Threaded Mode | Linear Mode

Gerson W. Barbosa · 09-26-2017, 04:37 PM

(09-25-2017 08:04 PM)emece67 Wrote: I have not read the whole thread, but I'm wondering if the fact that the base resistor values form a, more or less, geometric series is used in some way.

Thus, the E12 series uses 12 values on each decade, this way the ratio between one value and the next is \(\sqrt[12]{10}=1.2115\ldots\). This way the E12 values are:

1

\(\sqrt[12]{10}=1.2115\ldots\approx1.2\)

\((\sqrt[12]{10})^2=1.4677\ldots\approx1.5\)

\((\sqrt[12]{10})^3=1.7782\ldots\approx1.8\)

\((\sqrt[12]{10})^4=2.1544\ldots\approx2.2\)

\((\sqrt[12]{10})^5=2.6101\ldots\approx2.6\) (E24 value is 2.7)

\((\sqrt[12]{10})^6=3.1622\ldots\approx3.2\) (E24 value is 3.3)

\((\sqrt[12]{10})^7=3.8311\ldots\approx3.8\) (E24 value is 3.9)

\((\sqrt[12]{10})^8=4.6415\ldots\approx4.6\) (E24 value is 4.7)

\((\sqrt[12]{10})^9=5.6234\ldots\approx5.6\)

\((\sqrt[12]{10})^{10}=6.8129\ldots\approx6.8\)

\((\sqrt[12]{10})^{11}=8.2540\ldots\approx8.3\) (E24 value is 8.2)

I'm not yet worked this, but perhaps it would be possible to only search for resistor pairs that are zero steps apart, then one, then two,... and so on.

Great insight! I know AWG wire diameters follow a geometric progression, but I wasn’t aware of this happening in resistor series.

This RPL program will generate all 192 values of the E192 series, if I have verified them correctly:

« PUSH -3. SF -105. SF 10. 192. XROOT 191. NDUPN { 1. } 1 ROT
FOR i DUP i GET ROT * +
NEXT 100. * 0. RND 186. 920. PUT POP
»

EVAL

{ 100. 101. 102. 104. 105. 106. 107. 109. 110. 111. 113. 114. 115. 117. 118. 120. 121. 123. 124. 126. 127. 129. 130. 132. 133. 135. 137. 138. 140. 142. 143. 145. 147. 149. 150. 152. 154. 156. 158. 160. 162. 164. 165. 167. 169. 172. 174. 176. 178. 180. 182. 184. 187. 189. 191. 193. 196. 198. 200. 203. 205. 208. 210. 213. 215. 218. 221. 223. 226. 229. 232. 234. 237. 240. 243. 246. 249. 252. 255. 258. 261. 264. 267. 271. 274. 277. 280. 284. 287. 291. 294. 298. 301. 305. 309. 312. 316. 320. 324. 328. 332. 336. 340. 344. 348. 352. 357. 361. 365. 370. 374. 379. 383. 388. 392. 397. 402. 407. 412. 417. 422. 427. 432. 437. 442. 448. 453. 459. 464. 470. 475. 481. 487. 493. 499. 505. 511. 517. 523. 530. 536. 542. 549. 556. 562. 569. 576. 583. 590. 597. 604. 612. 619. 626. 634. 642. 649. 657. 665. 673. 681. 690. 698. 706. 715. 723. 732. 741. 750. 759. 768. 777. 787. 796. 806. 816. 825. 835. 845. 856. 866. 876. 887. 898. 909. 920. 931. 942. 953. 965. 976. 988. }

For E96, take the first element of the list and every second element, counting from the second;
For E48, take the first element of the list and every fourth element, counting from the second... and so on. For series with two significant digits, the values should be rounded accordingly. I haven’t checked these, though.

Regards,

Gerson.