Radio Broadcast (Nov 1926-Apr 1927)

APRIL, 1927 AN ANALYSIS OF LOUD SPEAKERS 589 N a FIG. 7 ligibly small by the simple expedient of keeping the ratio ?, large. Space will hardly permit a discussion of this point. Suffice it to say that good design dictates a limit to this ratio which must necessarily be determined by efficiency, and saturation of armature and pole pieces. Moreover, if a large permanent magnet is used, a stiff armature suspension will be required. Since the reed itself has a resonant period, great care must be exercised to properly fix this period in the frequency spectrum and to provide proper damping. Greatest apparent efficiency will, of course, be obtained by allowing the resonant period of the reed to fall between, say, 800 cycles and 2500 cycles. Best quality can generally be obtained if the resonant period falls near 100 cycles, and is highly damped. It is at once apparent that there are a number of factors which limit both the efficiency and the quality of this type of instrument. Another type of motor of more recent design, which is very much in favor at present, is the balanced armature type shown in Fig. 7. Among other advantages, this type of structure will take larger loads without producing second harmonics of the signal. Using the same nomenclature as above, we have: Force due to one set of poles = K (<j> + a sin tot)2 Force due to the remaining set of poles = K (<j> — a sin tot)2 The total force acting on the armature is obviously the difference of these two, or: P = K (<J> + a sin tot)2 — K (4> — a sin o>t)2 = 4 K <J) a sin cot In this case, the overtone and the additional steady pull, due to the signal, which were present in the output of the reed type motor, vanish. This results, then, in an armature vibration, which is proportional to the signal and which contains no distorting components. It is also a fact that the balanced type of unit will in general reproduce much stronger signals without undue distortion than is the case with the reed type unit. Moreover, if the load contains sufficient damping, the response-frequency characteristic will obviously be more uniform than that of the reed type motor. This type of unit is, of course, not entirely free from resonance, although its fundamental resonant peak is generally not as serious as that of the reed type unit. Fig. 8 shows the moving coil type of motor. Its operation is, in general, similar to that of the units described above, and lack of space forbids further comment here. This type of instrument may be made very free of mechanical resonant effects, since the mass and stiffness of the armature and its suspension system may be reduced. CAUSES OF DISTORTION *"THERE are numerous causes of distortion * in loud speaker motors in addition to those already mentioned. Probably the worst offenders are: 1. Saturation of armature and pole faces. 2. Iron losses, including hysteresis and eddy currents. A detailed discussion of the effects of saturation is beyond the scope of this paper. A simple analysis will, however, serve to point out the general effects to be expected. Saturation occurs in practically all commercial loud speaker motors, at relatively large armature excursions. This particularly applies to reed type motors and balanced armature type motors. It seems reasonable to suspect that the saturation of armature and pole faces in these instruments may FIG. 8 be due, not to the alternating current in the windings directly, but rather to the permanent magneto-motive force producing large momentary fluxes through the pole faces and armature at large armature excursions. As is often the case, a direct current bias in the windings of a loud speaker, used directly in the plate circuit of an amplifier, may cause armature saturation at very small armature excursions. Be the cause what it may, the effects are the same in that they add odd harmonics of the signal output. Consider FIG. 9 a sinusoidal signal as shown in Fig. 9, and for simplicity, consider the magnetization curve of the iron involved to be shown in Fig. 10. This, of course, neglects hysteresis and the curvature of the B-H curve, but it is sufficient to illustrate the point. A sine wave signal of sufficient amplitude will produce an armature flux as shown. That is, the peaks of the sine wave will be flattened. Let the signal magneto-motive force be: A = a sin tot. The resulting flux may then be represented as5 (see bibliography on page 590): B = Pi sin tot -f @3 sin 3 tot + {3s sin 5 tot for the case in hand. In addition, there will also be a series of even harmonics for any practical case. Using the previous nomenclature, we have for the reed type instrument, operating at low flux density*: P = K (<j> + Si sin tot + S3 sin 3 tot + S5 sin 5 tot ... )2 = K (J)2 + K Si2 sin2 tot + K S32 sin2 3 tot + K B52 sin2 5 tot + . . . + 2 K <j> £1 sin tot + 2 K 4> S3 sin 3 tot + 2 K t|> S5 sin 5 tot + 2 K Si S3 sin ut sin 3 tot + 2 K Si S5 sin tot sin 5 tot + 2 K S3 S5 sin 3 tot sin 5 tot + . • . = Y(2<PtPi2 + P.!tP52 + ...) + 2 K 4> (Pi sin wt + B3 sin 3 tot + 65 sin 5 wt + . . • ) (Sr cos 2 tot + S32 cos 6 wt + S52 cos 10 tot 2 + ...) + K Si 63 cos (wt — 3 tot) — K Si B3 cos (tot + 3 wt) + K Si S5 cos (tot — 5 tot) — K Si S6 cos (wt + 5 wt) + K S3 S5 cos (3 tot — 5 tot) — K S3 S5 cos (3 tot + 5 «*)+ • . . = 2 K ({> 61 sin iot + 2 K 4> S3 sin 3 tot + 2 K <}> S5 sin 5 tot + + K(Si S3 + S3 S5 — ^) cos 2 tot 2 + K (Si S5 — Si S3) cos 4 tot cos 6 tot — K S3 S5 cos 8 tot — cos 1 o tot + K (Si S5 + =.) K + -(2ti>2 + Si2-r 632 -r-S52~f2 .) Interpreted, this amounts to a force acting on the armature equivalent to the signal and a number of even and odd harmonics as shown above. It is apparent that the amplitude of the harmonics increases with the degree of saturation. Similarly, for the balanced armature motor we have: P = K (4> + Si sin tot + S3 sin 3 tot + S6 sin 5 tot + ... )2 — K (4> — Si sin tot — S3 sin 3 tot — S5 sin 5 "t + . . . )2 = 4 K t|> ft sin tot + 4 K tp 63 sin 3 tot + 4 K tj) S5 sin 5 tot + . . . Obviously, the odd harmonics are still present in their original relative amplitudes in the mechanical force acting on the armature. It will be H noticed, however, that the conglomeration of added even harmonics present in the vibrating reed type motor, balances out in this case. In addition to the introduction of harmonics due to saturation, there are present numerous other forms of distortion, even for very minute armature vibrations. Copper losses in general are negligible, but iron losses are responsible for a great deal of distortion at high frequencies. *A rigorous treatment, would of course, involve even harmonics as well as odd ones since there is always a permanent uni-directional magnetic flux in the armature of the reed type instrument. For simplicity, the shift in axis due to the permanent flux has been neglected. FIG. IO