# [PEDA] Chart for Speed of a Signal

```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
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

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