In this second installment on RF and speaker cables we’ll look at bi-wiring. There are those who contend using separate wires for the HF and LF drivers improves sound by minimizing interaction at the speaker terminals, moving it to the amplifier’s output terminals. Since the impedance is lower right at the amplifier outputs (versus at the other end of the cable) any electrical coupling is reduced. For the record, aside from the possible benefit of doubled wires, I do not subscribe to the audibility of bi-wiring, but it makes for an interesting thread. Disclaimer: as usual, because I do not hear anything, does not mean you will not.

First, I set up an ideal speaker with a simple first-order crossover network. With 8-ohm drivers (modeled by pure 8-ohm resistors), a 1.273 mH inductor is in series with the “woofer” and 19.894 uF capacitor in series with the “tweeter” provide a 1 kHz crossover. The crossover frequency is not terribly important for illustrating the effect of bi-wiring, so 1 kHz is just a convenient choice.

Figure 1 shows the frequency response with an 8-ohm speaker cable. The overall response (top light blue line) is perfectly flat, and the crossover frequency to the woofer and tweeter is 1 kHz as designed.

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Figure 1: Crossover frequency response.

Figure 2 shows the response into the speaker using a single 8-ohm wire. The amplifier’s output and speaker’s input are essentially the same (with the expected time delay, barely visible at this scale). Recall, or realize, that an inductor will reject high frequencies while a capacitor rejects low frequencies. The inductor looks like an open to a high-frequency signal, and the capacitor looks like a short. With the step input signal used, the tweeter responds immediately, then falling as the capacitor charges since as the pulse stays high it looks more and more like a d.c. signal. The inductor blocks the high-frequency step from the woofer and thus its voltage rises only very gradually.

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Figure 2: Single 8-ohm speaker wire.

Now what happens if bi-wire and we look at the speaker terminals? See Figure 3… The woofer inputs with 8-ohm and 93-ohm (Monster cable) lines are in the top plot, and the tweeter inputs are in the bottom plot. The tweeter input response looks very similar to that of the single wire and simple load of the previous thread, with the 8-ohm cable providing an immediate step and the Monster Cable’s line mismatch yielding reflections that result in a slower, “stepped” rise time. The capacitor is essentially a short circuit as discussed earlier and so initially the system is virtually identical to the test case in the previous speaker cable thread.

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Figure 3. Bi-wiring response.

The woofer input is much more interesting. Since the inductor is an open to high-frequencies, the initial (fast) step “sees” an open circuit, causing a reflection that doubles the signal level at the terminals. The reflection travels back to the amp, is inverted and reflected by the zero-ohm (amp) source, travels back to the speaker terminal, and the cycle repeats. A little more energy goes into the woofer as time goes on, and eventually will settle to its final value. The lossy Monster Cable line (green) actually appears to settle a little faster, primarily due to band-limiting and the resistive loss.

So, bi-wiring does affect the voltage at the speaker terminals, though ideally does not affect the actual speaker’s response. The extra reflections introduced could make it tougher on the amplifier, though we must remember a real amp will have higher output impedance (especially at high frequency) and thus damp the ringing more quickly. While these are the expected waveforms from an RF engineering perspective, I am guessing it is news to many audiophiles…

FYI - Don