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The Response of a Non-Linear Electric Circuit to an Impulse

Published online by Cambridge University Press:  24 October 2008

A. K. Nuttall ,
D. R. Hartree  and
A. Porter
A. K. Nuttall
Affiliation:
Trinity Hall*
D. R. Hartree
Affiliation:
St John's College
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Extract

Some apparent anomalies in oscillograms obtained in the course of electrical impulse tests of a material used in the construction of lightning arresters have led to a fuller investigation of the behaviour of the test circuit as applied to the study of a material with a non-linear voltage-current characteristic.

This investigation has been carried out by evaluation of solutions of the equations of a simplified form of the circuit numerically and by means of the differential analyser, and by further oscillograms taken under conditions suggested by the behaviour of these solutions.

The apparent anomalies which originally gave rise to the investigation have been shown to be a real feature of the response of the circuit, and not a spurious effect due to the recording apparatus, and the study of the initial response of the circuit to the impulse leads to the interpretation of another feature of the oscillographic records which had been previously regarded as an instrumental error.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 2 , May 1936 , pp. 304 - 320
Copyright
Copyright © Cambridge Philosophical Society 1936

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References

‡ Burch, F. P. and Whelpton, R. V., J. Inst. Elect. Eng. 71 (1932), 380.Google Scholar

§ Bush, V., J. Franklin Inst. 212 (1931), 447CrossRefGoogle Scholar; Hartree, D. R., Nature, 135 (1935), 940.CrossRefGoogle Scholar

* Burch, F. P., Phil. Mag. (7), 13 (1932), 760.CrossRefGoogle Scholar

* For an inductive circuit, the characteristic has to be used in such a way that i is the variable supplied to an input table by the machine, and V is the variable supplied to the machine by an operator following the (i, V) curve on the input table, and not vice versa, since the highest derivatives in the equation are the inductive terms L ldi l/dt and L 2di 2/dt, and i = i l – i 2 has to be deduced from the results of integrating these terms, not from V.

† Another solution, taken on a less open time scale, showed that there is no further subsidiary maximum.

* These solutions were carried out numerically as the differential analyser was engaged on other work at the time.