UDC 621.374.2

SQUARE-WAVE VOLTAGE PULSE GENERATORS

G. I. ZAIDMAN

(Presented by the scientific seminar of the Department of Radio Engineering)

The article presents four circuits of square-wave voltage pulse generators based on the method of bipolar switching of the load resistor. The causes determining the instability of the output voltage of the generators are considered. Expressions are given for determining the amplitude value of the voltage when calibrating the generators with direct current.
Illustrations 7, references 6.

For calibrating electronic voltmeters, in built-in verification devices, etc., promising sources of rectangular voltage having a Π-shaped form (square-wave voltage) are used. With a Π-shaped form, all three voltage values—amplitude, rms, and average—are equal [1]. Such a standard voltage can be obtained with the aid of a calibrator. The basis of a rectangular-voltage calibrator is a generator that determines its metrological characteristics and serves in amplitude meters [2] as a standard source.

Several methods of forming square-wave voltage are known, each of which is characterized by a number of advantages. This article is devoted to square-wave voltage pulse generators based on the method of bipolar switching of the load resistor [3, 4, 5], which, in comparison with generators of similar purpose but without bipolar switching of the load resistor, make it possible to double the utilization factor of the DC-source voltage, to reduce by a factor equal to the stabilization coefficient the instability of the switching elements in the closed state [3, 4], and to increase the stabilization coefficient [4] and efficiency [4, 5].

Let us consider the functional circuit of a pulse generator with switching of the load resistor in the diagonal of a bridge circuit with transistor switches and linear resistors in the bridge arms [3]. Such a bridge circuit, together with the pulse generator, is shown in Fig. 1. The generator contains a multivibrator M, a trigger, a switching circuit on transistors T₁ and T₂, to whose collectors are connected temperature-compensated Zener diodes D₁, D₂, the load resistor \(R_{\text{n}}\), and linear ballast resistors \(R_1\) and \(R_2\), forming a diode voltage stabilizer. The latter chiefly determines the metrological characteristics of the pulse generator [3].

The instability of the output voltage of the stabilizer (Fig. 1) is determined both by the instability of its elements and by the instability of

of the input voltage. Let us determine the requirements on the elements of the diode voltage regulator. To do this, we shall establish the relationship between the regulation coefficient of the diode voltage regulator and the values of its elements. The regulation coefficient of the diode voltage

Fig. 1

regulator (Fig. 1), in terms of relative voltage changes, can be written as follows:

\[ K=\frac{\Delta U_{\text{in}}/U_{\text{in}}}{\Delta U_{\text{out}}/U_{\text{out}}} =\frac{1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_i} {1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_{\text{st}}}. \tag{1} \]

Here \(R_{\text{b}}\) is the resistance of the ballast resistor, \(R_i\) is the dynamic resistance of the stabilitron, and \(R_{\text{st}}\) is the static resistance of the stabilitron. Let us denote \(\Delta U_{\text{in}}/U_{\text{in}}=A\), \(\Delta U_{\text{out}}/U_{\text{out}}=B\); consequently, \(B=A/K\), or

\[ dB=d\frac{A}{K}=\frac{K(dA-A/K\,dK)}{K^2}. \]

Assuming that \(A=\text{const}\), then \(dA=0\), and we have

\[ dB/B=-\,dK/K. \tag{2} \]

Let us express the relative change in the regulation coefficient through the relative instability of the elements of the regulator. At a constant ambient temperature, the regulation coefficient \(K\) is a function of four quantities,

\[ K=f(R_{\text{n}}, R_{\text{b}}, R_{\text{st}}, R_i). \]

Having determined the values of the partial derivatives

\[ \frac{\partial K}{\partial R_{\text{b}}},\quad \frac{\partial K}{\partial R_{\text{st}}},\quad \frac{\partial K}{\partial R_i},\quad \frac{\partial K}{\partial R_{\text{n}}}, \]

substituting their values into (1) and taking into account that \(R_{\text{st}}\gg R_i\), we obtain

\[ \frac{dB}{B}\simeq -\frac{1} {(1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_i) (1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_{\text{st}})} \left[ \frac{R_{\text{b}}}{R_i}\cdot\frac{\Delta R_{\text{b}}}{R_{\text{b}}} +\right. \]

\[ \left. +(1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_{\text{st}}) \frac{R_{\text{b}}}{R_{\text{st}}}\cdot \frac{\Delta R_{\text{st}}}{R_{\text{st}}} \right. \]

\[ \left. -(1+R_{\text{b}}/R_{\text{n}}+R_{\text{b}}/R_{\text{st}}) \frac{R_{\text{b}}}{R_i}\cdot \frac{\Delta R_i}{R_i} + \frac{R_{\text{b}}^{2}}{R_{\text{n}}R_i}\cdot \frac{\Delta R_{\text{n}}}{R_{\text{n}}} \right]. \tag{2a} \]

It follows from relation (2a) that the contribution to the instability of the relative change in the output voltage is made by the instabilities of the ballast-

... of the resistor and the load resistor, as well as the instability of the static and dynamic resistances of the stabilitron. In the particular case in which \(R_{\mathrm{b}}=R_{\mathrm{n}}\), the effect of their instability on \(\dfrac{\Delta K}{K}\) is equivalent.

Consequently, the stability requirements for the load resistor must be the same as for the ballast resistor. With \(R_{\mathrm{b}}=R_{\mathrm{st}}\),

\[ \frac{\Delta R_{\mathrm{st}}}{R_{\mathrm{st}}}=\frac{\Delta R_i}{R_i}, \]

and \(R_{\mathrm{b}}\gg R_i\), a change in \(R_i\) has a stronger effect on \(\dfrac{\Delta K}{K}\) than a change in \(R_{\mathrm{st}}\) of the stabilitron. The total instability of \(R_{\mathrm{st}}, R_i\) of the stabilitron is determined by the technology of its manufacture and, for the best domestic specimens of type KS 194, amounts to \(2.5\cdot 10^{-2}\%\) over 2000 hours.

Let us analytically estimate the limiting \(K\) of a diode stabilizer if the values of the resistances \(R_{\mathrm{b}}\) and \(R_{\mathrm{n}}\) are varied. Assuming that \(R_{\mathrm{n}}\to\infty\), from equation (1)

\[ R_{\mathrm{b}}=\frac{(K-1)R_i R_{\mathrm{st}}}{R_{\mathrm{st}}-KR_i}. \tag{3} \]

It is evident from expression (3) that, at \(K=\dfrac{R_{\mathrm{st}}}{R_i}\), the resistance of the ballast resistor tends to an infinitely large value. Thus, the ratio of the static resistance of the stabilitron to its dynamic resistance at the specified operating point determines the limiting value of the stabilization coefficient of a diode voltage stabilizer in the no-load mode.

Fig. 2

For a finite value of \(R_{\mathrm{n}}\), Fig. 2 gives the dependences of \(K\) on the ratio \(R_{\mathrm{b}}/R_{\mathrm{eqv}}\) for three cases: 1) \(R_{\mathrm{n}}\gg R_{\mathrm{st}}\) (curve 1),

2) \(R_{\mathrm{n}} = R_{\mathrm{st}}\) (curve 2), 3) \(R_{\mathrm{n}} = \dfrac{1}{2} R_{\mathrm{st}}\) (curve 3), where \(R_{\mathrm{eq}} = R_{\mathrm{n}} \parallel R_{\mathrm{st}}\).

As is seen from Fig. 3, for curves 2 and 3 the value of the ballast-resistor resistance, for a given load resistor, should be selected from the condition \(\dfrac{R_{\mathrm{b}}}{R_{\mathrm{eq}}} = 1 \div 1.5\), since at larger ratios the increase in the stabilization coefficient decreases, while the power dissipated in it increases, which lowers the efficiency of the stabilizer.

The limiting switching frequency of the shaper [3] is limited mainly by the frequency of the diode stabilizer, which is limited by the minimum duration of the input-voltage pulse \(t_{\mathrm{i}} = t_{\mathrm{r}} + t_{\mathrm{f}}\). Here \(t_{\mathrm{r}}\) and \(t_{\mathrm{f}}\) are, respectively, the rise and fall times of the pulse.

The problem of calculating the transient process of switching on a temperature-compensated Zener diode in a diode voltage-stabilizer circuit (Fig. 1) reduces to finding the time for establishment of the steady-state amplitude value during charging of the Zener-diode capacitance, since the switching time of the Zener diode itself is \(2.5 \div 80\) ns.

Fig. 3.
Vertical axis: \(C_{\mathrm{eq}}, 10^3\).
Horizontal axis: \(I_{\mathrm{st}}, \mathrm{mA}\).
Legend: \(\blacktriangle\) — sample No. 7; \(\circ\) — sample No. 11.

The solution of this problem can be divided into two stages. The first stage describes the duration of the process of establishing the voltage on the Zener diode when it is switched from the neutral state to the breakdown voltage [6], and the second stage—on the stabilization branch. In solving the problem for the second stage, the dependence of the capacitance (Fig. 3) and of the dynamic resistance on the stabilization current \(I_{\mathrm{st}}\) was determined experimentally, and the dependence \(\tau_{\mathrm{c}} = f(I_{\mathrm{st}})\) was plotted (Fig. 4). Here \(\tau_{\mathrm{c}} = C_{\mathrm{eq}} R_i\), where \(C_{\mathrm{eq}}\) is the value of the equivalent capacitance of the Zener diode.

Fig. 4.
Vertical axis: \(\tau_{\mathrm{c}}, \mu\mathrm{s}\).
Horizontal axis: \(I_{\mathrm{st}}, \mathrm{mA}\).
Legend: \(\blacktriangle\) — sample No. 7; \(\circ\) — sample No. 11.

It is seen from Fig. 4 that for \(I_{\mathrm{st}} > 3\) mA the change in \(\tau_{\mathrm{c}}\) is insignificant, which makes it possible to use an averaged value. In this case, the change in the voltage on the Zener diode with time when a unipolar pulse is applied to the input of the stabilizer is determined by the relations:

\[ U(t) = U_{\mathrm{st}}\left(1 - e^{-t/\tau_{\mathrm{c}}}\right) \tag{4} \]

for the rise,

\[ U(t)=U_{\mathrm{st}}e^{-t/\tau_c} \tag{5} \]

for the fall, where \(U_{\mathrm{st}}\) is the voltage drop across the stabilizing branches of the stabilitron within the averaged value \(\tau_c\).

The calculation of the transient process of voltage rise for a system of stabilitrons (Fig. 1) is analogous to the calculation of the transient process of voltage rise on a single stabilitron, since the value of the capacitance of a reverse-biased stabilitron (see Fig. 1) [6] is approximately three orders of magnitude smaller than its equivalent capacitance in the stabilization mode (Fig. 3). The duration of the transient process of switching on the stabilitrons on the stabilizing section of their current-voltage characteristic can be determined from the equation

\[ t_{c_2}=\tau_c \ln \frac{\left|2E_{\mathrm{st}}\right|+\left|U_{\mathrm{st}}\right|}{\left|2E_{\mathrm{st}}\right|}, \tag{6} \]

where \(E_{\mathrm{st}}\) is the value of the stabilization voltage of the stabilitron.

From a comparison of (6), (8), (12), (14) of work [6] and (4), (5), it follows that the dominant quantities are the durations of the transient processes on the stabilizing section of the current-voltage characteristic of temperature-compensated stabilitrons.

Analysis of (1) shows that the relative change in output voltage, for a specified instability of the input, is determined by the stabilization coefficient \(K\). An increase in \(K\) is especially desirable in the case of large instability of the supply voltage of the shaper [3]. However, the diode voltage stabilizers with a linear ballast resistor considered above cannot provide \(K\) greater than 50. In this case, from the point of view of increasing the stabilization coefficient, circuits of diode stabilizers with a nonlinear ballast resistor are promising. A technical implementation of such a stabilizer [5] is shown in Fig. 5 and represents a connection of a current stabilizer with a stabilitron.

Fig. 5

The stabilization coefficient of the voltage stabilizer is determined by the relation

\[ K= \frac{ 1+\dfrac{R_{\mathrm{b,dyn}}}{R_{\mathrm{n}}}+\dfrac{R_{\mathrm{b,dyn}}}{R_i} }{ 1+\dfrac{R_{\mathrm{b,st}}}{R_{\mathrm{n}}}+\dfrac{R_{\mathrm{b,st}}}{R_{\mathrm{st}}} }, \tag{7} \]

where \(R_{\mathrm{b,dyn}}\) is the dynamic resistance of the ballast two-terminal network;
\(R_{\mathrm{b,st}}\) is the static resistance of the ballast two-terminal network.

Let us examine the effectiveness of increasing the stabilization factor of such a diode voltage stabilizer in comparison with an analogous diode stabilizer, but with a linear ballast resistor. Taking the ratio of the stabilization factors (7) and (1), assuming the input-voltage magnitude of the stabilizers to be the same, and also assuming their parameters to be identical for \(R_{\mathrm{L}}\to\infty\) and \(\dfrac{R_b}{R_i}\gg 1\), \(R_b=R_{b.\mathrm{st}}\), we obtain

\[ \chi_1=\frac{R_{b.\mathrm{dyn}}}{R_{b.\mathrm{st}}}, \tag{8} \]

where \(\chi_1\) is the effectiveness of increasing the voltage-stabilization factor of a diode stabilizer with a nonlinear ballast resistor, whose operating current depends only weakly on the applied voltage. Taking the load resistor into account, the effectiveness of increasing the stabilization factor is equal to

\[ \chi_2= \frac{ 1+\dfrac{R_{b.\mathrm{dyn}}}{R_{\mathrm{L}}}+\dfrac{R_{b.\mathrm{dyn}}}{R_i} }{ 1+\dfrac{R_b}{R_{\mathrm{L}}}+\dfrac{R_b}{R_i} }. \tag{9} \]

It follows from (8) and (9) that the effectiveness of increasing the stabilization factor grows with an increase in the dynamic resistance and a decrease in the static resistance of the nonlinear ballast two-terminal network. The use of a nonlinear two-terminal network as a ballast resistor makes it possible to increase both the stabilization factor and the efficiency. However, the instability of the output voltage also increases because of the instability of the ballast two-terminal network. When stringent requirements are imposed on the stability of the output voltage, it is expedient to use such a stage as the input stage of a two-stage diode stabilizer. In this case, “rough” stabilization is performed by a diode voltage stabilizer with a nonlinear ballast two-terminal network. The instability of the two-terminal network is eliminated by a diode voltage stabilizer with a linear ballast resistor connected at its output.

Let us consider the sequence for determining the amplitude value of the voltage of pulse generators [3, 4] when they are calibrated on direct current. The change in the stabilization voltage of a Zener diode in the pulsed operating mode is caused by variation in the temperature of its junctions. The magnitude of the temperature increment of a compensated Zener diode depends on the change in the power dissipated at its \(p\)–\(n\) junctions and on the ambient temperature. Taking into account transient processes in the pulsed operating mode of Zener diodes, the amplitude value of the stabilization voltage is equal to

\[ E_{\mathrm{st}}^{*} = U_0 - P_0(1-G/Q)R_{\mathrm{tc}}\alpha_c \pm \alpha_c \Delta t^0, \tag{10} \]

where \(U_0\) is the value of the stabilization voltage measured on direct current at room temperature; \(P_0\) is the power dissipated in the Zener diode on direct current at room temperature; \(G=\dfrac{P_1}{P_2}\); \(P_1\) is the pulse power dissipated in the Zener diode with allowance for its transient processes during the rise and fall of the voltage; \(P_2\) is the pulse power dissipated in the Zener diode without allowance for its transient processes during the rise and fall of the voltage; \(Q\) is the duty factor of the rectangular voltage pulses; \(R_{\mathrm{tc}}\) is the total value of the thermal resistance of the Zener diode; \(\alpha_c\) is the temperature coefficient of the Zener diode stabilization voltage; \(\Delta t^0=t_2^0-t_1^0\) is the change in tempera-

of the ambient temperature (in this case the plus sign before the expression \(\alpha_c \Delta t^\circ\) is taken when the temperature is increased, and the minus sign when it is decreased); \(t_1^0\) is the room temperature at which \(U_0\) is measured; \(t_2^0\) is the ambient temperature at which the stabilitron operates. Relation (10) is valid for the steady-state operating mode of the pulse shapers [3, 4] when \(t_i \ll \tau\), where \(\tau\) is the time constant for establishment of the voltage on the stabilitron.

Measurement of the value \(E_{\text{st}}^*\) is accompanied by two systematic relative errors \(\eta_1, \eta_2\).

The error \(\eta_1\) is due to the change in the residual voltage of the transistor switch as its temperature varies,

\[ \eta_1=\frac{\alpha_t(\Delta t_t^0 \pm \Delta t^0)}{K E_{\text{st}}^*}, \tag{11} \]

where \(\alpha_t\) is the temperature coefficient of the voltage of the transistor switch; \(\Delta t_t^0\) is the increase in the temperature of the transistor switch when the pulse shaper changes from the static to the dynamic operating mode.

The error \(\eta_2\) is caused by the increment of the thermal current of the closed transistor switch \(\Delta I_t\) and of the reverse current of the temperature-compensated stabilitron \(\Delta I_c\) in the dynamic operating mode of the pulse shaper,

\[ \eta_2=\frac{(\Delta I_t+\Delta I_c)}{E_{\text{st}}^*}\cdot R_i . \tag{12} \]

Despite a number of substantial advantages of voltage pulse shapers [3, 4], they have certain drawbacks:

— a somewhat increased output resistance, determined by the dynamic resistance of the stabilitrons used;

— granularity of the output voltage because of the spread in the stabilization voltage of the stabilitrons;

— a limited range of stabilization voltage owing to the lack of a broad assortment of stabilitrons.

The listed drawbacks are largely eliminated when shapers based on trigger key circuits are used. One functional circuit of this type of shaper is shown in Fig. 6 [5]. As can be seen from Fig. 6, the pulses of multivibrator M, after being differentiated, trigger the high-frequency trigger T, which operates in counting mode and is used to control the transistor switching circuit.

Fig. 6

The amplitude value of the generator output voltage [5] is

\[ E_{\phi}=E_{\mathrm{k}}-U_{\tau_1}-U_{\tau_2}, \tag{13} \]

where \(E_{\mathrm{k}}\) is the voltage of the generator power-supply source; \(U_{\tau_1}\), \(U_{\tau_2}\) are the residual voltages of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) transistors. When measuring the amplitude of the pulse voltage, the systematic errors \(\eta_3,\eta_4\) should be taken into account.

The component \(\eta_3\) is due to the change in the residual voltages of the transistor switches of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types in the dynamic operating mode of the generator,

\[ \eta_3= \frac{ \alpha_{\tau_1}\left(\Delta t_{\tau_1}^{0}\pm \Delta t_{1}^{0}\right) + \alpha_{\tau_2}\left(\Delta t_{\tau_2}^{0}\pm \Delta t_{2}^{0}\right) }{E_{\phi}}, \tag{14} \]

where \(\alpha_{\tau_1}, \alpha_{\tau_2}\) are the temperature coefficients of the voltage of the transistor switches in saturation, respectively, of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types; \(\Delta t_{\tau_1}, \Delta t_{\tau_2}\) are the temperature increases of the transistor switches, respectively, of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types in the dynamic operating mode of the generator.

The appearance of the error component \(\eta_4\) is caused by an increase in the reverse currents of the closed transistor switches of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types when the generator changes from the static to the dynamic operating mode, because of the increase in the power dissipated in them,

\[ \eta_4= \frac{R_{\tau_1}\Delta I_{\tau_1}+R_{\tau_2}\Delta I_{\tau_2}}{E_{\phi}}, \tag{15} \]

where \(R_{\tau_1}, R_{\tau_2}\) are the resistances of the transistor switches in the saturated state, respectively, of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types; \(\Delta I_{\tau_1}, \Delta I_{\tau_2}\) are the increments of the leakage currents of the transistor switches of the \(p\)-\(n\)-\(p\) and \(n\)-\(p\)-\(n\) types.

Fig. 7

The generator [5] can be simplified (Fig. 7). Such a switching circuit is triggered by differentiated pulses from the IPS source.

In conclusion, we note that on the basis of the generators considered, compact, economical standard sources of rectangular voltage with high metrological characteristics can be built.

LITERATURE

1. R. A. Valitov. Radio-Engineering Measurements. “Sovetskoe radio,” 1963.

2. M. S. Roitman, G. I. Zaidman. Method for measuring the amplitude value of an alternating voltage. Author’s certificate No. 310187, Bulletin of Inventions No. 23, 1971.

3. G. I. Zaidman. Square-pulse generator. Author’s certificate No. 303720, Bulletin of Inventions No. 16, 1971.

4. G. I. Zaidman. Square-pulse generator. Author’s certificate No. 320032, Bulletin of Inventions No. 33, 1971.

5. G. I. Zaidman. Pulse generator. Author’s certificate No. 403041, Bulletin of Inventions No. 42, 1973.

6. G. I. Zaidman, S. A. Zaidman. Transient processes in temperature-compensated stabilitrons. Izvestiya VUZov SSSR, “Priborostroenie,” vol. 15, 1972, No. 2.