Signal Strength - Relationship To Average Radiated Power

Relationship To Average Radiated Power

The electric field strength at a specific point can be determined from the power delivered to the transmitting antenna, its geometry and radiation resistance. Consider the case of a center-fed half-wave dipole antenna in free space . If constructed from thin conductors, the current distribution is essentially sinusoidal and the radiating electric field is given by


E_\theta (r) =
{-jI_\circ\over 2\pi\varepsilon_\circ c\, r}
{\cos\left(\scriptstyle{\pi\over 2}\cos\theta\right)\over\sin\theta}
e^{j\left(\omega t-kr\right)}

where is the angle between the antenna axis and the vector to the observation point, is the peak current at the feed-point, is the permittivity of free-space, is the speed of light in a vacuum, and is the distance to the antenna in meters. When the antenna is viewed broadside the electric field is maximum and given by


\vert E_{\pi/2}(r) \vert = { I_\circ \over 2\pi\varepsilon_\circ c\, r }\, .

Solving this formula for the peak current yields


I_\circ = 2\pi\varepsilon_\circ c \, r\vert E_{\pi/2}(r) \vert \, .

The average power to the antenna is

where is the center-fed half-wave antenna’s radiation resistance. Substituting the formula for into the one for and solving for the maximum electric field yields


\vert E_{\pi/2}(r)\vert \, = \, {1 \over \pi\varepsilon_\circ c \, r}
\sqrt{{ P_{avg} \over 2R_a}} \, = \,
{9.91 \over r} \sqrt{ P_{avg} } \quad (L = \lambda /2) \, .

Therefore, if the average power to a half-wave dipole antenna is 1 mW, then the maximum electric field at 313 m (1027 ft) is 1 mV/m (60 dBµ).

For a short dipole the current distribution is nearly triangular. In this case, the electric field and radiation resistance are


E_\theta (r) =
{-jI_\circ \sin (\theta) \over 4 \varepsilon_\circ c\, r} \left ( {L \over \lambda} \right )
e^{j\left(\omega t-kr\right)} \, \quad
R_a = 20\pi^2 \left ( {L \over \lambda} \right )^2 .

Using a procedure similar to that above, the maximum electric field for a center-fed short dipole is


\vert E_{\pi/2}(r)\vert \, = \, {1 \over \pi\varepsilon_\circ c \, r}
\sqrt{{ P_{avg} \over 160}} \, = \,
{9.48 \over r} \sqrt{ P_{avg} } \quad (L \ll \lambda /2)\, .

Read more about this topic:  Signal Strength

Famous quotes containing the words relationship to, relationship, average and/or power:

    Poetry is above all a concentration of the power of language, which is the power of our ultimate relationship to everything in the universe.
    Adrienne Rich (b. 1929)

    Strange and predatory and truly dangerous, car thieves and muggers—they seem to jeopardize all our cherished concepts, even our self-esteem, our property rights, our powers of love, our laws and pleasures. The only relationship we seem to have with them is scorn or bewilderment, but they belong somewhere on the dark prairies of a country that is in the throes of self-discovery.
    John Cheever (1912–1982)

    The average Ph.D. thesis is nothing but a transference of bones from one graveyard to another.
    J. Frank Dobie (1888–1964)

    He has served me too well; by increasing my power he has stolen it away: he is now my subject only so long as he pleases.
    Pierre Corneille (1606–1684)