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:

    “Artists have a double relationship towards nature: they are her master and her slave at the same time. They are her slave in so far as they must work with means of this world so as to be understood; her master in so far as they subject these means to their higher goals and make them subservient to them.”
    —Johann Wolfgang Von Goethe (1749–1832)

    “If the relationship of father to son could really be reduced to biology, the whole earth would blaze with the glory of fathers and sons.”
    —James Baldwin (1924–1987)

    “The idea that leisure is of value in itself is only conditionally true.... The average man simply spends his leisure as a dog spends it. His recreations are all puerile, and the time supposed to benefit him really only stupefies him.”
    —H.L. (Henry Lewis)

    “What you fail to understand is the power of hate. It can fill the heart as surely as love can.”
    —Earl Felton, and Richard Fleischer. Captain Nemo (James Mason)