Question

An TEM transmission line is designed with a perfect dielectric that

has zero conductivity. The dielectric material separates the two conductors,
and it has a relative permittivity ∊r = 10.132 and unity relative permeability.
In addition, the conductors are made of a material with very high (infinite)
conductivity.
For this transmission line whose characteristic impedance is 50 and at 300
MHz, answer the following parts:

Find the line resistance R', conductance G', inductance L' and
capacitance C'. Is this line a lossless transmission line?
Explain your answers in detail.

Answer 1

The line resistance R', conductance G', inductance L', and capacitance C' of a TEM transmission line with a perfect dielectric can be calculated using specific formulas. In this case, the line is lossless due to the absence of resistance or conductance.

Step-by-step explanation:

The line resistance R' of a TEM transmission line can be calculated using the formula:

R' = sqrt(πfμ0/σ')

Where f is the frequency (300 MHz in this case), μ0 is the permeability of vacuum (4π × 10^-7 H/m), and σ' is the conductivity of the material (infinite for perfect conductors, so σ' = ∞).

Since the conductance G' is reciprocal of the resistance, it is G' = 1/R'.

For a perfect dielectric, the inductance L' and capacitance C' can be calculated using the expressions:

L' = μ0εr/2π

C' = 1/(2πfεr)

Since the line is made of a perfect dielectric and the conductors have infinite conductivity, the line is lossless as there is no resistance or conductance to cause energy loss in the form of heat.