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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING The mystique of short antennas. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Antennas. Theory When they want to praise the high sensitivity of the receiver, they often say that it, they say, receives signals from radio stations even on a "piece of wire". In this article, the author theoretically and experimentally proves that the notorious "piece of wire" is far from the worst antenna, and with proper coordination with the receiver input, it can provide a very large signal voltage. For broadcasting reception on long and medium waves, they used to be widely used, and even now, despite the widespread use of ferrite magnetic antennas, electric antennas are still often used in the form of a piece of ordinary wire located vertically. When working with such an antenna, grounding or a counterweight is required for good reception. In the simplest case, the body of the receiver serves as a counterweight, and if it is powered by the mains, then the wires of the power cord and the electrical network itself will be the counterweight. Horizontal wire antennas are rarely used, since all radio stations in the LW and MW bands emit waves exclusively with vertical polarization, which is associated with the properties of the Earth's surface that are close to those of a conductor for these ranges. Radio amateurs, especially those who have experimented with the simplest and insufficiently sensitive direct gain receivers, know that short wire antennas are very effective, in particular, a piece of wire 1 ... 2 m long often develops a much larger signal than a ferrite antenna. What is the secret? After all, the length of a wire antenna is immeasurably less than the wavelength, and according to all the canons, it should not be effective. Attempts to analyze the operation of a short vertical radio receiving antenna, as well as the desire to optimize it, led to very curious, and even surprising results, which the author offers to inquisitive readers. Optimization, in the sense of obtaining the maximum voltage at the receiver input (namely voltage, not power!), was reduced to the exclusion of the input circuit capacitor and replacing it with the capacitance of the antenna itself, as shown in Fig. 1. At the same time, the input impedance of the URF was assumed to be infinitely large, which is close to true when using a field-effect transistor on the DV and SV. The input capacitance of the URF and the capacitance of the coil are added to the capacitance of the antenna. We will not take them into account in our analysis.
On fig. 1 also shows the current distribution in the antenna, which is the initial section of the sinusoid. With sufficient accuracy, it can be considered triangular. Replacing it with a rectangle of the same area, we obtain the effective height of the antenna h, equal to half of its geometric height. The inductance of the coil is chosen such that, together with the capacitance of the antenna, to obtain resonance at the received frequency. The equivalent circuit of the resulting circuit is shown in fig. 2.
At resonance, the capacitive resistance of the antenna - Xc is equal to the inductive Xt (in absolute value) and the reactances compensate each other, therefore the current in the circuit is maximum and equal to e / R, where e is the EMF of the signal developed in the antenna (e \uXNUMXd Eh: E is the intensity field), and R is the active resistance of the circuit. Since the voltage at the input of the URC (U) is removed from the coil, it is equal to the current in the circuit multiplied by the inductive resistance of the coil: U = EhXL / R. We have a simple formula for calculating the voltage developed by the described antenna. The absolute value of the parameter XL =Xc is determined by the length of the antenna (the antenna capacitance is 7...15 pF per meter of length) and the received signal frequency f. Therefore Xc = 1/2πfC. The corresponding inductance is also easy to find: L = XL /2πf. E must be known, ah can be measured with a ruler. But the formula can be further simplified by noting that the ratio XL /R is nothing more than the quality factor Q of the antenna circuit: U = EhQ. With a short antenna, the quality factor of the entire circuit is almost equal to the quality factor of the coil. As an example, let's calculate a signal from a not too distant LW or MW radio station with a field strength of 10 mV/m, received on a piece of wire 2 m long (h = 1 m). We set the quality factor of the antenna circuit equal to 100. Having made simple multiplications of numbers, we arrive at a very surprising result - U = 1 V! This voltage is quite enough to detect a signal even without URF. But some reservations must be made. First, the coil must have a fairly large inductance. In our example, even in the middle of the MW band at a frequency of 1 MHz, the reactance XL is about 10 kOhm. the inductance is about 1.5 mH, and the resonant impedance of the antenna circuit, equal to XLQ, is close to 1 MΩ. The input impedance of the RF amplifier or detector should be even higher. This is the payment for the high voltage developed by the antenna. The question arises, is it possible for a large inductance coil in the circuit of Fig. 1 to be replaced by a conventional oscillatory circuit? Of course, it is possible, but the signal voltage developed on the circuit will be less. To save the reader from a rather laborious mathematical analysis, we will only say that the signal voltage decreases (approximately) in proportion to the ratio of the antenna capacitance to the total loop capacitance. This is explained by the fact that additional reactive currents, flowing through the resistance of the coil R, cause additional losses. It is clear that the self-capacitance of the coil and the input capacitance of the RF also play a harmful role, reducing the voltage developed. In the example shown, using a standard 200 uH medium wave inductor with a capacitor of about 130 pF connected in parallel to tune to 1 MHz. we will get a signal voltage of about 0,15 V on the circuit. Which, in general, is also not small! Further, for the sake of interest, let us assume that the coil is ideal and has no losses. Now the equivalent circuit will look like in Fig. 3. By the way, in this case, you can painlessly reduce the inductance of the coil and connect a loop capacitor in parallel. The resulting circuit will have to be tuned to a slightly higher frequency than the desired one, at which it will have the inductive nature of resistance, the greater, the smaller the detuning. Selecting the detuning, we obtain the inductive resistance of the circuit Xt, which is exactly equal to the capacitance of the antenna - Xc, and again we arrive at the equivalent circuit in Fig. 3. In practice, tuning is performed as usual, according to the maximum signal voltage on the circuit, and corresponds to the exact resonance of the circuit at the desired frequency, taking into account the capacitance of the antenna.
What is the active resistance of the antenna circuit now? Previously, it consisted of the loss resistance of the coil and the radiation resistance of the antenna, the latter being much smaller and we neglected it. Now the loss resistance of the coil is zero, the capacitor, if any, also practically does not introduce any losses, and only the radiation resistance remains. As is known from theory, for short antennas Rid = 1600h/λ2. Substituting this expression into the formula we obtained for the voltage developed on the coil, we get U = EXLλ2 / 1600h, i.e. when the antenna is shortened, the voltage even increases! I anticipate objections; this fantastic result was obtained, they say. for unrealistic conditions, i.e., when there are no losses in the coil, and its quality factor tends to infinity. Of course, no one is going to put a coil in liquid helium to achieve superconductivity and zero losses - although this can be done, it will be too expensive and troublesome. Another way has long been known and widely used - compensation for losses in the coil using positive feedback, or regeneration. When approaching the self-excitation threshold in the regenerator, the equivalent quality factor of the circuit increases significantly, and with it, both the signal voltage and sensitivity increase. It turns out that the legends about the extraordinary receiving qualities of Q-multipliers using regeneration in the input circuit did not arise at all from scratch! At long and medium wavelengths, regeneration in the input circuit is not often used, mainly because with a high quality factor, the bandwidth (B) narrows and the higher frequencies of the AM audio spectrum are attenuated, because B \u10d f / Q. But at short wavelengths, the required bands are narrower and the frequencies are higher, so there a large quality factor of the input circuit can only be welcomed. According to the measurements made by the author, it is quite possible to obtain a fairly stable quality factor of 000 in a well-designed Q-multiplier. Let's calculate what voltage a rather weak signal with E = 10 μV / m will develop in our antenna 2 m long connected to such a circuit: U = EhQ = 0,1 V. Comments, as they say, are superfluous. To confirm what was said, the author assembled the device shown in Fig. 4. This is a "source" field-effect transistor detector (in the past, detectors similar in their properties were made on lamps and were called cathode detectors). The resistance in the source circuit is chosen to be quite large, the transistor operates near the cutoff, at the lower bend of the characteristic, and therefore detects the AM signal well. A large gate-off bias (relative to source) guarantees high input impedance, and 100% audio feedback ensures low distortion. Capacitor C2 and the R3C4 circuit filter out high-frequency components, and the variable resistor R4 serves as a volume control. From it, an audio signal was fed to a simple UMZCH (V. Polyakov. "Universal amplifier 3Ch". - Radio. 1994. No. 12. p. 34, 35). The input circuit capacitor replaces the capacitance of the antenna, the coil, and the input capacitance of the transistor. The antenna is a one and a half meter piece of wire stretched from the desktop to the window, and the central heating pipe serves as grounding under the window. The coil was taken ready-made, from the magnetic antenna of an industrial DV receiver. It contained about 250 turns of PEL 0,2 wire, wound in one layer turn to turn on a frame 12 mm in diameter. For tuning, a magnetic rod of the same antenna was inserted into the coil. Due to the low capacitance, the circuit tuning turned out to be on the frequencies of the medium wave range. Four Moscow radio stations developed a signal from 0,5 to 1,5 V on the transistor gate. So the theory was completely confirmed - the volume control had to be set to a minimum! It was not at all easy to measure the high-frequency voltage at the gate - an oscilloscope cannot be connected to the gate due to signal shunting. The oscilloscope probe was connected to the source, instead of the capacitor C2. In this case, detection became worse, but the transistor transmitted a high-frequency signal in the source follower mode. Decreasing capacitance C2. regeneration and even self-excitation can be observed. Feedback in this case is obtained according to the capacitive three-point scheme. formed by the gate-source capacitance and capacitor C2. With sufficient regeneration, it was possible to listen to distant stations in the evening. An interesting fact is that when during the experiment the antenna wire came off the circuit, the reception of Moscow stations continued (albeit at a much lower volume) on the ferrite rod. Author: V.Polyakov, Moscow
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