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A half-wavelength (l = λ/2) dipole is connected to a transmission line with a characteristic impedance of 75 ohms. Determine the following:

(a) Reflection coefficient. Magnitude and phase (in degrees).

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Final answer:

The question is about determining the reflection coefficient for a half-wavelength dipole antenna connected to a transmission line with known impedance. the reflection coefficient's magnitude is approximately 0.0135 and the phase is -180 degrees, assuming a typical 73-ohm impedance for the dipole.

Step-by-step explanation:

The student's question pertains to antenna theory in physics, specifically to the concept of a reflection coefficient for a half-wavelength dipole antenna connected to a transmission line. However, to determine the reflection coefficient, additional information is required, such as the impedance of the antenna itself. Typically, a half-wavelength dipole has an impedance of about 73 ohms in free space. The reflection coefficient (Γ) is determined using the formula:

Γ = (Z_{L} - Z_{0}) / (Z_{L} + Z_{0})

Where Z_{L} is the load impedance (antenna impedance) and Z_{0} is the characteristic impedance of the transmission line. Assuming the antenna's impedance is 73 ohms, the reflection coefficient would be calculated as follows:

Γ = (73 - 75) / (73 + 75) = -2 / 148 ≈ -0.0135

The magnitude of the reflection coefficient is the absolute value, which is approximately 0.0135. Since the reflection is negative, that indicates a 180-degree phase change. Thus, the phase in degrees of the reflection coefficient is -180 degrees.

User Carles Andres
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