Modified Owen Bridge for Measuring Instantaneous Values of the Dynamic Reversible Permeability of a Sample
Abstract Generated abstract
A modified Owen bridge method is presented for measuring instantaneous active and reactive components of a periodically varying complex impedance, with application to dynamic reversible permeability in ferromagnetic specimens. The approach uses a high-frequency bridge supply, selective amplification of the unbalance voltage, and phase-synchronized stroboscopic observation to identify balance at chosen instants of a low-frequency magnetizing current. From the bridge balance conditions, the sensor resistance and inductance are converted into the real and imaginary components of reversible permeability. Experiments on a toroidal specimen indicate that alternating-field magnetization produces larger amplitude and phase changes than comparable direct-current magnetization, including a measurable lag of permeability relative to magnetizing current, attributed to low-frequency magnetic skin effect.
Full Text
PROCEEDINGS OF THE TOMSK POLYTECHNIC INSTITUTE
named after S. M. Kirov
Vol. 208 1974
A MODIFIED OWEN BRIDGE FOR MEASURING INSTANTANEOUS VALUES OF THE DYNAMIC REVERSIBLE PERMEABILITY OF A SPECIMEN
A. M. GRUZNOV, B. B. VINOKUROV, I. G. LESHCHENKO
(Presented by the scientific seminar of the Department of Information and Measuring Technology)
By dynamic reversible permeability we understand the reversible permeability obtained when a specimen is magnetized not by a constant field, but by an alternating field. In this case the frequency of the magnetizing field is much lower than the frequency of the field that leads to the formation of a minor cycle loop.
Since, in the process of measuring dynamic reversible permeability, the components of the complex resistance are determined, a technique may be used for measuring the instantaneous values of the components of a periodically varying complex resistance.
Let the complex resistance connected into one of the arms of an AC bridge vary in time according to an unknown law \(Z = Z(t)\), as a result of a harmonic action upon it
\[ p = P_m \sin(\Omega t - \varphi) \]
(Fig. 1, a). The frequency \(\omega\) of the voltage feeding the bridge is chosen much higher than the action frequency \(\Omega\). The voltage of the measuring diagonal is fed through a selective amplifier to the input of an electronic oscillograph. With a sweep duration equal approximately to
\[ \frac{2\tau}{\Omega}, \]
in the general case the oscillogram of the bridge unbalance voltage, amplitude-modulated, will have the form shown in Fig. 1, b. The shape of the envelope of this voltage will depend in a complex manner both on the law of variation of \(z\) and on the parameters of the bridge circuit.
If, for some instant of time \(t_i\), the condition of bridge balance is fulfilled, then in the oscillogram for this instant the upper and lower envelopes touch at a point (Fig. 1, c).
Fig. 1.
The unbalance voltage of the bridge circuit, obtained by the method described, in addition to the fundamental frequency \(\omega\), contains frequencies of the form \(\omega \pm n\Omega\), where \(n\) in the general case takes the values of even and odd integers from 0 to \(\infty\). However, first, because the spectral composition \(z\) can always be bounded above by the frequency \(\Omega_i\), and second, because of the frequency ratio \(\omega \gg \Omega\), the harmonics of the unbalance voltage will prove to be very close to the frequency \(\omega\). It is at this frequency that balancing of the bridge circuit practically takes place.
The Owen bridge is frequency-independent, i.e., the equilibrium condition can be fulfilled simultaneously for all harmonics.
The frequency \(\omega\) in the experiment was equal to \(2\pi \cdot 4.7\) kHz, and the frequency \(\Omega\) to \(2\pi \cdot 0.05\) kHz.
To determine the value of the harmonic action \(p_i\) corresponding to the instant of time \(t_i\), a device was constructed which, synchronously with \(p\), generates short strobe voltage pulses and illuminates, at the instant \(t_i\), the oscillogram of the bridge unbalance voltage. The calibrated phase shifter of this device makes it possible to vary the phase of the strobe pulse in the range \(0\)--\(2\pi n\).
If “0” on the phase-shifter scale corresponds to the instant at which \(p\) passes through zero, then the instantaneous value of the harmonic action for the instant of time \(t_i\) can easily be determined:
\[ p_i = P_m \sin \Theta, \tag{1} \]
where \(\Theta\) is the angle on the phase-shifter scale corresponding to the instant \(t_i\).
The procedure for obtaining the dependence \(z = f(p_i)\), where \(p_i\) is the instantaneous value of the harmonic action, is as follows. With the aid of the phase shifter, values of the angle \(\Theta\) are set at small intervals; from these, the corresponding values \(p_i\) are determined. For each of these values \(p_i\), using the balancing elements of the bridge circuit, the upper and lower envelopes of the unbalance voltage are brought into contact at the luminous point. Then, from the bridge equilibrium conditions, the active and reactive resistances of the sensor are determined from its parameters at balance.
The circuit (Fig. 2), operating by the proposed method, was calculated for the experimental determination of the dependence of the dynamic reversible permeability of ferromagnetic specimens on the instantaneous value of the magnetizing current of 50 Hz. The components of this permeability are determined from the equation
\[ j\omega L_d + R_d = j\omega \mu_0 \frac{S_{\mathrm{zh}}}{l_c} W^2 \left(\mu_{\mathrm{rev}}' - j\mu_{\mathrm{rev}}''\right), \tag{2} \]
where
\(\omega\) is the operating frequency of the bridge circuit,
\(L_d\) is the inductance of the sensor,
\(\mu_0\) is the permeability of vacuum,
\(S_{\mathrm{zh}}\) is the cross section of the magnetic circuit,
\(l_c\) is the mean length of the magnetic line of force,
\(W\) is the number of turns of the sensor [1],
\(\mu_{\mathrm{rev}}'\) and \(\mu_{\mathrm{rev}}''\) are, respectively, the active and reactive components of the dynamic reversible permeability.
Transforming expression 2, we obtain:
\[ \mu_{\mathrm{rev}}' = \frac{L_d \cdot l_c}{\mu_0 S_{\mathrm{zh}} W^2} = A L_d, \tag{3} \]
\[ \mu_{\mathrm{rev}}'' = \frac{R_d \cdot l_c}{\omega \mu_0 S_{\mathrm{zh}} W^2} = A' R_d. \tag{4} \]
where \(A\) and \(A'\) are coefficients constant under the experimental conditions.
The ideal balance conditions of the Owen bridge are
\[ L_{\mathrm{d}} = C_2 R_2 R_1, \tag{5} \]
Fig. 2. Schematic diagram of a modified Owen bridge for measuring dynamic reversible permeability
\[ R_{\mathrm{d}} = R_2 \frac{C_2}{C_1}. \tag{6} \]
The parameters of the bridge circuit were calculated in such a way as, on the one hand, to satisfy the condition of maximum sensitivity of the bridge at the operating frequency of \(4.7\ \text{kHz}\), and, on the other, to make the biasing current practically insensitive to changes in the balancing—
Fig. 3. Loops of reversible permeability at various values of the biasing fields:
a) under biasing by constant fields; b) under biasing by alternating fields.
elements of the bridge circuit. The choke Dr and capacitor \(C_3\) serve to separate the bridge power supplies from one another.
The action \(p\) in the circuit is the current \(i=I_m \sin(\Omega t-\varphi)\), from whose value it is not difficult to determine the magnitude of the magnetizing field.
Tests were carried out with the proposed circuit for a toroidal specimen. First, values of the reversible permeability of the specimen were obtained under magnetization by direct current, and then under magnetization by alternating current. The amplitude value of the alternating current corresponded to the value of the direct current. The frequency of the voltage feeding the bridge was the same in both cases—4.7 kHz.
The results of the experiments are presented in Figs. 3 and 4.
Fig. 4. Changes in the components of reversible permeability at different values of magnetizing fields: a) with magnetization by a constant field; b) with magnetization by an alternating field.
On the basis of the data obtained it is evident that:
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The reversible permeability under magnetization by an alternating field undergoes more significant changes, both in amplitude and in phase, than under magnetization by a constant field with the same maximum value.
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There is a clearly expressed phase lag of the dynamic reversible permeability relative to the alternating magnetizing current: the minimum of the permeability is observed after the current passes through its maximum value. The phenomenon of time lag is explained by the presence of the magnetic skin effect of the low-frequency field.
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The maximum value of the reversible permeability under magnetization by an alternating field is greater than the maximum value of the same permeability under magnetization by a constant field.
REFERENCES
- Z. Faktor, L. Grudnyi, I. Staryi, Z. Tisher. Magnetically Soft Materials, “Energiya,” 1964.
- K. M. Polivanov. Ferromagnetics, GEI, 1957.