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:

    “Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.”
    —Igor Stravinsky (1882–1971)

    “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)

    “The average American is a good sport, plays by the rules. But this war is no game. And no secret agent is a hero or a good sport—that is, no living agent.”
    —John Monks, Jr., U.S. screenwriter, Sy Bartlett, and Henry Hathaway. Robert Sharkey (James Cagney)

    “If all power is in the people, if there is no higher law than their will, and if by counting their votes, their will may be ascertained—then the people may entrust all their power to anyone, and the power of the pretender and the usurper is then legitimate. It is not to be challenged since it came originally from the sovereign people.”
    —Walter Lippmann (1889–1974)