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# Understanding Impedance Curves & Phase Angles

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### Impedance Curves

So far we’ve discussed impedance as a single number for a loudspeaker; it’s true that the most information you will ever see for a great many speakers is its nominal impedance. However, it is important to understand that a speaker’s impedance isn’t just one number; its actual value will vary by frequency, and it will sometimes be well above 20 ohms, and sometimes below 2 ohms, depending on the speaker in question. Part of how hard a speaker is on an amplifier depends on the actual impedance curve itself; for example, low impedance values in the octave of 10kHz-20kHz is generally not considered the end of the world given that real world content carries very little energy in that part of the spectrum. On the other hand, a stretch of low impedance from 80Hz-500Hz, which will have no shortage of energy with real world content, could be a serious problem if your partnering amplifier isn’t up to the task.  The speaker below has a 2.7 ohm dip right at 30Hz and 60Hz.  This can wreck havoc on an amplifier not capable of supplying enough output current.

Impedance curve of the Status Acoustics Titus 8T. Impedance Caries between ~2.7 ohms and ~18 ohms.

### The Mysterious Phase Angle

The phase angle, which also varies by frequency, is probably one of the less well understood aspects of a speaker’s electrical profile. The phase angle determines how much the current will lead or lag the voltage waveform in a reactive circuit. In an inductive circuit, the current will lag behind the voltage, and you’ll get a positive phase angle. In a capacitive circuit, the current will lead the voltage, leading to a negative phase angle. The phase angle will resultantly determine how much apparent power the speaker will see.

In spite of the phase angle’s role in equation (2), from the amplifier’s perspective we are not concerned with apparent power at the speaker. In one sense, you can consider the effects of phase angle being built into the frequency response (which represents voltage sensitivity over the full bandwidth): whether the phase angle is 0 degrees or 60 degrees, the voltage demanded from the amplifier remains the same. As a result you don’t have to worry that an amplifier is going to have to swing loads of extra voltage and current in order to cover the effects of a difficult phase angle.

From the amplifier’s standpoint there are two things we’re concerned with. The first is heat/power dissipation at the amplifier. In this respect, 45 is a magic number; at 45 degrees of phase shift, an amplifier’s output transistors will have to dissipate double the heat than if the load were purely resistive (i.e. 0 degrees of phase shift). Fortunately, 45 degrees is the worst case scenario for a real world loudspeaker; both above and below this point, the amount of power an amplifier is required to dissipate falls off.

Power Factor, Normalized Amplifier/Load Dissipation Vs. Phase; Courtesy of Sound.Westhost.com

In the table above, Power Factor refers to COS(Ф) from our equations (2) through (4); Power (Amp) denotes the amount of power the amplifier must dissipate, while Power (Load) refers to the power through the loudspeaker.

The second effect of electrical phase from the amplifier’s standpoint could be qualified as an apparent cut in the load impedance. Remember, the voltage waveform is no longer in phase with the current, so peak current is no longer being sourced from an amplifier at the same time as peak voltage. At the extreme of 90 degrees (which would never happen with a real world loudspeaker), peak current is being sourced when voltage is 0, which isn’t too far off from the conditions of a short circuit.

So now that we understand just how hard a phase angle like +/- 45 degrees can be on an amplifier, what can we take away? First, it is important to understand that your average bench test into an 8 ohm resistive load (and even a 4 ohm resistive load) isn’t capable of telling you the whole story on how an amplifier will perform into a real world load. To handle a real world loudspeaker, a good quality amplifier must be built with the challenges of a less than benign phase angle in mind. Naturally, that takes a lot of heat sinking or active cooling and a robust output stage.

### Conclusion

It is my hope that after reading and properly digesting this article, you the reader have a better understanding of the electrical characteristics of a loudspeaker, and how they matter when selecting an amplifier. Things are far more complicated than saying “Speaker X is 100dB sensitive, so you could power it with a potato!” Voltage sensitivity, impedance, and electrical phase all intertwine to determine just what you need in terms of amplification, and understanding how they interact is vital to making an informed decision. Use this knowledge well, and you’ll not need to spend thousands of dollars on an amplifier to drive reasonably sensitive speakers with relatively benign electrical phase and impedance, or conversely skimp on the amplifier when your speakers demand much more. Happy listening!

### Acknowledgements

• Sergiu Ignat, Electronics Designer of Classe Audio

Steve81 posts on February 19, 2013 17:08
What I am taking from the article is that phase angles are OK as long as they don't hover around 45 degrees? Is it as simple as that? So 60 degrees is fine and 30 is fine, but 45 is not fine, at least if you don't have a amp with good cooling? What would the most perfect, most ideal phase angle profile a speaker could have?

If you look at the table included in that section, specifically under the Power (Amp) column, you'll note that as the phase angle goes up, power dissipated in the amplifier goes up until you reach 45 degrees. At that point it falls off until you reach 90 degrees, which no real world loudspeaker will present. Nonetheless, at 30 and 60 degrees, while the power dissipated in the amplifier isn't as high as 45 degrees, it's still significantly higher than at 0 degrees, which is a purely resistive load.
shadyJ posts on February 19, 2013 15:09
What I am taking from the article is that phase angles are OK as long as they don't hover around 45 degrees? Is it as simple as that? So 60 degrees is fine and 30 is fine, but 45 is not fine, at least if you don't have a amp with good cooling? What would the most perfect, most ideal phase angle profile a speaker could have?
shadyJ posts on February 17, 2013 23:08
3db posts on February 15, 2013 12:17
I knew I would get the order wrong. In a capacitive circuit, current leads voltage and an in inductive circuits, current lags voltage. Its been 30+ years since I played with this. :o As current begins to flow across the capacitor, a charge is being created, hence the voltage build up across the capacitor ....still 90 degrees difference in a pure capacitive circuit. With a pure inductive circuit, the voltage applied across the inductor causes a field to build across the coil which in turns induces current flow. My apologies for having that mixed up earlier.

Here's a pic that illustrates pure resistance, inductance, and capacitance circuits.

Steve81 posts on February 15, 2013 10:17