Junior Comprehensive Presentation(Quantitative Problem)By Harrison Wood

Problem Statement

1.At the instant when the incident electric field is max, sketch the charge distribution along the antenna.

2.If the power absorbed by the antenna goes like a square of the maximum voltage induced across the antenna, how does the power absorbed depend on the angle between the antenna dipole and the plane of polarization of the EM wave?

For all cases consider a plane polarized electromagnetic wave incident on a λ/2 dipole rectenna in the microwave frequency region.

Problem Statement Continued

• 3. Derive an expression for a net EM wave that is the superposition of 2, 3, and 4 plane waves whose polarization direction and phase are random with respect to each other. Graph the absorbed power vs. time of the resultant wave. Compare this to the case where all four waves are in phase and have the same polarization.

• 4.Discuss the efficiency of using a rectenna for harvesting waste thermal heat.

Charge Distribution along the Antenna when the Incident Electric Field is Max.

λ/2Dipole Antenna

Power absorbed by the antenna

• Power Goes like the square of the maximum voltage induced across the antenna.

P=(E^2/R

The Net Electromagnetic Wave

• Random number Generator to generate values

• Phase Angle Φ=(1.76π rad, 1.99π rad, 1.16π rad, 1.75π rad)• Angle of Polarization γ=(1.07π rad, 0.32π rad,

1.71π rad, 1.13π rad)• Wave 1= E0cos(1.07π)*cos(ωt+1.76π)

• Wave 2=E0cos(0.32π)*cos(ωt+1.99π)

• Wave 3=E0cos(1.71π)*cos(ωt+1.17π)

• Wave 4=E0cos(1.13π)*cos(ωt+1.75π)

4-Component cosine Wave

P≈3.1, ϕ≈(π/4)

P

t

4-Component Cosine Wave*

*All four waves have the same phase and plane of polarization.t

P

Both Waves TogetherP

t

The Efficiency of using a rectenna for harvesting waste thermal heat

• In reality the waste heat given off in a thermally produced electromagnetic field is a superposition of large numbers of individual waves, each with their own random planes of polarization, phases, and amplitudes.

• Assuming that the waves are coming in parallel to the antenna, to maximize the power absorbed, the resultant wave would be calculated in a manner similar to that of the 4-component cosine wave.

Efficiency Continued• The second 4-component wave is an idealization that will not

be found in reality.• The first wave is made up of only four components. These

were just four of the many possible phase angle and plane of polarization combinations.

• As you can see in the case of the random superposition the Power absorbed is about one quarter the Power absorbed in the case with coherent superposition.

• The different planes of polarization and phases of the waves reduce the voltage induced, which is then squared greatly reducing the power absorbed by the antenna.

References• Knight, R. (2013). Physics for Scientists and Engineers (3rd ed.,

Vol. 4). Glenview, Ill: Pearson Education.• Mathematica (program)