The best layed plans . . . It seems that I can't do anything right the first time . . .
The number of picoseconds it takes to travel an inch is inversly proportional to the speed in inches per picosecond, which means it goes up, and not down, as the speed goes down, and therefore the numbers in the second and fourth columns of my first chart were in error. Oh, well . . . Throw the other chart away and use this one . . . JaMi Smith * * * * * * * * * * * This post, as well as all of the discussion on this topic, is in response to the first question: "Is there a formula to determine picoseconds per inch?", which was soon followed by the question / statement: "There must be a neat little chart somewhere that shows board materials and their respective prop. delays." I have look all over for such a "little chart", and failing to find one, I decided to come up with my own, which is reproduced below. I must firstly explain that the answer to the question is really quite simple, and that the data is out there in many places in plain sight, but that I myself was looking for such a complex answer that I couldn't even see the real answer that was right under my own nose. In fact I actually copied the answer into a previous post of my own here in response to this thread, without even realizing that it was in fact the answer. The primary question here, whether one approaches it from the perspective of the speed of the signal, or the propagation delay, or the velocity factor, is simply how fast does an electrical signal travel with respect to the dielectric constant of the medium in which the signal is traveling (in which the conductor is embedded). The answer to that question can be determined by the formula: velocity of signal equals the speed of light divided by the square root of the dielectric constant of the material that the signal is traveling through, or v = c /(sqr(Er)). In order to keep things in perspective, we must remember what we are really talking about is the speed (velocity) of a signal in a given medium or material, as compared to its full speed in a air or a vacuum; and that the propagation delay of that signal is simply the amount of time that the signal is slowed down, as compared to its full speed in air or a vacuum; and that the velocity factor is just the percentage of the slower speed in a given medium or material, as compared to its full speed in air or a vacuum. Respecting the speed of a signal in air or in a vacuum, it needs to be stated that there is a very small difference. In a vacuum, light (and consequently an electrical signal also) travels at 299,792,458 meters per second (0.011803 inches per picosecond (84.7253 picoseconds per inch)); while the speed of light in air is a little slower at 299,702,547 meters per second (0.011799 inches per picosecond (84.7507 picoseconds per inch)). To complicate matters even worse, some people round off the speed of light to 300,000,000 meters per second (0.011810 inches per picosecond (84.6667 picoseconds per inch)); or even to 186,000 miles per second (0.011785 inches per picosecond (84.8539 picoseconds per inch)). All of the above numbers here are so close that you certainly are not going to see the difference between them on your PC Board, but I bring them up simply to let you know that there is a very minor difference, and that because of this minor difference, sometimes the numbers in the chart below might be slightly off from similar numbers from a different source. This simply means that they used a slightly different number for the speed of light, or that there are slightly different rounding errors in the calculations. Most people use the actual speed of light in a vacuum as the basis for all of their electronic calculations, and notwithstanding that it might be more appropriate here to use the speed of light in air since we are dealing with dielectric constants based on air, since the difference is so minor I will follow convention and use the speed of light in a vacuum as the basis for the below calculations in the chart below. The real problem in figuring out the actual speed of a signal on or inside of a PC Board does not come from which number you use for the speed of light, but rather just which number you use for your dielectric constant, or more correctly, your "effective" dielectric constant. The dialectric constant of a material can vary significantly throughout the medium of the material, such as in the case of FR4, which varies between the fiber and the resin, which is one reason that different materials are sometimes used in PCB's operating at higher frequencies. This can be compounded by the fact that there may be extra resin and less fiber in the immediate area of the actual conductors (traces) internal to a PCB due to the stack up and lamination process. The "effective" dielectric constant is therefore in essence the "average" dielectric constant of the material in which the conductor (trace) is embedded. This problem is compounded on the outer surfaces of a PCB where the conductors (traces) are sitting on top of a base material of a given dielectric constant, and where the top of the conductors (traces) are exposed to air or covered with a material such as a soldermask, which has yet a different dielectric constant (usually much lower than the base material). I am not even sure if there is an exact way in which to calculate the actual "effective" dielectric constant in cases such as this, although it is said to be somewhere within the range between one half of the dielectric constant of the base material and the base material itself, which is usually written as 1/2 Er < Er Eff < Er, where Er Eff is the "effective" dielectric constant. Polar Instruments has just released an excellent Application Note presentation on their website which addresses the issue of "effective" dielectric constant of certain materials, including FR4, as it relates to determining the impedance of traces in a PCB, and gives an excellent presentation of the problem of the "effective" dielectric constant as also applicable to the speed of a signal thru that material. The Application Note, AP165, can be viewed at the following link: www.polarinstruments.com/support/cits/cits_index.html In a previous post, I directly copied a paragraph from the Rogers website (the duriod folks), although I left out the formula because it didn't copy correctly. I will reproduce it again here, except this time I will include the formula. "A signal traveling through a circuit board has a velocity that is dependent on the dielectric constant of the material, v = c /(sqr(Eeff)), where c is the speed of light (3.0x108 m/sec) and Eeff is the effective dielectric constant of the medium. In the case of multilayer constructions, the effective dielectric constant is the dielectric constant of the material, while for double sided constructions it is somewhere in the 1/2Er <Eeff< Er range. This is due to the non-homogenous medium that exists between the PCB material and air." Please remember that here when they speak of "multilayer construction", they are talking about internal layers where the conductors (traces) are embedded in the material, and when they speak of "double sided" construction, they are talking about external layers where the conductors (traces) is either exposed to air or is covered with a soldermask of a lesser dielectric constant than the base material. The actual frequency of the signal also has a lot to do with the "effective" dielectric constant. For further information on this, the whole article can be viewed at the following link. http://www.rogers-corp.com/mwu/techtip9.htm Now on to the actual chart itself. The first column is the actual "effective" dielectric constant of the material. This information is usually available from your board shop. Don't forget to ask them about the differences based on internal versus external layers, and whether or not the external traces are exposed or covered in solder mask. The second column is the speed (velocity) of the signal in a material of that "effective" dielectric constant, in picoseconds per inch. The third column is the same as second column, except expressed in inches per picosecond. The forth column is the actual delay, or "propigation delay" of the signal. The last two columns are the velocity factor and the inverse of the velocity factor, which can be used to determine the "equivalent electrical length" of a conductor when the conductor is embedded in a material of a given "effective" dielectric constant. For example, if you are told that the length of a conductor needs to be exactly 2.000 inches in physical length (based on wavelength or some timing factor), that specified length is usually specified as the physical length of the conductor in a vacuum or in air. If the conductor is embedded in a material with a .75 velocity factor, then the equivalent "electrical" length of the conductor is determined by multiplying the original conductor length in air by the velocity factor to determine the physical length of the embeded conductor, which in this case is actually shortened to 1.500 inches in physical length so that it will be "electrically equivalent". In the opposite scenario, if you know a conductor has a physical length of 1.600 inches embedded in a material with a .80 velocity factor, and you want to find out its "equivalent electrical length" in a vacuum or in air, then multiply the embedded physical length by the inverse of the velocity factor to obtain the actual physical length of the conductor in a vacuum or in air, which in this case would be 2.500 inches physical length to be "electrically equivalent". Chart for determining the speed of a signal in relationship to the Effective Dielectric Constant of the Material in which the signal is embedded, by JaMi Smith Er psec inch dly psec velocity velocity eff per inch per psec per inch factor factor / 1 1.00 84.7253 0.011803 0.0000 1.0000 1.0000 1.05 86.8176 0.011518 2.0923 0.9759 1.0247 1.10 88.8606 0.011254 4.1353 0.9535 1.0488 1.15 90.8577 0.011006 6.1325 0.9325 1.0724 1.20 92.8119 0.010774 8.0866 0.9129 1.0954 1.25 94.7257 0.010557 10.0005 0.8944 1.1180 1.30 96.6017 0.010352 11.8764 0.8771 1.1402 1.35 98.4419 0.010158 13.7166 0.8607 1.1619 1.40 100.2483 0.009975 15.5230 0.8452 1.1832 1.45 102.0227 0.009802 17.2975 0.8305 1.2042 1.50 103.7668 0.009637 19.0416 0.8165 1.2247 1.55 105.4821 0.009480 20.7568 0.8032 1.2450 1.60 107.1699 0.009331 22.4447 0.7906 1.2649 1.65 108.8316 0.009189 24.1063 0.7785 1.2845 1.70 110.4682 0.009052 25.7430 0.7670 1.3038 1.75 112.0810 0.008922 27.3557 0.7559 1.3229 1.80 113.6709 0.008797 28.9456 0.7454 1.3416 1.85 115.2388 0.008678 30.5136 0.7352 1.3601 1.90 116.7857 0.008563 32.0605 0.7255 1.3784 1.95 118.3124 0.008452 33.5871 0.7161 1.3964 2.00 119.8196 0.008346 35.0944 0.7071 1.4142 2.05 121.3081 0.008243 36.5829 0.6984 1.4318 2.10 122.7786 0.008145 38.0533 0.6901 1.4491 2.15 124.2316 0.008049 39.5064 0.6820 1.4663 2.20 125.6679 0.007957 40.9426 0.6742 1.4832 2.25 127.0879 0.007869 42.3626 0.6667 1.5000 2.30 128.4922 0.007783 43.7670 0.6594 1.5166 2.35 129.8814 0.007699 45.1561 0.6523 1.5330 2.40 131.2558 0.007619 46.5306 0.6455 1.5492 2.45 132.6160 0.007541 47.8908 0.6389 1.5652 2.50 133.9624 0.007465 49.2371 0.6325 1.5811 2.55 135.2954 0.007391 50.5701 0.6262 1.5969 2.60 136.6154 0.007320 51.8901 0.6202 1.6125 2.65 137.9228 0.007250 53.1975 0.6143 1.6279 2.70 139.2178 0.007183 54.4926 0.6086 1.6432 2.75 140.5010 0.007117 55.7757 0.6030 1.6583 2.80 141.7725 0.007054 57.0472 0.5976 1.6733 2.85 143.0327 0.006991 58.3075 0.5923 1.6882 2.90 144.2819 0.006931 59.5567 0.5872 1.7029 2.95 145.5204 0.006872 60.7952 0.5822 1.7176 3.00 146.7485 0.006814 62.0232 0.5774 1.7321 3.05 147.9663 0.006758 63.2411 0.5726 1.7464 3.10 149.1742 0.006704 64.4490 0.5680 1.7607 3.15 150.3725 0.006650 65.6472 0.5634 1.7748 3.20 151.5612 0.006598 66.8359 0.5590 1.7889 3.25 152.7407 0.006547 68.0154 0.5547 1.8028 3.30 153.9111 0.006497 69.1858 0.5505 1.8166 3.35 155.0727 0.006449 70.3474 0.5464 1.8303 3.40 156.2257 0.006401 71.5004 0.5423 1.8439 3.45 157.3702 0.006354 72.6449 0.5384 1.8574 3.50 158.5065 0.006309 73.7812 0.5345 1.8708 3.55 159.6347 0.006264 74.9094 0.5307 1.8841 3.60 160.7549 0.006221 76.0296 0.5270 1.8974 3.65 161.8674 0.006178 77.1421 0.5234 1.9105 3.70 162.9723 0.006136 78.2470 0.5199 1.9235 3.75 164.0698 0.006095 79.3445 0.5164 1.9365 3.80 165.1600 0.006055 80.4347 0.5130 1.9494 3.85 166.2430 0.006015 81.5177 0.5096 1.9621 3.90 167.3190 0.005977 82.5937 0.5064 1.9748 3.95 168.3882 0.005939 83.6629 0.5032 1.9875 4.00 169.4506 0.005901 84.7253 0.5000 2.0000 4.05 170.5063 0.005865 85.7811 0.4969 2.0125 4.10 171.5556 0.005829 86.8303 0.4939 2.0248 4.15 172.5985 0.005794 87.8732 0.4909 2.0372 4.20 173.6352 0.005759 88.9099 0.4880 2.0494 4.25 174.6656 0.005725 89.9404 0.4851 2.0616 4.30 175.6901 0.005692 90.9648 0.4822 2.0736 4.35 176.7086 0.005659 91.9833 0.4795 2.0857 4.40 177.7212 0.005627 92.9960 0.4767 2.0976 4.45 178.7282 0.005595 94.0029 0.4740 2.1095 4.50 179.7295 0.005564 95.0042 0.4714 2.1213 4.55 180.7252 0.005533 95.9999 0.4688 2.1331 4.60 181.7155 0.005503 96.9902 0.4663 2.1448 4.65 182.7004 0.005473 97.9751 0.4637 2.1564 4.70 183.6800 0.005444 98.9547 0.4613 2.1679 4.75 184.6545 0.005416 99.9292 0.4588 2.1794 4.80 185.6238 0.005387 100.8985 0.4564 2.1909 4.85 186.5881 0.005359 101.8628 0.4541 2.2023 4.90 187.5474 0.005332 102.8221 0.4518 2.2136 4.95 188.5018 0.005305 103.7766 0.4495 2.2249 5.00 189.4515 0.005278 104.7262 0.4472 2.2361 5.05 190.3964 0.005252 105.6711 0.4450 2.2472 5.10 191.3366 0.005226 106.6113 0.4428 2.2583 5.15 192.2723 0.005201 107.5470 0.4407 2.2694 5.20 193.2034 0.005176 108.4781 0.4385 2.2804 5.25 194.1300 0.005151 109.4047 0.4364 2.2913 5.30 195.0522 0.005127 110.3270 0.4344 2.3022 5.35 195.9701 0.005103 111.2449 0.4323 2.3130 5.40 196.8838 0.005079 112.1585 0.4303 2.3238 5.45 197.7932 0.005056 113.0679 0.4284 2.3345 5.50 198.6984 0.005033 113.9731 0.4264 2.3452 5.55 199.5995 0.005010 114.8742 0.4245 2.3558 5.60 200.4966 0.004988 115.7713 0.4226 2.3664 5.65 201.3897 0.004965 116.6644 0.4207 2.3770 5.70 202.2788 0.004944 117.5535 0.4189 2.3875 5.75 203.1641 0.004922 118.4388 0.4170 2.3979 5.80 204.0455 0.004901 119.3202 0.4152 2.4083 5.85 204.9231 0.004880 120.1978 0.4134 2.4187 5.90 205.7970 0.004859 121.0717 0.4117 2.4290 5.95 206.6672 0.004839 121.9419 0.4100 2.4393 6.00 207.5337 0.004818 122.8084 0.4082 2.4495 6.05 208.3966 0.004799 123.6713 0.4066 2.4597 6.10 209.2560 0.004779 124.5307 0.4049 2.4698 6.15 210.1119 0.004759 125.3866 0.4032 2.4799 6.20 210.9642 0.004740 126.2390 0.4016 2.4900 6.25 211.8132 0.004721 127.0879 0.4000 2.5000 6.30 212.6588 0.004702 127.9335 0.3984 2.5100 6.35 213.5010 0.004684 128.7757 0.3968 2.5199 6.40 214.3399 0.004665 129.6146 0.3953 2.5298 6.45 215.1755 0.004647 130.4502 0.3937 2.5397 6.50 216.0079 0.004629 131.2826 0.3922 2.5495 6.55 216.8371 0.004612 132.1119 0.3907 2.5593 6.60 217.6632 0.004594 132.9379 0.3892 2.5690 6.65 218.4861 0.004577 133.7608 0.3878 2.5788 6.70 219.3059 0.004560 134.5807 0.3863 2.5884 6.75 220.1227 0.004543 135.3974 0.3849 2.5981 6.80 220.9365 0.004526 136.2112 0.3835 2.6077 6.85 221.7473 0.004510 137.0220 0.3821 2.6173 6.90 222.5551 0.004493 137.8298 0.3807 2.6268 6.95 223.3600 0.004477 138.6347 0.3793 2.6363 7.00 224.1620 0.004461 139.4367 0.3780 2.6458 7.05 224.9612 0.004445 140.2359 0.3766 2.6552 7.10 225.7575 0.004430 141.0322 0.3753 2.6646 7.15 226.5510 0.004414 141.8257 0.3740 2.6739 7.20 227.3418 0.004399 142.6165 0.3727 2.6833 7.25 228.1298 0.004383 143.4045 0.3714 2.6926 7.30 228.9151 0.004368 144.1898 0.3701 2.7019 7.35 229.6977 0.004354 144.9724 0.3689 2.7111 7.40 230.4777 0.004339 145.7524 0.3676 2.7203 7.45 231.2550 0.004324 146.5297 0.3664 2.7295 7.50 232.0297 0.004310 147.3044 0.3651 2.7386 7.55 232.8019 0.004295 148.0766 0.3639 2.7477 7.60 233.5715 0.004281 148.8462 0.3627 2.7568 7.65 234.3385 0.004267 149.6133 0.3616 2.7659 7.70 235.1031 0.004253 150.3778 0.3604 2.7749 7.75 235.8652 0.004240 151.1399 0.3592 2.7839 7.80 236.6248 0.004226 151.8995 0.3581 2.7928 7.85 237.3820 0.004213 152.6567 0.3569 2.8018 7.90 238.1368 0.004199 153.4115 0.3558 2.8107 7.95 238.8892 0.004186 154.1639 0.3547 2.8196 8.00 239.6393 0.004173 154.9140 0.3536 2.8284 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * To post a message: mailto:[EMAIL PROTECTED] * * To leave this list visit: * http://www.techservinc.com/protelusers/leave.html * * Contact the list manager: * mailto:[EMAIL PROTECTED] * * Forum Guidelines Rules: * http://www.techservinc.com/protelusers/forumrules.html * * Browse 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