A wire antenna that is oriented along the x-axis is used to receive a signal from...
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A wire antenna that is oriented along the x-axis is used to receive a signal from an incoming wave, which may be modeled as a plane wave traveling in the z direction in free space. The open-circuit (phasor) voltage V, at the terminals of the antenna (the Thévenin voltage for the receiving antenna) can be expressed as V₁ =hE", where h is the "effective height" of the antenna and Eis the x component of the electric field of the incident plane wave (in the phasor domain). Calculate the magnitude of the normalized Thévenin voltage (defined as V₂ = V₂ / h) for the following incident plane waves, assuming that each plane wave has an incident time-average power density of 1 [W/m²]. a) A linearly polarized plane wave, polarized in the x direction and traveling in the z direction. b) A RHCP wave, traveling in the z direction. c) A LHCP wave, traveling in the z direction. Hint: For each of the cases, first calculate what the expression for the electric field vector should be, using the fact that the power density in the plane wave is known. The time- average power density comes directly from the real part of the complex Poynting vector. a) 27.43 V b) 19.41 V c) 19.41 V A wire antenna that is oriented along the x-axis is used to receive a signal from an incoming wave, which may be modeled as a plane wave traveling in the z direction in free space. The open-circuit (phasor) voltage V, at the terminals of the antenna (the Thévenin voltage for the receiving antenna) can be expressed as V₁ =hE", where h is the "effective height" of the antenna and Eis the x component of the electric field of the incident plane wave (in the phasor domain). Calculate the magnitude of the normalized Thévenin voltage (defined as V₂ = V₂ / h) for the following incident plane waves, assuming that each plane wave has an incident time-average power density of 1 [W/m²]. a) A linearly polarized plane wave, polarized in the x direction and traveling in the z direction. b) A RHCP wave, traveling in the z direction. c) A LHCP wave, traveling in the z direction. Hint: For each of the cases, first calculate what the expression for the electric field vector should be, using the fact that the power density in the plane wave is known. The time- average power density comes directly from the real part of the complex Poynting vector. a) 27.43 V b) 19.41 V c) 19.41 V
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