Question

The separation between adjacent maxima in the voltage standing wave on a lossless transmission line is 3 metres when sinusoidal excitation at 27.3 MHz is applied to the line.

a. What is the value of the phase propagation coefficient beta associated with the sinusoidal travelling waves on the line?

Answer 1

The phase propagation coefficient beta (β) for sinusoidal traveling waves on a lossless transmission line is π/3 per meter, calculated using the relationship between the separation of adjacent maxima in a standing wave (3 meters in this case) and the wavelength (which is double this separation).

Step-by-step explanation:

The student asked about the phase propagation coefficient beta associated with sinusoidal traveling waves on a lossless transmission line. To calculate beta, we need to understand the relationship between the wavelength and the separation between adjacent maxima in a standing wave pattern.

The separation between adjacent maxima (or nodes) of a standing wave on a transmission line represents half the wavelength. Since the separation is given as 3 meters, the wavelength (λ) is therefore 6 meters. In a lossless transmission line, the phase propagation coefficient beta (β) is defined as 2π divided by the wavelength (λ).

Thus, the phase propagation coefficient beta is calculated as:

β = 2π / λ

β = 2π / 6m

β = π / 3m-1

Hence, the value of beta is π/3 per meter.