Equivalence of electric and magnetic antennas. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Antennas. Theory

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This article, which considers some issues of electrodynamics, is not only of theoretical interest, but also leads to important practical conclusions that may be useful in designing and calculating antennas for long and medium waves, as well as in understanding the features of their operation.

Even the founder of electrodynamics and radio engineering, Heinrich Hertz, experimenting with various receiving antennas at the end of the 1th century, used a short split vibrator with a capacitive load at the ends in the form of balls or disks (electric antenna) and a wire ring (magnetic antenna), shown in Fig. 1a and fig. XNUMXb. The field indicator was a very small discharge gap between the X-X antenna terminals.

In the theory of antennas, the concepts of an elementary electric dipole (Hertzian dipole) and an elementary magnetic dipole - a ring with current are widely used. Both elementary antennas are small compared to the wavelength. With the development of the theory, the principle of duality was formulated, which follows from the relationship between electric and magnetic fields. Using it, A. Pistohlkors in 1944 pointed out an analogy between vibrator and slot antennas [1].

On the LW, electrical antennas are made in the form of vertical wires or a mast with a capacitive load in the upper part in the form of a horizontal wire or a network of wires. The earth on the LW is a good conductor, and only vertically polarized waves can propagate near it. Therefore, only one half of the Hertz dipole usually rises above the ground (Fig. 1c), the other half is its mirror image in the ground (shown by dashed lines). Such antennas need very good grounding.

Magnetic antennas are made either in the form of small frames or very small coils on a ferrite rod. Magnetic antennas do not need grounding, and they have higher noise immunity. However, the effectiveness of common magnetic antennas is very low, so they are not suitable as transmitters. But magnetic antennas were not always small - in the early 20s of the last century, LW loop antennas with a diameter of up to 20 m were used at receiving centers! Interest in large loop antennas has continued to this day, due to the desire to get the maximum signal from the antenna, for example, for a detector receiver [3].

So the question arises, which antenna is more efficient, electric or large frame magnetic? And does the principle of duality apply in this case? It cannot be said that the question was raised for the first time - it was solved back in the 20s of the last century, naturally, at the level of knowledge and ideas of that time [4]. The answer was obtained based on the concept of the effective height of the antenna - for an electric antenna, it turned out to be much larger and was given preference.

On the LW, it is almost impossible for radio amateurs to build a full-sized antenna commensurate with the wavelength. Therefore, we consider only small antennas used as receiving ones. Antennas will be placed near the surface of the conductive earth (Fig. 2).

On the left (Fig. 2, a) the vectors of the electromagnetic wave coming from the radio station are shown: the electric field strength E (vertical polarization), the magnetic field strength H and the energy flux density P. From the Maxwell equations for waves in free space it follows that P = E H, or only for modules (absolute values) P \u2d E - H \u120d EXNUMX / XNUMXπ.

On fig. 2b shows an electric L-shaped antenna in the form of a vertical drop with a height h, loaded with a horizontal wire of length L. To facilitate calculations, we put L >> h, then almost the entire capacitance of the antenna will be concentrated between the horizontal wire and the ground. The current in any section of the vertical conductor will be the same, and the effective height of the electric antenna hde = h.

It should be noted that a vertical drop with X-X terminals can also be connected in any other place of the horizontal wire, for example, in the middle, getting a T-shaped antenna. This will not affect the results of our analysis in any way. Moreover, grounding can be replaced by a counterweight - a piece of wire with a length L, laid along the ground (dashed line in Fig. 2, b). The strong capacitive coupling of the counterweight to ground will provide a near short circuit for high frequency currents.

We will make a magnetic antenna (Fig. 2, c) in the form of a rectangular single-turn frame of the same dimensions. The bottom wire of the frame will run directly at the ground, so its inductance will be very small compared to the inductance of the top one. Note that the lower wire can be replaced by two grounds, but their loss resistance will actually be greater than the resistance of the wire. The effective height of the magnetic antenna will be hdm = 2πS/λ = kS, where S is the frame area; k \u2d XNUMXπ / λ.

It is easy to derive this formula: on the vertical sides of the frame, an EMF equal to Eh is induced, and on the far (right) side of the frame, the EMF lags behind in phase by a small angle kL. EMF at terminals X-X will be EhkL. Since S = hL. we get hdm = kS. Considering that L<<λ, it becomes clear that the effective frame height hdm is much less than hde. For both antennas, the EMF developed at the X-X terminals is Ehd, which is why in [4] preference was given to electric antennas, since they develop a large EMF.

But the efficiency of antennas should be evaluated not by EMF (after all, it can be increased by a conventional transformer), but by the power of the signal taken from the antenna at a given field strength. The maximum power is removed when the load is matched to the signal source (antenna). Matching, in turn, consists in the fact that the load reactance is equal in absolute value, but in reverse sign, to the source reactance, and their active resistances are simply equal.

The first part of the matching condition (reactivity compensation) can be achieved by connecting a reactance -jX in series with the load r, as shown in fig. 3. For an electric antenna, this will be the inductance that compensates for the capacitance of the antenna, and for a magnetic antenna, it will be the capacitance that compensates for the inductance of the frame. Such compensation, in fact, means tuning the antenna into resonance at the frequency of the received radio station. Equivalent circuits of oscillatory circuits formed by electric and magnetic antennas are shown in Figs. 4a and fig. 4b.

The second part of the matching condition - the equality of the active resistances of the source and load - we will not be able to fulfill. The fact is that the active resistance of an ideal (lossless) antenna is its radiation resistance. For our antennas, it is very small due to the smallness of their sizes, so we will not even give formulas. If you choose the same low load resistance, then the quality factor of the circuit (Fig. 4) will turn out to be too high, and the bandwidth will be too narrow for the signal of the broadcasting station.

We will have to choose the load resistance r based on the required quality factor of the circuit Q. For example, if we are going to receive the Mayak radio station at a frequency of 198 kHz, then the quality factor of the circuit should be no more than 20 to provide a bandwidth of about 10 kHz. The quality factor will determine the value of the active resistance of the load r = X / Q, and the small active resistance of the antenna can now be neglected. It is practically inconvenient to include a small load resistance in series with the antenna circuit, it is much better to connect it in parallel with the circuit, as shown in Fig. 4, c and fig. 4, city The parallel resistance R will be XQ, and the conversion formula looks like this: R = X2 / r.

The power developed by the antenna in the load resistance chosen in this way will be P \u2d (Ehd) 1 / r, and r is determined by the reactance of the antenna X and the quality factor Q. So, now we need to calculate the reactance of both antennas: He \uXNUMXd XNUMX / ωSant - for electric and Хм =ωLant - for magnetic. Taking into account our assumption L>> h, it is easiest to use the formulas for open and closed at the end of long lines: Xe = W ctgL = W/tgkL and Xm = W tgkL. In view of the smallness of the value of kL, the tangents can be replaced by their arguments, then Xe = W/kL and Xm = WkL.

The wave impedance of the line W= (L/C)1/2 is given by the formula (taking into account the conductive earth) W = 60 ln(h/d), where the natural logarithm is taken from the ratio of the distance between the wire and the ground h to the wire diameter d.

From the above formulas, we calculate the power given off by the electric antenna: P \u2d (Ehde) 2 Q / Xe \u2d E2Qkh2L / W. Let's do the same for the magnetic antenna: P = (Ehdm)2 Q/Xm, = EXNUMXQkhXNUMXL/W. The same formula was obtained, which proves the same efficiency of small electric and magnetic antennas. In the conditions we have chosen, they give equal power at the same size. It is logical to assume that the pattern is more general and the principle of duality always works.

Let us now see whether it is expedient to use multi-turn frames. Having wound N turns with the same dimensions, we will get N times the EMF, but the reactance X will increase N2 times, since the inductance is proportional to the square of the number of turns. The load resistance will also have to be increased by the same amount, while maintaining the same quality factor Q. As a result, the power given off by the antenna will not change. Thus, the use of a multi-turn loop is just a way to transform resistances, but not a way to increase efficiency.

The formula we obtained for the power given off by the antenna deserves a more detailed analysis. First of all, the power P is proportional to the square of the field strength E, i.e., the energy flux density. This result has already been obtained in [5] for an ideal antenna without losses when the load is matched to its radiation resistance. Recall the formula derived there: Po = E2λ2/6400. Now we got it for the mismatched antenna.

The dependence on the wavelength λ is now different, λ is in the denominator, entering the formula through the wave number k, however, if we express the dimensions of the antenna in wavelengths, then the former dependence on the wavelength will be restored. Thus, if the dimensions of the antenna h and L are fixed (in meters), then it is more advantageous to use shorter wavelengths. If, however, we fix the dimensions of the antenna in wavelengths, i.e., change the antenna in proportion to λ, then long and extra-long ones are more profitable.

To get the maximum power from the antenna, it is advisable:

- to reduce the wave impedance of the antenna W, which is practically done by increasing the capacitance and lowering the inductance of the antenna by connecting several parallel and spaced wires;

- increase the quality factor of the antenna system Q by choosing the appropriate load and reducing losses in the "ground", insulators and conductors;

- increase the volume occupied by the antenna field.

The last point needs some explanation. On fig. 5 shows the field line configuration of both the electric (solid lines) and magnetic fields of the antenna (dashed lines). The antenna is shown from the end, and it can be seen that the width of the space where the lines of force are most dense is of the order of h. Therefore, the product h2L is the volume in which the antenna fields are predominantly concentrated. It is this volume that is beneficial to increase.

To illustrate all that has been said, we present one practical approximate calculation of the electric and magnetic antennas according to Fig. 2b and c. Antenna height h = 10 m and length L = 30 m. Wavelength λ = 1500 m, quality factor of the antenna circuit Q = 20. At a field strength E = 0,1 V / m, the power taken from both antennas will be about 5 mW, which is quite sufficient for loud-speaking detector reception. At the same time, the conditions for matching and loading the antennas will be completely different.

The wave impedance of the line formed by the horizontal wire of the antenna above the ground with a wire diameter of 1 mm will be W = 60 In104 = 550 Ohm, and kL = 0,125. This gives He = 550 / 0,125 = 4,4 kΩ, and Xm = 550 0,125 = 70 Ω. The reactance of the compensating coil for an electric antenna (inductance L is about 3 mH) and the compensating capacitor for a magnetic one (capacitance of about 10 pF) should be the same. Accordingly, the resistance of the antenna circuit at resonance will turn out (to be multiplied by the quality factor) 000 and 88 kOhm. It is this load resistance R, or the input resistance of the detector, that should load the circuit. With an electric antenna, one cannot do without matching elements [1,4]. It is easier with a magnetic antenna - a detector with a low input impedance can be connected directly to capacitor C.

Literature

1. Belotserkovsky G. B. Antennas. - M.: Oborongiz, 1956.
2. Polyakov V. Radio receiving antennas. - Radio, 1998, No. 2. p. 60.
3. Besedin V. Another one ... - Radio amateur, 1994, No. 6, p. 34, 35.
4. Slepyan L. Calculation of receiving frames. - Radio amateur (Radio), 1925, No. 10, p. 224, 225.
5. Polyakov V. On the supply of radio receivers with "free energy". - Radio, 1997, No. 1, p. 22, 23.
6. Polyakov V. Improvement of the detector receiver. - Radio, 2001, No. 1, p. 52, 53.

Author: V.Polyakov, Moscow

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