Theory: calculation of oscillatory circuits. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur
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The considerations below are valid not only for oscillator circuits, but also for any others used in radio engineering devices, for example, in radio receivers. We have already given the formula for the tuning frequency of the circuit, and it can be successfully used by substituting all the data in basic units: capacitance - in farads, inductance - in henry. The answer will, of course, be in hertz. To simplify the calculations, you can substitute the capacitance in nanofarads (thousands of picofarads), and the inductance in millihenry, then the answer will be in megahertz: f = 0,16 / (LC) 1/2
RF oscillatory circuits are often tuned in frequency using variable capacitors (CPCs). Typical capacitance ranges for such capacitors are 5 ... 180, 5 ... 360 or 17 ... 500 pF. When calculating, it is also necessary to take into account the small intrinsic capacitances of the coil, installation and the input capacitance of the cascade connected to the circuit. They add relatively little to the maximum capacitance of the KPI, but significantly increase the minimum capacitance of the circuit, narrowing the tuning range.
In order to equalize the minimum capacitances of several simultaneously tunable circuits, trimmer capacitors (C1 and C3 in Fig. 52) are connected in parallel to the sections of the KPI block.
In practice, the capacitance of the tuned circuit changes no more than 10 times, which gives only a threefold change in frequency. Coincidence of the circuit settings at the low-frequency edge of the range is achieved by changing the inductance of the coils, for which they are supplied with magnetodielectric trimmers (ferrite, magnetite, etc.). Typical values of the inductance of medium-wave coils are about 200 μH, long-wave - 2 mH.
The greatest difficulty for radio amateurs is the calculation of the number of turns of coils. The exact formula is derived for a solenoid with a winding length much larger than the diameter: L = μμ0N2S/L1 where μ is the magnetic permeability of the magnetodielectric; μ0 = 4π 10-7 H/m - magnetic constant; N is the number of turns; S is the cross-sectional area of the coil; (- winding length. When substituting the dimensions in meters, the answer is in henry. The same formula gives very good results for toroidal coils wound on ferrite rings. The winding length in this case is the circumference of the ring's center line.
For ferrite antennas, the formula is also suitable, but since the magnetic circuit is not closed, it is necessary to take the effective value of μ, which for widely used rods with a magnetic permeability of 400-1000 is only 50 ... 150. Typical values of the number of turns of the coils of magnetic antennas of the MW range are 50 ... 70, LW - 200 ... 250.
As already mentioned in section 7.3, to increase the quality factor of the DV and MW, the coils are wound with a LESHO wire twisted from several (from 7 to 81) thin insulated conductors. In the absence of such a wire, it can be made independently from a PEL wire with a diameter of 0,07-0,1 mm. When desoldering the leads, they are stripped, twisted and soldered together. Broken or unsoldered conductors reduce the Q factor of the coil.
Short-wave coils are wound with a single-core copper wire with a diameter of 0,4-1,5 mm, preferably silver-plated, but PEL brand wire can also be used. The inductance of a single-layer cylindrical coil (in μH) can be determined by the empirical formula: L \u2d DN102 / (45L / D + 10), into which the diameter D and the length of the winding L are substituted in cm. To increase the quality factor, winding should be carried out in increments (i.e. . gap between the turns), approximately equal to the diameter of the wire. Do not try to make the coil too small - the quality factor of small coils is less! The number of turns of KB coils usually does not exceed 20...XNUMX.
Often, radio amateurs have to use ready-made coils, for example, from the circuits of old broadcasting receivers or televisions. The question arises, how to rebuild the circuit to a different frequency? Here it is useful to mention a few simple laws: the inductance of a coil with fixed dimensions is always proportional to the square of the number of turns, therefore, in order to double the inductance, for example, it is necessary to increase the number of turns by 1,4 times. In this case, the circuit tuning frequency with a fixed capacitance decreases by a factor of 1,4 - it is inversely proportional to the number of turns. It is curious that the wavelength to which the circuit is tuned is directly proportional to the number of turns of the coil, and hence the length of the wire.
In conclusion, we note that circuits with a very large inductance with a small capacitance look ridiculous and work poorly, or vice versa. Indeed, with a small circuit capacitance, all kinds of parasitic capacitances begin to play an important role: the interturn capacitance of the coil, the mounting capacitance, the intrinsic capacitance of the parts connected to the loop, etc. Too low loop inductance at high capacitance leads to an increase in the role of parasitic inductance of the connecting wires, as well as lowering the resonant resistance of the circuit, equal to pQ. The characteristic resistance of the circuit p \u1d (LC) 2/XNUMX is usually chosen from hundreds of Ohms to several kOhms.
Author: V.Polyakov, Moscow
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