# [PEDA] Corrected Chart for Speed of a Signal

```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
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

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