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Antenna Gain by huang1tx2

Posted in Uncategorized on January 20th, 2010

Gain is a measure of the ability of the antenna to direct the input power into radiationin a particular direction and is measured at the peak radiation intensity. Consider thepower density radiated by an isotropic antenna with input power P₀ at a distance R:S = P₀/4πR². An isotropic antenna radiates equally in all directions, and its radiatedpower density S is found by dividing the radiated power by the area of the sphere4πR². The isotropic radiator is considered to be 100% efficient. The gain of an actualantenna increases the power density in the direction of the peak radiation:

S = = or |E| = = (1)

FIGURE 1 Antenna pattern characteristics.

Gain is achieved by directing the radiation away from other parts of the radiationsphere. In general, gain is defined as the gain-biased pattern of the antenna:

S(θ, φ) =  power density

U(θ,φ) = radiation intensity

The surface integral of the radiation intensity over the radiation sphere divided by theinput power P₀ is a measure of the relative power radiated by the antenna, or theantenna efficiency:

= sinθ dθ dφ = η_eefficiency

wherePr is the radiated power. Material losses in the antenna or reflected powerdue to poor impedance match reduce the radiated power. In this book, integrals inthe equation above and those that follow express concepts more than operations weperform during design. Only for theoretical simplifications of the real world can we findclosed-form solutions that would call for actual integration. We solve most integralsby using numerical methods that involve breaking the integrand into small segmentsand performing a weighted sum. However, it is helpful that integrals using measuredvalues reduce the random errors by averaging, which improves the result.

In a system the transmitter output impedance or the receiver input impedance maynot match the antenna input impedance. Peak gain occurs for a receiver impedanceconjugate matched to the antenna, which means that the resistive parts are the sameand the reactive parts are the same magnitude but have opposite signs. Precision gainmeasurements require a tuner between the antenna and receiver to conjugate-matchthe two. Alternatively, the mismatch loss must be removed by calculation after themeasurement. Either the effect of mismatches is considered separately for a givensystem, or the antennas are measured into the system impedance and mismatch loss isconsidered to be part of the efficiency.

Path Lossof Antenna

We combine the gain of the transmitting antenna with the effective area of the receivingantenna to determine delivered power and path loss. The power density at thereceiving antenna is given by Eq. (1), and the received power is given by Eq. (2).

S(θ, φ) =  power density

U(θ,φ) = radiation intensity—(1)

P_d= SA_eff—(2)

By combining the two, we obtain the path loss:

=

Antenna 1 transmits, and antenna 2 receives. If the materials in the antennas arelinear and isotropic, the transmitting and receiving patterns are identical (reciprocal). When we consider antenna 2 as the transmitting antenna and antenna 1 as thereceiving antenna, the path loss is

=

Since the responses are reciprocal, the path losses are equal and we can gather andeliminate terms:

= = constant

Because the antennas were arbitrary, this quotient must equal a constant. This constantwas found by considering the radiation between two large apertures:

=

We substitute this equation into path loss to express it in terms of the gains or effectiveareas:

= G₁G₂( )²=

We make quick evaluations of path loss for various units of distance R and for frequencyf in megahertz using the formula

path loss(dB) = K_U + 20 log(fR) − G₁(dB) − G₂(dB)

where K_U depends on the length units:

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