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0.513021060240902701203001503301800Figure 7-7MATLAB. Radiation pattern for a short dipole antenna.
Short electric dipole antenna606Example 7-4.A small antenna that is 1 cm in length and 1 mm in diameter is de-signed to transmita signal at 1 GHz inside the human body in a medical ex-periment. Assuming the dielectric constant of the body is similar to that of distilledwater (εr= 80) and that the conductivityσcan be neglected, compute themaximum electric field at the surface of the body that is approximately 20 cmfrom the antenna. The maximum current that can be applied to the antenna is 10μA. Find the new distance from the antenna1ρ, where the signal will beattenuated by 3dB.Answer: The wavelength of the electromagnetic wave within the body is com-puted to becm3.38010103fc98r×=ε=λThe characteristic impedance of the body is=εεµ=4280377Zr00CSince the dimensions of the antenna are much less than the wavelength, we canapply (7.20) for090=θand replaceC0ZZ.Thereforem/V3202.01033.0242410101kZ4IL|E|25Cµ×π××π×=ρπ=θThe attenuation of 3dB implies that the power changes by a factor of 2 an electricfield changes by a factor of 1.41.The distance is found to becm28m28.02.041.121=×=ρ=ρThe far field region is the most interesting for antenna applications.In thisregion, both of the electromagnetic field components are transverse to thedirection of propagation.This is clearly seen from equations (7.19) and (7.20).In order to calculate the radiated power from this antenna, one just has to
Short electric dipole antenna607perform the surface integration of the time-average Poynting vector as wasshown in Example 5-13.()∫ ∫π=φπ=θϕφθθρ=×=20022av0Sav*rddsin|H|Z21Re21PdsHE(7.21)After a substitution from (7.19) into (7.21) and performing the integration over thevariableφwhich yields to 2πthe expression (7.21) becomes()θθπ=θθπ=ππcosdcos116)LI(kZdsin16)LI(kZP022av20032av20rThe last integral gives a factor of 4/3. The radiated power from this antenna isπ=12I)kL(ZP2av20r(7.22)Here the constant current I can be replaced with its average value Iavassumingthat there is a slow variation in space.
Long dipole antenna6087.3. Long dipole antennaWe have now covered the basic idea of the radiation of electromagneticwaves from a short electric dipole antenna. As we take a short trip away from thisbook and into the hinterlands, we may see some tall structures that reach into theheavens and have flashing red lights at the top to warn passing airplanes. Theseantennas certainly do not seem to fall into the class of being “small”. Herein wewill describe a technique to generalize our treatment of antennas so that morerealistic antennas can be studied.

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Term
Spring
Professor
Abhisek bhachan
Tags
The Land, Coordinate system, Polar coordinate system, Coordinate systems

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