http://iet.metastore.ingenta.com
1887

The order of complexity of electrical networks

The order of complexity of electrical networks

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
Proceedings of the IEE - Part C: Monographs — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The natural frequencies of an electrical network are defined, and the number of these natural frequencies is called the order of complexity of the network. RLC networks are considered, and the order of complexity, σ, is shown to be given byσ = BL + N + SSCSCR.Here, BL is the number of inductors in the network, N is the number of nodes, S, SC and SCR are the connectivities, i.e. the number of separate parts of, respectively, the given network and those subnetworks formed of the capacitors only and of the capacitors and resistors only. Other expressions for σ are also obtained.It is shown that this order of complexity is also the number of arbitrary integration constants in the complete solution of the network equations, and the number of dynamically-independent network variables. Complete sets of such dynamically-independent variables are obtained by a process of elimination from the network equations. A particular type of complete set is classified topologically, such sets being made up of voltages across capacitors forming a forest of the capacitor-only network obtained by open-circuiting all the resistors and inductors, together with the currents through inductors forming a set of chords of the inductor-only network obtained by short-circuiting all the capacitors and resistors.

Inspec keywords: circuit theory; multipole networks

Subjects: Circuit theory

References

    1. 1)
      • A.C. Aitken . (1939) , Determinants and Matrices.
    2. 2)
      • T.R. Bashkow . The A Matrix, New Network Description. Transactions of the Institute of Radio Engineers on Circuit Theory
    3. 3)
      • P.R. Bryant . A Topological Investigation of Network Determinants. Proceedings I.E.E.
    4. 4)
      • R.A. Frazer , W.J. Duncan , A.R. Collar . (1952) , Elementary Matrices.
    5. 5)
      • E.A. Guillemin . (1935) , Communication Networks.
    6. 6)
      • E.A. Guillemin . (1957) , Synthesis of Passive Networks.
    7. 7)
      • Definitions of Terms in Network Topology. Proceedings of the Institute of Radio Engineers
    8. 8)
      • C. Lanczos . (1949) , The Variational Principles of Mechanics.
    9. 9)
      • W. Mayeda , S. Seshu . Topological Formulas for Network Functions. University of Illinois Engineering Experiment Station Bulletin No. 446
    10. 10)
      • Reed, M.B., Seshu, S.: `On Topology and Network Theory', Proceedings of the Symposium on Circuit Analysis, 1955, University of Illinois.
    11. 11)
      • Reed, M.B., Seshu, S.: `On Cut Sets of Electrical Networks', presented at the Symposium on Circuit Theory, December 1956, Michigan, E. Lansing.
    12. 12)
      • Reza, F.M.: `Order of Complexity and Minimal Structures in Network Analysis', Proceedings of the Symposium on Circuit Analysis, 1955, University of Illinois.
    13. 13)
      • H.M. Trent . A Note on the Enumeration and Listing of all Possible Trees of a Connected Linear Graph. Proceedings of the National Academy of Sciences, U.S.A.
    14. 14)
      • E.T. Whittaker . (1937) , A Treatise on the Analytical Dynamics of Particles and Rigid Bodies.
http://iet.metastore.ingenta.com/content/journals/10.1049/pi-c.1959.0031
Loading

Related content

content/journals/10.1049/pi-c.1959.0031
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address