1. CHAPTER 3: LOUDSPEAKERS

2. Introduction:
Loudspeaker is another very important device present in any audio and video system such as public address systems, radios, televisions etc. This will convert back the electrical signal into acoustic signal which is the original signal and the required signal after necessary amplification and signal processing.

3. 3.1 Characteristics of Loudspeakers:
Loudspeaker is a trasducer which converts electrical signals of audio frequency into sound waves of the same frequency.
A loudspeaker’s performance is determined by the following characteristics:

4. Efficiency:
It is defined as the ratio of output sound power to the input audio(electrical power).
2. Noise:
The unwanted sound, not contained in the input signal but present in the output of the loudspeaker is called noise. The mechanical parts may vibrate at some resonant frequency, causing noise. What is more important is signal to noise ratio (S/N) which is defined as the ratio of ‘signal output’ to the ‘output of noise in the absence of signal’.

5. 3. Frequency response:
It indicates loudspeaker’s response for the audible frequency range of sound. Ideally, response of a loudspeaker should be flat within + 1 dB for the frequency range of 16 Hz to 20 kHz . However, due to mass of the diaphragm assembly, high frequencies are attenuated.

6. 4. Distortion: 5. Directivity:
Any change in the frequency, phase and amplitude complexion of the output sound as compared to the input audio signal is called distortion.
5. Directivity:
Ratio of actual sound intensity at a point in the direction of maximum intensity to the sound intensity that would have been available there, had the loudspeaker been omnidirectional.

7. 6. Impedance:
This input impedance of the loudspeaker is represented in ohms and is an important parameter, as its matching with the impedance of source amplifier is necessary.
7. Power handling capacity:
A loudspeaker can handle some maximum power (indicated in watts) for which it is designed. Power more than the maximum will damage the speaker.

8. 3.2 Moving coil cone type loudspeaker:
Principle:
The moving coil loudspeaker works on the principle of interaction between magnetic field and current in the same way as an A.C. motor works.
A coil, called voice coil, is placed in a uniform magnetic field. When audio current passes through the voice coil, there is an interaction between the magnetic field and the coil, resulting in a force working on the movable coil.

9. This force is proportional to the audio current and hence causes vibratory motion (motor like action) in the coil, which makes a conical paper diaphragm to vibrate and produce pressure variations in air, resulting in sound waves.
The force in Newtons on the coil due to interaction between current through the coil and magnetic field is given by ,
F=B l i SIN α
Where, f= force in newton
B= flux density in wb/m2(or tesla)
L = length of coil wire in meter
I = current in ampere
Α = angle between the coil and field, Normally, α =900 , and hence, f=Bli

12. Construction:
Construction of a cone type moving coil loudspeaker is shown in fig. 3.1
The moving coil loudspeaker consist of voice coil , wound on a cardboard or fibre cylinder.
Audio current is fed to it through two terminals.
The coil is placed in a magnetic field.
The magnet is a pot type permanent magnet which has a central pole (south pole) and peripheral pole (north pole).

13. The magnet is made of high grade magnetic material, like AlNiCo (composition of AlNiCo is Aluminium 10%, Nickel 18%, Cobalt 12%, Copper 6% and Iron 54%) which retains the magnetism extremely well.
Because of the use of permanent magnet, it is also called ‘permanent magnet type speaker’.
The coil is attached to a conical diaphragm, made of paper .
It is called ‘papercone’.
The spider springs are used to support the complete diaphragm and also provide the required stiffness to restrain the motion.
The spiders also keep the coil centered so that the motion is vertical and linear.

14. Leads from the voice coil are cemented to the cone surface.
From there, these are brought to the terminals mounted on the metal frame or basket.
Functioning:
When audio current flows through the voice placed in a magnetic field, a force equal to Bli Newtons acts on the coil and moves it to and fro.
The paper cone attached to the coil also moves and causes compression and rarefaction cycles in the air.
Thus, audio current is finally converted into sound waves.

16. The equivalent circuit of the cone speaker is shown in fig. 3.2.
Rs is the D.C. Resistance of the voice coil, Ls its inductance.
Cm and Lm represent mechanical capacitance (compliance) and mechanical inductance (mass) of the moving unit (coil and cone assembly).
Cm is high and hence its reactance is negligible.
The resistance of air to the changes in its pressure is reflected in the electrical circuit as an equivalent load resistance.

17. The value of reactance of Cm(Xc) being negligible, Ls and Lm play an important role in determining frequency response of the loudspeaker.
At low audio frequencies inductive reactance of Lm is low and is across Rl and hence it reduces the output.
At high frequencies inductive reactance of Ls is high which, being in series, attenuate high frequencies.
Typical frequency response is shown in fig.3.3

19. Why cone type speaker is known as direct radiating type?
The whole paper in cone type loudspeaker acts as a diaphragm and causes pressure variations direct in the listeners’ area.
Hence it is called ‘direct radiating type loudspeaker’.

20. Characteristics of the cone-type speaker:
Efficiency:
The efficiency of a cone speaker is quit low,about 5 to 10 percent only. The poor efficiency is due to the fact that it acts as a direct radiator, and so there is complete mismatch between the low acoustic load presented by the large volume of air and the high mechanical load presented by the voice coil and cone assembly.
Signal to noise ratio:
It is 30 db or better.

21. Frequency response:
It is restricted to mid frequencies only. Frequency response drops at low and high audio frequencies for typical loudspeaker. However, massive loudspeaker (called woofer) for low frequencies and small size speaker (called tweeter) for high frequencies can be designed. Frequency response of a typical speaker is 200 Hz to 5000 Hz. Low frequency woofer speakers with baffles will give frequency response up to 40 Hz. High frequency tweeters extend the frequency response to 10 KHz or even higher.

22. Distortion:
Non-linear distortion due to non-uniformity in the magnetic flux density causes severe distortion up to about 10%.
Directivity:
Basically the loudspeaker is Omni-directional. But baffles and enclosures modify the directivity so that most of the power is in the frONT.

23. Impedance:
The effective impedance taking into account the mechanical and accoustical loads varies from 2 ω to 32 ω . the common impedances in commercial speakers are 4,8 or 16 ω . (200 to 300ω impedances are obtained in electro-dynamic type cone speaker).
Power handling capacity :
Power range of speakers lies between a few milli watts (for 2 cm speaker) to about 25 watt for large size speakers. (Electrodynamic speakers can withstand a few hundred watts of input power).

24. 3.3 Electrodynamic Loudspeaker:
To provide very strong magnetic field for high wattage speakers, electromagnet is used instead of permanent magnet.
The working principle of an electrodynamic speaker is the same as that of permanent magnet type.
Its construction is shown in fig. 3.4.
Loudspeaker of more than 25 watt and up to a few hundred watt are of electro-dynamic type.
The strong and steady magnetic field is produced by a large field coil wrapped around a core.

27. It is placed in the annular gap.
The special shape of the core allows magnetic flux to remain concentrated in the annular gap between pole pieces.
The voice coil is wound on fibre or aluminium (to keep it light weight).
It is placed in the annular gap.
The audio signal from the amplifier’s output transformer is applied to the voice coil .
This signal causes a varying magnetic field.

28. The resultant interaction between the two magnetic fields (one due to electromagnet and the other due to audio current in the voice coil) produces mechanical vibrations (motor action) in the coil assembly, which correspond to the audio signals.
The vibrations of the coil are transmitted to the attached cone which create sound waves in the air in listener's’ area, and hence, radiate sound energy directly.

29. Advantages and disadvantages of electro-dynamic speaker:
Higher power can be obtained.
Frequency response is better.
Disadvantages:
Power supply is needed for field coil.
Heavier in weight.
Costlier.

30. 3.4 Horn type loudspeaker:
Principle:
A horn type loudspeaker uses a moving coil placed in a magnetic field (similar to paper cone type), but instead of radiating acoustic power directly in open space of listeners’ area, the power is first delivered to the air trapped in fixed non-vibrating tappered or flared(one that widens gradually) horn, and from there to the air in the listeners’ area.
Thus, it radiates sound power to the air in space not directly from the diaphragm but indirectly through the horn.

31. This is the reason why the horn type loudspeaker is called “indirect radiating loudspeaker”.
The horn acts as an accostic transformer.This allows better impedance match between low impedance of the free air and the high impedance of the vibrating voice coil assembly.
This results in increased efficiency.
The efficiency of a horn type speaker is 30-50% as against only 5% efficiency of cone type speaker. But the sound produced is not natural.
Construction:
The horn is a trappered enclosure whose diameter increases from a small value at one (called ‘throat’) to a large value at the other end, (called ‘mouth’).

34. There is an air chamber trapped between throat and diaphragm.
The driver unit is similar to direct radiating type except that the paper cone is not present.
A basic horn (called exponential horn) type speaker is shown in fig. 3.5.

35. 3.6 Baffles and Enclosures:
Rigid flat material used to extend the edges of a loudspeaker cone is called ‘baffle’.
It is shown in fig. 3.9.
The term baffle is commonly used for a plane surface.
A baffle increases the effective length of the acoustical transmission path between the front and the back of the radiator.

37. Necessity of a baffle:
There is air on both sides of the cone, the front as well as the back.
Hence, the cone radiates sound from both sides.
However, when the cone moves forward, there is compression of the air in the front, but rarefaction at the back.
When the cone moves backwards, compression in the back and rarefaction in the front occurs.
Thus, the sound waves produced in the rear air are of opposite phase (i.e. Phase difference is 1800 relative to the sound waves produced in the front).

38. The sound waves from the rear leak round the sides and meet the sound waves in the front.
If the path difference is small as compared to λ/2, the two waves will almost cancel each other causing response of the speaker to drop off sharply.
When the frequency of radiated waves is low, the wavelength λ is large and hence the path difference between rear and front sides is quit small in terms of λ.
This will allow low frequency waves to arrive from rear to the front almost 1800 out of phase, reducing the radiated energy substantially.

39. The baffles are made of a good sound insulating material.
To save the low frequencies from attenuation, it is necessary to increase the path difference by using a physical barrier, the baffle.
At high audio frequencies, a baffle is not needed because compression and rarefactions are very closely spaced and occur in quick succession, and hence there is no general cancellation.
The baffles are made of a good sound insulating material.

40. Type of baffles:
There are four type of baffles:
Finite baffle.
Infinite baffle.
Enclosure.
Bass-reflex baffle.
1. Finite baffle:
The wooden cabinets as in radio receiver or T.V. Receiver acts as ‘finite baffle’. Such baffles, being of finite size, are not very effective and do cause some loss of low audio frequency signals.

42. 2. Infinite baffle:
An ideal infinite baffle is the one which has infinite lateral dimension. Such a baffle will not be feasible.
However, if baffle dimensions are so large that the frequency at which the path length is λ/2, is far below the lowest frequency to be used, such a baffle can be called ‘infinite baffle’.
For example, let a speaker be fixed in a hole in the wall will acts as natural barrier for the rear sound to come in front of the speaker. The wall will act as ‘infinite baffle’ .

45. Enclosures:
When a loudspeaker is mounted in a closed box with an opening in the front (to enable the cone to transmit its vibrations to the air in front), the box serves the purpose of infinite baffle because the waves from the back of the cone will not be able to come to the front side.
Such a closed box is called an enclosure, and is shown in fig The best material for enclosures is about 18 mm thick plywood. Board. The box must be air tight.

49. Bass reflex enclosure:
In this system, radiation from the back of the cone is used to strengthen the front radiation rather than weaken it. This design is shown in fig
Here, the port or cut is so designed that it permits flow of air from the rear to the front with additional path difference of λ/2 (or phase difference of 1800). Thus, the phase difference between the back wave coming out from the port and the front wave caused directly by the cone is = 3600 (equivalent to zero), and therefore, the two waves reinforce each other.

53. 3.7 Multi-way speaker system (woofers and tweeters):
A single loudspeaker can not have flat response for the whole audio frequency range from 16 Hz Hz, and not even for the practical Hi-Fi range of 40 Hz to Hz.
Low frequencies are weakened by the back sound waves of reverse phase in open speaker.
In closed box (encloser), the compliance(capacitive effect) of the entraped air comes in series with the compliance of the cone system and hence increases the resonance frequency of the loudspeaker.
The loss at high frequencies is due to mass (or inductive effect) of the diaphragm (including cone).

54. Thus, a single speaker can not produce both, the good solid bass and the smooth crisp treble.
The best of them can only produce just acceptable bass and treble which will not satisfy the Hi-Fi requirements.
To solve the problem, the audio frequency spectrum is divided into at least 2 and preferably 3 parts.
Separate speakers are designed for each part, so that each speaker has to cover only a small range of frequency.
The speakers which cover low frequencies from 16 Hz to 1000 Hz are called ‘woofers’.

55. The speakers which cover higher audio frequencies are called ‘tweeters’.
Many a time, a third speaker, called ‘squawker’ is used for mid frequency range from Hz and in that case woofer works upto 500 Hz and tweeter from 5000 Hz onwards.

56. 3.8 Cross-Over Networks:
When a multi-way loudspeaker system is used to get flat frequency response for the entire range of audio frequencies, it is essential to have a cross-over network to divide the incoming signal into separate frequency ranges for each speaker .
In the absence of cross-over networks, the speakers will suffer overheating and the output will be distorted when full power at frequencies outside their range is fed to them.
Over efficiency will be much reduced in the absence of cross-over networks.

57. A basic cross-over network is illustrated in fig. 3.19.
Cross-over networks make use of the fact that the capacitive reactance decreases with increase in frequency [xc =1/(2∏fc)], and the inductivereactance increases with increase in frequency (xl =2∏fl).
A basic cross-over network is illustrated in fig
The circuit consists of a low-pass LC filter across the woofer and a high-pass LC filter across the tweeter.
The low-pass filter permits only low audio frequencies (16 Hz to 1000 Hz) to go to the woofer.

60. The series reactance of L and shunt reactance of C for high audio frequencies prevents these frequencies from going to the woofer .
The high-pass filter consisting of C in series and L in shunt allows the high audio frequencies to pass to the tweeter and blocks the low frequencies .
The response curve of a typical cross-over network (of figure 3.19) is shown in fig It gives attenuation of 12 dB per octave.

62. Equations below gives the values of L and C,
L = RL √ 2 / 2 ∏ fc
C = 1 / 2 ∏ fc RL √ 2
Where, RL is the impedance of loudspeaker in ohms and fc is the cross-over frequency in Hz, L is the inductance and C, the capacitance of LC circuits.

65. A commercial three way divider network is shown in fig. 3.21.
In this circuit, capacitor Ct of 1 µf in series with tweeter prevents low frequencies and mid frequencies from reaching the tweeter.
Similarly , inductance Lw of 5mh in series with woofer prevents high frequencies from reaching the woofer.
Inductances Ls-1 and Ls-2 of 0.5mh and 5mh, respectively in the squawker circuit allow only mid frequencies and prevent too low and too high frequencies from reaching the squawker.
Typical divider curve for three way network of fig is shown in fig Single element filtering gives 6dB per octave attenuation and double elements give 12 dB per octave.

67. Considerations for designing cross over networks:
The cross over frequency for woofer tweeter circuit is where the woofer output curve crosses the tweeter output curve. This is normally 1000 hz. Hence woofer gives output between hz and tweeter from hz for 2 speaker system.
Attenuation beyond the cut-off frequency for woofer and before the cut-off frequency for tweeter should preferably be 12 db per octave although 6 db per octave is acceptable for economy models.

68. For a three way speaker system, frequency coverage to the cross-over point is as given below:
Woofer: 16 hz to 500 hz.
Squawker: 500 hz to 5000 hz
Tweeter: 5000 hz to hz
While for two way speaker system, it is as follows:
Woofer: 16 hz to 1000 hz.
Tweeter: 1000 hz to hz
Inductors and capacitances should be calculated correctly.
Electrolytic capacitors cannot be used as there is no polarisation DC current.

70. 3.9 Consequence of mismatch between amplifier output and loudspeaker impedance
Maximum power transfer theorem shows that power transferred from source to the load will be maximum when the internal impedance of the source is equal to the impedance of the load. When there is mismatch, the first consequence is that power developed in the load is reduced.
The matching of source impedance with the load impedance is done with the help of a matching transformer.

71. Relationship between the turns ratio of secondary turns(N2) to primary turns(N1) and ratio of impedance in the secondary circuit(Z2) to impedance in the primary circuit(Z1) is given by:
N2/N1 = (Z2/Z1)½