AMPLITUDE-STABLE SINE-WAVE VOLTAGE GENERATOR

M. S. ROITMAN, Yu. K. RYBIN, V. I. CHUFISTOV

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

The construction of generators based on a highly selective frequency-selective system and an inertia-free nonlinear element makes it possible to approach the resolution of the contradiction between the requirements of a low level of nonlinear distortion and the stability of the amplitude of self-oscillations [1].

The main difficulty in implementing such a generator consists in creating a selective frequency-selective system with a low level of introduced nonlinear distortions and a significant suppression factor (more than 1000) at the frequencies of the higher harmonic components.

One version of an amplifier satisfying the stated requirements is shown in Fig. 1. Its principal difference from an amplifier with negative feedback (NFB) through a rejector filter is the presence of an additional path for the signal to pass to the output. In this circuit the signal from the output of the rejector filter is supplied, as usual, through the NFB circuit to the amplifier input and simultaneously to the output subtracting summator. Here it is possible to increase the suppression factor and reduce the level of introduced distortions both through the NFB circuit and by compensation of the isolated signal in the summator. In this case, to achieve large suppression factors one may limit oneself to comparatively shallow NFB, which sharply simplifies the implementation of the selective amplifier as a whole.

Fig. 1

The transfer coefficient of the amplifier has the form

\[ K(j\omega)=K\frac{1-T(j\omega)}{1+KT(j\omega)}\ldots \tag{1} \]

where
\(K\) is the gain coefficient of the broadband amplifier,
\(T(j\omega)\) is the transfer coefficient of the active rejector filter (ARF).

It follows from formula (1) that, in order to increase the effectiveness of the additional subtraction circuit and to obtain the inequality \(1-T(j\omega)<0.05\) already at the frequencies of the 2nd and 3rd harmonics, it is necessary to have a filter with a quality factor of \(20 \div 30\). All these requirements are met by a filter containing a passive \(RC\) network and a repeater. If, as the \(RC\)-ne…)

... and use a \(2T\!-\!RC\) bridge, then the transmission coefficient of the ARF can be represented as

\[ T(j\omega)=K_{\mathrm{p}}\frac{T_0+jQY}{1+jQY}\ldots, \tag{2} \]

where \(K_{\mathrm{p}}\) is the transmission coefficient of the follower,

\(T_0\) is the transmission coefficient at \(Y=0\),

\[ T_0 \simeq \frac{t_0}{1-K_{\mathrm{p}}}, \]

\(Y\) is the generalized detuning, \(Y=\dfrac{\omega}{\omega_0}-\dfrac{\omega_0}{\omega}\);

\(\omega_0\) is the rejection frequency;

\(Q\) is the quality factor of the ARF, \(Q=\dfrac{q}{1-K_{\mathrm{p}}}\);

\(q\) is the quality factor of the \(2T\!-\!RC\) bridge;

\(t_0\) is the transmission coefficient of the \(2T\!-\!RC\) bridge at \(Y=0\).

Taking (2) into account, expression (1) can be written in the form

\[ K_{(j\omega)}=K_{(jY)}=K\frac{1-T_0}{1+T_0K}\cdot \frac{1}{1+jQ\frac{1+K}{1+KT_0}Y}\ldots \tag{3} \]

This expression coincides (apart from the first factor) with the transfer function of an amplifier with a single-tuned \(LC\) filter [2], with equivalent quality factor:

\[ Q_{\mathrm{e}}=Q\frac{1+K}{1+KT_0}\simeq q\frac{1}{1-K_{\mathrm{p}}}\cdot\frac{1+K}{1+KT_0}\ldots \tag{4} \]

With careful adjustment of the null circuit in the ARF, \(T\to 0\), and then

\[ K_{(jY)}\simeq \frac{K}{1+jQ_{\mathrm{e}}Y} \quad \text{and} \quad Q\simeq \frac{q}{1-K_{\mathrm{p}}}(1+K)\ldots \tag{5} \]

From formula (5) it may be concluded that the equivalent quality factor of the selective amplifier is determined by the quality factor of the \(2T\!-\!RC\) bridge, the transmission coefficient of the follower \(K_{\mathrm{p}}\), and the depth of the negative feedback \(F\simeq 1+K\); consequently, with a small negative-feedback depth \((30\div 50)\), \(K_{\mathrm{p}}=0.98\div 0.99\), and \(q=0.25\), it is comparatively easy to obtain \(Q_{\mathrm{e}}=1000\) and more. It should be noted that, to realize the same quality factor in an amplifier with a passive \(RC\) circuit, the required depth of negative feedback is \(F=4000\), which is practically unattainable over a wide frequency range.

A large value of the equivalent quality factor also makes it possible to provide high suppression at the frequencies of higher harmonics; thus, the suppression coefficient at the frequency of the \(n\)-th harmonic is

\[ K_{\mathrm{r}n}=\frac{|K_{(\omega_0)}|}{|K_{(n\omega_0)}|} =\sqrt{1+Q_{\mathrm{e}}^2Y_n^2}, \]

where \(Y_n\) is the generalized detuning at the frequency of the \(n\)-th harmonic; it can reach 1500 (for \(Q=1000\)) already at the 2nd harmonic and increases as the harmonic number increases. Here it is necessary to note that, at the boundaries of the frequency range, the nonideality of the output adder may have an effect. Clearly, the adder must not introduce amplitude- and phase-frequency distortions at the harmonics, nor additional nonlinear distortions. These requirements are best satisfied by a passive adder using resistors or a transformer.

Important for the generator under consideration is the question of the constancy of the amplitude of self-oscillations, which is determined primarily by the stability of the transfer coefficient of the selective amplifier at the quasiresonance frequency, which in turn is determined mainly by the stability of the transfer coefficient of the notch circuit at the rejection frequency.

The sensitivity of the transfer coefficient to a change in \(t_0\) is determined by the expression

\[ S^{t_0}=\frac{\dfrac{dK}{K}}{\dfrac{dt_0}{t_0}} \simeq \frac{1+K}{1-K_{\mathrm{p}}}\,t_0 \ldots \tag{6} \]

In the case under consideration, \(S^{t_0}\) depends on the value of \(t_0\) and worsens in proportion to the increase in the quality factor \(\left(Q_{\mathrm{e}}=q\,\dfrac{1+K}{1-K_{\mathrm{p}}}\right)\). Consequently, serious attention must be paid to the quality of the elements of the \(RC\) circuit and to the accuracy of its tuning, so as to reduce \(t_0\) as much as possible. Very good results in this respect are obtained by using monolithic notch filters based on a distributed \(RC\) line. Such filters are distinguished by high stability of the transfer coefficient near the rejection frequency.

Here it is also necessary to point out one possibility for increasing the suppression coefficient at the frequencies of the higher harmonics without increasing the quality factor and, consequently, without worsening the stability of the transfer coefficient at the quasiresonance frequency. It consists in forming an attenuation pole at the frequency of one of the harmonics; since the predominant higher harmonic at the output of a symmetrical limiter is the 3rd harmonic, it is desirable to provide the attenuation pole precisely at the frequency of the 3rd harmonic. For this purpose a phase-correcting section is introduced into the selective amplifier (Fig. 2).

Fig. 2

The idea of the solution consists in creating, for the 3rd harmonic, two transmission channels to the output summing circuit, in which, when the transfer coefficients are equal and opposite in phase, their mutual compensation is ensured. To provide exact phase opposition, a phase-correcting section is introduced, which does not have a noticeable effect on the stability of the transfer coefficient at the tuning frequency. As the phase-correcting section one may use a proportional-integrating filter, which is shown in Fig. 3.

Fig. 3

To ensure the required constancy of the oscillation amplitude in the generator, an automatic voltage-control system may be used. If, as the measuring transducer (MT), a rectifier with a single-section filter is used, then a second-order system is obtained.

Fig. 4. Schematic diagram of the amplitude-stable sine-wave voltage generator.

order (the selective amplifier for the envelope is a first-order link), stable for any value of the stabilization coefficient. In this case, amplitude stability is determined by the quality of the PS and the constancy of the reference dc voltage.

The schematic diagram of an amplitude-stable generator based on a highly selective amplifier is given in Fig. 4.

The selective amplifier is assembled on transistors \(T3 \div T10\); its wideband amplifier is made according to a circuit with a dynamic load on transistors \(T3 \div T5\), the active rejection filter is made on small-size rejection filters RF1–3 of type FRM-1 and transistors \(T6, T7\), and the output summator is on transformer Tr. The automatic output-voltage stabilization circuit includes an operational rectifier on integrated circuit 1UT401A and diodes \(D11 \div D15\), a comparison circuit on resistors \(R36, R39\), a mismatch amplifier made on another 1UT401A integrated circuit, and a regulating element, for which field-effect transistor \(T1\) is used.

Main characteristics of the mock-up

1. Output voltage . . . . . \(10\ \text{V}\)
2. Load resistance . . . . . \(200\ \Omega\)
3. Frequency range \(20\ \text{Hz} \div 20\ \text{kHz}\), discrete.
4. Nonlinear-distortion coefficient over the entire frequency range . . . . . \(< 0.04\%\)
   at mid-range frequencies . . . . . \(< 0.003\%\)
5. Amplitude instability . . . . . \(< 0.03\%\)

REFERENCES

1. M. S. Roitman, “Precision Measures of Alternating Voltages,” in the present collection.

2. N. S. Gonorovskii. Radio-Engineering Circuits and Signals. Moscow, “Sovetskoe radio,” 1972.