biwiring (cables in parallel) lowers the overall resistance (if the wires are the same gauge as the single wire) and inductance, but capacitance in parallel is additive, and in most cables the capacitance is the higher value component of reactance, and therefore normally has the most effect.
Actually, the loss from parallel capacitive reactance in a low impedance interface isn't even worth deriving because it's so insignificant.
The output impedance of a typical amplifier is around .02 ohms connecting usually to a load of about 8 ohms. This is a very low impedance circuit where the amplifier acts as a voltage source. Unlike inductance, capacitance provides us with a 'parallel' reactance. This frequency dependant resistance is across or in parallel with the 8 ohm load. A typical parallel load that the capacitance in a speaker cable provides is many, many orders higher than 8 ohms. It's in the thousands of ohms. It's not significant enough to consider. If we were discussing interconnects, of course the opposite is true because it's a high impedance connection.
Inductance though, is quite significant in a speaker circuit since it provides a series reactance that can be an appreciable portion of the 8 ohms that the speaker offers. This acts as a low pass filter and will indeed roll off high frequencies.
With respect to bi-wiring, one of the often mentioned explanations that it theoretically doesn't work, is that if you move one pair of speaker wires to the same terminals where the other pair is connected, absolutely nothing changes electrically. The law of physics that says so is called the superposition principle. In terms of electronics, the superposition theorem states that any number of voltages applied simultaneously to a linear network will result in a current which is the exact sum of the currents that would result if the voltages were applied individually.
I would contend that this is only partially true, since it assumes that the bi-wire speaker cables present a zero impedance, and that distortion from one driver will not affect the performance of the other driver. Superposition only holds true for a linear system.
Bi-wiring will only theoretically be a benefit when drivers distort and linearity is no longer maintained (non-linear).
With sufficient voltage a driver can deviate from ideal linearity so the current in that connection between the low output impedance of the amplifier and the woofer (in this case), will carry harmonic distortion components which can create intermodulation products. In a simple non-bi-wire situation, the tweeter driver terminals will see these distortion components through the speakers (low to zero) impedance straps (when a single non bi-wire set of cables is used).
The theoretical advantage is now valid if you assume a set of bi-wire speaker cables has some finite impedance (obviously, the longer the cables, the more pronounced the effects will be). When bi-wire cables are used rather than single wires with straps, the distortion components (caused by the woofer driver) will have a lower impedance path to the amplifiers low output impedance sink, rather than travel back and down the tweeters speaker cable.
Yes, it's a small advantage and you could argue that the tweeters crossover would help to reduce the problem, but I suppose you could argue that the harmonic and intermodulation products will be at a higher frequency and may pass through to the tweeter driver.
The entire advantage is gained by asking this question. From the perspective of the woofer driver terminals, which is the lower impedance path to the tweeters driver terminals? Is it a set of straps in a non bi-wire situation, or is it the route of a set of bi-wire cables that has a theoretical ideal voltage source (amplifiers low output impedance) in the path?.......... The answer is the bi-wire configuration.
Unfortunately, the benefit would be about the same result as attempting to slow your car down by putting your hand out the window? I doubt anyone could hear the benefits of bi-wiring, but the theory is there to prove it works.
brucek
