SECOND HARMONIC OF THE HIGH-FREQUENCY COMPONENT OF A COMPLEX PULSATING FIELD AND ITS RELATION TO THE BARKHAUSEN EFFECT

A. M. GRUZNOV, I. G. LESHCHENKO

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

In studying the behavior of a ferromagnet in a complex pulsating field [1], we encountered a phenomenon which, apparently, has not yet been described in the literature.

A ferromagnetic specimen with two short coils in its middle part is placed in a solenoid connected to the mains through a LATR-2 (Fig. 1). A high-frequency signal from a G3-7A generator, freed of the second harmonic by means of a notch filter, is fed into one of the coils in current-generator mode. The second coil is connected to the input of a V6-1 selective voltmeter tuned to twice the frequency of the generator, and the signal from the output of the voltmeter amplifier is fed to an S1-19 oscilloscope.

Fig. 1. Block diagram of the experiment

It must be noted at once that in the case under consideration the high-frequency field is many orders of magnitude smaller than the low-frequency field:

\[ H_{\mathrm{hf}} \ll H_{\mathrm{lf}} \]

in contrast to the conditions under which magnetic amplifiers with second-harmonic output and ferrozondes operate:

\[ H_{\mathrm{hf}} \gg H_{0}, \]

where \(H_{0}\) is the constant component of the field.

The scheme described above makes it possible to observe the following:

1. The second harmonic at the output of the selective voltmeter appears when only the ferromagnetic specimen is magnetized, and only by an alternating field. Magnetization by a constant field, as well as the absence of any magnetization, does not lead to the appearance of the second harmonic.

2. The amplitude of the second harmonic does not remain constant, but changes according to a periodic law, which becomes more complex as the amplitude of the magnetizing field increases (Fig. 2).

1. With biasing fields that bring the specimen to saturation, pauses appear in the pattern of the second harmonic, corresponding to the saturated state.

2. If the high-frequency generator is switched off and the sensitivity of the voltmeter is increased by several orders of magnitude, a pattern of magnetic noise appears on the oscilloscope screen. The magnetic noise coincides with the second harmonic in time and in the shape of the envelope.

It follows quite obviously from items 1, 3, and 4 that there is a connection between the second harmonic and the Barkhausen effect.

Our explanation of the cause of the occurrence of the second harmonic is based on the discrete character of magnetization. During cyclic remagnetization, at any moment of time, except for the time spent in the saturated state, there exist in the ferromagnet domains to which the low-frequency field has indeed supplied an energy \(\Delta E\), but this energy is still less, by an amount \(\Delta\Delta E\), than that at which irreversible processes of displacement of the boundaries of the domains under consideration begin. It is precisely this missing energy that is supplied to the ferromagnet by that half-wave of the high-frequency field which coincides in direction with the low-frequency field. For the other half-wave of the high-frequency field there are no longer slightly “underexcited” domains in the corresponding direction in the ferromagnet, and therefore the change in magnetization caused by it will be smaller than in the preceding half-period. The resulting asymmetry of the high-frequency component of the magnetization relative to the time axis gives rise to the appearance of the second harmonic.

Fig. 2. Dependence of the envelope of the second harmonic on the magnitude of the biasing current

If the envelope of the second harmonic has a clearly pronounced character, then one can speak of an envelope of the magnetic noise only conditionally, since the noise amplitude at any moment of time varies slightly about the mean value according to a random law.

These variations are explained by two causes:

1. During cyclic remagnetization, the magnitude of each jump, its location in the specimen, and its critical field are not repeated from cycle to cycle [2].

2. A selective voltmeter is a narrow-band filter to the input of which the noise voltage is applied. It is known [3] that the instantaneous voltage at the output of this filter will oscillate with a frequency \(f_0\), approximately equal to the center frequency of the filter, while the voltage envelope will fluctuate with a frequency close to half the passband \(\Delta f\) of the filter. The V6-1 selective voltmeter has two discrete passbands, 10 and 1 kHz; i.e., the fluctuation period should be, respectively, 0.2 and 2.0 ms. In our opinion, the second cause is the dominant one and consists in the fact that the fluctuation maxima are in continuous motion from cycle to cycle. It is important here to emphasize that the “ragged” character of the envelope of the magnetic noise is caused mainly by the measuring circuit.

The instantaneous values and the envelope of the second harmonic do not depend on the passband. On this basis one may assume

that the domains responsible for the second harmonic have a spectrum lying above the generator frequency.

REFERENCES

1. L. I. Rabkin. High-Frequency Ferromagnetics, Fizmatgiz, 1960.

2. A. M. Rodichev. Proceedings of Higher Educational Institutions, vol. 4, no. 3. Gorky University Press, 1961.

3. I. S. Gonorovsky. Radio-Engineering Circuits and Signals, “Sovetskoe Radio,” 1964.

4. S. V. Vonsovsky and Ya. S. Shur. Ferromagnetism, Moscow–Leningrad, Gostekhizdat, 1948.