BASICS.HTM --- Part of Manual for Driver Parameter Calculator --- by Claus Futtrup.
Created 1. January 2000, last revised 23. August 2003. Ported to XHTML 1.0 on 2. October 2004. Last modified 25. October 2004.

1. Introduction
2. The Loudspeaker System
3. The Driver
• The Impedance Curve
• The Frequency Response Curve
• The Tweeter
4. Driver Quality

## Introduction

Originally this was a separate work, which should have become a webpage. After an extensive time work I decided to put this document with Driver Paramter Calculator instead and reduce the content of the document by focusing entirely on drivers.

The document starts with the very basics, but I hope as it progresses that you, the reader, will find it enlightening, educational and/or informative. The goal is to explain to the reader how loudspeaker drivers work.

I have the following limitations---first of all, the loudspeaker drivers I treat here are based on the most common principle called the electro-dynamic principle - and second, the loudspeaker systems treated very briefly here use several driver units in a loudspeaker cabinet and split the work between them with a socalled passive filter. This concept cover 99 % of all high-quality loudspeaker systems on the world market, so I do not consider it much of a limitation.

## The Loudspeaker System

We start at the end product. Everybody knows it. The loudspeaker. Professionals call it the loudspeaker SYSTEM to make sure that everybody understands what it is about. On the outside you see a number of drivers, usually on the front of the system. The drivers are surrounded by a cabinet. Inside the cabinet you will find (at least) a filter. So generally speaking we can conceptually split a loudspeaker system into three parts:

• DRIVER
• FILTER
• CABINET

The driver has several names, eg. unit or loudspeaker driver/unit or just speaker or loudspeaker (latter two mentioned are bad terms because they are a basis for confusion, mixing with the loudspeaker system). Besides the driver has names like transducer, electro-dynamic transducer or most advanced is electro-mechano-acoustic transducer, which I will explain in the next section.

Similarly the filter may also be called the crossover or the x-over (filter being the most general term), and the cabinet may be called the box or the enclosure.

In this tutorial we will be talking about the driver, first of all because it is the most high-technology single component in a loudspeaker system, second because physically very fundamental things happen here, and they have very important effects.

## The Driver

If we take apart a driver, one of the hidden parts shows up, the voice coil. It is located on the back of the diaphragm and attached through a voice coil bobbin / voice coil former. There is also a spider attached to the voice coil bobbin, the spider is the yellow part (normally the spider is yellow, but other colours exist as well).

The voice coil (or any coil for electrical means for that matter) is an electrically conducting wire that is wound in a helix. When current is applied, the circular motion of the electrons is resisted, but if forced it will build a magnetic field through the center of the circle. The magnetic field is actually a storage of energy, which it takes time to build and this is why a coil is resistant at first, but as the current continues, it becomes easier. As soon as the current is changed the magnetic field has to follow and if the current is stopped then the magnetic field is taken down. This is related to the electrical domain.

Besides the voice coil, a driver also has a permanent magnet attached, which generates a permanent magnetic field. We all know what happen if two magnets are forced together. Either the magnetic field resists the motion (when North-North, or South-South), or the magnetic field will help put the two magnets together (when North-South, South-North is the same difference). What we feel is a socalled force. And the force will accelerate the objects into motion. So when a current is applied to the voice coil and the magnetic field is built, then due to the permanent magnetic field the voice coil will try to move. We have now entered the mechanical domain.

The voice coil is connected to the diaphragm, which then makes the air around the voice coil move. This creates pressure waves in the air. If the motion is frequently enough, say between 20 and 20000 cycles per second, and the pressure changes are loud enough for the human ear to hear, then we have produces sound. In other words two things are required for the pressure waves to be classified as sound. First of all, the pressure waves must be within the frequency range that the human ear can hear (usually the audible band is standardized as 20 to 20000 Hz). Second, the pressure waves must be high enough for the human ear to register, i.e. the intensity of the pressure waves must be higher than the hearing threshold. This is the acoustic domain.

These three domains and the accompanying transformations can be plotted as below:

• electrical domain
• electro-mechanical transformation
• mechanical domain
• mechano-acoustic transformation
• acoustical domain

This is why a driver is called an electro-mechano-acoustic transducer. A driver treats these three physical domains, and the transformations between them. This is also why I consider the driver to be the most advanced single device in a loudspeaker system.

As you may be able to read from the description of the three physical domains, the transformation between electrical and mechanical means is handled by the magnetic motor system, whereas the transformation between mechanical and acoustical means is handled by the driver diaphragm.

When we examine a driver, and try to describe its behaviour, we describe the electrical side (the input) as well as the acoustical side (the output). When describing the electrical side, we do it by electrical means. To be more specific, we measure the impedance curve (impedance versus frequency). When describing the acoustical side, we do a similar approach since we describe it by acoustical means. We measure the socalled frequency response curve (sound pressure level versus frequency).

These two curves essentially describes the behaviour of a driver.

### The Impedance Curve

Looking at an impedance curve we see that it is dominated by phenomena.

To the left a peak shows the resonance of the driver. This resonance appears as always, when a moving system has a mass and a spring stiffness. These mechanical parameters reflects into the electrical domain, as seen on the curve, because they are connected by the electro-mechanical transformation from the magnetic motor system. Below the resonance frequency the driver is stiffness controlled (same as compliance controlled, which means that the force from the motor system is primarily used to overcome the force-resistance by the spring) and above the resonance frequency the driver is mass controlled (which means that the force in the motor system is primarily used to overcome mass intertia).

The mass comes from the voice coil, the bobbin, the diaphragm and the moving parts of the spider and cone surround. The spring stiffness is primarily given by the spider, but also partially by the cone surround. The mass and the spring stiffness tells us where the resonance top is placed on the x-axis, ie. the frequency axis.

The height of the peak tells us how much damping is present at the resonance frequency. Damping is a desired factor, which keeps the resonance under control, but too much damping is possible. The total damping is a combined damping from the electrical and the mechanical domains.

The mechanical damping is created by friction phenomena, normally resistive air-flow, viscous and visco-elastic materials, but in the worst case it includes dry friction (such friction is called coulomb friction and would cause rub and buzz problems). Mechanical damping usually is smaller than the electrical damping.

All these mechanical parameters "reflects" back into the electrical impedance, and the acoustical parameters too. The reason is the conversion in the motor system, where the force applied gives a counter force named "back EMF." Back EMF is actually the reason why it is possible to measure the T/S parameters electrically.

The electrical damping is given by the electrical resistance in the voice coil, where smaller resistance gives better electrical damping properties, and the strength of the magnetic motor system, where a strong magnet gives better electrical damping.

In this way the impedance peak tells us a lot about the driver and its electro-mechanical system.

To the right an almost constant rise appears because of the voice coils resistance to changes of the electric current. Higher frequency means quicker cycles of change in the applied current, which means higher resistance from the voice coil due to the energy storage phenomenon described earlier.

Between the two phenomena we see a plateau of minimum impedance. This is where the resonance and the voice coil inductance have even influence, and therefore the slopes cancels each other.

### The Frequency Response Curve

The most important observation on the frequency response curve is the fact that the driver gives approximately horizontal/linear output in a limited range of frequencies. This is so because all drivers are bandpass designs. They let a certain range of frequencies pass whereas frequencies outside the operation range gets reduced output, more or less.

At the lower frequencies the behavior is very much decided by the mass/spring and damping relations, which also were described by the resonance peak on the impedance curve. At these frequencies the diaphragm behaves much like a point source. As the input frequency is increased the behaviour changes to that of a flat circular piston. While the driver operates in these states, the behaviour of the driver is given by the fundamental driver parameters, like spring stiffness, damping, moving mass etc.

At the higher frequencies the behavior changes. First of all, the increasing impedance from the voice coil gives a reduction of the totally radiated sound.

Parts of the diaphragm goes into vibration modes, where the modes are represented by local resonances at certain frequencies. Parts of the diaphragm becomes more or less disconnected to the voice coil movements and therefore moves more or less uncontrolled. This reduces the mass load and therefore a smaller force is required for a given acceleration. The drawback is that less sound is radiated to the sides (socalled off-axis) when compared straight in front of the driver (socalled on-axis) and further up in the frequency domain heavy nonlinearities will appear even on-axis. Such vibration modes may be more or less well damped. High damping is desired.

At high frequencies the geometry of the diaphragm becomes very important, but also the termination to the other parts, ie. the surround and the voice coil. If the surround is not properly glued to the diaphragm and the basket, then odd behaviour and increased levels of distortion will be the result.

Small assembly tolerances is critical to obtain smooth high-frequency response and small frequency response tolerances in the production. Assembly is also critical in regard to low-frequency response, primarily distortion, when considering the exact placement of the voice coil and the desired concentric placement in the magnetic motor system / voice coil gap as well as its exact placement in/out of the voice coil gap.

The limited bandwidth of the driver means that if the loudspeaker system is to cover a range of frequencies from 20 to 20000 Hz, then it should be done with several drivers, at least if a high quality system is the goal. In a high fidelity loudspeaker system this is considered to be the goal because this is the range of frequencies the human ear can observe. This means that a quality system based on the concept described above always will be a multiway system. This is so because the electro-dynamic driver concept, which is described above, will not play the full range of frequencies. It is limited for scientific reasons, given the current technology and materials.

For best possible adaption to different frequency ranges, this calls for specialized drivers. This is why a loudspeaker system typically utilizes a woofer and a tweeter (at least one of each kind). The above description is based on a woofer. The tweeter will be described shortly below, though Driver Parameter Calculator is not dedicated to this kind of drivers.

### The Tweeter

Fundamentally the tweeter works exactly the same way as the woofer and it is also an electro-dynamic transducer. This is why the impedance curve looks similar.

Since the tweeters job is to fill out the missing frequency band from about 2-20 kHz, not covered by the woofer, it has a much higher resonance frequency, for example around 1 kHz. This comes from a lower mass and a higher stiffness in the mechanical system. Sometimes we also see that the peak is much lower than what we find from woofers. The top is only about 50% above the minimum, and very broad. This is so because the construction has much higher damping at the resonance frequency.

The inductance value given by the size of the voice coil is much lower, which you can see because it starts rising at a much higher frequency. This also provides for a better high-frequency performance.

On the frequency response we see that the higher resonance means that the curve drops at lower frequencies, now situated much higher in frequency than for the woofer.

The curve from a tweeter is typically very smooth. This is so because it is a very easy construction. It only handles one decade of frequencies, from 2-20 kHz, whereas the woofer above should handle two decades. Such a limitation in the requirements of the tweeter design makes it easy to get a smooth response. High damping, as observed on the impedance curve, combined with good engineering are the reasons for the smoothness.

## Driver Quality

Here follows a small warning or wake-up call to the DIY speaker builder:

As it may be obvious from the above description, the Thiele-Small (T/S) parameters, which is the main focus with Driver Parameter Calculator, is not a good indicator of the driver quality if the quality is based on T/S parameters alone. More fundamental qualities could be present, for example whether the driver is produced with high or low precision, whether it produces a ticking noise at a specific frequency, or whether it is dominated by wind noise behind the driver, or a kind of "cry" is audible in certain frequency ranges.

These fundamental qualities are handled (more or less) by the engineers and can be studied by the DIY speaker builder, especially if there are alternative products to compare with.

The T/S model is as simple as it possibly gets. The nonlinear behavior of the driver is not explored with the T/S parameters at all. Einstein once said that a model must be as simple as possible, but no simpler than that. This statement is two-fold because it implies that you may not abuse a model by conclusions based on limited information. Garbage in produces garbage out.

Thiele-Small parameters are suitable for comparing two drivers on paper, or for studying a given parameter set and its suitability in a certain application (eg. closed box or alternatively bass reflex).