To avoid diagonal clipping, the capacitor voltage must decay faster than the envelope voltage, that is,
t = -;;— ^^—^—'—77;—tt;t = 19 . 89 x 10—6 s . (3. 4 . 36)
3.4.7 Audio-Frequency Amplifier
The audio-frequency amplifier was discussed in Section 2.7. A few minor changes may be necessary in the design of the final stage of the amplifier so that it can drive a loudspeaker efficiently.
So far, the audio-frequency signal is in an electrical form. To convert it to an acoustic signal, an electrical-to-acoustic transducer is required. This can take two basic forms: the loudspeaker and the headphone. The more common of the two devices is the loudspeaker [3, 4]. There are two basic types of loudspeakers: the direct radiation and the horn loudspeaker. The diaphragm of the direct radiation loudspeaker is coupled directly to the air whereas that of the horn loudspeaker (as the name suggests) is through a horn. The horn loudspeaker is generally more efficient due to the better matching between its diaphragm and the air provided by the horn. However, it is usually large, heavy, and expensive. A direct radiation loudspeaker, by contrast, has a simple construction, occupies a small space, and has a relatively uniform response over a moderate frequency band. The design of loudspeakers is a highly specialized field, and therefore outside the scope of this book. However, a qualitative description of the behavior of loudspeakers is a subject that should be of interest to radio engineers.
A cross-section of the direct radiation loudspeaker is given in Figure 3.18. It consists of a paper cone, the apex of which is mechanically connected to a cylinder on which the voice coil is wound. The voice coil is located in a magnetic field provided by a permanent magnet. The outer rim of the cone is corrugated to permit the cone to move along its axis with the minimum of mechanical resistance. The whole cone may be viewed as the diaphragm of the loudspeaker. The
corrugation is referred to as the suspension of the cone. The outer edge of the suspension is fastened to the frame of the loudspeaker and the frame is secured to the baffle.
An ideal loudspeaker should produce a uniform sound pressure at all frequencies with non-directional characteristics, have a good dynamic range, high efficiency, and produce no distortion. The characteristics of the practical loudspeaker are quite different from the above and the reason is that the properties required to produce a low-frequency vibration are quite different from those required to produce a high-frequency sound. Furthermore, the environment in which the loudspeaker operates has a significant effect on its performance.
When a current is passed through the voice coil, a force is exerted on the voice coil by the interaction of the flux due to the permanent magnet and the flux generated by the current in the voice coil. The result is that the voice coil moves and so does the cone to which it is attached. When an ac signal is applied, the cone will vibrate in accordance with the signal, producing a sound. The cone, the voice coil, and the cardboard former on which it is wound have a finite mass, as has the air which the cone has to displace as it moves back and forth. Although the suspension is designed to offer the minimum mechanical resistance to motion, this resistance is not zero. When suitable assumptions have been made about the stiffness of the cone and the linearity of the suspension system and so on, a differential equation describing the motion of the cone can be written and used to study the effects of changing the parameters of the system on its performance. The following broad conclusions can be drawn from both theory and practice.
(1) The force driving the cone is proportional to the magnetic flux density in the air gap (B), the length of the conductor in the voice coil (l) and the current flowing in the coil (i):
A high flux density can be obtained by using a large powerful magnet in conjunction with a small air gap. The minimum air gap is dictated by the thickness of the voice coil former and the diameter of the conductor used to wind the coil and the need to keep the voice coil from touching the magnet assembly. The longer the wire in the coil the greater its mass and, since it is part of the cone, a larger force will be required to drive it. A large coil current makes demands on the amplifier required to drive it.
(2) A good low-frequency response requires a large (area) cone. A large cone will, in general, have a relatively large mass. However, a good high-frequency response requires a cone of very small mass. It would appear that it is not possible to use one cone for the complete range of frequencies in the audio signal. A reasonable compromise, one which comes with a suitable price tag, is to use a filter to divert the low-frequency components of the signal to a large loudspeaker (woofer) and the high frequency to a small loudspeaker (tweeter).
(3) When the frequency is low, the cone moves as one lumped mass, that is, all points on the cone remain in the same position relative to each other as the cone moves back and forth. As frequency increases, the cone starts to behave like a distributed mass and a phase difference between different parts occur. The result is that the response becomes irregular, with peaks and troughs depending on whether the radiated signals from the different parts of the cone add or subtract from each other at a given point within its field of radiation.
(4) The sound wave from the front of the loudspeaker must be separated from the back wave. Otherwise, at low frequency the high pressure created by the forward movement of the cone is neutralized by the low pressure created at the back of the cone. The energy put into the loudspeaker simply moves the air around the edge of the loudspeaker instead of being converted into radiated energy. This can be prevented by mounting the loudspeaker on a large baffle whose dimensions are at least greater than one-quarter the wavelength of the lowest frequency. Similar results can be obtained by enclosing the back of the loudspeaker in a closed box.
(5) The cone, as a mass supported on its suspension, is a system which can have a resonant response when suitably excited. It so happens that the resonant frequency is usually in the low-frequency end of the loudspeaker response. By adjusting the mass of the cone, the characteristics of the suspension and the damping, the peak of the resonant response can be moved to a frequency that improves the low-frequency performance of the loudspeaker.
The loudspeaker will generate harmonic distortion when the force-displacement characteristics of the cone suspension are non-linear. Another source of distortion is the non-uniformity of the flux density in the air gap, especially when the voice coil is at the extremities of its excursion.
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