Bulletin of the Tomsk Polytechnic Institute named after S. M. Kirov
Vol. 285, 1975

Synchronization of a Magnetotransistor Multivibrator

M. A. Zhitkov, A. A. Kuvshinov, A. K. Luzginov

(Presented by the Scientific and Technical Seminar of the Research Institute of Automation and Electromechanics)

In power conversion technology and automation, magnetotransistor multivibrators have found wide application; they are used as low-power converters and frequency dividers, as well as master oscillators.

Synchronization of a magnetotransistor multivibrator (MTM) is usually carried out by an alternating voltage that forcibly switches the transistors of the multivibrator. Remagnetization of the core of the MTM transformer occurs along a partial cycle of the hysteresis loop, obtained by limiting the value of induction “from below” or “from above,” or simultaneously “from below” and “from above.”

The synchronization processes of an MTM have different characters depending on the shape of the synchronization voltage.

The synchronization voltage may be of a two-half-period rectangular or sinusoidal form (complete synchronization), or may have the form of short unipolar pulses (pulse synchronization) [1].

With such synchronization methods, duration-controlled bipolar voltage pulses can be obtained only by the geometric addition of the output voltages of two multivibrators [3]. However, the known synchronization methods do not make it possible to obtain a duration-controlled bipolar voltage directly at the output of the multivibrator.

The method considered in this article for synchronizing an MTM with emitter-base couplings, controlled in duration by unipolar pulses (pulse-width synchronization), makes it possible to obtain at its output a controlled bipolar voltage.

Below are presented the results of a theoretical and experimental investigation of pulse-width synchronization of an MTM.

In the general case, remagnetization of the core (Fig. 1) occurs along a symmetrical cycle with natural frequency

\[ f_0=\frac{(U_{\mathrm{p}}-\Delta U_{\mathrm{ke}}-U_{\mathrm{sm}})\cdot 10^8}{4w_1\cdot S_{\mathrm{st}}\cdot B_s}, \tag{1} \]

where

\(U_{\mathrm{p}}\) — supply-source voltage;

\(U_{\mathrm{sm}}\) — bias voltage formed by means of the circuit D5-D7 and C1;

\(W_1\) — number of turns of the primary winding;

$S_{\text{st}}$ — cross section of the transformer core;
$B_s$ — saturation induction.

Fig. 1.

Positive synchronizing pulses, adjustable in duration, are applied simultaneously through diodes D1 and D2 to the bases of transistors T1 and T2 of the multivibrator. In this case, depending on the ratio of the natural frequency $f_0=\dfrac{1}{T_0}$, the synchronizing frequency $f_c=\dfrac{1}{T_c}$, and the duration of the synchronizing pulse $t_i$, three operating modes of the MTM are possible.

For $f_c<2f_0$, the MTM operates at its natural frequency for a time $T_c-t_i$. If $T_c-t_i<\dfrac{T_0}{2}$, then bipolar pulses are formed at the MTM output, adjustable in duration within a range limited by $\dfrac{T_0}{2}$.

When $T_c-t_i>\dfrac{T_0}{2}$, an adjustable-duration burst of pulses is formed at the output, containing an integer or fractional number of pulses.

To obtain bipolar pulses adjustable in duration over the full range, it is necessary to satisfy the following condition:

\[ f_c>2f_0. \tag{2} \]

When a positive synchronizing pulse is applied to the bases of transistors T1 and T2, a positive bias voltage is applied, and the transistor that had previously been on is cut off.

At the same time, owing to the decrease in the magnetizing current of the MTM transformer, its operating point lies on the return curve of the hysteresis loop, which leads to a change in the sign of the derivative of the flux and of the emf. As a result, in the base circuit of the transistor that was off at the moment the synchronizing pulse arrived, the self-excitation condition is satisfied, and when the synchronizing pulse is removed, the circuit switches.

When the next synchronizing pulse is applied, the circuit operates similarly.

The transition time of the MTM from its natural frequency to the synchronizing frequency depends on the magnitude of the time interval $\Delta t$ between the leading edge of the positive synchronizing pulse and the moment of the preceding switching of the MTM transistors. A detailed consideration

these processes under complete (CS) and pulsed (PS) synchronization was carried out in [1]. The duration of the transient processes in CS, for \(\Delta t < \dfrac{1}{2 f_c}\), does not exceed half the synchronization period, while for \(\Delta t > \dfrac{1}{2 f_c}\) it is equal to zero.

A characteristic feature of PS is the presence of two operating modes: two-half-period synchronization (THS), when the duration of the transient process is equal to zero, and one-half-period synchronization (OHS), which occurs when \(0 < \Delta t < \dfrac{1}{f_c}\). The OHS mode is considered nonoperational because of distortion of the waveform of the MTM output voltage.

With pulse-width synchronization (PWS) of a magnetotransistor multivibrator, the OHS mode is also possible; however, the region in which it arises is determined not only by the synchronization frequency but also by the duration of the synchronizing pulses.

Figure 2 shows diagrams illustrating characteristic cases of the occurrence of OHS (Fig. 2, a) and THS when the time \(\Delta t\) is varied (Fig. 2, b), the synchronizing-pulse duration \(t_i\) is varied (Fig. 2, c), and the synchronization frequency \(f_c\) is varied (Fig. 2, d).

On the basis of the foregoing, the width of the zone of one-half-period synchronization under PWS is determined by the following expression:

\[ \Delta t \leq \frac{1}{f_c} - t_i . \tag{3} \]

Fig. 2.

Denoting by \(\Delta \tau = \dfrac{2 \Delta t}{T_0}\) the relative width of the OHS zone, expression (3) can be represented in the form

\[ \Delta \tau \leq \frac{1-\tau_i}{k}, \tag{4} \]

where

\[ \tau_i=\frac{t_i}{T_c} \]

is the relative duration of the synchronizing pulse,

\[ K=\frac{T_0}{2T_c}=\frac{f_c}{2f_0} \]

is the coefficient of multiplicity of the synchronization frequency.

In Fig. 3, according to equation (4), a family of straight lines has been plotted that are the lower boundaries of the zone of two-half-period synchronization.

Fig. 3.

Analysis shows that STS is an intermediate mode between the PS modes \((\tau_i=1)\) and IS \((\tau_i\approx 0)\), and, in order to obtain stability of two-half-period synchronization, it requires the use of a device that determines the moment of arrival of the first synchronizing pulse.

It should be noted that, when the adjustment range is limited from below, the multiplicity of the frequencies \(K\) can be reduced and even brought down to unity. This makes it possible to substantially reduce the precision requirements on the time-setting device and the dimensions of the MTM transformer.

The expressions obtained are valid for a magnetic core with a rectangular hysteresis loop. In the case of using magnetic cores for which \(B_s>B_r\), the width of the OIS zone is also determined by the rectangularity coefficient of the hysteresis loop

\[ K_p=\frac{B_r}{B_s} \]

[2]. This is explained by the fact that, when the operating point moves from \(B_s\) to \(B_r\), the state of the MTM transistors before and after the arrival of the synchronizing pulse does not change.

The time of motion of the operating point along the return curve is equal to

\[ \Delta t_r=\frac{B_s-B_r}{4f_0B_s}. \tag{5} \]

Thus, in the present case the width of the OIS zone decreases by the amount \(\Delta t_r\) and, in relative units, is determined by the expression

\[ \Delta \tau \leq \frac{1-\tau_i}{K}-\frac{1-k_p}{2}. \tag{6} \]

The experiments carried out confirmed the operability of the considered method of synchronizing the MTM and the correctness of the results of the analysis of transient processes under one- and two-half-period STS.

Conclusions

1. The considered method of pulse-width synchronization of the MTM makes it possible to obtain at its output a bipolar voltage adjustable in duration.

2. In the case of PWS, the width of the zone of single-half-period synchronization is determined not only by the ratio of the natural frequency of the MTM to the synchronization frequency, but also by the duration of the synchronizing pulses.

3. The width of the zone of single-half-period synchronization under PWS can be significantly reduced by using an MTM transformer core with a nonrectangular hysteresis loop.

Literature

1. V. K. Tikhomirov. Pulse synchronization of transistor converters. Elektrotekhnika, 1966, No. 8.

2. N. F. Il’inskii, V. V. Mikhailov. Transistor-magnetic converters of a continuous signal into a sequence of pulses. Moscow–Leningrad, Energiya, 1966.

3. O. A. Kossov. Power amplifiers using transistors in switching mode. Moscow, Energiya, 1971.