Speaker Impedance: Resistance and Phase Question

Just one clarification. The voltage is fixed with zero phase angle. It is the current that either lags or leads the voltage. Depending on whether there exits a capacitive, inductive or combination of the two load.

enjoy

Thanks for the nice words, Mesch. Yes, JA's measurements, and the interpretations he provides in the associated text, certainly represent major contributions to the hobby. I couldn't begin to count the number of times I and many others have referred to them in threads here, in identifying potential mismatches when components are being considered for purchase, and in diagnosing problems. And it has been extremely rare that I've ever sensed that his measurement-related comments might be in error in some way.

Good follow-up by Larry in his above post.

Regarding your question:

Would it be fair to say that capacitance becomes a most critical issue over inductance or resistance in regards to speaker and speaker cable interaction with cables having adequate isolation between the = and - strands and of an adequate gauge?

I think that the following comments address the intent of your question, but let me know if I'm misinterpreting your post.

Generally speaker cable capacitance is not a significant concern, except in those few cases where it is extremely high. A few cables, such as Goertz, achieve ultra-low inductance at the expense of having ultra-high capacitance. Those kinds of cables should, especially if driven by solid state amplifiers, generally be used with a Zobel network, or otherwise their extremely high capacitance can adversely affect the sonic performance of the amplifier, or even cause it to oscillate and self-destruct.

In typical situations, though, speaker cable capacitance is a non-issue. It can, however, be a quite significant consideration in the cases of line level interconnects and phono cables.

Given adequate gauge, and correspondingly low resistance, speaker cable inductance can be the one of the three parameters that is particularly important. But its criticality will depend on the impedance characteristics of the speaker at high frequencies. Inductive reactance (the inductive form of impedance, which is measured in ohms) is directly proportional to frequency, and will be negligible for any reasonably designed cable at low and mid audio frequencies. It can become significant at high frequencies, though, especially if speaker impedance is low at those frequencies. The impedance of many box-type dynamic speakers tends to increase in the upper treble region, fortunately. But many electrostatic speakers have impedances which descend to 1 ohm or thereabouts at 20 kHz, which will make cable inductance particularly critical. Once again, JA's measurements can help to sort things like that out.

Best,
-- Al

Al, I think you touched on my question in your post above about "[t]he phase angle of the impedance of a speaker, at a given frequency, is the angle of the "vector sum" of the magnitudes of the resistive, inductive, and capacitive components of the impedance." But let me try to break this down a little bit.

Let's focus on what a speaker's phase angle might look like at a x-over point. Say for example the x-over point is where the woofer rolls off and the midrange picks up. Would the designer use an inductor in series in the woofer driver to roll off frequencies over a certain point. If so, I would surmise the phase angle might be inductive, or positive.

But at the same time, the designer might want to filter low frequencies from reaching the midrange below a certain point by using a capacitor in series with the midrange driver. Again, I surmise the phase angle might be negative.

So both a inductor and a capacitor might be in the circuit within the same frequency range. How would the interaction of these two passives plot as a phase angle?

P.S. My example is intentionally oversimplified in order to make a point. I suspect that the drivers themselves could be inductive or capacitive at certain frequencies. Plus I also suspect that modern x-overs don't simply insert one passive in series with a driver to achieve the desired roll-offs.

Thanks

Bruce

Bruce, I'm not totally certain, but I believe the answer to your question is that at the crossover frequency the phase angle of the speaker's impedance will be zero degrees, i.e., it will appear to the amplifier to be resistive. Per your well stated question, this is based on the hypothetical assumptions that the driver impedances are purely resistive and are equal in value, and that the rolloffs of the low and mid frequency parts of the speaker are symmetrical.

Best,
-- Al

The phase angle is zero at resonance. That is when the capacitive load and the inductive load components cancel each other out at a specific frequency and you are left with only a resistive load.

enjoy