FullPower

Power Distribution

When large currents (from, say, 100mA or more) are involved we can no longer consider the wiring carrying it to be an ideal zero resistance. At a current of 1A every milliohm of resistance becomes a millivolt voltage drop and typical systems using pcbs and ribbon cables have voltage drops in hundreds of mV. Furthermore the distribution structure compounds the problems as different varying currents are combined in common wiring.

The following diagram shows the significant resistances in power and 0V wiring involved in powering two modules patched to each other:

Important points to note are:

  • Although the mains Earth is used as the reference for signal 0V every point connected to it is separated by a resistance and they are only at the same potential if no current is flowing in them.
  • Current will flow in the 0V paths, both through the power distribution and cable screens, in an unbalanced system.
  • Only one point in each power rail is regulated. This may be considered fixed and every other point is a variable voltage drop away.

In the diagram the resistance of the common wiring between the PSU and the distribution is shown as Rd. The resistances of the individual power cables to the modules is shown as Rc. A system supplying 1A or more will have all that current flowing through the Rds and to limit the voltage drop to <10mV these must be lower than 10mΩ. The voltage drops in the Rds will be seen by all modules in the system as their power supply. This is the major mechanism that causes audio bleed and module interaction when modules switching between two or more states taking different currents create waveforms on the distribution rails. The lower the resistance value that Rd can be made the more this effect can be reduced.

The individual power cable resistances, Rc+ and Rc-, would normally be in series with other resistances within the modules and so are not so critical, but the 0V cable resistance, Rc0, is supplying the 0V reference for the whole system and the module will be moved from this potential by the difference between its power currents multiplied by this resistance, (I+ - I-) x Rc.

 

Wire Resistances

Wire Size
mΩ/metre
mΩ/foot
7/0.12 (Ribbon) 28 AWG 219.9 64.9
7/0.2 24 AWG 84.22 25.67
16/0.2 20 AWG 33.31 10.15
24/0.2 18 AWG 20.95 6.385
32/0.2 17 AWG 16.61 5.064
64/0.2 14 AWG 8.286 2.525
 

A typical 200mm ribbon cable will have theoretical resistance of 42mΩ per conductor, but by the time IDC and contact resistances are included will be over 50mΩ. The same length of a KK 0.156" power cable with 24/0.2 wire will be 12mΩ per conductor including the headers each end.

 

Resistances of Metals

To calculate the resistance of a uniform cross-section solid multiply the resistivity (ρ) by the length in metres and divide by the area in square metres.
Metal
nanoρ Ω-m @ 20°C
Silver 15.9
Copper 16.8
Gold 24.4
Aluminium 28.2
Aluminium Alloys 28.7 upwards*
Bronze 35.9 upwards*
Zinc 59.0
Brass 59 to 71*
Nickel 69.9
Tin 109
Stainless Steel 690

* alloy mixtures and impurities will increase these figures. Most metals used for electrical connectors have platings and irregular shapes so the real resistances involved will always be higher than theoretically calculated ones.

A 400mm pcb trace 1.5mm wide in 2oz copper, typical of many buscards, will have a resistance of 63.5mΩ @ 20°C. A 400mm aluminium bar 20mm x 10mm will have a resistance of 56µΩ at the same temperature. Voltage drops from the same current in the two will be over 60dB different.

 
 
 
 
Last updated: 23 January 2015