Question

A coaxial cable has impedance of Z0=50Ω. A horn antenna has impedance of ZL=100−j10Ω. Assume the frequency of operation is 1GHz and the velocity of propagation on the transmission line (vp) is 0.9c where c is the speed of light in vacuum.

a) Calculate the reflection coefficient between the coax line and horn antenna ( ΓL).

Answer 1

The reflection coefficient (ΓL) between the coaxial cable and horn antenna with given impedances is approximately 0.3363 - 0.0442j.

Step-by-step explanation:

To calculate the reflection coefficient (ΓL) between the coaxial cable and horn antenna, you can use the following formula:

ΓL = (ZL - Z0) / (ZL + Z0)

Where Z0 is the characteristic impedance of the coaxial cable and ZL is the load impedance of the horn antenna. In this case, Z0 = 50Ω (Ohms), and ZL = 100 - j10Ω. Using the given values, you get:

ΓL = ((100 - j10) - 50) / ((100 - j10) + 50)

ΓL = (50 - j10) / (150 - j10)

Now, calculate the numerator and denominator separately to get:

ΓL = (50 - j10) * (150 + j10) / (150 - j10) * (150 + j10)

ΓL = ((50 * 150) + (50 * j10) - (j10 * 150) - (j10 * j10)) / (150² + j10²)

ΓL = (7500 + 500j - 1500j - (-100)) / (22500 + 100)

ΓL = (7600 - 1000j) / 22600

The real part of ΓL is 7600 / 22600, and the imaginary part is -1000j / 22600. Calculating these, you get:

Real(ΓL) = 0.3363
Imag(ΓL) = -0.0442j

Therefore, the reflection coefficient is approximately 0.3363 - 0.0442j.