FEATURES OF MEASURING PULSE CHARACTERISTICS OF FERRITES IN STRONG FIELDS

R. B. Bakshit

(Presented by the scientific seminar of the Research Institute of High Voltages)

When measuring the pulse characteristics of ferrites in strong fields, difficulties arise associated with the short magnetization-reversal time (of the order of \(10^{-9}\) sec) in the field range \(40 \div 300\) Oe. In the present work the influence of the self-inductance of the measuring turn and the influence of the surface effect on the magnetization reversal of ferrites are evaluated. A block diagram of the setup for investigating pulse characteristics is shown in Fig. 1. The pulse of the magnetizing field \(H_m\) was formed by discharging line \(L_1\) through a spark switch with nitrogen under high pressure and, after the peaking unit 2, had a front of \(0.5\) nsec with a duration of \(250\) nsec. The ferrite torus under study was placed in container 4 at the short-circuited end of line \(L_2\). The magnetization-reversal voltage \(U(t)\) from the measuring turn was fed along line \(L_3\) directly to the deflection plates of oscilloscope 6. The magnetization-reversal time was determined at the level 0.1 of the maximum value of the voltage \(U(t)\). The possible maximum equivalent resistance of the ferrite element is [1]:

\[ R_{\max}=\frac{r_m S}{l}, \]

where \(r_m\) is a parameter determined by the properties of the ferrite,
\(S\) is the core area,
\(l\) is the length of the mean magnetic path.

For the ferrites studied \(r_m=200 \div 300\ \Omega/\text{cm}\), \(S=1 \div 3\cdot 10^{-2}\ \text{cm}^2\), \(l=2 \div 4\ \text{cm}\). Then \(R_{\max}=1 \div 3\ \Omega\), which is much less than the wave resistance of line \(L_2\), \(\rho=75\ \Omega\). To make sure that the equivalent resistance of the ferrite element does not affect the shape of the magnetizing pulse, we carried out an experiment according to the circuit shown in Fig. 2. Here 1 is a G5-12 generator producing pulses with an amplitude of \(100\) V and a front of \(0.7\cdot 10^{-9}\) sec, 2 is an oscilloscope, and 3 is a container with the ferrite torus under study. On the oscilloscope screen the pulse incident on the ferrite torus and the signal reflected from it were observed. As the experiment showed, the front and amplitude of the reflected pulse do not differ from the front and amplitude of the incident one.

As already indicated above, the change in the magnetization vector was observed by us according to the usual scheme, with the aid of a measuring loop; it is obvious that the self-inductance of the measuring loop \(L_n\) will

distort the form of the signal \(U(t)\). These distortions will be absent if the time constant of the measuring circuit \(T\) is much smaller than the remagnetization time \(\tau\). In [2], the following expression is given for the inductance of a ring:

\[ L_{\mathrm{n}}=\mu_0 R \ln\left(8\frac{R}{a}-2\right), \tag{1} \]

where \(R\) is the radius of the ring,
\(a\) is the radius of the wire cross section.

For our case \(R=0.25\cdot 10^{-2}\ \text{m}\), \(a=0.35\cdot 10^{-3}\ \text{m}\), and \(L_{\mathrm{n}}=5\cdot 10^{-9}\ \text{H}\), which gives the damping time constant of the measuring circuit:

\[ T=\frac{L_{\mathrm{n}}}{\rho}=10^{-10}\ \text{s}. \]

Thus, the damping time constant of the measuring circuit is an order of magnitude smaller than the minimum duration of the signals being measured; nevertheless, in view of the fundamental importance of the question of the influence of the inductance of the measuring loop on the objectivity of measuring the remagnetization time of a ferrite, we carried out the control experiment described below.

Fig. 1.

Fig. 2.

A resistance \(R=310\ \Omega\) was connected in series with the measuring turn, whereby the damping time constant of the measuring circuit was reduced by a factor of 6; this should have led to a corresponding decrease in the duration of the measured signal in the event that its duration were determined by the inductance \(L_{\mathrm{n}}\). As follows from Fig. 3, the duration of the signal changed practically not at all when the damping time constant was reduced.

In studying the magneto-viscous properties of a material, it is necessary to take into account the influence of the surface effect. The presence of the latter may lead to a lengthening and a change in the form of the remagnetization process. For a preliminary estimate of the influence of the surface effect, we used the method proposed by Vitkov [3]. The change in the magnetic state of the surface layers of a ferromagnet can be expressed through the impulse of the remagnetizing magnetic field:

\[ Q_1=\int_0^t (H_1-H_0)\,dt, \tag{2} \]

\[ \frac{dB}{dt}=r_m\left(1-\frac{B^2}{B_S^2}\right), \tag{3} \]

\[ B=B_S\,\operatorname{th}\left(\frac{r_m}{B_S}Q-\varphi\right). \tag{4} \]

Here \(B_S\) is the saturation induction,

$r_m$ and $H_0$ are experimentally determined parameters characterizing the dynamic magnetic properties of the core,

\[ \varphi = ar \operatorname{th} \frac{B_r}{B_s}. \]

The reversal of the magnetization of the inner layers is associated with the pulse of the external field in a more complicated way. The eddy currents initiated during magnetization reversal of the plate create an additional pulse for the inner layers $Q_v$, and $Q = Q_e + Q_v$.

Fig. 3. Oscillograms of magnetization-reversal pulses: $a$—without an additional resistance (through a 15-db attenuator); $b$—additional resistance of 300 ohms switched in. Frequency of the calibration oscillations: 500 MHz.

The correction of the first approximation consists of a correction depending on the conductivity of the ferrite,

\[ Q_\sigma = -\frac{1}{2}(b^2 - x^2)\sigma(B + B_r) \tag{4a} \]

and a correction depending on the dielectric permittivity,

\[ Q_\varepsilon = -\frac{1}{2}(b^2 - x^2)\varepsilon \cdot \varepsilon_0 \left(1 - \frac{B^2}{B_s^2}\right) r_m (H - H_0). \tag{5} \]

In expressions (4a) and (5), $b$ is the thickness of the core (in our case

\[ b = \frac{D - d}{2}, \]

where $D$ is the outer diameter and $d$ is the inner diameter of the core), and $x$ is the distance of the layer undergoing magnetization reversal from the mean axis of the core. G. A. Tatur [4], in calculating the magnetization-reversal time with allowance for viscosity and the surface effect on an electronic digital computer, showed that the influence of dielectric permittivity on the processes of re-

the magnetization begins to have an effect only at \(\varepsilon > 10^{-2}\). However, according to [5], the dielectric permittivity of all ferrites at high frequencies falls to 10. Consequently, the correction for displacement currents may be neglected.

The largest magnitude of the correction associated with the shielding effect of eddy currents, and consequently the greatest possible distortion of the pulse shape, pertain to the middle layer of the remagnetized core. The largest correction for a core of grade 0.16VT \((10 \times 7.5 \times 2)\), \(\sigma = 0.2 \cdot 10^{-6}\ \text{mho/cm}\). The magnitude of the pulse of the remagnetizing field for this ferrite is \(1\ \mu\text{s}\cdot\text{mho/cm}\). Consequently, the correction for eddy currents is comparable with the magnitude of the pulse of the remagnetizing field only when \(\sigma = 10^{-1}\ \text{ohm}^{-1}\text{cm}^{-1}\). For the ferrites we investigated, the specific conductivity is \(\sigma = 10^{-1} \div 10^{-4}\ \text{ohm}^{-1}\text{cm}^{-1}\). However, there are grounds to assume [5] that the conductivity increases sharply with increasing amplitude of the remagnetizing field as a result of the growth of the fraction of high-frequency components arising at nanosecond ferrite remagnetization times. A final answer to the question of the influence of specific conductivity on the pulse characteristics of ferrites in strong fields can be given only by studying these characteristics over a wide temperature range.

REFERENCES

1. A. I. Pirogov. Magnetic Cores with RRG. Energiya, 1964.
2. V. S. Tseitlin. Handbook for Calculating Inductances. Moscow, 1959.
3. M. G. Vitkov. Avtomatika i telemekhanika, vol. XXI, issue 10, 1960.
4. G. A. Tatur. Izv. vuzov—Elektromekhanika, No. 2, 1962.
5. J. Smit, H. P. J. Wijn. Ferrites. IL, Moscow, 1962.