Audio Power - Some basic concepts - Edited and expanded

[bandcoach]

This is taken from a set of notes written for a PA operators workshop at the school I worked at in 2005. The references are to Australian power circuits, so you may need to adjust to reflect your countries power grid.

1.1 Mains Electricity
This electricity comes in three varieties:
1. single phase which comes out of the wall socket
2. Three-phase, which is what is used to drive some industrial machinery and kitchen appliances, as well as theatre lighting.
3. High voltage, which is used to transmit electricity across large distances.
We will be mainly concerned with single phase electricity.
Single phase electricity is delivered with Active, Neutral and Earth lines. Electricity nominally comes out of the Active line and returns through the Neutral line, although as it is an alternating current, the electricity is going backwards and forwards between these two lines. The Earth line is provided to ensure electrical safety, and is directly connected to some metal item that is placed into the ground/soil, hence the term Earth. In some countries the Electricity regulations require that the Neutral line also be connected to ground( strange but true)

1.1.1 Current
There are two types of current:
1. Direct current, this is usually found in batteries. It is usually shown as a straight line, although it will decay towards 0 over time.
2. Alternating current, this is the current found in household and industrial mains. It is shaped like a sine wave, although depending on where you are int he grid, this sine wave may have a lot of noise on it by the time it comes out of your wall sockets.

If you remember nothing else, remember this: current kills. Current is the flow of electrons through a point every second. The higher the current, the more electrons there are moving.
Everything contains electrons in their atomic structure. Some things give their electrons up easily, allowing electricity to move fast (high current). Other things have a hard time giving up their electrons, stopping electricity from flowing or only allowing it to move slowly (low current). One thing stands – if the current is high enough, it will flow through anything.
Most mains circuits are rated at either: 8, 10 or 15 Amperes (Amps for short). The circuits we will be using for school functions are rated at 15 Amps.

1.1.2 Voltage
Voltage is the push that an electron receives as it moves around a circuit. Mains electricity is rated at 240 volts RMS. This is an average value for the voltage. The peak value of this voltage is 340 volts. The peak to peak value is 680 volts (positive and negative sides of the waveform). The mains voltage cycles up and down 50 times each second, this means it has a frequency of 50 Hz. This is an important point to consider later when setting up the system and trying to identify possible points of noise and interference – we usually hear this cycle as a hum consisting of both 50 and 100 HZ tones, both of which are musically close to “G”. Eliminating ground loop hum is a difficult and dangerous business and better left undone than poorly done. We will NOT cover how to do this in this workshop.

1.1.2.US
US voltages are quoted as being either 110-120V or 240V. So the peak values are 155V-170V and the peak to peak values are 310V-340V. The mains frequency in the US is normally quoted as being 60Hz, although one of the reasons that we use drop frame time code is because this is actualy closer to 59.7Hz, having a direct impact on circuit design for television scanning in the pre-LCD/Plasma days.

1.1.3 Power
Joule's Law states
W (Power in watts) = I (Current in Amps) x V (Electro-Motive Force in Volts RMS).
Power is the energy created or consumed by the flow of a current caused by an RMS voltage. The higher the current, the higher the power. The higher the voltage, the higher the power.

This is similar in function to Ohms Law
E (Volts) = I (in Amps) x R (resistance in Ohms).

1.2 Amplifier Power
Amplifier power is rated in watts RMS. However, they are also rated into a given load, stated as impedance in Ohms. Impedance is the AC equivalent of resistance.

1.2.1 Current
Amplifier current is high, usually about 5 Amps. It is an alternating current. All of the advice given for mains current still applies.

1.2.2 Voltage
Amplifier voltage varies between 25 volts and 50 volts RMS, although some amplifiers do go up to 100 volts RMS.

1.2.3 Power
Amplifier power is usually quoted as one of three ratings:

RMS: This is the smallest value quoted, but the most sensible to use. It is the continuous average power of the amplifier under load. (it is the same as the Peak power divided by 0.707 (1/square root of 2))
Peak: This is the RMS value multiplied by the square root of 2 (1.414). It is a larger number and is often quoted to improve sales of the amplifier, particularly to teenage boys.
Music Power: This is the Peak power multiplied by 2. Sometimes called the Instantaneous Music Power (IMP) or Peak Music Power (PMP), this is the value the amplifier can generate very briefly before blowing up. Again, often quoted to improve sales to young men.

Shane

[bandcoach]

Following on from the first post, here is ana example, taking mrberts question about his 12W Marshall head (I'll assume that it is 12W RMS into an 8ohm load)

RMS Power: If it is an 8ohm load then the power is as quoted, 12WRMS.
Peak Power: This becomes near enough to 17W peak to peak.
Music Power: This is near enough to 34W Instantaneous.

Assuming we have a constant load over the frequency response of the speakers (not likely, but it helps to simplify the math), then if the current is constant, say 2 amps, the voltage varies as follows (even though this seems to refute Ohms Law about V=IR, it doesn't because the voltage is being described in different units at each point):

Joule's Law says

W = V x I

rearranging we get

V = W / I

Code: Select all

          Power     Voltage
RMS:      12W       6V
Peak:     17W       8.5V
PMP:      34W       17V


Shane

[bandcoach]

What if Mrberts Marshall head was rated into an 8-ohm load but the box he connected it to was rated at 2-ohms, 8-ohms, or 32-ohms? This might seem silly except that these are three of the possible combinations of impedances possible depending on how you wire the four speakers found in a quad box together.

Some basic ideas about speaker connections, based on their DC resistance rather than their AC impedance.

1.1 Wiring speakers (resistors) in series
As we wire speakers so that the positive of one speaker is connected to the negative of the next speaker, we end up with the speakers wired in series. We add the impedance of each speaker in the chain to get the final impedance (load).

Using 8-ohm speakers

Series: resulting impedance = impedance 1 + impedance 2 (speaker 1 + speaker 2) in this case, 8 + 8 = 16 ohms.



1.2 Wiring speakers in parallel
The word inverse simply means that we take a number and turn it into a fraction with one on top of it. Example: if the number is 8, then its inverse is 1/8.

As we wire speakers so that the positive of both speakers are connected together and the negatives are also connected together, we end up with speakers wired in parallel. We add the inverse impedance of each speaker in the chain to get the final inverse impedance, i.e. we need to invert the final result to get the actual impedance

Parallel: resulting inverse impedance = inverse impedance 1 + inverse impedance 2
i.e.
1/the result = 1/8 + 1/8 = 2/8 = 1/4

To get the final impedance turn the resulting fraction upside down (invert it) and reduce if necessary

i.e. 1/4 inverted is 4 ohms



1.3 Wiring a quad box - getting 2ohms, 8ohms, 32ohms, 6 ohms and 10 2/3 ohms

a) Wire everything in series and you get 32 ohms.

b) Wire pairs in parallel and then wire these pairs in series
Parallel: 1/8 + 1/8 = 2/8 = 1/4 => 4ohms
Series: 4 + 4 = 8 ohms

c) Wire pairs in series and then wire these pairs in parallel (same result as b, different wiring scheme)
Series: 8 + 8 = 16 ohms
Parallel: 1/16 + 1/16 = =1/8 => 8ohms

d) Wire everything in parallel and you get 2 ohms
Parallel: 1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 2/4 = 1/2 => 2 ohms

e) wire three in series and the remaining speaker in parallel with them
Series component: 8 +8 + 8 = 24 ohms
Parallel component: 1/24 + 1/8 = 1/24 + 3/24 = 4/24 = 1/6 => 6 ohms

f) wire three in parallel and the remaining speaker in series with them
Parallel component: 1/8 + 1/8 + 1/8 = 3/8 => 2 2/3 ohms
Series component: 2 2/3 + 8 = 10 2/3 ohms

e and f both give strange impedances. Your amp won't mind but the configurations won't work efficiently, because one or more of the drivers will be soaking up more power than others.

2 How does impedance affect power?

Impedance affects power because of Ohms Law.

Remember that Power is defined by Joule's law to be W = I x V

Ohms Law says that

V = I x R

rearranging, we also get

I = V / R

Combining the two laws we can look at power in two other ways:

a) W = I x I x R = I squared x R

b) W = V/R X V = V/R x V

Put into words

Power is proportional to Impedance

2.1 Mr Berts Marshall reappears

Going back to the example of Mr Berts Marshall head going into our rewired quad box and keeping all of the other factors the same we get the following results


All power values have been rounded to the nearest whole number.

2.2 But what really happened here - how did the power change?

It comes back to what happened to the current.

Remember that I = V/R.

Well if the load (resistance) changes, the current must increase or decrease proportionately to compensate for the change in the load if the voltage is held constant.

So for each of the Loads and assuming a constant voltage we get the following currents:



The table shows that for each load a different current is required to keep the voltage constant. This is why in some cases amplifiers can be cooked. If the amplifier is not designed to sink so much current into the external load, it will damage its circuitry, most probably the power output stage.

2.3 Real life vs examples

If the amplifier can't increase the current it sinks into the load, the voltage may be increased to compensate for the current limit. This is how speakers get cooked and some amplifiers as well.

For the amplifier to increase the voltage, it has to swing it further and further through the range supplied by the power rails. If it tries to exceed the range of the power rails, the amplifier isn't able to do this. What happens instead is the amplifier ends up clipping the waveform at the peak voltage the power rails can deliver (i.e. it doesn’t reproduce the waveform accurately once it reaches the limit of the power rails, it just stops at the maximum positive or negative voltage). If this continues and the load becomes increasingly smaller, the output waveform starts to look like a square wave. This type of waveform is likely to damage the voice coil in your speakers and the output circuitry of your amplifier as well.

a square wave produced by multiple odd harmonics

a waveform driven to clipping showing portions that resemble a square wave
Shane

[mrbert]

So...in theory my 12watt head which can drop impedance no lower than 8ohms (it comes as standard with two cabs loaded with 10" 25w 16 ohm spkrs) can drive my 2x12" cab which is loaded with 2 100w 8ohm spkrs as long as they are wired in series so that the final impedance is 16ohms?

Or am I still a dufus? And does the power handling of the speakers have something to do with it? ie the little amp is too wee pumping out only 12watts to drive big 100watt spkrs?

[bandcoach]

So...in theory my 12watt head which can drop impedance no lower than 8ohms (it comes as standard with two cabs loaded with 10" 25w 16 ohm spkrs) can drive my 2x12" cab which is loaded with 2 100w 8ohm spkrs as long as they are wired in series so that the final impedance is 16ohms?

It can drive this cabinet whether it is wired as 16-ohms (in series) or 4-ohms (in parallel). The difference is how the amplifier tries to drive it. In the 16-ohm load it will deliver the expected voltage, current and therefore wattage (power). In the 4-ohm load both the voltage and the current will increase to achieve the expected 4 x power (the values will be some complex multiples depending on current limits and the voltage rails supplying the output stages). What will happen with the 4-ohm load is that it will allow the amplifier to easily clip the waveform.

The clipping of this waveform by the way is not what happens when a normal valve amp does its so-called soft clipping; valve-amp clipping is actually output transformer loading imperfections which introduces 2nd harmonic distortion. Even a solid-state amplifier can do this if it uses an output transformer as well.

Any amplifier driven in the way that the 4-ohm load would require to achieve the expected power required by the load will actually introduce harsh clipping which is lopping off the top and bottom of the waveform, introducing harmonic distortion across the odd harmonics: creating a square wave. Fourier, Helmmholtz and Ohm all agreed that waveform could be broken into its consituent sine waves; a square waveform is the sum of all the odd harmonics of the fundamental at decreasing amplitudes

f(x) = sin(x) + 1/3sin(3x) + 1/5sin(5x) + 1/7sin(7x) + ....

Or am I still a dufus? And does the power handling of the speakers have something to do with it? ie the little amp is too wee pumping out only 12watts to drive big 100watt spkrs?

The power handling of the speakers has a lot to do with it. Two schools of thought
1) you want speakers that are rated several factors higher than your amplifier to allow for the instantaneouos power spikes.
2) you want an amplifier that is rated higher than the speakers it will be driving.

School 1 asserts that you need to cover all your bases to avoid speaker burnout.
School 2 says if the amplifier is being overdriven (generating square waves because of hard clipping) then it and the speakers won't last long, better to run the amplifier at a lower level with a higher overall power rating to avoid driving it so that it is continuously clipping.

To come back to your 12W amp - the amp will be easily overdriven before it is actually driving the speakers efficiently. Remember that a speaker is designed to move air. It is damped to stop it continuously moving or overshooting. The air provides additional resistance on the front of the speaker as does the cabinet design (closed vs open vs ported) on the rear of the speaker. It is rated at a particulalr power handling capacity to indicate how much power is required to move it efficiently. You can drive it with a small amp or a large amp and not do much damage until you either overdrive the amp or send too much power to the speaker - I have not personally seen voice coils glowing because they are recieving too much power, but I have heard tales of it - sure way to start a fire too.

Shane