First the basics.
To understand what you are actually doing when wiring a speaker up to an amplifier, it is important to understand the concept of ohms law.
This is a very basic explanation. (For a more comprehensive explanation, have a look at the links at the bottom of this post, or do a search on the internet, or study a textbook on the subject.)
Basically for something to be done (ie, for sound to occur), some work needs to be done. Power is the amount of work that is done at a specific point in time. In an electronic circuit, through an electrical conductor, this work is done by the movement of charged particles (usually electrons).
Next, for something to be done, a force needs to be applied. In an electronic circuit, this force is known as voltage, sometimes referred to as electromotive force (EMF). Voltage is the potential difference (of force) between two points.
This force causes the electrons in an electrical conductor to move.
Next, we move on to current. Current is the measure of the flow of charged particles passing through a particular point in an electrical circuit in a given period of time.
One ampere (amp) is defined as one coulomb per second.
Next, it is important to consider resistance. If there was no resistance, then when you apply a force, there would be an unlimited amount of current flow. Resistance is the measure of the opposition to the current flow.
One volt when applied across a resistance of one ohm will cause one amp of current to flow through the circuit.
As you can see, an increase in resistance results in a decrease of current flow.
As I stated earlier, power is the amount of work done at a specific point in time. The amount of work done is measured in watts. The power equals the voltage multiplied by the current. For example, if you had one volt and one amp, there will be one watt of work done. If you had a resistor of one ohm, applied a voltage of one volt, then there would be one watt of power dissipated as heat.
Voltage is expressed in volts
Current is expressed in amperes (amp/amps)
Resistance is expressed in ohms
Impedance is expressed in ohms
Power is expressed in watts
So we have two base formulas:
Power = Current multiplied by voltage
Voltage = Current multiplied by resistance
And we can derive the needed formulas from there:
P = Power
E = Electromotive force (voltage)
I = Current
R = Resistance
sqrt = Square root
^2 = Squared
To find the power: P = I x E, P = E^2 / R, P = I^2 x R
To find the voltage E = I x R, E = P / I , E = sqrt(P x R)
To find the current: I =P / E, I = E / R, I = sqrt(P / R)
To find the resistance: R = E^2 / P, R = E / I, R = P / I^2
It is important to consider that in car audio, the purpose of some electronic components, is not to create heat, but to reproduce sound. For example, the purpose of an amplifier is to increase the voltage that is able to be sent to a speaker. The purpose of a speaker is to produce sound waves from this voltage. However, these components are not perfectly efficient and will dissipate some power out as heat. For example, a (average Class A/B) amplifier may only be around 60% efficient at full volume. (Less efficient at lower volumes.) This means that 40% of the power that enters the amplifier will be dissipated as heat through the heatsink. If you increase the power into the amplifier, for example you turn up the volume, or increase the battery/alternator voltage, or reduce the resistance of the speaker that the amplifier is driving, then there will also be an increase in the heat output of the amplifier.
In the case of audio, we reproduce the sound in the form of alternating current, rather than direct current. This means that you will have a wave that will alternate back and forth a certain amount of times per second. These cycles are usually referred to frequency, which is the amount of times the wave cycles per second. The scale ranges between DC (direct current), which has no cycles per second, to infinity where the wave alternates an infinite amount of times per second. As the frequency increases, so does the tone of the sound. For example, bass tones are low frequencies and treble tones are high (relative to our hearing) frequencies. Music is a complex wave that comprises of many sine waves at different frequencies and amplitudes (volume).
Now in electronics, there are components (capacitors and inductors) that will have a resistance that actually varies with frequency. This is referred to as reactance and measured in impedance. These components will have an impedance curve that varies with frequency. Then there are more complex reactive loads which have both capacitance and or inductance and or resistance.
Speakers contain both resistive, capacitive and inductive effects (as well as the effects of passive crossover filters etc). So the impedance of a speaker will change with frequency. So the "nominal" impedance is basically the average impedance. For example, a common speaker may have a DC resistance of 3.5 ohms and a nominal impedance of 4 ohms. This basically means that over a wide range of frequencies, the impedance will be around 4 ohms. It is important to note, that while the impedance can rise to many times the DC resistance at certain frequencies, in the case of normal speakers, the impedance will typically not drop any lower than the DC resistance.
Next, we move on to series and parallel wiring.
When you have multiple components, the total resistance (load) on the amplifier will change, depending on how you wire them up. This will happen, whether you have several resistors, or several speakers, or a dual voice coil subwoofer etc
The possible methods of wiring are:
Series wiring to a single channel
Parallel wiring to a single channel
Independent wiring to two separate channels
When you have more than a few loads, then you can combine both series and parallel wiring.
Independent wiring is fairly obvious, basically you do not wire the components together at all, but instead you wire them up to separate amplifier channels. (voltage sources)
Example of independent wiring of a dual voice coil subwoofer:
Series wiring is fairly straightforward to understand. In a series circuit, the current will flow through one device to the other. This will mean that in a series circuit, the current flow through all devices is the same. The voltage across each component depends on the impedance/resistance and the current flowing through the circuit.
To work out the load on the voltage source, you simply add the impedance/resistance of the various devices together.
If the voltage remains constant, when additional components are wired in series (thus increasing the resistance/impedance), the current flow will decrease.
The math:
In this example, there are three components (Za, Zb, Zc) wired in series and we would like to calculate the total resistance (Zt).
Zt = total resistance
Za = resistance of the first component, ie 1 ohms
Zb = resistance of the second component, ie 3 ohms
Zc = resistance of the third component, ie 4 ohms
Zt = Za + Zb + Zc (+Zd etc if you had more components)
Zt = 1 + 3 + 4
Zt = 8 ohms
Example of series wiring a dual voice coil subwoofer :
Note, it is occasionally mentioned that series wiring of separate speakers is not recommended. However, provided you are using quality speakers, the speaker wire used has low resistance, then series wiring of separate speakers should not be a problem.
Parallel wiring is also fairly straight forward.
In a parallel circuit, basically each component is wired directly to the voltage source. This will mean that in a parallel circuit, each component will each receive the same amount of voltage. The current flow across each component depends on the resistance/impedance of that component. As additional components are wired in parallel (thus decreasing the resistance), the current flow from the voltage source will increase.
The math:
In this example, there are three components (Za, Zb, Zc) wired in parallel and we would like to calculate the total resistance (Zt).
Zt = total resistance
Za = resistance of the first component, ie 1 ohms
Zb = resistance of the second component, ie 3 ohms
Zc = resistance of the third component, ie 4 ohms
1/Zt = 1/Za + 1/Zb + 1/Zc (+ 1/Zd etc if more components are used)
1/Zt = 1/1 + 1/3 + 1/4
Zt = 12/19 ohms ~ 0.63 ohms
Example of parallel wiring a dual voice coil subwoofer:
It is important to remember, that when wiring to amplifier, make sure amplifier is stable at that load. If you present the amplifier with a impedance load that is too low, the amplifier will attempt to output more current. If the amplifier is not designed to output this much current, then the amplifier will likely overheat, possibly causing damage.
Moving on to dual voice coil speakers.
What is the advantage of a dual voice coil?
The advantage of dual voice coils is wiring flexibility. Dual voice coils are basically voice coils that have two (or more) layers that are wired independently. Dual voice coil subwoofers will have two pairs of wiring terminals. Although there are multiple layers, dual voice coils don't necessarily have any performance advantage over a single voice coil. There are single voice coils that have multiple coils, as well as single layer coils that have as many turns in the gap, as well as similar thickness. So therefore the advantage of dual voice coil speakers is the flexibility of wiring them up as different loads.
The voice coils can be wired up in series, parallel, independently as well as hooking up just a single coil.
Here are some guidelines:
When hooked up in series, parallel, independently as already mentioned, the power handling etc will be exactly the same. The way you would hook it up, depends on the amplifier channels available. Some amplifiers are only stable at 4 ohm (when bridged for example), others may be stable at 2 ohm, or 1 ohm.
For example, if you had a dual 2 ohm coil, you could:
Wire the coils in series, to an amplifier channel that is 4 ohm stable.
Wire the coils in parallel, to an amplifier channel that is 1 ohm stable.
Wire the coils separately/independently, each to an amplifier channel which is 2 ohm stable.
When wiring the coils independently, you would aim to set the gains on each channel fairly close. However, there will not be an increased chance of damage if the gains are not set perfectly. For example, if you were to set the gains by eye, there is no reason why the speaker would magically blow (contrary to some advice given on some forums). Secondly, even if the signal to each coil is not exactly the same, the speaker will not magically blow. The signal will just cancel electrically. So you don't need to worry about that. Obviously, it is not recommended that you wire each coil out of phase, because that would result in virtually no sound from the speaker.
There is of course another method of wiring a dual voice coil subwoofer.
That is, wiring just one of the coils up to an amplifier.
However, there are some important points to consider about this:
If you only wire up one of the coils, then the power handling will be significantly decreased. (I generally don't recommend it for this reason)
If you only wire up one of the coils and leave the other open, the motor strength will be halved and the speaker parameters will shift dramatically. (different efficiency, frequency response etc)
However, if you wire up one of the coils to an amplifier, but short out the coil that is not hooked up to any amplifiers with a short bit of wire, then the parameters will be the same, as if you had hooked up both coils to an amplifier.
So for example, if you had a dual 2 ohm coil, you could hook up one of the coils to a 2 ohm stable amplifier channel and short out the other coil that is not hooked up to anything.
Example of hooking up just a single coil:
For more information:
http://sound.westhost.com/beginners.htm (very good)
http://www.bcae1.com/ (good)
For more diagrams on how to wire multiple subwoofers (including dual voice coils), have a look at this page:
http://www.jlaudio.com/tutorials/wiring/index.html