## Effective Length of Receiving Magnetic Loop AntennaPart 2: Multi-turn Wire Loop Antenna

In the first part, the definition of the effective length of the receiving antenna in general was given, the relationship between the electric and magnetic fields induced by the electromagnetic wave at the receiving point was shown, and an expression was obtained for calculating the effective length of the loop antenna, consisting of one turn of the electric wire.

### The effective length of the multi-turn loop antenna

The emf on the open-circuited terminals of a electrically small loop antenna of several turns of wire located in close proximity to each other, will be equal to the sum of emf induced in each of the turns:

(14)

where is:

Si – the area of the surface enclosed by each turn of the wire loop antenna;
n – number of turns.

From expression (14) it follows that the effective length of a multi-turn loop antenna is equal to:

(15)

When all of turns of the loop antenna are the same, this mean that the areas of the surfaces enclosed by these turns are equal. In this case it is correct to write:

where is:

S = S1 = S2 = … = Sn

Then the effective length of the multi-turn loop antenna is determined by the expression:

(16)

So, the effective length of a multi-turn loop antenna, consisting of n identical turns of wire, is n times greater than the effective length of a single-turn loop of the same dimensions.