## Effective Length of Receiving Magnetic Loop AntennaPart 3: Resonant Loop Antenna

A loop antenna, supplemented with a variable capacitor to tune into resonance with the received signal, converts the energy of an electromagnetic wave into signal voltage much more efficiently, that is, its effective length is much more than that of an ordinary loop antenna. Here, in the third part, the determining of how much more is given.

### Effective length of the resonant loop antenna

In a resonant loop antenna, the wire loop operates as an inductor L as part of an oscillatory circuit tuned by a variable capacitor C to resonance with the received signal (see Fig. 2).

Let the emf induced in the loop by an electromagnetic wave, in accordance with expression (1), be equal to:

where is:

heff – effective length of the non-resonant loop antenna, determined by expression (16), m;
E – intensity of the electric component of the electromagnetic field produced by the electromagnetic wave at the receiving point, V/m.

An equivalent circuit for including such a loop in the oscillatory circuit as an inductor is shown in Fig.3. The inductor L in the schematic diagram is a wire loop with inductance L, and the emf source (designated as ) is the equivalent of the emf induced in the loop by an external magnetic field of thr received signal. Capacitor C adjusts the oscillatory circuit to resonance with the received signal. The resistor rk in the schematic diagram represents the total equivalent loss resistance in the elements of a real oscillatory circuit.

If such an oscillating circuit is tuned to resonance with the received signal, the voltage on the variable capacitor C, and hence on the open-circuited terminals of the resonant loop antenna, will be many times greater than the emf induced in the loop:

(17)

where is:

Q – quality factor of the oscillatory circuit; – effective length of the resonant loop antenna.

Thus, the value of the effective length of a resonant loop antenna is Q times greater than that of a non-resonant loop antenna of the same dimensions:

(18)

where is:

n – number of turns of the wire in the loop;
S – the area of the surface enclosed by each turn of the wire loop antenna, m2; – signal angular frequency, rad/s;
Q – quality factor of the oscillatory circuit with a loop as a contour inductor;
c – speed of light in vacuum, m/s.

### Effective length of the active receiving loop antenna

Receiving loop antennas are often made as active, that is, with a built-in antenna amplifier that requires power. But an active receiving magnetic antenna should be considered as a single, functionally complete unit. It cannot be divided into passive and active parts, it cannot be considered as an ordinary serial connection of functionally completed nodes. This approach is due to the fact that the “antenna itself”, that is, the part of the device that directly converts the energy of radio waves into emf, works as a signal source with a complex output impedance, to which the active four-terminal circuit is connected – the antenna amplifier. Both the “antenna itself” as a signal source and the antenna amplifier are matched with each other as a whole, as a functionally complete device, to the output of which, in turn, as well as to a passive antenna, you can already connect, for example, a coaxial cable any length, radio receiver, etc.

As already noted, the effective length of the receiving antenna in its physical meaning is the coefficient of conversion of the intensity of the electromagnetic field at the point of radio reception into the voltage of the received signal on the open-circuited output terminals of the antenna. Nothing prevents the use of this characteristic in relation to active antennas, in the design and manufacture of which it is only necessary to take into account both the effective height of the “antenna itself” and the amplifying and noise properties of the built-in antenna amplifier.