Marconi's law

If H is the height (i.e. the length) of the antenna and D the maximum signalling distance, then we have, according to Marconi's law

${\displaystyle H=c{\sqrt {D}}}$,

where c is some constant.

Marconi's law can be deduced theoretically as follows:[3]

Hertz has shown that distances large compared with its length the magnetic force of a linear oscillator varies inversely as the distance. The maximum value of the current set up in any given receiving antenna varies as its length, also as the magnetic force of the waves incident on it, and as the maximum value of the current in the transmitting antenna. Hence, if ${\displaystyle M}$ is the magnetic force of the waves incident on a receiving antenna of height H, and if ${\displaystyle D}$ is the distance between the sending and receiving antenna, and if ${\displaystyle I_{1}}$ and ${\displaystyle I_{2}}$ are the maximum values of the currents in the sending and receiving antennæ, we have—

${\displaystyle M\propto {\frac {I_{1}}{D}}}$ and ${\displaystyle I_{2}\propto MH}$

Hence ${\displaystyle I_{2}\propto {\frac {I_{1}H}{D}}}$

Also, since for a given charging voltage the current ${\displaystyle I_{1}}$ in the sending antenna varies very nearly as its capacity—that is, as its height—and if the sending antenna has the same height, ${\displaystyle H}$, as the receiving aerial, we have—

${\displaystyle I_{1}\propto H}$

But ${\displaystyle I_{2}\propto {\frac {I_{1}H}{D}}}$

Therefore ${\displaystyle I_{2}\propto {\frac {H^{2}}{D}}\propto }$ some constant

For any given receiving apparatus a certain constant minimum value of the maximum current in the receiving antenna is necessary to cause a signal. Therefore it follows that, with given receiving and sending apparatus, we must have ${\displaystyle {\frac {H^{2}}{D}}}$ a constant, or—

${\displaystyle H=c{\sqrt {D}}}$

That is, the maximum signalling distance with given apparatus will vary as the square of the height of the antenna.

The above law is, however, much interfered with by the nature of the surface over which the propagation takes place.

• Arco-Slaby (Telefunken)
• Electrical lengthening
• Radio propagation
• Radio antenna

General

• Fleming, J. A. (1906). The principles of electric wave telegraphy. London: Longmans, Green, and Co. Pg Page 601+.
• Fleming, J. A. (1906). Hertzian wave wireless telegraphy. Pages 42 - 46

Citations