jneutron said:
Not to worry about typos, etc.
That LC looked like inductance and Capacitance at first
so don't worry about units. Thanks for the rest.
L and C are indeed inductance and capacitance. First, the easy method, then the more rigorous one...
We know that for a constrained system such as a coax, this equation holds:
LC = 1034 DC.... L in nanohenries/ft, C in pf /foot.
Now, lets look at belden type 9222...
L = 77 nh/ft
C = 30.8 pf/ft
published Z 50 ohms
published V 66% lightspeed.
First, calc of impedance.. Z = sqr(L/C)
L = 77,000 pH/ft, C = 30.8 pF/ft..(make both same power of ten)
77000/30.8 = 2500
sqr(2500) = 50. Ok, Z worked..they don't have a gross error in their specifications (I found 3 errors in belden's spec sheets out of 31 cables I looked at)
Now, V = 1/sqr(LC), and V=c/sqr(epsilon mu)...c being lightspeed.
V = c times (1/sqr (epsilon mu))..for coax, this boils down to:
V (% lightspeed)= 1 / sqr(DC)....for example, if DC = 4, V =50%...if DC=9, V = 33%
Here's the easy method: use second equation by calculating the DC. (assume mu =1)
LC = 1034 DC.... DC = LC/1034.
DC = (77 times 30.8)/1034
DC = 2371.6 / 1034 = 2.293617
sqr(2.293617) = 1.5144
V = c times (1/ 1.5144) = c times .66029
V is 66% lightspeed, just what belden posted..
((Edit: The significance? For ALL coaxes made using that dielectric will have the exact same prop velocity. This is absolutely independent on the impedance of the coax, or it's physical size. All coaxes which are made with an insulator which has that same dielectric coefficient, will also have the exact same velocity of propagation..
This equation is useful for ALL wire pairs...coax is special in that the magnetic field is confined to inside the outer conductor while a wire pair does not do that..so a slight mod is in order.. The DC in the LC=1034 DC must be considered as an Effective Dielectric Constant, or EDC, to reflect the spillage of magnetic field outside the working dielectric. Cable EDC's in the 5 to 10 range are common, and that indeed reflects the prop velocity of those wires.))
Hard way:
sqr(LC) = sqr(77* 10<sup>-9</sup> * 30.8 * 10<sup>-12</sup>)
= sqr(2371.6 * 10<sup>-21</sup>)
= sqr(2371.6) * sqr(10<sup>-21</sup>) = 48.699 * sqr(10<sup>-22</sup>) * sqr(10)
=48.699 * 3.162 * 10<sup>-11</sup>
= 159.986 * 10<sup>-11</sup>..now, this is the denominator of the first eq..
1/(159.986 * 10<sup>-11</sup>) = 6.494 * 10<sup>-3</sup> * 10<sup>11</sup>
6.494 * 10<sup>8</sup> (remember, this is using feet as origional units, lets convert..
6.494 * 10<sup>8</sup> ft/sec * 12 in/ft * 1 meter/39.4 inches =
6.494 * 12 / 39.4 * 10<sup>8</sup> = 1.97786 * 10<sup>8</sup> meters/sec
Lightspeed is 2.99792 * 10<sup>8</sup> meters/sec.
so, fraction of lightspeed is:
1.97786 / 2.99792, or .6597, this is 65.97% of lightspeed.
A heck of a lot of calcs to do it the hard way, I prefer the easy method..
Cheers, John
ps..finally fixed all the eq typo's, sheesh..