hovan@bgsuvax.UUCP (09/11/87)
Can anyone explain how coax cable specifications are derived? Does 75ohm coax get its designation by ohms per thousand foot or is this a rating given from a measurement of impedance at frequency? Any technical information pertaining to coax cable will be appreciated. John Hovan BGSU Hardware Support hovan@bgsuvax.uucp
rep@genrad.UUCP (Pete Peterson) (09/16/87)
In article <1284@bgsuvax.UUCP> hovan@bgsuvax.UUCP (John Hovan) writes: > > Can anyone explain how coax cable specifications are derived? >Does 75ohm coax get its designation by ohms per thousand foot or is this >a rating given from a measurement of impedance at frequency? > The characteristic impedance of a coax cable depends primarily on its geometry (log of ratio of shield diameter to inner conductor diameter) and the permittivity (or dielectric constant) of the dielectric material separating the conductors. It can also be expressed in terms of the inductance per-unit-length and capacitance per-unit-length of the cable. For low-loss cables: Characteristic impedance: (ohms) Zo=sqrt(L / C) where Zo is in ohms, L is in henrys/meter and C is in farads/meter. or Zo= 138 * sqrt (mu / epsilon) * log10 (b / a) mu = permeability of dielectric in henrys/meter; epsilon = permittivity of dielectric in farads/meter; b = shield diam; a = inner conductor diam. Propagation velocity: (meters-per-second) Vp = 1 / sqrt(L * C) or Vp = 3.0E8 / sqrt (mu * epsilon) Your 75 ohm coax with a resistive load of 75 ohms will look like 75 ohms resistive at the other end independent of the frequency and the length of the line. If terminated in any other load, the driving end will see a complex impedance which depends on the length of the cable and the frequency (actually the distance in wavelengths modulo 1/2 wavelength). Also, if the line is terminated in its characteristic impedance, there are no reflections from the load. Really, these are equivalent statements. For the time it takes for the applied signal to get to the load and back, you will see a 75 ohm resistive load regardless of what's on the other end of the cable. You can use any of the above properties to determine the Zo empirically depending on what you have for instrumentation. Note that cables having dielectrics containing newt's eyes and bat's wings have been shown to give an improved reproduction of the polish on the floor of the sound stage. Unfortunately, these cables must be made only during a particular phase of the moon since the moon phase at time of manufacture has important effects on the phase effects in the cable. This restriction results in limited production and great cost. To appreciate the importance of phase errors resulting from differences in propagation velocity with frequency, you should observe that speaker cables might have a delay corresponding to a phase shift of a whole 0.1 degrees at 20khz. The fact that this total phase shift (let alone variations in it) is negligible compared to phase errors in any realizable phono-cartridge equalization circuit should, of course, not disturb you. pete peterson {decvax,linus,wjh12,mit-eddie,masscomp}!genrad!rep
henry@utzoo.UUCP (Henry Spencer) (09/17/87)
> Can anyone explain how coax cable specifications are derived? > Does 75ohm coax get its designation by ohms per thousand foot or is this > a rating given from a measurement of impedance at frequency? Sort of the latter. Consider a longish cable with *something* at the other end. Suddenly we apply a voltage to the near end. How much current flows? Remember that speed-of-light lag means that the impedance at the other end is unknown and cannot influence the answer! The answer is that the properties of the cable (and its immediate environment) determine a "characteristic impedance" which is what you plug into Ohm's Law to find the instantaneous current. Of course, after speed-of-light lag has had time to occur, then there will be trouble if the impedance at the other end doesn't equal the cable's characteristic impedance. What happens then is "reflections", which propagate back (and forth) until everything eventually settles down to the steady-state situation that you would expect if you ignored the finite speed of light. Unfortunately, reflections are usually undesirable, because they can be mistaken for signal changes when fast circuits are involved. To avoid reflections, the basic approach is to keep the same impedance all the way along, from the transmitter output to the other end. In particular, this means cable with fairly constant characteristic impedance and a terminator of that same impedance at the other end. The c.i. of a single wire varies a lot depending on what is near it, although various tactics can limit the variations. Coax's c.i. is largely insensitive to its surroundings, making a constant-impedance system much easier to build. Some of the serious electron-pushers may want to correct or elaborate on the above; I'm just a software type with one foot in hardware... -- "There's a lot more to do in space | Henry Spencer @ U of Toronto Zoology than sending people to Mars." --Bova | {allegra,ihnp4,decvax,utai}!utzoo!henry
ron@topaz.rutgers.edu (Ron Natalie) (09/17/87)
Yes, remember that the cable termination is to make it appear infinitely long.