Electronic Switch

V. K. Zhukov

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

Measurement of small increments of capacitances and inductances can be carried out with high accuracy by generator circuits using the method of automatic substitution [3], the essence of which consists in the alternate connection of the monitored and reference inductances (or capacitances) to the measuring generator. Implementation of this method is possible when there is a switch satisfying the following conditions: since switching is performed in the potential circuits of the generator (at high-frequency voltage), the switch key must be weakly coupled to the points of zero potential, i.e., it must have a large active and reactive resistance of coupling to the “ground” of the generator at frequencies of tens of megahertz; the forward resistance of the switch key proves to be connected in series into the oscillatory circuit of the generator, therefore, in order not to introduce significant damping into it, this resistance must be small; for reliable disconnection of the element being switched, the reverse resistance of the key must be large. These requirements are best satisfied by an electromechanical switch based on an electric motor. However, it has a low switching frequency, large dimensions, and is unreliable in operation.

Fig. 1. Schematic circuit diagram of the switch.

The described circuit of the electronic switch (Fig. 1) is free from the indicated shortcomings and at the same time satisfies the requirements listed above for the switch.

Point semiconductor diodes $D_1$ and $D_2$, having a small differential resistance in the open state, are used as the switch keys. Among the diodes manufactured by domestic industry, in this respect the best are diodes D11 and D13. Figure 2 presents the current–voltage characteristics of selected D13 diodes at temperatures of $20^\circ\text{C}$ and $60^\circ\text{C}$. With a direct current through the diodes of 50 mA and $T = 20^\circ\text{C}$ they have a differential resistance of less than 2 ohms. A temperature change of $40^\circ\text{C}$ causes a decrease in the resistance $r_{\text{pr}.1}$ of diode $D_1$ by $(0.12)$ ohm, while the resist-

of the forward resistance \(r_{\mathrm{pr}\cdot 2}\) of diode \(D_2\) by \((0.11)\ \Omega\), while the difference \(r_{\mathrm{pr}\cdot 1}-r_{\mathrm{pr}\cdot 2}\) changes by no more than \(0.01\ \Omega\). The latter circumstance is especially important in the present case, since it means that the temperature dependences of the diodes will have little effect on the difference of the packet frequencies generated by the oscillator. In the closed state a diode represents a large active resistance shunted by the capacitance of the \(p\)—\(n\) junction, which for D13 diodes does not exceed \(1\ \mathrm{pF}\).

The switching diodes are connected in the collector circuits of the trigger. When triode \(PT_1\) is open, a forward voltage is applied to diode \(D_1\), and therefore it is also in the open state. The inductance \(L_1\), through the small resistance of the open diode, is connected to the oscillator tank circuit. At this time the other triode, \(PT_2\), is in the closed state and a blocking voltage is applied to diode \(D_2\). The inductance \(L_2\) is connected to the oscillator tank circuit through the large resistance of the closed diode, and therefore it has practically no effect on the oscillator frequency.

Fig. 2. Current-voltage characteristics of diodes: \(A\)—at \(20^\circ\mathrm{C}\), \(B\)—at \(60^\circ\mathrm{C}\).

To obtain the voltage blocking the diodes, the resistors \(R_{k0}\) and \(R_{k1}\) are used. When one triode is open, for example \(PT_1\), and the other is closed, the voltage drop across the resistor \(R_{k0}\), produced by the collector current of the open triode, exceeds the voltage drop across the resistor \(R_{k1}\), produced by the base current of the open triode. As a result, diode \(D_2\) is blocked. Opening of triode \(PT_2\) and closing of \(PT_1\) are accompanied, respectively, by unlocking \(D_2\) and blocking \(D_1\). The high-frequency choke \(D_p\) serves to decouple the oscillator and trigger circuits in order to eliminate the influence of the latter on the frequency of the generated oscillations. To prevent the circuit of the open switch from shunting the source of the blocking voltage of the closed switch, capacitors \(C_1\) and \(C_2\) are used.

Fig. 3. Equivalent circuit of the commutator.

To obtain the basic design relations, let us consider the equivalent circuit of the trigger shown in Fig. 3. Suppose that triode \(PT_1\) is open and \(PT_2\) is closed. To obtain a stable operating mode of the trigger, it is necessary to bring the open triode into saturation. The potentials of the collector and base of the saturated triode differ little from the emitter potential; therefore the triode may be regarded as a point with a single potential at all electrodes. The closed triode is replaced by two current generators, \(I'_{k0}\) and \(I'_{e0}\). In [1] it is shown that the base current of the closed triode is \(I_b=I_{k0}'\), where \(I_{k0}'\) is the temperature current of the collector junction.

Triode \(PT_2\) will be reliably blocked under the condition that the base potential is positive relative to the emitter, i.e. \(U_{be}>0\). Taking \(I_{k1}\simeq I_{e1}\gg I'_{k0}\) and \(I_{k1}\gg I_{R1}\), from the equivalent circuit of the trigger one can obtain:

\[ (I_{k0}+I_{R2})\cdot R_b+I_{R2}\cdot R=I_{k1}\cdot R_e . \tag{1} \]

The collector current of the transistor in the saturation mode is

\[ I_{k1}=\frac{E_k}{R_e+R_{k e}}, \tag{2} \]

where \(R_{k e}\) denotes the equivalent resistance of the collector load, equal to

\[ R_{k e}=\frac{(R_k+R_{k0})R_{k1}}{R_k+R_{k0}+R_{k1}} . \tag{3} \]

The forward resistance of the diode \(r_{\mathrm{fr}}\ll R_k\), and therefore it is not taken into account in determining \(R_{k.e}\).

From expression (1), taking (2) into account, we find

\[ U_{b2}=I_{R2}\cdot R =R\frac{E_k\cdot R_e-I_{k0}\cdot R_b(R_e+R_{k.e})}{R_e+R_{k.e}} . \tag{4} \]

For the condition \(U_{b2}\gg 0\) to be fulfilled, the numerator of expression (4) must be greater than zero, whence we obtain the condition for cutoff of the transistor

\[ R_e>\frac{R_b\cdot R_{k.e}\cdot I_{k0}}{E_k-I_{k0}\cdot R}. \tag{5} \]

The open transistor will be in the saturation state if its base current is

\[ I_b\gg\frac{E_k}{\beta(R_{k e}+R_e)} . \tag{6} \]

From the equivalent circuit of the trigger it follows that

\[ R_e(I_{k1}+I_{b1})+R\cdot I_{R1}+R_{k1}(I_{R1}+I'_{k0})=E_k \tag{7} \]

and

\[ I_{R1}=I_{b1}+\frac{R_e(I_{k1}+I_{b1})}{R_b}. \tag{8} \]

Assuming \(I_{k1}\gg I_{b1}\) and \(I_{k1}=\beta\cdot I_{b1}\), from equations (7) and (8), after transformations, we obtain

\[ I_{b1}=\frac{E_k}{\beta\cdot R_e+R+R_{k1}} . \tag{9} \]

The transistor will be in the saturation mode if the expression obtained for \(I_b\) exceeds the value \(E_k/\beta(R_e+R_{k e})\), which is satisfied when

\[ R\ll \beta\cdot R_{k.e}-R_{k1}. \tag{10} \]

This will be the condition for saturation of the open transistor.

At the moment the trigger flips, both switching diodes are open. The voltage on capacitor \(C_k\) during the regenerative stage does not have time to change; therefore the equivalent resistance of the collector load of each transistor is equal to

\[ R'_{k e}=R_k\parallel R_{k1}=\frac{R_k\cdot R_{k1}}{R_k+R_{k1}} . \tag{11} \]

The value \(R'_{k.e}\) is less than \(R_{k.e}\), determined by expression (3), as a result of which fulfillment of the conditions for reliable cutoff of the closed transistor (5)

and saturation of the open one (10) may prove insufficient to ensure an unstable state of the flip-flop when both triodes operate in the active region of the characteristics. To prevent this, it is necessary to make the current gain coefficient of the circuit, “κ,” greater than 1 (the flip-flop consists of two cascaded amplifiers, the output of each being connected to the input). It can be shown that

\[ \kappa=\frac{\beta \cdot R_{\mathrm{k}}\parallel R_{\mathrm{k}1}}{R+R_{\mathrm{k}}\parallel R_{\mathrm{k}1}}, \]

whence instability of the states corresponding to the active region of the triodes will occur for \(R<\beta\cdot R_{\mathrm{k}}\parallel R_{\mathrm{k}1}\).

Expression (13) gives a somewhat smaller value for \(R\) than expression (10); therefore, in the calculation it is necessary to use formula (13).

It was noted above that when one of the switching diodes is open, a blocking voltage must be applied to the other. This requirement is fulfilled by providing a definite ratio between the resistances \(R_{\mathrm{k}0}\) and \(R_{\mathrm{k}1}\), for which \(I_{\mathrm{d}}\cdot R_{\mathrm{k}0}>I_{\mathrm{b}}\cdot R_{\mathrm{k}1}\) (for the state of the circuit shown in Fig. 3). Using expression (2) and the dependence \(I_{\mathrm{b}1}=S\cdot I_{\mathrm{k}1}/\beta\), where \(S\) is the saturation coefficient of the triode, the last inequality can be transformed into the form

\[ \beta\cdot R_{\mathrm{k}0}>S\cdot (R_{\mathrm{k}0}+R_{\mathrm{k}})+S\cdot R_{\mathrm{k}1}. \tag{14} \]

The resistance \(R_{\mathrm{k}0}+R_{\mathrm{k}}\) is found from the condition of ensuring the maximum permissible current through the open diode at the specified voltage \(E_{\mathrm{k}}\), which is done in order to obtain a small forward resistance of the diode. The value of the resistance \(R_{\mathrm{k}1}\) must be considerably greater than \(R_{\mathrm{k}0}+R_{\mathrm{k}}\), since otherwise a significant part of the collector current of the open triode branches into \(R_{\mathrm{k}1}\); and if one takes into account that the current through the diode must be significant (50–70 mA), it becomes clear that decreasing \(R_{\mathrm{k}1}\) leads to large collector currents and to the necessity of using power triodes. However, an excessively large value of \(R_{\mathrm{k}1}\) is also undesirable, because in order to satisfy the condition for blocking the diodes (14) it will be necessary to increase \(R_0\), which, at an unchanged current through the open diode, is associated with an increase in \(E_{\mathrm{k}}\). Values of \(R_{\mathrm{k}1}\) equal to \((5\div 10)\cdot (R_{\mathrm{k}0}+R_{\mathrm{k}})\) may be recommended.

If we denote \(R_{\mathrm{k}1}=K\,(R_{\mathrm{k}0}+R_{\mathrm{k}})\), then condition (14) can be written as

\[ R_{\mathrm{k}0}>S\,\frac{1+K}{\beta}\,(R_{\mathrm{k}0}+R_{\mathrm{k}}), \tag{15} \]

With the aid of the last expression, having specified the value of the saturation coefficient \(S\) and the value \(K=5\div 10\), and having preliminarily determined \(R_{\mathrm{k}0}+R_{\mathrm{k}}=E_{\mathrm{k}}/I_{\mathrm{d}}\), one can readily find \(R_{\mathrm{k}0}\), \(R_{\mathrm{k}}\), \(R_{\mathrm{k}1}\) corresponding to stable operation of the flip-flop and ensuring the application of blocking voltage to the diodes.

The described switch circuit was used for switching sensors in an instrument for measuring the diameter of fine wires. Tests showed that it can be used successfully for switching elements of the tank circuit in an oscillator.

REFERENCES

1. S. M. Gerasimov, I. N. Nikulin, V. N. Yakovlev. Calculation of Semiconductor Amplifiers and Oscillators. Gostekhizdat, Ukrainian SSR, 1961.

2. B. N. Kononov. Symmetrical Flip-Flops on Planar Semiconductor Triodes. Gosenergoizdat, 1960.

3. V. K. Zhukov, V. E. Dreizin, M. S. Roitman, I. G. Leshenko. Measuring circuits for monitoring the diameter of fine wires by the eddy-current method (article being printed in the present collection).