Question

For a lossy transmission line, the characteristic impedance does not depend on

• A. Operating frequency of the line
• B. Length of the line
• C. Conductivity of the conductors
• D. Conductivity of the dielectric separating the conductors

Hint:

Characteristic impedance depends on the distributed parameters \(R,L,G,C\), but not on the physical length of the transmission line.

Answer 1

The Correct Option is B

Concept: The characteristic impedance of a lossy transmission line is \[ Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}} \] where
• \(R\) = resistance per unit length
• \(L\) = inductance per unit length
• \(G\) = conductance per unit length
• \(C\) = capacitance per unit length

Step 1: Identify the parameters affecting characteristic impedance.
From the formula, \[ Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}} \] it depends on: \[ R,\;L,\;G,\;C,\;\omega \] Thus it depends on conductor conductivity, dielectric conductivity and operating frequency.

Step 2: Check dependence on length.
Since \(R,L,G,C\) are per-unit-length quantities, the total length of the line does not appear in the expression. Therefore characteristic impedance remains unchanged with line length.

Step 3: Final Answer.
\[ \boxed{\text{Characteristic impedance is independent of line length}} \] Hence, \[ \boxed{\text{Correct Option (B)}} \]