Electromagnetics

Question 1

State the equation for the intrinsic impedance of free space? How does this differ from the equation for a lossy medium?

Answer 1

Z = SQRT ( U_o / e_o ) = 377 Ohm / m^2

Z_lossy = SQRT ( jwU / conductivity + jwe )

Question 2

State the equation for the power radiated in a particular polarisation? How is the cross polar power ratio then derived?

Answer 2

P_v = integral (integral(|E_theta^2|sin(theta))dtheta)dphi
P_h = integral (integral(|E_phi^2|sin(theta))dtheta)dphi

XPR = P_v / P_h

Question 4

What does the equation for a circularly polarised wave look like?

Answer 4

1. Two perpendicular components that have pi/2 phase difference:

E=Eocos(wt-kx)az + Eocos(wt-kx-pi/2)ax

Question 5

What are the different phase relations of the perpendicular components for 1) linear polarisation 2) circular polarisation 3) elliptical polarisation

Answer 5

1. In phase
2. 90 degrees out of phase
3. between 0 and 90 degrees