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Sonnet User's Guide - Sonnet Software

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Chapter 19 Antennas and Radiation<br />

Z TE<br />

η<br />

= ------------------------- f > f c<br />

f c<br />

1 ⎛<br />

⎝<br />

--- ⎞ 2<br />

–<br />

f ⎠<br />

Waveguide<br />

Walls<br />

Waveguide<br />

Termination<br />

f c<br />

Z TM = η 1 – ⎝<br />

⎛---<br />

f ⎠<br />

⎞2 f><br />

f c<br />

f c<br />

=<br />

v<br />

----- c<br />

2π<br />

mπ<br />

-------<br />

⎝<br />

⎛ A ⎠<br />

⎞ 2 + nπ -----<br />

⎝<br />

⎛ B ⎠<br />

⎞2<br />

Array<br />

Patches<br />

Substrate<br />

The waveguide simulator for infinite arrays inspired the technique described here. In this<br />

side view, the waveguide walls form images of the array of microstrip patches, simulating<br />

an infinite array. v c is the velocity of light in the medium filling the waveguide.<br />

In a phased array with the array scanned to a specific direction, a single waveguide<br />

mode is generated. The em software can model the waveguide simulator of that<br />

infinite array just by setting the top cover impedance to the impedance of the excited<br />

waveguide mode.<br />

Modeling an Open Environment<br />

If we can use a closed (i.e., terminated) waveguide to model an infinite array, we<br />

can also model radiation from a finite array; although, it must be done under certain<br />

conditions. It is important to keep in mind that, unless the analysis is carefully<br />

prepared, these conditions are easily violated, yielding incorrect results. When the<br />

conditions are met, useful results can be obtained, as shall be demonstrated.<br />

275

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