Speaker sensitivity, impedance, and calculating amp power

daledeee1 2-20-2020
How can an amp have different current output with the same "wattage" as a different brand?

With a very few exceptions, nearly all solid state amps are designed such that for a given input voltage their output voltage remains essentially constant regardless of the load impedance, as long as the amp is operated within the limits of its voltage, current, power, and thermal capabilities. And for a given output voltage from the amp, per Ohm’s Law the current drawn by a given load impedance will increase as that impedance decreases. And correspondingly the power delivered into that load will increase as that impedance decreases, since the power delivered into a resistive load corresponds to the voltage applied to it multiplied by the current it draws when that voltage is applied to it. (Speaker impedances are not purely resistive, of course, but I won’t get into that for purposes of this explanation).

So as an example if we consider two amps rated at say 100 watts into an 8 ohm resistive load, one amp may be able to deliver 200 watts into a 4 ohm resistive load, and 400 watts into a 2 ohm resistive load, if it is able to provide the correspondingly increased amounts of current. The other amp might be able to deliver only 150 watts into 4 ohms, and 200 watts into 2 ohms. So the second amp has less current capability than the first amp, even though they are both rated at 100 watts into 8 ohms. (This assumes, of course, that both ratings are accurate, and it also assumes that the 100 watt/8 ohm rating of the first amp has not been understated to create a false impression that the amp can double the maximum amount of power it can deliver into halved load impedances).

Tube amps are a different story altogether, though. While most solid state amps have output impedances that are near zero, which enables them to maintain essentially constant voltage into varying load impedances (within some limits), tube amps have output impedances which are significant relative to speaker impedances, and which vary widely among different tube amps. As a result, depending mainly on their output impedance, and assuming they are operated within their capabilities, different tube amps tend to fall at various points along a spectrum whose end points are maintaining constant voltage and maintaining constant power into varying load impedances. Usually not at either of the end points of that spectrum, but somewhere in between.

Finally, as you probably realize the majority of speakers these days are designed to be driven by solid state amps having near zero output impedances, while others are designed such that they are best driven by tube amps, while others are happy with either type.

Regards,
-- Al

P.S: @dwmaggie, thank you for the kind words.

What is the formula for calculating what the SPL would be at 3 meters (typical listening position) rather than 1 meter?

For a single speaker, and assuming it is a conventional box-type (i.e., it is non-planar and non-line source), and neglecting room reflections, the attenuation of SPL resulting from the increase in distance is:

20 x log(distance from listener/1 meter)

where "log" is the base-10 logarithm.

So in this case, and under those assumptions:

20 x log(3 meters/1 meter) = 9.5 db of attenuation relative to the SPL produced at 1 meter (rounding off slightly).

For Erik’s example that you quoted:

109 db - 9.5 = 99.5 db SPL at 3 meters.

The presence of a second speaker and the effects of room reflections will typically add several db to that.

The 20 x log formula is built into the online calculators which have been linked to in some of the posts above.

Regards,
-- Al

Another way to have asked the question would have been:

"What role does impedance have, if any, alongside other factors in the calculation of how much power should be used to drive a speaker comfortably?"

In modern times speaker sensitivities are usually (although not always) based on the SPL produced at 1 meter in response to an input of 2.83 volts, rather than in response to an input of 1 watt. 2.83 volts into 8 ohms corresponds to 1 watt, so in the case of an 8 ohm speaker (that is truly 8 ohms) both numbers will be the same. However 2.83 volts into 4 ohms corresponds to 2 watts, which is 3 db greater than 1 watt. So 3 db should usually be subtracted from the specified sensitivity of a 4 ohm speaker to derive the SPL it will produce in response to 1 watt.

In the case of a 6 ohm speaker the corresponding figure to subtract is about 1.25 db.

Often such specs do not indicate whether they are based on 2.83 volts or 1 watt. In those cases it would be a good bet that they are based on 2.83 volts.

Note though, that since most solid state amplifiers can provide considerably more power into 4 ohms than into 8 ohms (sometimes as much as a factor of 2 more) that increase in amplifier power capability will partially or fully compensate for the 3 db subtraction. That would not be the case with tube amps, though, or with McIntosh solid state amps which have autoformers at their outputs. Tube amps and McIntosh solid state amps having autoformers are usually designed such that maximum power capability when a 4 ohm load is connected to their 4 ohm tap is essentially the same as when an 8 ohm load is connected to their 8 ohm tap.

On another note, the 80 db average and 100 db peak listening levels you mentioned are fairly similar to mine, my listening being mostly to classical music. Although I’ve found that some (relatively few) classical symphonic recordings that have been well engineered with minimal or no dynamic compression can produce 105 db peaks at my 12 foot listening distance while being listened to at average levels in the mid-70s.

Also, here is another SPL calculator you may find useful:

https://myhometheater.homestead.com/splcalculator.html

In contrast to the Crown calculator you cited this one adds 3 db if two speakers are specified, which is a reasonable approximation, and it attempts to address the effects of room reflections, i.e., what is sometimes referred to as "room gain."

Also, be aware that these calculators will significantly underestimate the resulting SPL in the case of planar speakers, such as electrostatics and Magnepans, for which SPL falls off much less rapidly as distance increases, compared to dynamic (box-type) speakers.

Finally, be aware that speaker sensitivity specs are frequently optimistic by a few db. Before using these calculators it would be prudent to Google the specific make and model of the speaker together with the word "measurements." If Stereophile, SoundStage, or some other publication has reviewed the speaker the measurements that may be presented in conjunction with the review will usually be much better to rely on than the manufacturer’s spec. And their measurements and the associated text will also often provide useful insight into the impedance of the speaker, how it varies as a function of frequency, and how accurate or inaccurate the specified number may be.

Regards,
-- Al