What length of hook-up wire (electronic circuit board) is equivalent to a 470 Ohm resistor? I want to place LEDs at some distance (max 6 feet/1.8 metres) from the TTL outputs that drive them, and normally one would include a 470 Ohm resistor per LED. But if the connecting wires (probably the individual cores in flat ribbon cable, like IDE drive cable) provide enough resistance, there may be no need for the resistors.
Temperature is of major importance when determining DC resistance. For 100 per cent IACS copper dc resistance can be found with the following equation: Rdc=( (Pc/CMA)*((tah+T)/(tah.+20)) )*(length in feet)
Where Pc is the circular mil ohm resistance in ohms at 20 degrees C. tah is the inferred temperature of zero resistance. T is the temperature in degrees C at which we wish to find the DC resistance CMA is circular mil area (diameter of conductor in thousandths of an inch squared) Example: For the resistance of a copper conductor at 75 degrees C. with a CMA of 1620 circular mils (No. 18 AWG) 1000 feet long the resistance would be: Rdc=(10.371 ohms/1620 cma)(234.5 degrees C+75 degrees C)/(234.5 degrees C+20 degrees C))(1000 ft)
Rdc=7.8 ohms per thousand feet This matches the value in Table 8 or Chapter 9 in the NEC. For resistance of other metals used the circular mil ohms resistance per foot at 20 degrees C in place of the value of 10.371 used for copper. Typical vaues for Pc and tah are: copper (100 per cent IACS) is 10.371 ,tah is 234.5 Aluminum (61 per cent IACS) is 17.002, tah is 228.1 Brass (27.3 per cent IACS) (70 cu, 30 Zn) is 38.0 and tah is 912 Lead (7.84 per cent IACS) 132.3 and tah is 236
Reference: Neher McGrath paper The Calculation of the Temperature Rise and Load Capability of Cable Systems published by AIEE (now the IEEE) October 1957
The source impedance is going to be several hundred ohms - and at the end of the line is a (conducting) LED that is going to present a very low impedance to any voltage transients over its knee voltage. You don't get a lot better than that for minimising reflected power. Add a ferrite core to the line and the "spike" isn't going to be fast - not that it would be very fast anyway, because of the source impedance.
Of course if things were different, say a very low impedance source and a very high impedance load, and the shape of the signals really mattered, etc, etc, then a lot more attention to the design would be needed.
The LEDs will be switched on/off at a rate comparable to MIDI when playing an average piece of music. That is, however many individually struck notes you would get in a bar/measure, that is the equivalent rate for the LEDs.
Peter, I'm open to any ideas! Basically, think of a small circuit board with CMOS 4099s or TTL equivalent latches. Each output pin shall drive an LED. I can, of course, choose between different LED types and sizes, but I want to aim for a 3 mm size, as the application needs these to be as compact as possible. There are also, apparently, LEDs now available that incorporate their own resistor. So here we have our latch with each output pin connected to an LED. Pin goes high, LED lights up.
Now extend the distance the LED is mounted from its driver pin by, say, 6 feet max. I could use ordinary hook-up wire from Maplins. Or I could use a strip of flat ribbon cable, separating out the inividual cores at the LED end. Ideally, my long mounting board could have copper tracks on it, but that is not feasible for a homebrew prototype.