Speaker Impedance: Resistance and Phase Question

I have enjoyed the learning curve presented by other threads regarding this issue and the issue of Voltage vs. Amperage driven amplifiers. I am not asking that what has been presented in other threads be repeated here.

Does the phase shift of a speaker (resulting in Capacitance) refer to a lag of current behind voltage? Or is this too simple of an explanation?

And to AL, Regards.
Voltage and current are not in perfect syncronization because the load stores energy and then feeds it back to the source on a delayed basis (reactive load). The type of load determines whether current will be leading or lagging behind voltage. An inductive load results in current lagging behind voltage. Speakers present an inductive load that varies with frequency which can make it more difficult to deliver power than a purely resistive load (e.g., power delivery to a light bulb is easy because it does not store electrical energy and feed back that power).
Thanks, Mesch. Regards to you as well :-)

I second Larry's comments, except that his last sentence might be taken to mean that speakers ALWAYS "present an inductive load," which of course is not the case. Speaker impedance will usually be inductive at some frequencies, to some degree, capacitive at other frequencies, to some degree, and purely resistive at a few frequencies, where it transitions from inductive to capacitive or vice versa.
Does the phase shift of a speaker (resulting in Capacitance) refer to a lag of current behind voltage? Or is this too simple of an explanation?
Actually it's the other way around, with voltage lagging current for a capacitive load. Current lags voltage for an inductive load.

But first, it should be made clear that in this context "phase shift of a speaker" does not refer to phase shifts that may be produced in the acoustic output of a speaker, which is a whole different subject. What you are referring to is the "phase angle" of the impedance of a speaker. Impedance consisting of a magnitude, measured in ohms, and a phase angle, measured in degrees.

If a sine wave at a single given frequency is applied to a hypothetical ideal resistor (having no inductive or capacitive component), voltage and current will be in phase with each other, meaning that both will reach their maximum, minimum, and corresponding intermediate values at the same time. If that signal is applied to a hypothetical ideal inductor (having no resistive or capacitive component), current will lag voltage by 90 degrees, or 1/4 of a cycle of the sine wave. If that signal is applied to a hypothetical ideal capacitor (having no resistive or inductive component) voltage will lag current by 90 degrees.

Inductive and capacitive loads are collectively referred to as reactive loads, as opposed to purely resistive loads.

The 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. If the three components were plotted on a graph, by convention the inductive component would be represented as a positive number along the y (vertical) axis, the capacitive component would be represented as a negative number along the y axis, and the resistive component would be represented as a positive number along the x axis. So an inductive phase angle will be a positive number of degrees; a capacitive phase angle will be a negative number of degrees; and a resistive phase angle will be zero degrees. The larger the number of degrees in the positive direction, up to a maximum of 90, the more purely inductive the impedance is. The larger the number of degrees in the negative direction, down to -90, the more purely capacitive the impedance is. Phase angles for most speakers at most frequencies tend to fall somewhere within a range of perhaps +/- 45 degrees or so.

Most of the speaker reviews in Stereophile, which can be found at their website, include measurements taken by John Atkinson of impedance magnitude (ohms) and phase angle, and some good associated commentary.

As Larry indicated, if a speaker load is significantly reactive its efficiency (acoustic power out vs. electrical power in) will be lower than if it were purely resistive, everything else being equal. Hypothetically speaking, if a speaker had an impedance of + or - 90 degrees at some frequency, it would be unable to produce any output at that frequency, as all of the power it received at that frequency would be returned to the source, and none would be absorbed and converted into sound.

Severely capacitive phase angles, especially if they occur at frequencies for which the impedance magnitude (the number of ohms) is low, are particularly demanding on the amplifier. In part because reactive phase angles lower efficiency, as was mentioned. And also because the current drawn by a capacitor increases in proportion to the rate of change of applied voltage, which results in larger demands for current when fast transients occur than would otherwise be the case. The current drawn by an inductor, on the other hand, varies in proportion to the "integral" of applied voltage, which is not as challenging to the amplifier.

Regards once again :-)
-- Al

Great expansion on the subject; I tried for a simpler answer, but, it is good to see a complete explanation.

For practical application of such information, the tests you mention that Stereophile publishes are helpful. They plot the imdedance of the speaker against frequency and also plot the phase angle against frequency. The most meaningful use of that data is to look at the low points of impedance and then look to see how far off the phase angle at that same frequency is from zero. A low impedance and high phase angle (positive or negative) represents a difficult load. If that point is also in a frequency range where there is a lot of musical energy, that makes the speaker even more demanding.

A lot of speakers have deceptive nominal ratings; for example, the manufacturer may claim 8 ohms because over much of the frequency range the impedance is close to 8 ohms but at some crucial point (e.g., 80 hz) the impedance drops closer to 2 ohms and the phase angle is more than 30 degrees. That would be a demanding impedance characteristic.

I run tube amplifiers so my experience is mainly with matching speakers with such amps. A lot of people look at efficiency numbers when trying to decide whether a low-powered tube amp will work with a particular speaker. To me, the impedance characteristics is much more telling than nominal efficiency. I have heard a 15 ohm speaker which, I believe, has a 83 db/w efficiency rating that played loudly in a large room with an 8 watt amp. I have heard supposedly 95 db/w speakers that could not play well with even 50 watt amps because of their difficult impedance characteristics.
Thanks very much Larryi and Al. When I stated speaker phase shift I meant to say phase angle. Given the relative 'lameness' of my question, I was provided exceptional feedback. It came as no surprise given the authors.

I wish to provide a little feedback on myself and my equipment given the the kind responses I have garnished. I have been involved in this hobby since I was 20, some 44 years ago. In that time I have developed only 3 systems, all on the budget end. My current system: Esoteric MG10s, Bel 1001MK5, Jolida Fusion 3000, Arcan DV137, PS Digital Link III w/Hiface USBtoSPDIF, Sonographe turntable (bought in 1983), Bluepoint N0. 2, Lounge phonostage, Kimber and Audioquest cables. Looking to replace the DAC and USB converter as evident from some of my other posts.

I only became involved in this forum this year and have enjoyed it immensely.
Thanks to all.
I should add to my previous post that I first became aware of the importance of speaker reactance via John Atkinson's writings and that aspect of Stereophile,s speaker evaluation I find most informative. I have long known that reactance =resistance+inductance+capacitance however am gaining a far better understanding. 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?
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.

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.

-- 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.


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.

-- 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.