I need some speaker cables. Long run ~40'
Looked options
Large gauge, 8 AWG (extreme)
// smaller 12 AWG
After reading up (a good thing) and thinking (seldom a good thing) I arrived at using low surge/characteristic impedance Zo as the main design parameter.
Zo = sqrt(L/C)
It can be lowered by decreasing L or increasing C.
L is in series, signal path
C is in //
Most papers say low L is key to avoid high end roll off. Any cable phase shift is moot vs. the speaker xover.
In //
Le = 1/L1 + 1/Ln ..., if L is the same L/n
Gets smaller in //
C is the inverse
Ce = C1 + Cn, ie, the sum
I am contemplating 2 cables of 4x14 AWG per speaker. Each cable 2 x + and 2 x -.
L/4, may be smaller
Cx4 (may be larger due to separation
Offsetting and making Zo smaller
Why Zo?
At a junction the Zo on each side determines reflection and refraction (or transmission). expressed as a factor 0 to 1.
Reflection 1 = 100% reflected
Refraction 1 = 100% passed, 0% reflected
At the amp you want 100% reflected, ie, low output Z. Not distorting the output.
At speaker ideally 0 reflected/100 absorbed. Obviously not possible in a reactive circuit. In my calcs the sign will change with phase, ie, C or L load at xover.
This determines whether the effected adds or subtracts with the incident.
Yes, my head is not wired normally.