The Application of Hyperbolic Functions to Electrical Engineering Problems

The Application of Hyperbolic Functions to Electrical Engineering Problems

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 edition. Excerpt: ...was first pointed out by Heaviside, the effect of distributed inductance in a telephone line is to diminish the attenuation of the telephonic current. The influence of increasing linear inductance on the attenuation-constant is clearly shown geometrically in Fig. 64, where OI is the vector linear impedance of the conductor, z = r + jx ohms per km. The linear admittance of the dielectric, y = g--jb mhos per km. is shown similarly at O A. The argument of z is fiv and of y, /32, radians. The product zy, or a2, is then indicated at OB, whose modulus is the product of the moduli z and y, and whose argument is Pi + Pv ne sum f tne arguments of z and y. At O C is indicated the square root of O B, or the vector attenuation-constant a in hyps, per km., where the argument is half the argument of O B. The real part Oe is the hyperbolic component, and the imaginary or/-part cC is the circular component. As the linear inductance / of the line is increased, the linear reactance x = lco increases proportionately. This has the immediate effect of increasing the modulus or length O I, and also of increasing the argument /3r The secondary effect of the change is to increase the modulus O C in the square-root ratio, and to increase the argument of O C by half the increase of fiv The vector attenuation-constant a is thus somewhat increased; but, owing to the increase in argument, the real component a, is markedly diminished; while the imaginary component c is increased. The increase in a2 merely diminishes the velocity of propagation, and shortens the wave-length; while the reduction in! reduces the attenuation. Limit to the Reduction in Attenuation with Increasing Distributed Inductance.--If, as generally happens, there is dissipation of power in the dielectric; so...show more

Product details

  • Paperback | 66 pages
  • 189 x 246 x 4mm | 136g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236545737
  • 9781236545732