The following is something that I put together in response to a question in another forum, dealing with the speed of a signal in a PCB. Since this is a question that many PCB Designers encounter sooner or later in their designs, I thought that it would be useful to some if I reposted it here.
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 82.6834 0.011518 2.0419 0.9759 1.0247 1.10 80.7824 0.011254 3.9429 0.9535 1.0488 1.15 79.0067 0.011006 5.7185 0.9325 1.0724 1.20 77.3432 0.010774 7.3820 0.9129 1.0954 1.25 75.7806 0.010557 8.9447 0.8944 1.1180 1.30 74.3090 0.010352 10.4163 0.8771 1.1402 1.35 72.9199 0.010158 11.8054 0.8607 1.1619 1.40 71.6059 0.009975 13.1193 0.8452 1.1832 1.45 70.3605 0.009802 14.3648 0.8305 1.2042 1.50 69.1779 0.009637 15.5474 0.8165 1.2247 1.55 68.0530 0.009480 16.6723 0.8032 1.2450 1.60 66.9812 0.009331 17.7441 0.7906 1.2649 1.65 65.9585 0.009189 18.7667 0.7785 1.2845 1.70 64.9813 0.009052 19.7440 0.7670 1.3038 1.75 64.0463 0.008922 20.6790 0.7559 1.3229 1.80 63.1505 0.008797 21.5748 0.7454 1.3416 1.85 62.2913 0.008678 22.4340 0.7352 1.3601 1.90 61.4662 0.008563 23.2591 0.7255 1.3784 1.95 60.6730 0.008452 24.0522 0.7161 1.3964 2.00 59.9098 0.008346 24.8155 0.7071 1.4142 2.05 59.1747 0.008243 25.5506 0.6984 1.4318 2.10 58.4660 0.008145 26.2593 0.6901 1.4491 2.15 57.7822 0.008049 26.9431 0.6820 1.4663 2.20 57.1218 0.007957 27.6035 0.6742 1.4832 2.25 56.4835 0.007869 28.2418 0.6667 1.5000 2.30 55.8662 0.007783 28.8591 0.6594 1.5166 2.35 55.2687 0.007699 29.4566 0.6523 1.5330 2.40 54.6899 0.007619 30.0353 0.6455 1.5492 2.45 54.1290 0.007541 30.5963 0.6389 1.5652 2.50 53.5850 0.007465 31.1403 0.6325 1.5811 2.55 53.0570 0.007391 31.6683 0.6262 1.5969 2.60 52.5444 0.007320 32.1809 0.6202 1.6125 2.65 52.0463 0.007250 32.6790 0.6143 1.6279 2.70 51.5622 0.007183 33.1631 0.6086 1.6432 2.75 51.0913 0.007117 33.6340 0.6030 1.6583 2.80 50.6330 0.007054 34.0922 0.5976 1.6733 2.85 50.1869 0.006991 34.5384 0.5923 1.6882 2.90 49.7524 0.006931 34.9729 0.5872 1.7029 2.95 49.3290 0.006872 35.3963 0.5822 1.7176 3.00 48.9162 0.006814 35.8091 0.5774 1.7321 3.05 48.5136 0.006758 36.2117 0.5726 1.7464 3.10 48.1207 0.006704 36.6046 0.5680 1.7607 3.15 47.7373 0.006650 36.9880 0.5634 1.7748 3.20 47.3629 0.006598 37.3624 0.5590 1.7889 3.25 46.9971 0.006547 37.7282 0.5547 1.8028 3.30 46.6397 0.006497 38.0855 0.5505 1.8166 3.35 46.2904 0.006449 38.4349 0.5464 1.8303 3.40 45.9487 0.006401 38.7765 0.5423 1.8439 3.45 45.6146 0.006354 39.1107 0.5384 1.8574 3.50 45.2876 0.006309 39.4377 0.5345 1.8708 3.55 44.9675 0.006264 39.7578 0.5307 1.8841 3.60 44.6541 0.006221 40.0711 0.5270 1.8974 3.65 44.3472 0.006178 40.3780 0.5234 1.9105 3.70 44.0466 0.006136 40.6787 0.5199 1.9235 3.75 43.7519 0.006095 40.9733 0.5164 1.9365 3.80 43.4632 0.006055 41.2621 0.5130 1.9494 3.85 43.1800 0.006015 41.5453 0.5096 1.9621 3.90 42.9023 0.005977 41.8230 0.5064 1.9748 3.95 42.6299 0.005939 42.0954 0.5032 1.9875 4.00 42.3626 0.005901 42.3626 0.5000 2.0000 4.05 42.1003 0.005865 42.6249 0.4969 2.0125 4.10 41.8428 0.005829 42.8824 0.4939 2.0248 4.15 41.5900 0.005794 43.1353 0.4909 2.0372 4.20 41.3417 0.005759 43.3836 0.4880 2.0494 4.25 41.0978 0.005725 43.6275 0.4851 2.0616 4.30 40.8582 0.005692 43.8671 0.4822 2.0736 4.35 40.6227 0.005659 44.1026 0.4795 2.0857 4.40 40.3912 0.005627 44.3341 0.4767 2.0976 4.45 40.1636 0.005595 44.5616 0.4740 2.1095 4.50 39.9399 0.005564 44.7854 0.4714 2.1213 4.55 39.7198 0.005533 45.0055 0.4688 2.1331 4.60 39.5034 0.005503 45.2219 0.4663 2.1448 4.65 39.2904 0.005473 45.4349 0.4637 2.1564 4.70 39.0809 0.005444 45.6444 0.4613 2.1679 4.75 38.8746 0.005416 45.8507 0.4588 2.1794 4.80 38.6716 0.005387 46.0537 0.4564 2.1909 4.85 38.4718 0.005359 46.2535 0.4541 2.2023 4.90 38.2750 0.005332 46.4503 0.4518 2.2136 4.95 38.0812 0.005305 46.6441 0.4495 2.2249 5.00 37.8903 0.005278 46.8350 0.4472 2.2361 5.05 37.7023 0.005252 47.0230 0.4450 2.2472 5.10 37.5170 0.005226 47.2083 0.4428 2.2583 5.15 37.3344 0.005201 47.3909 0.4407 2.2694 5.20 37.1545 0.005176 47.5708 0.4385 2.2804 5.25 36.9771 0.005151 47.7481 0.4364 2.2913 5.30 36.8023 0.005127 47.9230 0.4344 2.3022 5.35 36.6299 0.005103 48.0953 0.4323 2.3130 5.40 36.4600 0.005079 48.2653 0.4303 2.3238 5.45 36.2923 0.005056 48.4330 0.4284 2.3345 5.50 36.1270 0.005033 48.5983 0.4264 2.3452 5.55 35.9639 0.005010 48.7614 0.4245 2.3558 5.60 35.8030 0.004988 48.9223 0.4226 2.3664 5.65 35.6442 0.004965 49.0811 0.4207 2.3770 5.70 35.4875 0.004944 49.2378 0.4189 2.3875 5.75 35.3329 0.004922 49.3924 0.4170 2.3979 5.80 35.1803 0.004901 49.5450 0.4152 2.4083 5.85 35.0296 0.004880 49.6957 0.4134 2.4187 5.90 34.8808 0.004859 49.8444 0.4117 2.4290 5.95 34.7340 0.004839 49.9913 0.4100 2.4393 6.00 34.5890 0.004818 50.1363 0.4082 2.4495 6.05 34.4457 0.004799 50.2796 0.4066 2.4597 6.10 34.3043 0.004779 50.4210 0.4049 2.4698 6.15 34.1645 0.004759 50.5607 0.4032 2.4799 6.20 34.0265 0.004740 50.6988 0.4016 2.4900 6.25 33.8901 0.004721 50.8352 0.4000 2.5000 6.30 33.7554 0.004702 50.9699 0.3984 2.5100 6.35 33.6222 0.004684 51.1031 0.3968 2.5199 6.40 33.4906 0.004665 51.2347 0.3953 2.5298 6.45 33.3605 0.004647 51.3647 0.3937 2.5397 6.50 33.2320 0.004629 51.4933 0.3922 2.5495 6.55 33.1049 0.004612 51.6204 0.3907 2.5593 6.60 32.9793 0.004594 51.7460 0.3892 2.5690 6.65 32.8551 0.004577 51.8702 0.3878 2.5788 6.70 32.7322 0.004560 51.9930 0.3863 2.5884 6.75 32.6108 0.004543 52.1145 0.3849 2.5981 6.80 32.4907 0.004526 52.2346 0.3835 2.6077 6.85 32.3719 0.004510 52.3534 0.3821 2.6173 6.90 32.2544 0.004493 52.4709 0.3807 2.6268 6.95 32.1381 0.004477 52.5871 0.3793 2.6363 7.00 32.0231 0.004461 52.7021 0.3780 2.6458 7.05 31.9094 0.004445 52.8159 0.3766 2.6552 7.10 31.7968 0.004430 52.9284 0.3753 2.6646 7.15 31.6855 0.004414 53.0398 0.3740 2.6739 7.20 31.5752 0.004399 53.1500 0.3727 2.6833 7.25 31.4662 0.004383 53.2591 0.3714 2.6926 7.30 31.3582 0.004368 53.3670 0.3701 2.7019 7.35 31.2514 0.004354 53.4739 0.3689 2.7111 7.40 31.1456 0.004339 53.5796 0.3676 2.7203 7.45 31.0409 0.004324 53.6843 0.3664 2.7295 7.50 30.9373 0.004310 53.7880 0.3651 2.7386 7.55 30.8347 0.004295 53.8906 0.3639 2.7477 7.60 30.7331 0.004281 53.9922 0.3627 2.7568 7.65 30.6325 0.004267 54.0928 0.3616 2.7659 7.70 30.5329 0.004253 54.1924 0.3604 2.7749 7.75 30.4342 0.004240 54.2911 0.3592 2.7839 7.80 30.3365 0.004226 54.3888 0.3581 2.7928 7.85 30.2397 0.004213 54.4855 0.3569 2.8018 7.90 30.1439 0.004199 54.5814 0.3558 2.8107 7.95 30.0490 0.004186 54.6763 0.3547 2.8196 8.00 29.9549 0.004173 54.7704 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 or Search previous postings: * http://www.mail-archive.com/[email protected] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
