Infinite One-Dimensional Periodic Systems—Characteristic Impedance

  • Ingram Bloch

Abstract

This chapter is a continuation of the last one, in which the periodic systems are infinitely long—strictly speaking, semi-infinite, having a beginning but no end. We can get an indication of what to expect by letting our chain of masses, or the equivalent ladder network with series L and shunt C, become infinitely long by addition of more and more sections like those already there. Thus we let N → ∞, without m or k (or L or C) changing. Then the spectrum of normal frequencies more and more densely fills the interval from 0 to 2ω0, while ω0 remains constant at (k/m)1/2 or (LC)−1/2. It seems reasonable to suppose that a semi-infinite system can oscillate at any frequency in this range, that the discrete spectrum becomes continuous in the limit. We shall see that this expectation is correct. Similarly, the series-C-shunt-L network, when infinitely long, permits any frequency above ω0/2, as might be expected from Equation 11.48.

Keywords

Phase Velocity Group Velocity Standing Wave Input Voltage Pass Band 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. 1.
    Brillouin, L. Wave Propagation in Periodic Structures. New York: McGraw Hill, 1946; Dover Reprint, 1953.Google Scholar
  2. 2.
    See also: French, A.P. Vibrations and Waves. New York: Norton, 1971; and Zeines, B. Introduction to Network Analysis Englewood Cliffs, NJ: Prentice-Hall, 1967.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ingram Bloch

There are no affiliations available

Personalised recommendations