Electromagnetism - Impedance

In transmitting high frequency signals on a coaxial cable, it is important that the cable be terminated at an end with its characteristic impedance in order to avoid

A. Leakage of the signal out of the cable
B. Overheating of the cable
C. Reflection of signals from the terminated end of the cable
D. Attenuation of the signal propagating in the cable
E. Production of image currents in the outer conductors

(GR9277 #18)

Solution:

Characteristic impedance of a transmission line is the ratio of the voltage and current of a wave travelling along the line.

When the wave reaches the end of the line, a reflected wave could travels back in the opposite direction. It could develop an interference and cause the voltage to fluctuates.

To avoid this problem, the receiving end of a coaxial cable should be terminated using a resistance value equals to its characteristic impedance.

Answer: C

Electromagnetism - Impedance

An alternating current electrical generator has a fixed internal impedance R_g + jX_g and is used to supply power to a passive load that has an impedance R_g + jX₁, where j =√(−1). R_g ≠ 0 and X_g ≠ 0. For a maximum power transfer between the generator and the load, X₁ should be equal to

A. 0
B. X_g
C. −X_g
D. R_g
E. −R_g

(GR8677 #64)

Solution:

Maximum power transfer theorem (Impedance matching): 

Maximum power is transferred from a source to a load when

• Load resistance = the internal resistance of the source, or 
• Load impedance = complex conjugate source impedance (Z_l = Z_s^*)

Z_s = R_g + jX_g  with  j =√(−1)

Z_s^* = R_g − jX_g

For max power transferred: 
Z_l  = Z_s^*
X₁ = −X_g

Answer: C