The Nuts & Bolts of Loudspeakers

A Closer Look at Speaker Impedance and Sensitivity, and How They Relate to Amplifier Requirements
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When someone asks whats the impedance of this speaker?, Im inclined to ask: at what frequency? To many, loudspeaker impedance is just a number quoted on some speakers spec sheet. But theres a lot more to it than that. But what is impedance, and why you should care?

The impedance of a loudspeaker system is a function of the impedance of the individual drivers that comprise the system, with the additional influence of the crossover network components. No impedance level is better than another, and no conclusions about a loudspeakers sonic performance or quality can be drawn from impedance.

The DC resistance of the voice coil is one of the dominant components of a drivers overall impedance. The coil is also an inductor, and the more turns there are on the voice coil, the greater its inductance. At DC, the speakers impedance will simply be the resistance of the voice coil. At higher frequencies, inductance will add to the impedance.

Figure 1 shows the impedance curve for the woofer used in Thiel Audios model CS1.6 speaker system. Note the prominent impedance peaks at about 51 Hz. This is a function of the woofers natural resonance frequency. When an input sine wave is slowly swept through this frequency range, driver excursion really goes up at resonanceeven though theres no change to the input voltage. The large excursions result in a back-EMF (back-electromotive force, or back-voltage). The high impedance at this frequency is due to the back-EMF.

All unmounted driversas well as those mounted in closed boxes, such as infinite-baffle and acoustic suspension enclosureswill exhibit a single impedance peak at their resonant frequency. Some tweeters may have so much mechanical and/or air-load damping at resonance that they hardly show a peak. Woofers mounted in ported (base-reflex) or passive-radiator enclosures will show a double peak, which is a product of the enclosure tuning.

Above the resonance frequency, the impedance declines again, but never goes quite down to the coils resistive value, because coil inductance is now also in play. The lowest point on the impedance curve above resonance frequency will typically be about 20 percent to 30 percent above the DC resistance, and its this pointin the saddle of the impedance curvethat many speaker manufacturers consider to be the drivers rated or nominal impedance. At yet higher frequencies, the effect of voice coil inductance can be seen, as impedance steadily rises.

Figure 2 shows the impedance curve for the complete Thiel CS1.6, a two-way, 4-Ohm, base-reflex system. It shows the characteristic double peak of a ported system.

The rest of this speaker systems impedance curve is remarkably flat. Thiel Audio co-founder, co-owner, and product design engineer Jim Thiel says that hes added components to the crossover network specifically to flatten the impedance curve. Many speaker systems show a prominent hump in the impedance curve around the crossover frequency, due to the action of the crossover network components. In other cases, there may be a dip around the crossover frequency, if the designer were trying to pump extra energy to the drivers in this region.

The important consideration regarding speaker impedance is to be sure that the amplifier that will be used is rated to drive loads of that impedance. But, of course, were faced with the problem that impedance varies with frequency. In light of that, how can we come up with a single number for a speakers impedance?

You cant just take an average, because a speaker with an impedance that varies from 2 Ohms to 25 Ohms may have a 9-Ohm average impedance; its the portion of the frequency range where the speakers impedance is 2 Ohms that will give the amplifier fits.

You could focus on the minimum impedanceessentially looking at the worst-case scenariobut that might be too extreme, especially if the speaker just dips low in one narrow frequency band. I havent seen a speaker that never dips below 8 Ohms, said Paul DiComo, marketing manager for Baltimore-based Polk Audio.

The best way to evaluate a speaker systems impedance is not to try to distill it down to a single number, but to gather as much data as possible. Consult the speakers impedance curve, if available. It essentially contains all the information you need. What is the systems minimum impedance? Does that occur at just one point, or across much of the spectrum? And finally, whats the manufacturers nominal impedance rating for the system? If a manufacturer is genuinely trying to be upfront with their customer base (as opposed to engaging in specsmanship), their nominal rating can be surprisingly on-target.

There are a couple of speakers in our line where the impedance curve is sufficiently low that we just rate them as 4-Ohm systems, DiComo said. Our top-of-the-line LSi series is an example. With them, the impedance curve stays below the 8-Ohm line a lot. So there, we thought it important to send the consumer a signal that they need to have an amplifier that can drive a 4-Ohm load.

The Thiel Audio CS1.6, which is represented by the impedance curves shown in Figures 1 and 2, is a 4-Ohm system, so its important to match it with an amplifier rated to handle 4-Ohm loads. Most modern amplifiers are so rated, and in fact, as Thiel points out, Many amplifiers can provide twice as much power into 4 Ohms as they can into 8 Ohms, which is why I design 4-Ohm speakers.
Thiels is a good point to keep in mind. If you want to find an amplifier that will really drive 4-Ohm loads to maximum power levels without breaking a sweat, compare how much power the amplifier delivers into various impedances. If maximum power into 4 Ohms is twice that into 8 Ohms, it should do well driving 4-Ohm loads.

To protect against over-current situations resulting from too low a load impedance, many amplifiers contain some type of automatic current-limiting circuitry that will disconnect the amplifier or hold the current to some acceptable value. If you find an amplifier cutting out erratically, producing audible distortion, or a suddenly reduced signal level, it may be the amplifiers protection circuitry in action, which could indicate a speaker load thats too low in impedance for that amplifier. Check the specs on both the speaker and the amplifier.

A loudspeakers sensitivity is closely related to its efficiency, though the two are not, strictly speaking, one and the same. Both are measured by placing a microphone at one meter (3.28 feet) directly in front of the speaker (on axis). The sound pressure level (SPL) is measured in decibels while the speaker under test is driven with an input signal offor sensitivity measurements2.83-volts RMS. For efficiency measurements, a one-watt input signal is used.

Sensitivity and efficiency measurements will yield the same number for 8-Ohm speakers, because 2.83-volts RMS into 8 Ohms produces one watt. (From basic electronics, we know that the power dissipated in a circuit can be calculated by taking the square of the voltage, and dividing that by the resistance. Two point eighty-three-squared equals eight, and that number divided by eight [the resistance, in Ohms] equals one watt.)

For speakers of other than 8-Ohm impedance, the sensitivity and efficiency numbers will differ. For 4-Ohm speakers, for example, two-volts RMS produces one watt. Thus, for a 4-Ohm speaker, youd need to use a 2-volt signal to test efficiency, and a 2.83-volt signal for sensitivity. You can also infer from this that a 4-Ohm speakers sensitivity rating will be three dB above its efficiency rating (because 2.83 volts into 4 Ohms produces two watts, twice the power used for the efficiency measurement; doubling the power will raise the SPL by three dB).

Sensitivity and efficiency measurements should be made under anechoic conditions, otherwise room reinforcement (sound reflected from the various room surfaces) could artificially add several dB to the measured SPL. Also, no loudspeakers frequency response is ruler-flat, so the speakers SPL should be averaged across a reasonable band of frequencies. Jim Thiel recommends taking the average in the octave from 500 Hz to one kHz. Others take a wider range.

DiComo noted that Polk Audio tests both the sensitivity and efficiency of its speakers, but that that they publishonly the efficiency spec.

So which number is more useful: sensitivity or efficiency? It depends on what type of comparison that you want to make. There is utility in the sensitivity rating, given that modern amplifiers are constant-voltage devices (the sensitivity rating compares speakers on an equal-voltage basis). The different sensitivity ratings for various speakers reflect the differences in sound level that you would hear if you were to hook up a bunch of them to an amplifier, through a speaker switch, and switch back and forth. The efficiency number would be more useful when calculating amplifier power needed to reach a given SPL, in a given setting (as it compares speakers on an equal-wattage basis).

Differences in speaker efficiency can affect amplifier power requirements a great deal. If one speaker has an efficiency rating three dB higher than another, the less-efficient speaker will need twice as much power, just to play at the same level, everything else being equal.
Of course, theres also room volume to take into consideration. As a rough approximation, doubling the room volume, in cubic feet, can double the power needed to achieve a given sound level. A very detailed discussion of speaker efficiency, room size and power requirements can be found on Crown Audios website, at (www.crownaudio.com/amp_htm/ amp_info/how_much_power.htm).

Theres even a calculator that will let you plug in your own numbers. (Crowns article is geared toward professional audio applications, such as outdoor concerts, but it also discusses how to apply the information to indoor venues. It uses the term sensitivity, but goes on to label that as being measured with one watt at one meterwhich is contradictory. It appears that if you replace the references to sensitivity with efficiency, the information still applies.)

Before you start trying to calculate power requirements to the fraction of a watt, it may pay to keep some words of Jim Thiel in mind: How sensitivity, power, and room size relate to the output level is especially important because theres significant misunderstanding out there. Many people think that the most significant variable in all of that is loudspeaker sensitivity, but I dont think it is.

In Thiels view, three main variables determine power needs: speaker sensitivity, room volume, and how loud the listener wants the music to sound. In my experience, by far the biggest factor is how loud you like to listen to it, he said. The second-biggest factor is the size of your listening space. In a way, the least important factor is the efficiency of your speaker.

To support that last point, Thiel points out that almost all home hi-fi speakers are somewhere between 85 and 90 dB sensitivitya range of a bit less than 6 dB. Compared to a speaker having sensitivity in the middle of that range, one that fell at the high end of the range would require about half as much power for the same SPL, while one at the low end would need nearly twice as much power. While thats a pretty significant range, you can have more variation than that in terms of room size. Some rooms are more than twice as big as the average room.

While I agree that the variation in preferred listening levels is the dominant variable affecting power requirements, Im not sure I buy room volume as the next-biggest factor. Im inclined to see speaker sensitivity variations as being at least a close tie with room size.

A former loudspeaker designer, Alan R. Frank (alanrfrank@earthlink.net) is a freelance writer and networking consultant.

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