A is transmission line connects a transmitter of 1.2 MHz to the antenna located 50 m away from it. If Z_o of the line equals 500 Ω, what the input impedance of this line if antenna end:

1-Open circuited
2-Short circuited

To determine the input impedance of the transmission line at the antenna end when it is open circuited or short circuited, we can use the principles of transmission line theory and reflection coefficient.

1- Open circuited: When the transmission line is open circuited at the antenna end, it means that the end is not connected to anything, resulting in complete reflection of the signal. In this case, the reflection coefficient (Γ) can be calculated using the following formula:

Γ = (Z_L - Z_0) / (Z_L + Z_0),

Where Z_L is the load impedance at the antenna end, which is infinite in the case of open circuit.

Using the given values, we can substitute Z_L = ∞ and Z_0 = 500 Ω:

Γ = (∞ - 500 Ω) / (∞ + 500 Ω)

Since the impedance of Z_L is infinite, the reflection coefficient is equal to 1 (Γ = 1).

The input impedance (Z_in) can be calculated using the following formula:

Z_in = Z_0 * (1 + Γ) / (1 - Γ)

Substituting the value of Γ = 1, we get:

Z_in = 500 Ω * (1 + 1) / (1 - 1)
= 500 Ω * 2 / 0

The input impedance is undefined since we are dividing by zero. This happens because an open circuit at the antenna end causes a perfect reflection, resulting in an impedance that cannot be determined.

2- Short circuited: When the transmission line is short circuited at the antenna end, it means that the end is connected directly to a short circuit, resulting in complete absorption of the signal. In this case, the reflection coefficient (Γ) can be calculated using the same formula:

Γ = (Z_L - Z_0) / (Z_L + Z_0),

Where Z_L is the load impedance at the antenna end, which is zero in the case of short circuit.

Using the given values, we can substitute Z_L = 0 and Z_0 = 500 Ω:

Γ = (0 - 500 Ω) / (0 + 500 Ω)
= -500 Ω / 500 Ω
= -1

The input impedance (Z_in) can be calculated using the same formula:

Z_in = Z_0 * (1 + Γ) / (1 - Γ)

Substituting the value of Γ = -1, we get:

Z_in = 500 Ω * (1 - 1) / (1 + 1)
= 500 Ω * 0 / 2
= 0 Ω

Thus, the input impedance of the transmission line at the antenna end is 0 Ω when it is short circuited.