STEP VOLTAGE GENERATOR WITH CONTROLLABLE CONVERSION COEFFICIENT

V. K. Zhukov, I. I. Tolmachev, Yu. A. Kilin

(Presented by the scientific seminar of the Department of Information and Measurement Technology)

The paper describes a uniformly stepped voltage generator (SVG) used in a pulse voltmeter of scanning balancing.

The construction of an SVG with a small number of steps can be carried out by means of relays or electronic threshold devices. When operating in an amplitude voltmeter, the number of SVG steps determines the number of quantization levels of the measured input voltage, i.e., determines the discreteness error. For a three-digit voltmeter, the number of pulses chosen was \(N = 1000\), which corresponds to a discreteness error \(\gamma_{\text{d}} = 0.1\%\). For constructing an SVG for such a number of pulses, the most acceptable is the SVG described in [1], based on a capacitive divider (Fig. 1).

Fig. 1. Step voltage generator based on a capacitive divider.

Fig. 2. Step voltage generator based on a capacitive divider with a cathode follower.

Rectangular pulses of constant amplitude \(U_0\) are applied to the input of the SVG. Diode \(D_1\) is open for positive input pulses, and capacitors \(C_1\) and \(C_2\) form a capacitive voltage divider. During passage of the first voltage pulse at the SVG output

\[ \Delta U_1 = U_0 \cdot \frac{C_2}{C_1 + C_2}. \tag{1} \]

In the interval between the first and second pulses, diode \(D_2\) opens and capacitor \(C_2\) discharges. Diode \(D_1\) is closed during this time, and the voltage \(\Delta U_1\) across capacitance \(C_1\) changes only slightly if the load resistance is large. The second input pulse increases the voltage on capacitor \(C_2\) by one more step,

\[ \Delta U_2 = \frac{C_2}{C_1 + C_2}\cdot (U_0 - \Delta U_1). \tag{2} \]

After the arrival of the \(N\)-th pulse, the output voltage will increase by

\[ \Delta U_N = \frac{C_2}{C_1 + C_2}\cdot \left( U_0 - \sum_{i=1}^{N-1} \Delta U_i \right). \tag{3} \]

It follows from this that, as \(N\) increases, the magnitude of the step decreases. The error of the SVG arising for this reason will be small if

\[ N \cdot \Delta U_1 \ll U_0. \tag{4} \]

However, in this case the utilization factor of the rectangular pulse will be small. To eliminate this shortcoming, a cathode follower is inserted into the circuit between the anode of diode \(D_2\) and ground; its input is connected to the SVG output, and its output to the anode of diode \(D_2\). Now, after the passage of the first pulse, capacitor \(C_2\), through the open diode \(D_2\) and the output resistance of the cathode follower, will discharge not to zero, but to the voltage

\[ U_{C_2} = \Delta U_1 \cdot K_{\text{cf}}, \tag{5} \]

where \(K_{\text{cf}}\) is the voltage transmission coefficient of the cathode follower.

In the case where \(K_{\text{cf}} = 1\), the second step of the output voltage is

\[ \Delta U_2 = \frac{C_2}{C_1 + C_2}(U_0 + U_{C_2} - \Delta U_1) = \frac{C_2}{C_1 + C_2}\cdot U_0 = \Delta U_1. \tag{6} \]

The \(N\)-th step of the output voltage is

\[ \Delta U_N = \frac{C_2}{C_1 + C_2}\cdot (U_0 + U_{C_2} - \Delta U_{N-1}) = \frac{C_2}{C_1 + C_2}\times \]

\[ \times (U_0 + \Delta U_{N-1} - \Delta U_{N-1}) = \Delta U_1, \tag{7} \]

that is, all the steps will be equal.

The main error of the SVG arises from the fact that the voltage transmission coefficient of the cathode follower \(K_{\text{cf}} \ne 1\).

Possible variants of constructing an SVG on a tube and on a field-effect transistor are possible. A generator using a pentode cathode follower has a large input resistance and better frequency properties, which makes it possible to apply short pulses with a high repetition frequency to its input. Field-effect transistors, in comparison with a pentode, have poorer frequency properties and high temperature instability. Therefore, in the present work an SVG with a pentode cathode follower is investigated.

The basic circuit diagram of the SVG is shown in Fig. 3. The circuit for controlling the amplitude of the pulses applied to the input of the SVG is assembled on transistors \(T_1\) and \(T_2\). An emitter follower is assembled on transistor \(T_2\), which repeats the voltage set at its base by means of a divider consisting of switch bank \(P58\) and resistance \(R_9\). This follower

Fig. 3. Schematic circuit diagram of the SVG.

sets the supply voltage for transistor \(T_1\), operating in the switching mode. By changing the voltage at the base of transistor \(T_2\), we change the pulse amplitude at the collector of transistor \(T_1\). Transistor \(T_3\) serves to reduce the nonlinearity of the characteristic for controlling the SVG conversion coefficient.

The SVG proper is assembled using capacitors \(C_1\), \(C_2'\), \(C_2''\) and diodes \(D_1\) and \(D_2\). The uniformity of the step voltage is achieved by connecting a cathode follower on a pentode. A special feature of the cathode-follower circuit is that a dynamic load is included in the circuit, on transistor \(T_4\), which is connected in a common-base configuration and operates as a current stabilizer.

In the initial state the storage capacitance is discharged and the grid potential is equal to zero. By means of resistor \(R_{11}\), a zero potential is set at the output of the cathode follower (at point A). Diode \(D_4\) serves to protect transistor \(T_4\) and limits its collector voltage at the level of \(+12\) V.

The block diagram for testing the SVG and the timing diagrams are shown in Fig. 4. In the initial state switch \(K_1\) is closed and shunts the collector-emitter junction of the transistor in one arm of the symmetrical multivibrator, operating as a pulse generator (PG), thereby ensuring disruption of oscillation. Switch \(K_2\) is also open and discharges capacitor \(C_1\) in the SVG. The working cycle begins with the single-pulse generator (SPG), upon an operator’s command, issuing short pulses that flip trigger \(T_g\) to position 1. Switches \(K_1\) and \(K_2\) close, and the PG begins to apply rectangular pulses to the SVG input. For each input pulse, the SVG produces a voltage step \(\Delta U\) at its output. From the SVG output, the step voltage \(U_x\) is applied to the comparison device (CD), where it is compared with the reference voltage \(U_e\). At the moment when \(U_e = U_x\), the CD operates and issues short pulses that reset the trigger to position 0. The circuit returns to its initial state; in this process, a packet of pulses passes to the pulse counter (PC), the number of which is equal to the number of steps in the SVG output voltage.

The number of pulses arriving at the SVG input can be determined as

\[ N = \frac{U_e}{\Delta U}. \tag{8} \]

Substituting \(\Delta U\) from (7) into (8), we obtain,

Fig. 4. Block diagram for testing the GSN and timing diagrams.

\[ N=\frac{U_{\mathrm{e}}}{U_0}\cdot\frac{C_1+C_2}{C_2}. \tag{9} \]

It follows from this that the number of pulses at the input of the GSN is directly proportional to the reference voltage at the SU and inversely proportional to the amplitude of the input pulses. Thus, by adjusting the amplitude of the input pulses \(U_0\), one can vary the conversion coefficient of the GSN and measure voltage ratios.

The main error of the GSN is the nonlinearity of the characteristic \(N=f(U_{\mathrm{e}})\), arising because the transfer coefficient of the cathode follower \(K_{\mathrm{cf}}\ne 1\). The results of testing the GSN for nonlinearity are shown in Fig. 5. In this case, the actual values \(N_{\mathrm{d}}\) were compared with the values of points lying on the approximating straight line drawn through the two end points (\(U_{\mathrm{e}}=0\) and \(U_{\mathrm{e}}=10\) V). From the table

Fig. 5. Testing the GSN for nonlinearity.

it is seen that the maximum relative error is \(\gamma_{\text{rel max}}=1.1\%\), and the maximum reduced error is

\[ \gamma_{\text{red max}}=\frac{278-275}{918}\cdot 100\% = 0.3\%. \]

The occurrence of temperature error in the SGV is due mainly to three factors:

1. Under the influence of temperature the capacitance values \(C_1\), \(C_2'\), \(C_2''\) change, and the ratio

\[ \frac{C_2' + C_2''}{C_1 + C_2' + C_2''}, \]

changes, that is, the magnitude of the generator step \(\Delta U\) changes. To eliminate this phenomenon, the TCCs of the capacitors were chosen so that, when the temperature changes, the ratio

\[ \frac{C_2' + C_2''}{C_1 + C_2' + C_2''} \]

changes only weakly. For this purpose the following were selected:

\[ \begin{aligned} C_1&=0.1\ \mu\mathrm{F}, && \mathrm{TCC}=-0.0075\ \%/\mathrm{deg},\\ C_2&=91\ \mathrm{pF}, && \mathrm{TCC}=-0.0050\ \%/\mathrm{deg},\\ C_2''&=8.2\ \mathrm{pF}, && \mathrm{TCC}=-0.07\ \%/\mathrm{deg}. \end{aligned} \]

1. As the temperature increases, the thermal current of transistor \(T_4\) increases and the potential of point \(A\) increases (Fig. 3), which is equivalent to an increase in the reference voltage \(U_{\mathrm{e}}\). To obtain good temperature stability of the generator, a thermistor with a positive TCR, wound from copper wire, is included in the emitter circuit of transistor \(T_4\); it compensates the increase in the transistor’s thermal current as the temperature rises.

2. As the temperature increases, the leakage currents of diodes \(D_1\) and \(D_2\) increase, which may cause the capacitance \(C_1\) to discharge in the pause between pulses. To eliminate this, silicon diodes \(D_{105}\) with low leakage currents were selected.

The results of testing the SGV for temperature instability are shown in Fig. 6. The curve has a markedly nonlinear character, since several temperature-dependent elements participate in the process. From the graph in Fig. 6 it is seen that, in the temperature range \((20\div 50)^\circ\mathrm{C}\), the SGV has a temperature error not exceeding \(\pm 0.2\%\).

To determine the control characteristic of the conversion coefficient, \(U_{\mathrm{e}}=10\ \mathrm{V}=\mathrm{const}\) was set. Then expression (9) can be written as

\[ N=\frac{U_{\mathrm{e}}}{U_0}\cdot \frac{C_1+C_2}{C_2}=\frac{K}{U_0}, \tag{10} \]

where \(K\) is a constant coefficient.

Fig. 6. Testing the SGV for temperature instability.

Fig. 7. Control characteristic of the conversion coefficient.

The dependence \(N=f(U_0)\) for \(U_{\mathrm{in}}=\mathrm{const}\) is shown in Fig. 7. Taking the middle point (at \(U_0=9\ \mathrm{V}\)) as the reference, we calculate the coefficient for it:

\[ K=N\cdot U_0=1310\cdot 9.0=11800. \]

Comparing this value with the coefficients at the edges of the range (at \(U_0=8\ \mathrm{V}\) and \(10\ \mathrm{V}\)), we find that the maximum nonlinearity of the coefficient is \(\gamma_{k\max}=0.4\%\).

REFERENCES

1. P. P. Ornatskii. Automatic Measuring Instruments. Kiev, “Tekhnika,” 1965.