HIGH-FREQUENCY TRANSISTOR-BASED CALIBRATOR GENERATOR

Yu. M. Fomichev, Yu. N. Varakuta

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

In connection with new developments of broadband converters of alternating current into direct current, it became necessary to expand the frequency range of the apparatus used for their testing. At present there is an urgent need for equipment that is simple to operate and has high metrological properties (of the GK-10 type [1]), with a frequency range extended to 1 MHz. The circuit solutions used in the GK-10 [1] prove unsuitable at frequencies above 100–200 kHz because of the sharp increase in nonlinear distortions. Therefore, in the new development of the broadband calibrator generator GK-11, it was necessary to change both the functional and the electrical circuit, although the principle of constructing the calibrator as a static automatic-control system with an rms-value comparator in the feedback loop [2] remained the same.

The GK-11 consists of two generator units: a low-frequency generator—10 Hz–30 kHz, and a high-frequency generator—30 kHz–1 MHz, which operate depending on the selected frequency and on a common loop for automatic stabilization and calibration of the output level (Fig. 1). In the low-frequency part of the GK-11 (up to 30 kHz), the circuit solutions adopted in the GK-10 [1] are used without any special changes.

At frequencies above 30 kHz, a circuit of a two-stage LC oscillator with inductive positive feedback is used.

Because of the high output resistance of the HF generator*) in order to improve its load characteristic, a large transmission coefficient is required in the stabilization loop for the rms value of the output level, and this requires providing a stability margin.

To reduce the order of the system, its regulating device is made on a field-effect transistor with an insulated gate (an inertia-free element), but this proves insufficient. Let us consider the structural diagram of the high-frequency generator together with the loops for stabilizing the rms value of the output level (Fig. 2), where

\(K_1(p),\ K_2(p)\) are the transfer functions of the first and second stages of the oscillator amplifier,

\(K_{\mathrm{FPC}}(p)\) is the transfer function of the photoelectric converter of the comparator.

*) In the adopted circuit it is not possible to introduce negative feedback with high effectiveness.

$K$ — transfer coefficient of the error amplifier,
$K_{\rho}(I, U_y)$ — transfer coefficient of the regulating device,
$K_{\text{п}}$ — transfer coefficient of the positive-feedback circuit.

Fig. 1

Fig. 2

Starting from this equivalent circuit, we write the characteristic equation in the form

\[ (1 + S_1 R_0)\tau_1 \tau_2 \tau_{\text{л}} \tau_{\phi} p^4 + (1 + S_1 R_0)\left[(\tau_1 + \tau_2)\tau_{\text{л}}\tau_{\phi} + \tau_1\tau_2(\tau_{\text{л}} + \tau_{\phi})\right]p^3 \]
\[ + \left\{\left[(1 + S_1 R_0) - K_1K_2K_{\text{п}}\right]\tau_{\text{л}}\tau_{\phi} + (1 + S_1 R_0)\left[(\tau_1 + \tau_2)(\tau_{\text{л}} + \tau_{\phi}) + \tau_1\tau_2\right]\right\}p^2 \]
\[ + \left\{\left[(1 + S_1 R_0) - K_1K_2K_{\text{п}}\right](\tau_{\text{л}} + \tau_{\phi}) + (1 + S_1 R_0)(\tau_1 + \tau_2)\right\}p \]
\[ + \left[(1 + S_1 R_0) - K_1K_2K_{\text{п}} + K_1K_2K_sK_yK_{\phi\text{п}}\right] = 0, \]

where

$\tau_1,\ \tau_2$ — time constants of the first and second resonant stages;
$\tau_{\text{л}},\ \tau_{\phi}$ — time constants of the incandescent lamp and of the photoresistor of the photoelectric comparator converter;
$S_1$ — transconductance of the transistor of the first stage;
$R_0$ — active resistance of the regulating transistor at the operating point.

\[ K_s=\frac{dR/R}{dU/U} \]
—the control slope.

According to the Routh–Hurwitz criterion, a system described by a fourth-order equation is stable when the following conditions are satisfied [3, 4]:

\[ a_1>0,\quad a_3>0,\quad a_4>0,\quad a_3(a_1a_2-a_0a_3)-a_1a_4^{\,2}>0. \tag{1} \]

In the case under consideration,

\[ \begin{aligned} a_0&=(1+S_1R_0)\tau_1\tau_2\tau_l\tau_\phi,\\ a_1&=(1+S_1R_0)\bigl[(\tau_1+\tau_2)\tau_l\tau_\phi+\tau_1\tau_2(\tau_l+\tau_\phi)\bigr],\\ a_2&=\bigl[1+S_1R_0-K_1K_2K_{\mathrm p}\bigr]\tau_l\tau_\phi +(1+S_1R_0)\bigl[(\tau_1+\tau_2)(\tau_l+\tau_\phi)+\tau_1\tau_2\bigr],\\ a_3&=(1+S_1R_0-K_1K_2K_{\mathrm p})(\tau_l+\tau_\phi) +(1+S_1R_0)(\tau_1+\tau_2),\\ a_4&=(1+S_1R_0)-K_1K_2K_{\mathrm p}+K_1K_2K_sK_yK_{\phi r}. \end{aligned} \]

For the real case, \((\tau_l+\tau_\phi)\gg\tau_1+\tau_2\) and \(S_1R_0\gg1\). Taking this into account, solving inequalities (1), we find the stability condition and the permissible stabilization coefficient:

\[ K_{\mathrm p}\ll \frac{R_0}{R_{0e}\cdot K_2}, \tag{2} \]

\[ G_{\mathrm{st}}<\frac{1}{2}\frac{\tau_l+\tau_\phi}{\tau_1+\tau_2}\cdot \frac{\bigl[(1+S_1R_0)-K_1K_2K_{\mathrm p}\bigr]^2}{1+S_1R_0}, \tag{3} \]

where \(G_{\mathrm{st}}=K_1K_2K_sK_yK_{\phi r}\).

It follows from expression (3) that the smaller \(K_{\mathrm p}\) is, the larger the stabilization coefficient that can be obtained. \(K_{\mathrm p}\) cannot be reduced to zero, since its value is determined by the condition for the balance of the amplitudes of the self-oscillator. In this connection, the positive-feedback circuit must be made so that it provides the self-excitation condition of the self-oscillator and at the same time has a small transfer coefficient for increments of the first harmonic. Such a characteristic is possessed by a two-sided limiter using diodes under deep limiting.

Description of the schematic diagram

It has already been noted earlier that the low-frequency part of the GK-11 is made identically to the GK-10. The high-frequency generator is a two-stage selective LC amplifier, made with identical high-frequency transistors 2T602, covered by positive feedback \((C_{40}, D_4, D_5, C_{41})\) and negative current feedbacks in each stage \((R_{42}, T_{10})\) and \((R_{45}, R_{46})\) (Fig. 3). To ensure stability, the positive feedback is made nonlinear (a limiter using diodes \(D_4, D_5\)). The limiting level is set by variable resistors \((R_{36}, R_{38})\). The depth of the negative current feedback in the first stage is varied by means of a field-effect transistor \((T_{10})\) when a mismatch signal appears from the output of the differential comparator \((LN_2R_{51},\ LN_3R_{54},\ R_{52},\ R_{53},\ R_{55},\ R_{56})\).

The output stage of the HF generator is assembled according to a push-pull circuit \((T_{11}, T_{12})\). Coupling to the load is by transformer.

Technical characteristics of the GK-11

1. The error in setting the rms value of the output voltage (5 V) is less than 0.05%.

Fig. 3. Circuit schematic of the GKT-1

1. Instability of the output voltage:
   less than 0.01% over 10–15 minutes,
   not more than 0.1% over 2 hours.

2. Frequency range: 10 Hz–1 MHz (15 fixed points).

3. Nonlinear distortion:
   not more than 0.04% at frequencies of 55 Hz–30 kHz,
   0.01% at frequencies of 30 kHz–1 MHz.

REFERENCES

1. Yu. M. Fomichev, Yu. I. Latonov, A. V. Sokolov. Source of calibrated voltage GK-10. In the present collection.

2. M. S. Roitman, E. I. Tsimbalist, Yu. M. Fomichev. Device for obtaining a stable voltage calibrated by rms value. Inventor’s Certificate No. 196114. Bulletin of Inventions, 1967, No. 11.

3. I. S. Gonorovsky. Radio Engineering Circuits and Signals. Moscow, “Sovetskoe radio,” 1971, p. 296.

4. V. S. Andreev. Theory of Nonlinear Electrical Circuits. Moscow, “Svyaz,” 1972, p. 125.