PSA: Power output lookup table

Or, how much air gets shifted when you hook things up

Figuring out whether you’re going to blow up your speaker cabinet seems to be a consideration that turns up more often than you might think. Here’s a run-through of the simple calculations to demystify the calculation.

Power output calculation

A quick recap on delivering power to speakers.

There are 2 things you can change: the Amp (make it smaller / bigger) and the speakers and their combined impedance. Now, for material reasons, similar speakers doing a similar job tend to have similar impedances.
Guitar speakers are around 8Ω (Ohms), with some at 4 and some at 16. When they are similar enough, it’s useful to combine them in series or parallel.

The formulae are

P = V² / R

also written as:

P = I² R (you can verify this is the same using Ohm’s law)

So, here is my favourite “real” amp right now. It’s a proper commercial amp separate and a home made by me speaker cabinet. I have recently upgraded the cables and added an isolator switch to allow the use of only one speaker, but apart from that, it’s been fine for over 20 years.

The mighty triumvirate

I clearly have not been playing loud enough, though…

detail of one speaker.

A Worked Example

So, to see how good this match is: let’s resort to the manuals. Yes, you heard me correctly: read the manuals.

Between these 2 manuals, which look similar only from the frontispiece, we glean 2 facts:

For connection to external loudspeakers. The minimum operating impedance for the VS100R, VS100H & VS102R is 4 Ohms. The internal speaker on the VS100R/VS102R is rated at 8 Ohms, therefore if using an external speaker in conjunction with the internal speaker, the external speaker should be rated at 8 Ohms

Output 100 Watts RMS -4 Ω

(technically: from the back panel diagram)

Note also

230V ~ 50 Hz 150 Watts

So, no great surprise: it’s an amp; able to deliver 100W; and what’s more, designed to do this into a 4Ω load. Let’s work out what happens when we connect the cabinet.

Simple Calculation

These are approximate calculations: simplest to consider that ALL values are RMS

At rated maximum:

P = 100W into 4Ω

V² / 4 = 100

V² = 400 (V= 20V)

My cabinet

In parallel:

16 || 16 => 8 Ω

P = 400 / 8 = 50W ✅

Solo => 16Ω:

P = 400 / 16 = 25W ✅

So, both configurations are comfortably under the rating.

Another approach to double check — max voltage

speaker rating is 65W @ 16Ω

Pₘₐₓ = Vₘₐₓ² / R

Vₘₐₓ² = 65 * 16

Vₘₐₓ = 32 V — which is below the maximum generated by the amp, so again✅

So, we’ll never* blow up that speaker with that amp.

Yet another double check — max current

Pₘₐₓ = Iₘₐₓ² R

100 / 8 = Iₘₐₓ²

Iₘₐₓ = 3.5A

Now, if the cables connecting the speakers internally and to the amp are not very comfortably capable of carrying that current, the risk is that the sound is distorted — trust me, it sounds terrible.

What does “comfortable”, look like?

• Lazy engineer’s approach #1

Iₘₐₓ R << Vₘₐₓ

so, R << 20 / 3.5 or R is much less than 5Ω

• Lazy engineer’s approach #2

“Just make sure the cable resistance is much less than the speaker resistance”

so, R << 8 or R is much less than 8Ω

which is basically the same as #1, with even less arithmetic.

You can buy speaker cables, and of course they will have an maximum amp rating, which should be a perfectly adequate yardstick to pick the right one for your connection.

Finally: A General table

As the VS100H (or any other 100W amp) is conveniently 100W, simply convert the power with the appropriate ratio to use this table for any amplifier output.

+-----------+----------------+-----------+---------------+
| Impedance | Configurations | Power (W) | dB power diff |
+-----------+----------------+-----------+---------------+
|         4 | 4Ω, 8Ω||8Ω     |       100 |             0 |
|         8 | 8Ω, 16Ω||16Ω   |        50 |             3 |
|        16 | 16Ω, 8Ω + 8Ω   |        25 |             6 |
|        32 | 16Ω + 16Ω      |      12.5 |             9 |
+-----------+----------------+-----------+---------------+

It might help to consider the 100W at 4Ω as equivalent to 100% at 40Ω. Hence an amp capable of 400W into 4Ω will deliver 100W into 16Ω, or 25%

Conclusion

In brief, it’s pretty easy to get approximate figures out how to safely connect up your speakers to get close, but not too close to the maximum output of your amp.

Why am I saying these are these figures are approximate?

• we’re relying upon manufacturer’s ratings

They could quote anything they want — most likely there is a non-trivial safety factor to protect their product’s reputation. The frequencies you push through the speaker will also make a difference.

• we’re not considering impulsive signals versus sustained

A speaker might only get a guitar feeding back on one note at 700Hz for a minute, or it might be subjected to a drum kit being played through it. These will materially affect how the speaker is strained. For the former it is pretty easy to calculate the energy consumed, for the latter we don’t even have a rating for the limit on the power of an impulse.

• rough averages work pretty well for our purposes, because speaker efficiency is amazingly low

No matter how the signals looks, we can be sure that if 65W is sent into the speaker, the vast majori^H^H^H^H^H^H^H^H^H^H all of that becames heat. Speakers are terribly inefficientin the range of percentage points http://www.sengpielaudio.com/calculator-efficiency.htm. Hence, your real worry is burning out or deforming the speaker.

The latter reinforces the message that if you want to get predictable performance from your speakers, use them in the intended way at the intended rating. Unless you are the Beatles.

Recording practices of the Beatles - Wikipedia

* famous last words !