1:25Intrinsic noise is very predictable.
28. 1:27Whereas extrinsic noise is typically difficult to predict.
29. 1:32In this noise video series we will focus on intrinsic noise.
30. 1:37As we mentioned before, our discussion
31. 1:39will focus on how to calculate, simulate and measure noise.
32. 1:43We will also discuss techniques for reducing noise.
33. 1:50This slide illustrates how an amplifier circuit
34. 1:53can be translated into a noise equivalent circuit.
35. 1:57Each resistor has a noise voltage source
36. 2:00associated with it.
37. 2:01The noise voltage source is denoted by a circle
38. 2:05with an asterisk inside.
39. 2:07The amplifier also has a noise voltage source,
40. 2:10and a noise current source.
41. 2:12The noise current source is denoted by a diamond
42. 2:15with an asterisk inside.
43. 2:17The magnitude of the noise sources inside the amplifier
44. 2:20is given in the amplifier's data sheet.
45. 2:24The magnitude of the noise associated with the resistor
46. 2:27is dependent on the resistance value, and can be calculated.
47. 2:32We will soon learn how to combine
48. 2:34the effects of all the noise sources
49. 2:36to determine the total output noise.
50. 2:38But first, let's look at some general categories of noise.
51. 2:43This slide shows the time domain waveform
52. 2:46for white noise, also known as broadband noise.
53. 2:50The time domain waveform is what you
54. 2:52would see if you measured noise with an oscilloscope.
55. 2:56Notice that the horizontal axis is 1 millisecond full scale.
56. 3:00Taking the reciprocal of the full scale time
57. 3:03gives the frequency of 1 kilohertz.
58. 3:06In general, broadband noise is considered
59. 3:08to be in the middle-to-high high frequency range.
60. 3:11That is frequencies greater than 1 kilohertz.
61. 3:15In the next slide we'll consider lower frequency noise sources.
62. 3:19Also note the statistical distribution
63. 3:21to the right-hand of the slide.
64. 3:24The distribution is Gaussian, with a mean value of 0 volts,
65. 3:28and the skirts of the distribution at approximately
66. 3:31plus or minus 40 millivolts.
67. 3:34The distribution indicates that the probability of measuring
68. 3:37noise near 0 volts is high.
69. 3:40Whereas the probability of measuring noise
70. 3:42near the skirts of the distribution is relatively low.
71. 3:46Later we will see how the distribution
72. 3:48can be used to estimate the peak-to-peak value of the noise
73. 3:52signal.
74. 3:54Flicker noise, also known as 1 over f, or low frequency noise,
75. 3:59is another category of noise.
76. 4:01This slide shows the time domain waveform, as well as
77. 4:04the statistical distribution for 1 over f noise.
78. 4:08The time domain waveform is what you
79. 4:10would see if you measured noise with an oscilloscope.
80. 4:14Notice that the horizontal axis is 10 seconds full scale.
81. 4:18Taking the reciprocal of the full scale time
82. 4:21gives a frequency of 0.1 hertz.
83. 4:24In general, 1 over f noise is considered
84. 4:27to be in the low-frequency range.
85. 4:29That is frequencies less than 1 kilohertz.
86. 4:35Another category of noise is called burst or popcorn noise.
87. 4:39Popcorn noise is a sudden change or step in voltage or current.
88. 4:44It does not follow a Gaussian distribution.
89. 4:47Instead it has a bimodal or multimodal distribution.
90. 4:51The example above jumps between three discrete modes
91. 4:55of operation.
92. 4:57Popcorn noise is low frequency from 0.1 hertz to 1 kilohertz.
93. 5:02Popcorn noise sounds like popping popcorn
94. 5:05when played on a speaker or headphones.
95. 5:08Popcorn noise is caused by defects in a device,
96. 5:11and unfortunately it cannot be mathematically predicted.
97. 5:15This presentation does not give further details
98. 5:17on popcorn noise.
99. 5:22As we have already seen, the various categories of noise
100. 5:25have many synonyms.
101. 5:27For example, broadband noise is also
102. 5:30called white noise, Johnson noise, thermal noise,
103. 5:34and resistor noise.
104. 5:36It can become very confusing to engineers
105. 5:38that are new to the subject, when
106. 5:40literature and presentations switch
107. 5:42between these different terms.
108. 5:47A brief background in statistics is helpful with noise analysis,
109. 5:51because most noise has a Gaussian distribution.
110. 5:54The probability density function creates the outline
111. 5:57of the Gaussian curve.
112. 5:59The probability distribution is derived
113. 6:02by integrating the probability density function.
114. 6:06The probability distribution function
115. 6:08gives the probability that an event will
116. 6:10occur in a certain interval.
117. 6:13For example, if the probability distribution function
118. 6:16is equal to 0.3 for x in the range of minus 1 to plus 1,
119. 6:22then there is a 30% chance that x
120. 6:24will be between minus 1 and plus 1 at any instant in time.
121. 6:30In the case of noise, we will use the probability distribution
122. 6:33function to estimate peak-to-peak noise.
123. 6:39The probability distribution function
124. 6:41indicates that there is a 68% chance
125. 6:44that a peak will occur between plus or minus 1
126. 6:47standard deviation or 2 sigma.
127. 6:50For plus or minus 3 standard deviations, or 6 sigma,
128. 6:54the probability increases to 99.7%.
129. 6:58This is often used as an estimate of peak-to-peak noise.
130. 7:02Keep in mind, however, that the tails of the Gaussian curve
131. 7:05are infinite.
132. 7:07So there's always a finite probability
133. 7:09that noise can be measured outside of the interval
134. 7:12of plus or minus 3 sigma.
135. 7:18The table shown here relates the number of standard deviations
136. 7:22to the probability that a measurement
137. 7:23is bounded by this range.
138. 7:26For example, there's a 68.3% chance
139. 7:30that any instantaneous noise measurement will
140. 7:32be in the range of 2 sigma, or plus or minus 1
141. 7:35standard deviation.
142. 7:386 sigma and 6.6 sigma are common ways
143. 7:41of estimating the peak-to-peak noise.
144. 7:44In the case of 6 sigma, for example,
145. 7:47there is a 99.7% percent chance that any instantaneous
146. 7:51measurement will occur within that range.
147. 7:54Thus the chance that a noise reading
148. 7:56is outside this limit at any instant in time is only 0.3%.
149. 8:02The 0.3% probability is considered to be negligible.
150. 8:06So 6 sigma is often used as an approximation
151. 8:09for peak-to-peak noise.
152. 8:12If you are familiar with noise analysis
153. 8:14you may have heard the term standard deviation and RMS
154. 8:18used interchangeably.
155. 8:20This leads one to wonder, is RMS equivalent
156. 8:23to standard deviation?
157. 8:27The answer is both yes and no.
158. 8:30If the signal has no DC offset, the answer is yes.
159. 8:34This is the case for most noise signals.
160. 8:37Notice that the equation for RMS and standard deviation
161. 8:40are the same, except that the standard deviation
162. 8:43equation subtracts out the average or DC offset.
163. 8:49In the case where a signal has a DC offset,
164. 8:51RMS will not be equal to the standard deviation.
165. 8:55Fortunately, op amp and resistor noise do not have a DC offset.
166. 9:00So we can consider RMS to be equivalent
167. 9:03to the standard deviation in these cases.
168. 9:06Some extrinsic noise, such as digital switching noise,
169. 9:11may not be symmetrical and thus will have a DC offset.
170. 9:15It is important to note, however, that some instruments
171. 9:18or simulation tools will report RMS noise, including
172. 9:22the offset term, AC plus DC, and others
173. 9:26will report RMS without the offset term, AC only.
174. 9:31An important concept in noise analysis is adding noise values.
175. 9:36Noise cannot be added algebraically, for example,
176. 9:403 plus 5 equals 8.
177. 9:43Noise must be added as a vector as shown here,
178. 9:46where we take the square root of 3 millivolts RMS squared,
179. 9:50plus 5 millivolts RMS squared for a result of 5.83
180. 9:55millivolts RMS.
181. 9:58It is important to note that this relationship applies only
182. 10:01to uncorrelated random noise.
183. 10:04If the noise source is correlated,
184. 10:06a different formula applies.
185. 10:12Do you remember that white light is
186. 10:14the combination of all colors?
187. 10:16Well, white noise is the combination of all frequencies.
188. 10:21This figure shows that when you add
189. 10:23several signals of different frequencies
190. 10:25together in the time domain, the result
191. 10:27is a random-looking signal.
192. 10:30In the frequency domain, each one of these signals
193. 10:33looks like an impulse.
194. 10:35Combining an infinite number of these signals
195. 10:37across all frequencies, creates what is called a noise spectral
196. 10:41density curve.
197. 10:44Voltage noise spectral density is often
198. 10:46a confusing parameter to engineers who are not
199. 10:49familiar with noise analysis.
200. 10:51Spectral density has units of nanovolts per square root hertz.
201. 10:56Multiplying spectral density by the square root of the noise
202. 11:00bandwidth gives the RMS noise, as shown in the equation
203. 11:04on the top right.
204. 11:06Looking at the units in the equation,
205. 11:08you can see how the square root hertz cancels out.
206. 11:12The spectral density curve is the main amplifier specification
207. 11:16used to describe an amplifier's noise characteristics.
208. 11:20In this video series we will use the spectral density curve
209. 11:23extensively in noise calculations.
210. 11:28At this point we have introduced many of the fundamentals needed
211. 11:31to understand noise.
212. 11:34This slide shows how to calculate the noise produced
213. 11:36by a resistor.
214. 11:38This noise is generated by the random motion
215. 11:40of charges within the resistor.
216. 11:43The equation shown above gives the total RMS noise
217. 11:47generated by a resistor.
218. 11:49Notice that the equation requires the temperature
219. 11:51in Kelvin, the resistance, the bandwidth, and Boltzmann's
220. 11:55constant.
221. 11:57Dividing both sides of the equation
222. 11:59by the square root of the bandwidth
223. 12:01yields the voltage spectral density equation.
224. 12:05Remember that amplifier's noise specifications are usually given
225. 12:09in terms of spectral density.
226. 12:11Determining the noise spectral density for a resistor
227. 12:14is useful.
228. 12:15Because it allows for easy comparison
229. 12:17of the noise generated by resistors and the noise
230. 12:20generated by amplifiers.
231. 12:24This plot was generated using the equation
232. 12:26given in the last slide.
233. 12:28Note that the equation was divided
234. 12:30by the square root of the bandwidth
235. 12:31to give a spectral density, which is useful,
236. 12:34because it provides a quick way of comparing resistor
237. 12:37noise to op amp noise.
238. 12:39Remember, most op amps specify noise
239. 12:42in nanovolts per square root hertz.
240. 12:46A very low noise amplifier may have intrinsic noise of only 1
241. 12:50nanovolt per root hertz.
242. 12:53Comparing to this plot, 1 nanovolt per root hertz
243. 12:56corresponds to a resistor value of approximately 70 ohms.
244. 13:01Thus for this example, you should
245. 13:03try to use resistors of 70 ohms or less with this op amp.
246. 13:08For best performance it's recommended
247. 13:10for the amplifier in a circuit to generate more noise
248. 13:14than the resistors.
249. 13:16Low noise amplifiers can be expensive.
250. 13:18And you would not want to pay extra
251. 13:20for an expensive low-noise amplifier,
252. 13:22and have resistor noise dominate the circuit's noise performance.
253. 13:28Neglecting resistor noise is a very common oversight
254. 13:31of engineers who are new to noise analysis.
255. 13:34For this reason, it is useful to have this chart available
256. 13:37for quick reference.
257. 13:40This slide shows the typical op amp noise model.
258. 13:43In some cases, it is important to have
259. 13:45two separate current noise sources,
260. 13:47as shown in the upper left.
261. 13:50In other cases, the simplified model
262. 13:52with a single noise source between the inputs, is adequate.
263. 13:57The noise sources represent the spectral density curves.
264. 14:01In the following videos discussing noise,
265. 14:03we will learn how to use the op amp noise
266. 14:05model to predict the total peak-to-peak output
267. 14:08noise for different amplifier configurations.
268. 14:13That concludes this video.
269. 14:15Thank you for watching.
270. 14:17Please try the quiz to check your understanding
271. 14:19of this video's content.