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METHODOLOGICAL NOTES
EDUCATIONAL DEMONSTRATION OF FREQUENCY-MODULATED OSCILLATIONS
V. S. Etkin
Frequency modulation is widely used in radio engineering and technical physics, but clear demonstrations of this relatively complex phenomenon are lacking. This is explained by the fact that the modulators with reactance tubes used in practice are rather complex in their circuitry and are designed to produce a relatively small change in frequency, which is difficult to observe. Increasing the modulation depth introduces distortions and leads to instability of the oscillations. To restore stability, additional devices are required, which further complicate the circuit.
For an educational demonstration it is desirable to have a modulation depth that would ensure clearly visible changes in the oscillation frequency on the screen of an electronic oscilloscope; in addition, it is desirable that the circuit used be as simple as possible.
In the device described, a method is used for changing a parameter of the circuit (the inductance), based on the nonlinearity of the magnetization curve of iron and on a change in the mutual-induction coefficient of coupled circuits.
The generator (Fig. 1) is assembled according to a three-point circuit with a midpoint in the capacitive branch; the coil of the circuit is inductively coupled to a modulating coil, supplied with current at the mains frequency (50 cycles). The change in modulation depth is achieved by the rheostat \(R_M\) and by moving the coils along a common iron core, which forms a closed magnetic circuit; the cross section of the iron is \(1 \text{ cm}^2\). The oscillation frequency of the generator in the absence of modulation is 650 cycles.
For all possible values of the frequency deviation (reaching 50%), the simplicity and clarity of the circuit are retained.
To obtain a stable, clear picture on the oscilloscope screen, it is necessary that the carrier frequency be a multiple of the modulation frequency and of the sweep frequency. To achieve this, use is made of,
V. S. ETKIN
besides the synchronizing devices of the oscilloscope, the rheostat \(R_c\) in the bias circuit, and the relative displacement of the coils of the circuit and the modulator.
Since, in order to obtain a sufficient frequency deviation, the modulation depth has to be chosen rather large, the frequency-modulated signal also turns out to be strongly modulated in amplitude. To eliminate the amplitude modulation, the signal
Fig. 1. Parameters.
| Tubes | Capacitances | Resistances | Inductances |
|---|---|---|---|
| Л1—6С5 | \(C_1=C_2=0.01\,\mu\text{F}\) | \(R_1=R_2=200\,\text{k}\Omega\) | \(L_1=1\,\text{H}\) |
| Л2—6Ф5 | \(C_3=150\,\text{pF}\) | \(R_3=2\,\text{k}\Omega\) | \(L\)—about 8000 turns on 10 cm |
| Л3—6Ф5 | \(C_4=C_5=0.005\,\mu\text{F}\) or \(0.01\,\mu\text{F}\) | \(R_{g0}=1.0\,\text{k}\Omega\) | \(L_M=5000\) turns on 2 cm |
| \(C_0=20\,\mu\text{F}\) | \(R_{g1}=R_{g2}=900\,\text{k}\Omega\) | ||
| \(C_6=0.01\,\mu\text{F}\) | \(R_c=4.7\,\text{k}\Omega\) | ||
| \(R_M=10\,\text{k}\Omega\) |
is passed through a limiter; thus, the given circuit can also serve as an independent demonstration of the operation of a limiter.
Frequency detection is carried out by connecting, in parallel to the output of the limiter, an oscillatory circuit tuned to a frequency somewhat different from the carrier frequency.
As a result, an amplitude-modulated signal is obtained, the depth of whose amplitude modulation is determined by the frequency modulation of the original signal. This amplitude-modulated signal can then be detected in the usual way. The frequency variation in this signal is preserved, but it does not affect the subsequent transformations of the signal—the extraction and amplification of the audio frequency.
The operation of the apparatus described is illustrated by the following oscillograms (Fig. 2):
Fig. 2.
Oscillogram 1 shows the unmodulated oscillation, and oscillogram 2 the frequency-modulated oscillation (the oscilloscope was connected at points 1—2).
Oscillogram 3 shows the unmodulated oscillation, and oscillogram 4 the modulated oscillation after it has passed through the limiter (the oscilloscope was connected at points 3—4); in this case the frequency detector was switched off.
Oscillogram 5 shows the unmodulated signal, and oscillograms 6 and 7 the modulated signal after passing through the frequency detector (the oscilloscope was connected at points 3—4 with the frequency detector switched on); oscillograms 6 and 7 correspond to different depths of frequency modulation.
The work was carried out in the radio-engineering laboratory of the Moscow State Pedagogical Institute named after V. I. Lenin at the suggestion of Prof. Malov, under the direction of assistant A. Ya. Volkova, to whom the author is deeply grateful for her attentive supervision.