Analog to Digital Converter: Single Slope and Dual Slope ADC Explained — Transcript

Full transcript

1. 0:12Hey friends, welcome to the YouTube channel ALL ABOUT ELECTRONICS.
2. 0:17In the previous introductory video, we understood the basics of ADC.
3. 0:21So, in this video, let's learn about the Dual Slope ADC.
4. 0:26So, this Dual-Slope ADC is integrating type ADC.
5. 0:31Meaning that it uses the integrator circuit for the conversion.
6. 0:35So, this type of ADC provides a high resolution with good accuracy.
7. 0:41But they have slow conversion time.
8. 0:44And due to that, they are not used for the data acquisition.
9. 0:49For example, they are not used in the single processing application where a lot of data
10. 0:55needs to be acquired continuously.
11. 0:58And they are preferred in the applications where the signal is changing very slowly.
12. 1:04But due to their good accuracy and high resolution, they are used in the measurement instruments
13. 1:09where good reliability is essential.
14. 1:13And in fact, they are commonly used in digital multimeters.
15. 1:17So, before we go through this dual-slope ADC, let's quickly go through the single slope
16. 1:23ADC.
17. 1:24Which will not only help us in understanding the working of this dual-slope ADC, but it
18. 1:30will also help us in understanding, why the dual slope ADC is used over the single slope
19. 1:35ADC.
20. 1:36So, in case of the single slope ADC, the reference voltage is integrated using the integrator.
21. 1:44And then it is compared with the input voltage using the comparator.
22. 1:48So, this reference voltage is integrated until the integrated output is equal to the input
23. 1:54voltage.
24. 1:55And this time T gives us the measure of the input voltage.
25. 1:59So, let's understand it.
26. 2:02So, in the case of the integrator, the output voltage can be given as minus 1 by RC times,
27. 2:09integration of input voltage.
28. 2:12And here as the reference voltage is negative, so the slope of the integrated output will
29. 2:18be positive.
30. 2:20And at time T, the output voltage Vout can be given as
31. 2:23T* Vref/RC.
32. 2:32And if you see over here, at time T, the output voltage is equal to the input voltage.
33. 2:38So, we can compare this expression with the input voltage.
34. 2:43So, from this, we can say that this input voltage Vin is equal to T* Vref/RC.
35. 2:51Now, for the given ADC, the reference voltage and the value of R and C are constant.
36. 2:59That means we can say that this magnitude of the input voltage is directly proportional
37. 3:04to this T. So, this time T gives us the measure of the
38. 3:09input voltage.
39. 3:11So, now let's understand how we can measure this integrating time.
40. 3:16So, as you can see in this diagram, the output of the comparator, is given to the AND gate.
41. 3:23And through this AND gate, the clock pulses are applied to this counter.
42. 3:27So, whenever the output of the comparator is high, then the clock pulses will be applied
43. 3:33to this counter.
44. 3:34So, as soon as this counter gets this clock pulses, it starts counting.
45. 3:39Now, before the conversion starts, the counter has been reset to the zero.
46. 3:45So, whenever the conversion starts, then the integrated output will be less than the input
47. 3:51voltage.
48. 3:53That means the output of the comparator will be high.
49. 3:56And due to that, these clock pulses will be applied to the counter.
50. 4:01Or we can say that during the integration time, this counter starts counting.
51. 4:07And as soon as, the output voltage of the integrator is just equal to the input voltage,
52. 4:13then the output of the comparator will become low.
53. 4:16And due to that, the output of this AND gate will also become low.
54. 4:21So now, no clock pulses will be applied to this counter.
55. 4:26And whatever count that is present at the output of this counter, is directly proportional
56. 4:31to the input voltage.
57. 4:33So, in this way, this single slope ADC converts the input voltage into the binary output.
58. 4:40Now, in this circuit, there is also a RESET switch.
59. 4:46And it will get closed momentarily, whenever the output of the comparator will become low.
60. 4:51So, basically, it ensures that no charge remains across the capacitor whenever we start the
61. 4:57new conversion.
62. 4:59So, this is the basic function of the single slope ADC.
63. 5:04Now, here as the reference voltage and the RC time constant is fixed, so the slope of
64. 5:11the integrator will remain fixed.
65. 5:14And depending on the input voltage, this time T will change.
66. 5:18So, if the input voltage is higher than the time which is required for the integration
67. 5:23will be higher.
68. 5:25But the slope of this integrator will remain the same.
69. 5:29And due to the single slope, this ADC is known as the single slope ADC.
70. 5:35And this is the very simple type of integrating ADC.
71. 5:39But in this case, if you notice, if the value of R or C changes, then the slope will also
72. 5:45change.
73. 5:46And now for the same input, we will get a different time.
74. 5:50For example, if the value of R reduces, then the time required by the integrator to reach
75. 5:57the input voltage will also reduce.
76. 6:00And now for the same input voltage, we will get the lesser time.
77. 6:06And practically this thing bound to happen because the value of R and C will not remain
78. 6:11constant and it will change over the period of time, either due to the aging or temperature.
79. 6:16So, due to that, the accuracy of this single slope ADC is very poor.
80. 6:23And that is why this ADC is not used for the measurement purpose.
81. 6:28But this problem can be solved by using the dual slope ADC.
82. 6:32So, now let's understand the working of the dual slope ADC.
83. 6:37So, in case of this dual-slope ADC, there is a switch at the input of the integrator
84. 6:43which can connect either to an input voltage or to the reference voltage.
85. 6:48But initially, during the start of the conversion.
86. 6:51the switch is connected to the input voltage.
87. 6:55So, once the conversion starts, then this integrator starts integrating this input signal
88. 7:00for a finite time.
89. 7:03And let's say, this time is equal to T1.
90. 7:08And if you see the output voltage of the integrator, then it can be given as, minus 1 by RC times,
91. 7:15integration of input voltage.
92. 7:18Or after the time T1, we can say that it is equal to -T1*Vin/(RC).
93. 7:26And let's say that is equal to V1.
94. 7:29Now, after this time T1, the switch will get connected to the reference voltage.
95. 7:35So, now the integrator will integrate this reference voltage.
96. 7:41And if you notice the sign of this reference voltage, it is negative.
97. 7:45And usually,m the magnitude of this reference voltage is larger than the input voltage.
98. 7:50Now, due to this negative reference voltage, the integrator integrates in the positive
99. 7:56direction.
100. 7:58And after time T1, it will integrate until the output of this integrator reaches the
101. 8:04zero volt.
102. 8:05So, this time T2 is the time that is required by the integrator to reach to the zero volt.
103. 8:12And this time T2 is the direct measure of the input voltage.
104. 8:15So, let's understand it.
105. 8:18So, after this time T1, the integrator output can be given as the initial voltage across
106. 8:24the integrator plus (-1/RC) times integration of input voltage.
107. 8:31And in this case, now the input to the integrator is equal to -Vref.
108. 8:35Now, if you notice over here, after this time T1, the initial voltage across the integrator
109. 8:42is equal to V1.
110. 8:45And for this time T2, this term can be written as -T2*(-Vref)/RC.
111. 8:55And the initial voltage across the capacitor is equal to V1.
112. 8:58So, this will be the total voltage across the integrator after the time T1+T2.
113. 9:05Now, in this expression, if we put the value of V1, then we can write the output voltage
114. 9:16Vout as (T2/RC)*Vref + (-T1*Vin/RC) Now, one more thing if you notice over here,
115. 9:23after this time, the output of the integrator will become zero.
116. 9:28that means we can say that, after this time T1+T2, the output of the integrator is equal
117. 9:34to 0.
118. 9:36So, if we rearrange the terms then we can write it as (T1/RC)*Vin = (T2/RC)*Vref
119. 9:47So, after canceling this RC and rearranging these terms we can write the T2 as T1*Vin/Vref
120. 9:57Now, in this dual-slope ADC, this time T1 and the reference voltage are fixed.
121. 10:04That means we can say that this time T2 is directly proportional to the input voltage.
122. 10:10So, as the input voltage changes, this time T2 will also change.
123. 10:16So, as you can see over here, as the input voltage increases, then this first slope will
124. 10:22also increase.
125. 10:24But the second slope will remain the same.
126. 10:27Because over here, the value of Vref and RC are fixed.
127. 10:31So, as the value of input voltage increases, then the time T2 will also increase.
128. 10:37So, in short, this time T2 gives the direct measure of the input voltage.
129. 10:44And now, let's understand how we can measure it.
130. 10:48So, as you can see in this diagram, the output of the integrator is connected to the comparator.
131. 10:55And the other input to the comparator is connected to the ground terminal.
132. 10:59So, initially, when the input is connected to the input voltage, then the integrator
133. 11:05integrates in the negative direction.
134. 11:07That means the inverting terminal of the comparator is negative with respect to the non-inverting
135. 11:14terminal.
136. 11:15And due to that, the output of the comparator will be high.
137. 11:19Now, this comparator output is connected to the AND gate.
138. 11:24And the clock signal is provided to this n-bit counter using this AND gate.
139. 11:29So, whenever the output of the comparator is high, at that time, this clock pulses will
140. 11:35be provided to this n-bit counter.
141. 11:38And due to that, this counter starts counting from zero onwards.
142. 11:43That means if we combine all these blocks then we can say that whenever the switch is
143. 11:48connected to the input voltage then the counter starts counting from zero onwards.
144. 11:54And it will count until this overflow bit will become 1.
145. 11:58So, let's say, if we have 4-bit counter then it will start counting from all zeros to all
146. 12:061's.
147. 12:08And after all 1's, during the next clock, the overflow bit will become 1.
148. 12:14And once this overflow bit becomes 1, then the switch toggles from the input voltage
149. 12:19to the reference voltage.
150. 12:21So, going from all zeros to all 1's, the counter will take total 2 to the power N minus 1 clock.
151. 12:29And after that in the next clock, whenever the overflow bit will become 1, then this
152. 12:35switch will toggle from the input voltage to the reference voltage.
153. 12:38So, we can say that this input signal will be integrated for total 2^N clocks.
154. 12:47And after that, this switch will get toggled to the reference voltage.
155. 12:51Now, here as the reference voltage is negative, so integrator starts integrating in the positive
156. 12:58direction.
157. 12:59But still, if you see the output of the integrator, it will still remain negative.
158. 13:03That means the output of the comparator is still high.
159. 13:08And due to that, the clock signal will be applied to this n-bit counter.
160. 13:13That means after generating this overflow bit when the reference voltage is getting
161. 13:17integrated, this counter starts counting from zero onwards.
162. 13:22And it will count, until the output of the integrator is equal to zero.
163. 13:27Because after that the comparator output will become low.
164. 13:32And these clock pulses will not get applied to this counter.
165. 13:35So, at that time, whatever is the binary output of this n-bit counter, it will be directly
166. 13:42proportional to the time T2.
167. 13:44And in a way, we can say that this binary output is directly proportional to the input
168. 13:49voltage.
169. 13:50So, in this way, using this dual-slope ADC, the input voltage can be converted into the
170. 13:57digital output.
171. 13:58So, here the total conversion time is equal to T1+T2.
172. 14:04Or we can say that it is equal to 2^N *Tc +T2.
173. 14:10Because the input will get integrated for 2^N clocks.
174. 14:16And here, Tc is the clock duration.
175. 14:19So, in general, we can say that the conversion time will be equal to (2^N*Tc + N*Tc)
176. 14:24where N is the output of this n-bit counter.
177. 14:32So, in the worst case, whenever the input voltage is same as the reference voltage,
178. 14:38in that case, both slopes will be equal.
179. 14:43And the total conversion time will be equal to 2*2^N*Tc.
180. 14:47Or we can say that it is equal to 2^(N+1)*Tc.
181. 14:54So, as you can see, it takes much longer time for the conversion.
182. 14:59And the conversion time of this ADC depends on the resolution that means the number of
183. 15:06bits of the ADC as well as the clock frequency.
184. 15:11And as we increase the resolution, that means the number of bits of the counter, then the
185. 15:15conversion time will increase.
186. 15:17So, to understand that let's put some numbers into this expression.
187. 15:24So let's say, we have 12-bit dual-slope ADC and it is operated at the clock speed of 10
188. 15:30MHz.
189. 15:32Then in the worst case, the maximum conversion time will be equal to 0.8 ms.
190. 15:38On the other end, for 16-bit ADC, with the same clock frequency, the maximum conversion
191. 15:43time would be roughly around 13 ms.
192. 15:47So, as you can see, as the number of bits increases, the conversion time will also increase.
193. 15:54And that is why we can not increase the resolution of this type of ADC beyond a certain extent.
194. 16:01And of course, by increasing the clock frequency we can reduce this conversion time.
195. 16:06But that too, can not be increased beyond a certain limit.
196. 16:11As the response time of the different components in the ADC is the limiting factor.
197. 16:16And due to that, this type of ADC is not used for the data acquisition.
198. 16:23But it provides good accuracy as well as noise immunity.
199. 16:26So, if you see this expression of T2 then it is independent of RC.
200. 16:33That means the value of R and C won't affect the conversion.
201. 16:37And hence, this dual slope ADC can provide good accuracy.
202. 16:42Apart from that this ADC also provides good noise immunity.
203. 16:47And particularly against the supply frequency noise.
204. 16:50So, due to its good accuracy and the noise immunity, this dual slope ADC is used in the
205. 16:56measurement instruments.
206. 16:57So, I hope in this video, you understood the working of this single slope as well as the
207. 17:03dual slope ADC.
208. 17:05So, if you have any question or suggestion, do let me know here in the comment section
209. 17:09below.
210. 17:10If you like this video, hit the like button and subscribe to the channel for more such
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