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:

    “Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.”
    —Friedrich Nietzsche (1844–1900)

    “Sisters is probably the most competitive relationship within the family, but once the sisters are grown, it becomes the strongest relationship.”
    —Margaret Mead (1901–1978)

    “Whether or not his newspaper and a set of senses reduced to five are the main sources of the so-called “real life” of the so- called average man, one thing is fortunately certain: namely, that the average man himself is but a piece of fiction, a tissue of statistics.”
    —Vladimir Nabokov (1899–1977)

    “You are evil. But even the power of evil cannot stand against the power of faith and goodness.”
    —Griffin Jay, and Randall Faye. Lew Landers. Lady Jane Ainsley (Frieda Inescort)