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Chapter 9: 9.37P (page 433)

A microwave antenna radiating at 10GHz is to be protected from the environment by a plastic shield of dielectric constant 2.5. What is the minimum thickness of this shielding that will allow perfect transmission (assuming normal incidence)? [Hint: Use Eq. 9. 199.]

Short Answer

Expert verified

The minimum thickness of the shielding is 9.5 mm.

Step by step solution

01

Expression for the minimum thicknesof the shielding:

Write the expression for minimum thickness.

d=蟺k ........(1)

02

Determine the minimum thickness of the shielding

Substitute k=蝇vand 蝇=2蟺谓in equation (1).

d=蟺蝇谓d=蟺2蟺谓vd=v2谓

Substitute 谓=cnand n=蔚渭蔚0渭0in the above expression.

d=cn2谓d=c2谓蔚渭蔚0渭0 ....... (2)

Here, 渭鈮�渭0and 蔚蔚0=蔚T.

Substitute 渭鈮�渭0and 蔚蔚0=蔚Tin equation (2).

d=c2谓蔚T........(3)

Substitute c=3脳108m/s,谓=10GHzand蔚T=2.5 in equation (3).

d=3脳108m/s2脳10GHZ脳109Hz1GHz2.5d=9.49脳10-3m脳103mm1md=9.5mm

Therefore, the minimum thickness of the shielding is 9.5 mm.

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