If you have a 300 ohm transmission line terminated with an antenna that presents a (400 ohm - j 600 ohm) load impedance:

What is the normalized load admittance? (I come up with 1.5 - j 2 but am uncertain if correct)

How far from the load should a short circuit stub be placed to match the load? (can 0.25λ be correct?)

How long should the stub be? (can 0.085λ be correct?)

What is the VSWR before matching at the load?

What is the VSWR after matching at the input of the transmission line?

To answer these questions, we'll need to use transmission line theory and impedance matching techniques. Let's go through each question step by step:

1. Calculating the normalized load admittance:
First, we need to convert the given load impedance into admittance. The admittance (Y) can be obtained using the formula:
Y = 1/Z, where Z is the complex impedance.
In this case, the load impedance is (400 ohm - j 600 ohm). So, we can calculate the admittance as:
Y = 1/(400 - j600) = (400 + j600)/(400^2 + (-600)^2)
Simplifying this expression, we get:
Y = (0.4 - j0.6) mhos (or siemens)
Therefore, the normalized load admittance is (0.4 - j0.6).

2. Determining the distance for a short circuit stub:
To match the load impedance, we can use a short circuit stub. The distance from the load to the stub (d) is given by the formula:
d = λ/(4n), where λ is the wavelength and n is an integer representing the quarter-wavelength sections.
Given the information provided, we don't have the frequency or wavelength values provided, so it's difficult to determine the exact distance. However, if we assume "λ" to be the wavelength on the transmission line, then 0.25λ could be a reasonable estimate for the distance of the short circuit stub.

3. Calculating the length of the stub:
The length of the stub depends on the wavelength and the distance determined in the previous step. To calculate the stub length (l), we use the formula:
l = λ/4
Again, since we don't have the wavelength value, we cannot determine the exact length. However, if we assume "λ" to be the wavelength on the transmission line, then 0.085λ could be a reasonable estimate for the length of the stub.

4. Calculating the VSWR before matching at the load:
To calculate the Voltage Standing Wave Ratio (VSWR), we need to know the magnitude of the reflection coefficient (Γ) at the load. The reflection coefficient is given by the formula:
Γ = (ZL - Z0)/(ZL + Z0), where ZL is the load impedance and Z0 is the characteristic impedance of the transmission line.
In this case, the characteristic impedance is not specified. Assuming a 300-ohm transmission line, we can substitute the values and calculate the reflection coefficient.
Γ = (400 - j600 - 300)/(400 - j600 + 300)
By simplifying the expression, we get:
Γ = -0.25 + j0.75
The magnitude of Γ is given by:
|Γ| = sqrt((-0.25)^2 + (0.75)^2)
By calculating the magnitude, we find:
|Γ| = 0.7906
The VSWR is then given by:
VSWR = (1 + |Γ|)/(1 - |Γ|)
Substituting the value of |Γ|, we find:
VSWR = (1 + 0.7906)/(1 - 0.7906)
Simplifying, we get:
VSWR = 4.1807
Therefore, the VSWR before matching at the load is approximately 4.1807.

5. Calculating the VSWR after matching at the input of the transmission line:
To calculate the VSWR after matching at the input of the transmission line, we need to determine the magnitude of the reflection coefficient at that point. Assuming the stub is perfectly matched and there is no further reflection, the reflection coefficient becomes zero (Γ = 0). Therefore, we can calculate the VSWR using the same formula as before:
VSWR = (1 + |Γ|)/(1 - |Γ|)
Substituting Γ = 0, we find:
VSWR = (1 + 0)/(1 - 0) = 1
Therefore, the VSWR after matching at the input of the transmission line is 1, indicating a perfect match.