Electricity and magnetism are sometimes thought to be two different subjects, but in fact they are intimately related. The fundamental unit of electricity is charge. Like charges repel and unlike charges attract, incredibly strongly. Through a random definition of polarity made long ago, electrons have a negative charge. They don’t know that, of course. Atoms are held together by the attraction between the positive charge of the proton and the negative charge of the electron, which are equal to as many decimal places anyone can measure.

Electrical charges cause electrical fields, which don’t need a medium to carry them and can exist in a vacuum. When charges move, magnetic fields are created. There is no other source of magnetic fields and there is no magnetic equivalent of the electron. Magnetic fields describe the direction and intensity of the magnetism across space. They are continuous, but we often sample them so they can be visualised. At each point we can draw a vector. Sometimes we join up the vectors to draw lines of flux.

Some elements, like metals, have loose bonding of some of their outer electrons, so they don’t care if a particular electron is lost and replaced by another. This allows a flow of electrons, so metals are classed as conductors. Some elements hold tight to their electrons and so are insulators. Some elements have an odd number of spinning electrons and so can produce a net magnetic field. Since magnetic fields come solely from moving electrons, they cannot originate from insulators. Another interesting property of magnetism is that there is no such thing as a magnetic insulator.

Magnetic fields can exist in a vacuum and there is no material known that can stop them. Superconductors can divert them, many materials that have no effect and some materials encourage magnetic fields. The parameter that describes it is reluctance. So if we really don’t want a magnetic field some place, the best we can do is to surround the place with a low reluctance material that encourages the field and so deflects it away from where we don’t want it, rather like putting honey on the deck to keep ants out of the house.

Electrons can move linearly or they can spin (or both). Linearly moving charge results in a magnetic field that encircles the direction of motion, so a series of electrons moving, for example along a wire, produce a cylindrical field where the vectors are all tangential. In a form of duality, a spinning electron will produce a magnetic field vector that aligns with the axis of spin. Fig.1 contrasts these fields. Magnetic fields interact. It is well known that like poles repel and opposite poles attract. The forces are tangible, and it appears that the lines of flux which we have visualised are under tension and mutually repel.

Fig.2 shows the circular field around a conductor and a parallel field between two pole pieces. When they are superimposed, the result is asymmetrical. On one side of the conductor the lines are deflected further away from their formerly straight path. The result is a force on the conductor.

More duality: a moving charge can create a magnetic field, but a changing magnetic field can induce an electromotive force (EMF) and cause a current. This means that the arrangement of Fig.2 can be a motor or a generator. If we supply the current in the conductor, it will produce a force. If we supply the motion, the conductor will produce the current. That is the basis for the moving coil loudspeaker and microphone. Early loudspeakers used a constant current flowing in a field coil to produce the linear flux of Fig.2. Today, permanent magnets are used.

Permanent magnet materials have been under development for some time and have become more powerful. All permanent magnets are described by two parameters. One is the amount of magneto-motive force they can produce per unit length and the other is the amount of flux they can pass per unit of area. Alnico magnets, for example are poor at creating mmf, but pass flux well, so Alnico magnets tend to be long and slender, like rods. Ferrite has the opposite attributes to Alnico. It can develop plenty of mmf per unit length, but its ability to carry flux is poor, so ferrite magnets tend to be short and fat.

Magnetic circuits are analogous to electric circuits and magnets have internal impedances. If we short circuit a magnet with low reluctance keeper, all of the mmf is developed across the interior of the magnet and very little is developed across the keeper. If we leave a magnet open circuit, the flux will be very small and the mmf will be developed across the open circuit.

There is thus a magnetic equivalent of impedance matching, where the reluctance of the air gap in a magnetic circuit needs to match the characteristics of the magnet so that the greatest magnetic energy appears in the gap. Today software exists to simulate magnetic circuits so that becomes quite easy.

The gap is where the coil goes. By passing current through the coil a force can be created to move the diaphragm, which is desirable, and heat will be dissipated by the coil resistance, which is undesirable. The depth of the flux in the gap is always slightly greater than the pole depth because of mutual repulsion between the lines of flux. Fig.3 shows that the coil can be the same length as the pole, shorter or longer. A shorter, or underhung, coil is ideal for a tweeter that has little travel, whereas an overhung coil is less efficient, but better for a woofer that will need long travel. Both approaches keep the amount of coil in the magnetic field constant. If it changes, the result will be distortion. The equal length coil works because the flux spreads out and is always a little deeper than the pole thickness.

Loudspeakers are classified by their impedance. What does that mean? There is no short answer.

The force produced by a coil is the product of the coil length l and the field strength B. There is space in the gap for a given volume of coil material. That volume can be occupied by a short length of thick wire, or a long length of thin wire. Let us assume that we have two coils that have the same volume, but one has a single layer of thick wire whereas the other has a double layer of wire of one half the diameter and one quarter the cross section. There will be four times as many turns of the thinner wire, so l will be four times greater, whereas the resistance will be sixteen times greater.

Suppose that the coil was glued solidly in place. The coil would appear as a resistance to a tester applied to the terminals. Since power is given by V²/R, the thinner coil would require four times as much voltage to get the same power. That would result in one quarter the current, but as the length is four times greater, the Bl product would be the same. The efficiency has not changed. All that has happened is that with more turns the same power has to be supplied with more voltage but less current. The impedance has changed.

Let us unblock the coil and allow it to move. Once the coil moves, it becomes a generator and produces an EMF proportional to the velocity. The polarity of the EMF is such that it subtracts from the applied voltage, hence the term Back-EMF. The Back-EMF makes the impedance appear higher, because for a given applied voltage there is less current. Fig.4 shows an impedance curve of a typical woofer. At the fundamental resonant frequency, the impedance has risen dramatically because very little power is needed to sustain motion at resonance and the back EMF approaches the applied EMF. Above resonance the impedance falls again.

As frequency rises further, the coil inductance will make the impedance rise again. Thus a loudspeaker doesn’t have constant impedance. The impedance quoted is a nominal figure which is the lowest value that can be found above resonance. That figure only applies at that frequency.

Uncontrolled resonance would produce an unwanted response peak, so the resonance has to be damped. This is achieved by using audio amplifiers that employ negative feedback so they have negligible output impedance. The Back-EMF produced by the coil then sees effectively a short circuit that maximises damping. If that is not enough, the amplifier can be modified to have negative output impedance.

It should be pointed out that the mass of the moving assembly reflects back through the moving coil as complex impedance. The current will not be in phase with the voltage and the amplifier will be working at a sub-optimal power factor. Switched-mode amplifiers are much more efficient for driving woofers since some of the power returned by the woofer can go back to the power supply instead of being converted to heat.  

Parts 1 - 5 of this loudspeaker series can be found at the links below.

Editor’s note;

John Watkinson has a new book readers may wish to view.