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

Generalized operators for the approximate steady-state analysis of linear and non-linear circuits

Generalized operators for the approximate steady-state analysis of linear and non-linear circuits

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.

A method of approximate analysis is given for linear and nonlinear circuits subjected to sinusoidal or non-sinusoidal applied voltages. In brief, the method may be said to be a periodic analogue of the technique of time series. Waveforms are represented by an n-component operator giving the values of the wave at each of n ordinates. For waves containing only odd harmonics, the half-cycle is divided into n parts, while for those containing even harmonics the complete cycle is divided into n parts. The central feature of the method is the use of a shift operator, u, which translates any waveform to the right by l/nth of a half-cycle or of a complete cycle as the case may be. The fundamental relations un = − 1 and un = 1 are obtained in the two cases respectively.For linear circuit work the method is advantageous where the periodic input is numerically or graphically specified and where a similar description of the output is required. The procedure is then to form, according to certain rules, an impedance operator for the circuit and to operate on the inverse of the impedance operator, i.e. the admittance operator, by the input wave of applied voltage. The waveform of the current, or the output in the case of a transfer-function operator, is then obtained. From this, r.m.s. values and powers are easily computed. Since the method relates basically to operations on non-sinusoidal waveforms displaced with respect to each other, it is also suitable for e.m.f. calculations in distributed coil groups moving in non-sinusoidal fields.In the solution of non-linear circuits, e.g. those containing ironcored coils or non-linear resistors, the current is obtained by a process of continued approximation. This can be done very simply. An initial solution is assumed or a very rough calculation made in order to start the procedure. One particular method of doing this is to assume that all of the applied voltage acts across the non-linearity. From the static characteristic of the non-linearity a second estimation can then be made of the voltage acting across the non-linearity using the imposed circuit equation. The two estimations are averaged and the procedure is repeated until there is only a small change in any of the waveforms. The method appears to be of fairly general application. Both sinusoidal and non-sinusoidal applied voltages may be handled with the same amount of work. It is suitable for instantaneous and non-instantaneous non-linearities, and since it provides a response waveform, r.m.s. currents and powers may be obtained. It is also suitable for circuits containing more than one non-linearity.The method, however, is approximate, numerical and relates to a fixed frequency. The accuracy is generally within 5% of the maximum ordinate in the waveform with the normal ordinate spacings employed. R.M.S. values and powers, however, may be obtained more accurately, the error in these seldom exceeding 2%.

References

    1. 1)
      • A. Tustin . A Method of Analysing the Behaviour of Linear Systems in Terms of Time Series. Journal I.E.E.
    2. 2)
      • Thomson, W.E.: `A Theory of Time Series for Waveform Transmission Systems', Monograph No. 53 R, Proceedings I.E.E., October 1952, 99, p. 397, Part IV.
    3. 3)
      • Lewis, N.W.: `Waveform Computations by the Time-Series Method', Paper No. 1382 R, Proceedings I.E.E., September 1952, 99, p. 294, Part III.
    4. 4)
      • Madwed, A.: `Numerical Analysis by the Number Series Transformation Method', Proceedings of a symposium on nonlinear circuit analysis, 1953, New York, Polytechnic Institute of Brooklyn, p. 320, Edwards, Ann Arbor, 1953.
    5. 5)
      • J.R. Ragazzini , A.R. Bergen . A Mathematical Technique for the Analysis of Linear Systems. Proceedings of the Institute of Radio Engineers
    6. 6)
      • Cruickshank, A.J.O.: `A Note on Time Series and the Use of Jump Functions in Approximate Analysis', Monograph No. 110 M, Proceedings I.E.E., October 1954, 102 C, p. 81.
    7. 7)
      • R. Boxer , S. Thaler . A Simplified Method of Solving Linear and Nonlinear Systems. Proceedings of the Institute of Radio Engineers
    8. 8)
      • Moullin, E.B.: `The Problem of a Non-Ohmic Resistor in Series with an Impedance', Paper No. 1048, Proceedings I.E.E., March 1951, 98, p. 87, Part I.
    9. 9)
      • Moullin, E.B.: `The Solution of a Certain Differential Equation', Monograph No. 99, Proceedings I.E.E., May 1954, 101, p. 290, Part IV.
    10. 10)
      • Slemon, G.R.: `A Method of Approximate Steady-State Analysis for Non-Linear Networks', Paper No. 1530, Proceedings I.E.E., September 1953, 100, p. 275, Part I.
    11. 11)
      • P.D. Crout . A Short Method for Evaluating Determinants and Solving Systems of Linear Equations with Real or Complex Coefficients. Transactions of the American I.E.E.
http://iet.metastore.ingenta.com/content/journals/10.1049/pi-c.1958.0013
Loading

Related content

content/journals/10.1049/pi-c.1958.0013
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address