Introduction

The Loudspeaker is the final component in the line of music reproduction. Present in every corner of society, it has more less stayed the same for over half a century, changing very little in basic concept albeit advances in electronics, materials and magnetism have helped improve vastly on its efficiency. Today it still remains a subject of intense engineering research. This blog attempts to explore the basic ideas and concepts in order to progress further into nature and design of transducers and enclosures.

The Transducer

The most common type of loudspeaker transducer (or driver) is the Moving Coil or Electro-dynamic a relatively mundane mechanical device. It is effectively an electromagnet suspended in a very high magnetic field. When a current is passed through the electromagnet thrust is generated using Fleming's left hand rule. This causes the electromagnet and thus, the diaphragm of the speaker attached to it, to move.

A Cross Section of a Moving Coil Loudspeaker

The Diagram above fully illustrates my point. The electromagnet or voice coil is housed in the coil assembly free to move a pre-determined displacement. The front and rear suspension ensure the movement is purely axial and to hold the voice coil in place. 

Cross Section of Transducer (1)

Typical Impedance of a Loudspeaker

Many of us hear of speakers being graded as 4 Ohms,6 Ohms and 8 Ohms and so on. So what is this impedance? How much of the power is real? How much is reactive?

The answer to this question requires modelling the loudspeaker as a coil in an electromagnet. This means that the system is a bit more complex than just a simple resistive load. The diagram below illustrates my point.

Impedance of a Loudspeaker against frequency (2)

As you can see the Impedance  Z of the Loudspeaker is rarely constant across its frequency range. A Loudspeaker's impedance is a constantly varying function of frequency. The peak at frequency Fs is called the free-space resonant frequency and is the speakers actual resonance. At this frequency the back E.M.F generated(according to Right hand Fleming rule) by the driver means that the effective resistance of the speaker is now at its maximum. Note that this is the point when the speaker has no reactance and is purely a resistive load. 

Any point of the graph with a positive gradient indicates an increase in with f thus an inductive nature and a negative gradient displays a capacitive nature. The min trough exhibits a generally resistive region. The rated or nominal impedance is always calculated as Z =  1.15 Zmin.

Another important aspect of loud speakers is that on the return stroke of the diaphragm they produce a back E.M.F which means they produce a reverse current. An amplifier with a low output impedance is essential to create a damping for the back E.M.F and thus to prevent ringing in a loudspeaker.

Equivalent model of a Loudspeaker

In our quest to understand the full functionality of a loudspeaker one must look into how a loudspeaker can be observed as an electronic circuit  Since it is both an electrical and mechanical device the equivalent circuit must accommodate both of those aspects into it.

Equivalent Circuit of speaker (3)

The left-hand side of the circuit represents the electrical circuit. The source is eg with Re and Le representing voice coil resistance and inductance parameters. A transformer models the conversion of electrical to mechanical force by a  turns ratio of Bl:1. 
The right hand side of the circuit models  the mechanical. BIL, as we all know is the force created by the voice coil when a current is passed through it and it is acted upon by three other external forces. Mms stands for the mechanical load presented by the air volume and cone mass, the resistance Rms represents the friction in the voice coil and other components and Cms represents the mechanical compliance. Compliance in this context is the resistive force  exerted by the front and rear suspension in order to return the speaker to its original/idle position.

Introduction to the Electrostatic Loudspeaker

The other more expensive and less common form of loudspeakers are the ESL or Electrostatic Loudspeakers. In this type of loudspeaker the force on the flat diaphragm is exerted by an Electrostatic field rather that a EM in a magnetic field.

The ESL Loudspeaker (4)

The charge on the diaphragm is maintained by a very high voltage supply called an EHT (Extra High Tension). From the image, it is visible that the EHT ground is midway of the transformer resulting what is now referenced as a ground. When a output signal is present the electrostatic force on the diaphragm changes causing it to mechanically vibrate.

Since this device is effectively just has a plate with variable distance it is acting as a variable capacitance and is also a high impedance device as opposed to the Electrodynamic speaker.

Enclosures

To maximise a transducers acoustic potential, it is necessary for it  to be come coupled with an enclosure. The Enclosure has several functionalities. The most important aspect of the enclosure is to isolate the sound waves generated from the rear diaphragm of the speaker from those of the front in order to prevent them interacting destructively. In addition to this they provide a strong stand for the speaker and dampen vibrations from the transducer itself.

Enclosures Designs 

There are many factors that have to be taken into careful consideration when designing enclosures. First is the type of driver or transducer that will be mounted to it. Then what acoustic range the enclosure is designed for, cost, efficiency and many other finer aspects.

I shall take the three most common types of enclosures available.

Enclosure types (5)

Infinite Baffle: This is simply separating the front of the speaker sound waves from the back with a single plane. This does not generally offer the same quality of bass resonance as closed or bass reflex enclosures as some cancellation does occur. 

Sealed Enclosure: In this type of enclosure the rearward sound waves are concealed in a sealed box (hence the name) and only the front of the speaker is exposed. Owing to the fact that the sealed interior will always be at constant pressure, such enclosures are simpler to tune and easier to build. However, you tend to require transducers that are purpose built and are capable of exerting larger thrust/force (preferably, high power woofers) as there is nowhere for the displaced volume of air to leave.

Ported or vented enclosures: This is the most common type of enclosures found and they are sometimes referred to as bass-reflex. The idea behind this is to utilise the backward sound wave and alter its phase by 180 degrees so that they interact constructively. However, this requires careful tuning. The enclosure is designed so that its cavity resonant frequency matches that of the free space resonant frequency, Fs of the speaker. This has a profound effect of extending the low frequency region as shown by figure 6.

Effect of Bass Reflex (Vented) Enclosure (6)

The disadvantage, however, is that mid to high frequencies could give unwanted sound coloration as they resonate from the enclosure. This design also proves to be much more complex to build as it requires careful consideration into size.

The VAS Of a Speaker
This represents the volume of air that exerts the same force as the compliance of the suspension when compressed to one cubic meter. 

Calculating Displacement volume (VD)
This is generally not a difficult thing to do as it is quite simply the maximum voice coil overhang (or the maximum excursion) multiplied by the the cone/diaphragm surface area 

Quality Factor of Suspension
Often referred to as the Q of a speaker's suspension, the Q factor will be a critical piece of information that will be required in order to create an enclosure for a speaker. The Q factor is a sought of 'damping factor' like in a car absorber. Excluding a few exceptions, as a general rule of thumb it is relevant to class transducers with Q of below about 0.5 in a vented enclosure, 0.5 < Q < 0.7 as a sealed enclosure and Q > 0.7 as an infinite baffle.

References

(1)(2000). Stereo Technical Information Centre. Available: http://www.stereotechnicalinformation.com/education/speakers/howtheywork.htm. Last accessed 29/10/2013.

(2)Electrical characteristics of dynamic loudspeakers. Available: Electrical chhttp://en.wikipedia.org/wiki/Electrical_characteristics_of_dynamic_loudspeakersaracteristics of dynamic loudspeakers. Last accessed 30/10/2013.

(3)Knud Thorborg , Andrew D. Unruh and Christopher J. Struck . (2007). An Improved Electrical Equivalent Circuit Model for Dynamic Moving Coil Transducers. Available: http://www.tymphany.com/files/resources/papers/AES122nd-Impedance.pdf. Last accessed 30/10/2013.

(4) Electrostatic loudspeaker. Available: http://en.wikipedia.org/wiki/Electrostatic_loudspeaker. Last accessed 31/10/2013.

(5) Outrageous Audio…. Available: http://www.outrageousaudio.com/page_files/enclosure_design.pdf. Last accessed 31/10/2013.

(6) Ported Bass-Reflex Enclosure. Available: http://hyperphysics.phy-astr.gsu.edu/hbase/audio/basref.html. Last accessed 31/10/2013. 

(7) SUPPORT UNDERSTANDING LOUDSPEAKER DATA. Available: http://www.eminence.com/support/understanding-loudspeaker-data/. Last accessed 21/12/2013.

Background: http://decibel.fi.muni.cz/models/cinema2011/xmatusk1/1/tex/Brushed%20Metal.jpg