RC Swept-Frequency Oscillator
Abstract Generated abstract
This paper describes a simplified swept-frequency oscillator for measuring the frequency characteristics of low-frequency four-terminal networks, using an RC oscillator with photoresistors in the positive-feedback path instead of a beat-frequency arrangement. The authors discuss the conditions for stable operation, emphasizing the need for matched photoresistor characteristics and suitable selection of components for amplitude-stabilizing negative feedback. They derive the expected frequency coverage from the photoresistor resistance ratio and note practical limits due to imperfect matching and lamp inertia. Experiments on a mock-up showed that frequency coverage above 100 is readily attainable with output-voltage variation of about 5 percent, provided the sweep frequency does not exceed roughly 1 Hz.
Full Text
RC Swept-Frequency Oscillator
V. K. Zhukov, A. V. Erokhin
(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)
For measuring the frequency characteristics of four-terminal networks (low-frequency filters, low-frequency amplifiers), it is convenient to use a swept-frequency oscillator (SFO). The most common circuit used for this purpose is a beat-frequency oscillator circuit, consisting of two high-frequency oscillators, a mixer, and a low-frequency amplifier. The frequency of one of the oscillators is stabilized by a quartz crystal, while that of the other is varied within small limits by a reactance tube.
A swept-frequency oscillator is simpler if an RC oscillator circuit is used with photoresistors in the positive-feedback circuit. The photoresistors are illuminated by incandescent lamp L₁, whose supply voltage varies according to a sawtooth law (Fig. 1). In accordance with the change in the supply, the value of the photoresistance will vary approximately according to a logarithmic law.
Fig. 1. Schematic diagram of an RC swept-frequency oscillator.
To stabilize the amplitude and reduce the harmonic coefficient, the oscillator is provided with reflex negative feedback through photoresistor \(R_3\) and lamp L₅. Operation of the oscillator at a fixed frequency with such amplitude stabilization is described in [1].
In order to obtain the greatest possible frequency deviation, it is necessary to use, in the positive-feedback circuit, photoresistors with a large ratio of variation, such as FS-D, FSK-M, and FSK-2N.
Stable operation of range RC oscillators is ensured under the condition that...
\[ \frac{1}{1+\sqrt{\dfrac{R_2^2}{R_1^2}+\dfrac{C_1^2}{C_2^2}+\dfrac{R_2C_1}{R_1C_2}}}=\text{const}, \]
which, for a constant ratio \(\dfrac{C_1}{C_2}\), is satisfied when \(R_1\) and \(R_2\) vary identically. In the present case this requirement leads to the necessity of selecting, for the positive-feedback circuit, photoresistors with identical characteristics \(R_\phi=f(U_l)\). Fulfillment of this condition can be achieved to some extent (in addition to selecting photoresistor specimens) by changing the distance between the filament of the incandescent lamp and the surface of the photoresistor.
It is known that the frequency of an \(RC\) oscillator is equal to
\[ \frac{1}{2\pi RC}\quad \text{for } R_1=R_2=R \text{ and } C_1=C_2=C, \]
and the coverage factor for a range oscillator is
\[ K=\frac{f_{\mathrm{v}}}{f_{\mathrm{n}}}=\frac{R_{\max}}{R_{\min}}, \]
therefore the range coverage factor will be equal to the ratio of the photoresistors used, which, in the case of using FSK-M or FSK-2N, gives a value of \(10^3\div 10^4\). In practice this value is somewhat lower because it is impossible to select photoresistors with identical characteristics \(R_\phi=f(U_l)\) over the entire range of variation of \(R_\phi\).
When choosing the type of photoresistor for the negative-feedback circuit, one must be guided by the following considerations.
The feedback coefficient of the oscillator is equal to
\[ K_{\mathrm{fb}}=\frac{R_4}{R_3+R_4}\simeq \frac{1}{3}. \]
\(R_4\) is chosen from the condition of ensuring the operating mode of tube \(L_2\), and for different types it may vary from 500 to 1.5 kΩ; consequently, the value of the photoresistor should be approximately \(1\div 3\) kΩ. Such a low resistance in the illuminated state is found in photoresistors of the FSK-2N type, whose minimum value may reach 100 Ω. The use of photoresistors with a low value of \(R_\phi\) in the illuminated state provides a large value of
\[ \frac{dR_\phi}{dU_l} \]
at the operating point, which has a favorable effect on the stability of the oscillator amplitude.
The proper choice of the sweep frequency has a great influence on the constancy of the oscillator amplitude over the sweep range. Experiments show that it should not exceed 1 Hz, since otherwise the inertia of the incandescent lamps \(L_4\) and \(L_5\) begins to have an effect, which is manifested in a decrease in the frequency deviation and in an increase in the amplitude variation over the sweep range.
The operation of the oscillator was investigated experimentally on a mock-up. The investigations showed that a frequency coverage exceeding \(10^2\) can readily be obtained with variation of the output voltage over
of the sweep range is about 5%. The deviation and the initial frequency \(f_{\min}\) are easily adjusted by changing the voltage on \(L_1\).
REFERENCES
- M. S. Roitman, V. K. Zhukov. Application of photoresistors for voltage stabilization. Proceedings of the Second Conference on Automatic Control and Methods of Electrical Measurements, Siberian Branch of the USSR Academy of Sciences, 1960.