Difference Equations, Z-Transforms and Resistive Ladders

Chapter

It is shown that the semi-infinite and infinite resistive ladder networks composed of identical resistors can be conveniently analyzed by the use of difference equations or z-transforms. Explicit and simple expressions are obtained for the input resistance, node voltages and the resistance between two arbitrary nodes of the network.

Keywords

Infinite networks Resistive ladders Difference equations Z-transforms 

Notes

Acknowledgments

This work was supported by the Indian National Science Academy through the Honorary Scientist scheme.

References

  1. 1.
    E.M. Purcell, in Electricity and Magnetism, Berkeley Physics Course—Vol. 2, 2nd edn. (New York, McGraw-Hill, 1985), pp. 167–168Google Scholar
  2. 2.
    F.W. Sears, M.W. Zemansky, in College Physics, World Students, 5th edn. (Reading, MA, Addison-Wesley, 1980)Google Scholar
  3. 3.
    R.M. Dimeo, Fourier transform solution to the semi-infinite resistance ladder. American J. Phys. 68(7), 669–670 (2000)CrossRefGoogle Scholar
  4. 4.
    L. Lavatelli, The resistive net and difference equation. American J. Phys. 40(9), 1246–1257 (1972, September)Google Scholar
  5. 5.
    T.P. Srinivasan, Fibonacci sequence, golden ratio and a network of resistors. American J. Phys. 60(5), 461–462 (1992)CrossRefGoogle Scholar
  6. 6.
    D. Thompson, Resistor networks and irrational numbers. American J. Phys. 65(1), 88 (1997)CrossRefGoogle Scholar
  7. 7.
    J.J. Parera-Lopez, T-iterated electrical networks and numerical sequences. American J. Phys. 65(5), 437–439 (1997)CrossRefGoogle Scholar
  8. 8.
    B. Denardo, J. Earwood, V. Sazonava, Experiments with electrical resistive networks. American J. Phys. 67(11), 981–986 (1999, November)Google Scholar
  9. 9.
    V.V. Bapeswara Rao, Analysis of doubly excited symmetric ladder networks. American J. Phys. 68(5), 484–485 (2000)CrossRefGoogle Scholar
  10. 10.
    A.H. Zemanian, Infinite electrical networks: a reprise. IEEE Trans. Circuits Sys. 35(11), 1346–1358 (1988)MathSciNetCrossRefGoogle Scholar
  11. 11.
    A.H. Zemanian, Infinite electrical networks. Proc. IEEE 64(1), 1–17 (1976)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    A.H. Zemanian, Transfiniteness for graphs, electrical networks and random walks (Birkhauser, Boston, MA, 1996)MATHGoogle Scholar
  13. 13.
    S.K. Mitra, in Digital Signal Processing—A Computer Based Approach, 3rd edn, Chapter 6 (New York, McGraw-Hill, 2006)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology DelhiNew DelhiIndia

Personalised recommendations