Amps: Watts and Decibels: a classic misunderstanding

Introduction

Note: this entry was already published in my old Spanish version of this blog around March 2011. I am just revisiting it here for it's interest.

Most of guitarist (and that included myself at some point of time) are confused about Watts and Decibels and, therefore, doesn't understand why some less powered amp can sound louder than a higher powered amp, by example.

The first time anyone hears a Vox AC30 is being impressed by its loudness, it seems louder than any Marshall half stack, by example. While the Vox AC30 is rated at around 30 Watts, typical half or full stacks are rated to 100 Watts.

One more typical confusion is to think that an amp with double power will sound double louder (by example, a 100 W amp = 2 times a 50 W amp).

To understand all this, we need to clarify some concepts, as: Power, Decibels and SPL, among other related ones.
So, let go ahead trying to clarify some things related to amps...

Electrical Power of an Amp (Watts)

Electrical Power definition

Power measures the amount of the Work done by any particular agent in a certain Time.

Imagine that we are a group of friends trying to lift a 1 Kg stone, up to 1 meter high (a table, by example). More or less, everyone will be able to easily lift that stone, in same time.
If we try the same with a 30 Kg stone, to some it will cost a bit more than to others and, the time that will need each one for it will slightly differ from individual to individual.
Now,  let try the same with a 80 Kg stone. Probably, most of people couldn't lift that weight up to the table and, those that were able, will need very differentiated times.

For each stone that everybody was able to lift to the same 1 meter high, EVERYONE had done the same amount of WORK (we had to apply same Force to move the stone 1 meter up), everybody burnt the same ENERGY (Energy = Work) but, each person should use a different time for same task.
The quickest is the most powerful, the slowest is the less powerful.

In electricity, power is the product of the electrical potential difference (energy level difference, voltage) and the intensity of the current (amperage) that can be produced by time unit.
Part of such an energy will be dissipated as Heat, most of such an energy will be used for the task which a circuit was designed for.

In the case of guitar amps, the remaining useful energy will be used just to move the coil(s) of your amp' speaker(s).

The Power measurement unit is being called Watt (W).

As any light bulb consumes electrical power from your mains, at a determined ratio / hour, any amp has a power consuming ratio.
The input energy is being transformed in Heat (dissipated by the electronics components of the amp and, specially by tubes, transformers and resistors) and, just part of the original input power remains to let the amp to do its job: to amplify the weak signal of our guitar, converting it into an electrical signal with power enough to move an speaker with ease.

The ratio of the input energy that the amp is able to deliver at its output it's being called: Performance or Efficiency. Given two amps delivering 50 W on their outputs, if the first one consumes 100 W and the second 75 W of mains power, clearly the one consuming 75 W is more efficient than the one consuming 100 W.
The amp consuming 100W was able to use just the 50% of the consumed energy, while the 75W amp was able to use a 66,66% of the consumed energy (or said in other way, wasted just a 33.33% of the consumed energy, against the 50% of the other amp).

Guitar Amps are very inefficient circuits and, waste a lot of energy.
A 50W amp can consume about 125 - 175W to produce just those 50W on its output!.
First surprise for you?.



Power of a tube amp

The power of a tube amp depends, basically, in the efficiency of its tubes and, such an efficiency depends on the tube limitations and on the rest of the amp design.

The so called Single-End designs (one single power tube, by example), are less efficient than the so called Pull-Push designs.
Each tube type can offer a different range of power, up to certain max, depending on the design of the amp.
By example, an EL84 can offer 12W in Single-End pure Class A, 15W in Cathode-Biased and, about 20W in a Pull-Push Class AB design with Fixed-Bias.



Maximum and RMS Power

So, tube types and amp design (Class, Bias type, topology) around those tubes will delimiter the maximum power of such an amp. But, this maximum power will depend on the impedance of the speakers, also.

Usually, an amp is being designed to stand some minimum impedance and several higher impedances.
The less the minimum impedance value is, the harder the amp works.
Typical minimum impedance levels for guitar amps are 4 or 8 Ohms and, can be lower (2 Ohm) in the case of solid state amps for bass guitars.

So, typically, the Power Ratio facilitated by the amp maker is often related the the output power of this amp at its minimum impedance.

If an amp has a maximum power of 100W@4 Ohms and, we plug to it an 8 Ohms cab, we will reduced the amp power approximately to half. Increasing the resistance of the load (impedance), we reduce the voltage and, since Power = voltage * current, delivered power drops.
With a 16 Ohms cab, we would reduce the power to approx a quarter part.

Ok. We can see now that if the cab has a higher impedance than the minimum impedance of the amp, we wouldn't get its maximum power (even that this trick can be used to lower the loudness of the amp).
Therefore, it's very important to read the technical specifications of your amp and, specially in the case of combos, to check which is the minimum impedance for this amp and which impedance have the paired cab.

It's not so rare to find amps with a minimum impedance of 8 Ohms using a paired cab or speaker (in case of combos) rated at 16 Ohm.
This is even more typical in PA systems.

But, things doesn't stop here.
While to measure things that happen in a Direct Current circuit is quite easy, when Alternate Current is involved things go more complex. The AC changes in phase and sign (positive and negative) in a cyclical way.
To approximate values of AC electrical variables to same values measured in DC, a complex mathematical formula was developed. This formula was named Root Mean Square (RMS) and, measures average values.

The amp doesn't delivers its power in a lineal and constant way. The average value between power peaks and valleys is the so called RMS Power and, it's the value that really matters, because it talks about the average power level that the amp can deliver is a constant way.
Peak values should be about 200% over RMS. If the amp is rated to 100W RMS, it's peaks can reach around 200W of maximum power.

Therefore, another important information in amp' specifications is to know if the nominal power is related to Peak or RMS Power. The rule for tube guitar amps is RMS (but, read your specifications).

Then, if our amp delivers 50W RMS, we will need at least an speaker (or cab) supporting 50W RMS (or higher, for higher security) at the same impedance than the amp's minimum impedance.
As amps, speakers rated to certain RMS value can support peaks the double of its RMS value.

So, watch out!. It's not the same a 50W Max amp and a 50W RMS amp. The 50W Max amp will have 50W peaks but, will deliver around 25W RMS, while the 50W RMS will have 100W peaks and will deliver 50W RMS (double power).

Well, mix this Max / RMS thing with impedance mismatching  and, you can start to understand how a theoretically powerful amp (75W Max) can sound quieter than a theoretically less powerful amp (50W RMS).

But, we are still missing the other big component: Speakers.



Speakers

At this point, it's clear that all that output energy (power) that the amp is delivering will be used just to move the big coil of our speaker(s), to move the membrane, to push the air (by pressuring it) and, creating the sound but... which role play speakers in all this confusion about loudness and power?.

In one side, we already discussed about the fact that the speaker impedance increases the resistance in the power stage of the amp, dropping the delivered power (and thus, the available energy that can be transduced into sound). But, neither the Watts of Power of an amp or an speaker tell us nothing about their own efficiency in to transform that available input energy (output of the amp, input of the speaker) to sound.

As in the case of amps, the speaker will waste part of its input energy (dissipated as heat) and use the remaining one to excite the coil to move its membrane. But, we need to clarify still some things, before going further.



Decibels (dB)

The Decibel is the 10th part of a Bel. A Bel establishes the logarithmic ratio for the power difference of a certain value related to a reference value.
In the case of sound, we arbitrary assigned a zero value to the threshold of human hearing (that is, 0 dB = threshold of human hearing).
This is so arbitrary and useful as to give a zero value to the level of the sea and then, to measure mountains, expressing their high related to that reference value.

It's important to say here that the Decibel, in fact, is an undimensional unit and, means nothing alone, at least that is being related to some other dimensional unit.
Together with the decibel symbol, we will need to add some dimensional symbol to properly define what are we measuring.
So, we can see 1 dB V (voltage) , 1 dB SPL (sound pressure level), 1 dB RMS (average level), etc.

As it's a logarithmic unit, each increase of 1 Bel means a power 10 times higher respect of the previous power level so, 1 dB is 10 times more powerful that 0 dB and, 2 dB 10 times more powerful than 1 dB and 100 times more powerful than 0 dB.

Since the Bel is a huge measurement unit, the decibel (a 10th of a Bel) is being used to measure loudness, instead. The Pain Threshold is about 140 dB (respect of the hearing threshold!).
To have a better idea, a quiet breathing sounds around 10 dB, a conversation around 40 dB, traffic noise around 90 dB, 98 dB is the standard for Cinema, 130 dB correspond to a reaction plane taking off and, the biggest measured sound level ever measured were the 180 dB produced by the explosion of Krakatoa Vulcan.



Sound Pressure Level (SPL)

The Sound Pressure Level measures the instantaneous intensity of the sound that reaches a certain spot.
Even that air pressure changes are being measured in Pascals, since there is a really wide range between the hearing threshold (20 micro-Pascals) and the pain threshold (200 Pascals), we use the decibel scale (logarithmic), taking as the reference value (0 dB SPL) the 20 micro-Pascals that correspond to the the hearing threshold.

Usually, speaker specifications say which are the maximum SPL that they can generate and, such a level is often referred to the level perceived at 1 meter of the speaker.

Since the sound is being produced when compressing the air molecules, that travel in the space as waves, pressuring our eardrum (inversely to how an speaker works), loudness changes are being measured in decibels SPL and, not in Watts. That's a common confusion.

There is some relationship between Watts and dB SPL but, this is not a 1 to 1 relationship. If we double the watts (by example, from 50W RMS to 100W RMS), we are increasing the sound pressure in about 3 dB (not doubling it!). If, by example, 50W produced 102 dB SPL, 100W will produce 105 dB SPL and not 204 dB SPL (remember that the loudest sound never recorded reached "just" 180 dB!!!).


Speaker efficiency

In the same way that amp are differently efficient transforming the input power into output power, not every speaker is equally efficient transducing the electrical power into sound pressure (sound).

In principle, speakers that support higher power levels should be able to move more air than speakers of lower power and, this is like this but, when comparing several speakers with equal power, not all them offer same efficiency levels (sound pressure).
By example, the Celestion G12 "Blue Bulldog", that were originally mounted in those Vox AC30 were able to deliver 100 dB SPL, while the Jensen of same epoch (Fender amps, basically) were generating between 90 and 96 dB SPL. The famous Celestion Greenback deliver 97 dB SPL, by example.

3 dB SPL more or less is the minimum difference that the common human hears as an stepped change in loudness. Remember that this is the difference between the loudness of a 100W amp and a 50W amp or, between a 50W amp and a 25W amp.


Speakers cab design

Size and geometry of the own speaker (membrane, coil, etc.) determines the amount of air that the speaker can push in a single stroke (movement of the membrane). Two speakers move more air than just one and, 4 move more than 2 and, 8 more than 4. That's clear.

Together with the number of speakers and their own efficiency, the design of the cab (dimensions, shape, components...) that holds them, contributes to how the sound is actually being projected and, also to which frequencies are more or less represented (what is very important, since the human hearing is more sensible to mid frequencies, the closer to the human voices).



Big Ass, walking or don't walking?

So nice so good. We have already seen that there are several factors that will determine if a certain amp will sound louder than other one and, this is not always directly proportional to their nominal  power so, everything depends on the efficiency of the set amp-speakers.
So, ok, I've got it: I will pair the speakers with the higher efficiency with the impedance level corresponding to the minimum impedance supported by my amp and... krank that shit!.

Errr.... NOT. This is not a competition to see who has the bigger thing. We are talking about music and, music is being perceived in a very subjective way.
The set amp-speakers is our main tool as guitarists (wasn't it the guitar?... then not... even a cheap guitar can sound nice in a great amp, the opposite is false) and, there are amps and speakers to cover every taste.

When an amplifier is being designed, the maker is also choosing certain speakers to achieve a certain sound. If that sound it's being achieved with the less efficient speaker then, this is the right speaker and, it doesn't matter if the amp of our neighbor sounds way louder, if it doesn't suits our needs.

As I find stupid to drive a Ferrari Testarrosa in the city (well, you look really cool and will attract some girls, this I can recognize but... can you really enjoy the potential of such a car?), it's absolutely stupid to have a Full Stack of 100W with two cabs of 4x12" speakers (and Blue Bulldog, why not), to play at 70 dB SPL (bellow traffic noise).
We will not extract the best of that amp and speakers, because both will be work way bellow their sweet spots, where they can deliver their magic voice.

Therefore, you will see often en Recording Studios (by example) little amps that you will be able to krank to their sweet spot to record harmonically rich guitars. Most of the tracks we love were recorded with little amps. Some samples are Fender Tweed, Champ, Blues Jr and similar.
The best disk of Clapton was recorded with a 18W RMS combo (called later BluesBreaker, because of the disk). In most of Zeppelin disks, guitars were recorded using a Supro amp rated at 15-20W RMS.
Clearly, you don't need same sound pressure to fill a stadium or to fill an small room.
The power and efficiency of your amp and speakers has to be the right one for the space and loudness that you need for each environment.


A side warning note about speaker cables

Unfortunately, I've seen many guitarists and, even some "sound engineer", using guitar cables to link the cab to the amp. This is definitively wrong.
Anyone that knows a bit about amps (and, I am not talking about myself, since I know nothing about), will say to you that you have to use speaker cables, otherwise you are in risk to damage your speaker and / or your amp (usually the Output Transformer is what deads here, costing an eye to repair).
You should had hear it but, nobody explained to you why, am I right? (and that's why you think it's bullshit).

We have seen above that the output power of an amp is the product of voltage and current. If the output voltage is 370 Volts and the amp is rated to 50W RMS, that means that the current value is:
P = V * I, then I = P / V
I = 50 W / 370 V = 0,135 A = 135 mA

In instrument cables, concretely guitar cables, travel voltage levels in the order of mili-volts (about 1000 times lower) and, very low current levels and, therefore, the energy travelling the cable is way lower (about 1000 times lower).

Depending on the power expected, the cable should have a different section (gauge).
Signals of low power can travel producing none or very low heating in conductors of a gauge similar to a hair but, higher power signals will need wider sections, to allow the conductor to "eat" electrons easily, and reducing the heat generated because of the resistance that the conductor offers to the travel of electrons.

Look at your mains power.
From the Energy Central there exit cables of a huge gauge, travelling all the country.
From those cables, smaller gauged cables reach your house's entry spot.
Then, from that entry spot, smaller gauged cables distribute the energy inside your home.
Your electric network will be protected by a therm-magnetic device that will jump if there is some overheating in your cabling.
This overheating can occur because your are hanging one or more electrical devices in the same line which, combined power summed up together is bigger than the power that the conductor can stand.
If that protective device wasn't there and the overheat stant for a long while, it will produce fire.
For this same reason, the cable that it's used to link the amp and the speaker or cab, must be a cable with TWO independent (positive and negative) conductors, of an adequate section.
Instrument cables have just a single signal conductor, wrapped in a mall or a metallic folder to ground such a signal. Those cable haven't the right section to support the power generated in the amp.
Therefore, the overheating of such a cables can even degenerate in a fire and, disappearing the load of the speaker, your amp can result seriously damaged (and even get fire).

So, please, buy some speaker cable for your amp and cab and, forget using instrument cables for that.
You never know when the overheat will be enough to cause the issue.