Characteristic impedance of transmission line depends upon

Question

Examoogle · Accepted Answer

Option C: Geometrical configuration of the conductor

Explanation & Concepts:
The characteristic impedance ($Z_0$) of a transmission line is a property determined by the distributed parameters of the line: resistance ($R$), inductance ($L$), conductance ($G$), and capacitance ($C$). These parameters are fundamentally dependent on the physical geometry, dimensions, and spacing of the conductors relative to each other and the return path.

Working Principle: For a lossless line where $R$ and $G$ are negligible, the characteristic impedance is given by $Z_0 = \sqrt{\frac{L}{C}}$. Since $L$ (inductance per unit length) is a function of the flux linkage path area and $C$ (capacitance per unit length) is a function of the electric field geometry between conductors, both $L$ and $C$ are entirely governed by the cross-sectional geometry and the dielectric constant of the medium surrounding the conductors.

Key Formulas: $Z_0 = \sqrt{\frac{L}{C}}$ — General expression for lossless line; $Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$ — General expression for lossy line

Key Points: Characteristic impedance is independent of the length of the transmission line.; It is a function of frequency in practical lines due to skin effect, but primarily defined by geometry at high frequencies.; Conductivity of the material only affects attenuation, not the fundamental $Z_0$ in the lossless approximation.

Advantages: Allows matching of load to source for maximum power transfer.; Eliminates signal reflections when matched.

Disadvantages: Mismatch leads to Standing Waves (VSWR).; Dependency on geometry makes manufacturing precision critical for high-frequency performance.

Applications: Power transmission systems; RF/Microwave circuit design; Telecommunication cabling

Additional Info: For an overhead line, $L$ and $C$ depend on conductor diameter and spacing distance (GMD and GMR).. Option B is incorrect because conductivity affects the internal resistance and losses, but $Z_0$ is dominated by the reactive components which are geometric constants.

Answer: C is correct — The characteristic impedance of a transmission line is inherently determined by its primary line constants ($L$ and $C$), which are functions of the conductor's physical geometry and spatial configuration.

Exam Tip: Always remember that characteristic impedance is an intrinsic property of the line structure, not the load or the length; it represents the ratio of forward-traveling voltage to current waves.

Examoogle · Answer

Option A: Shape of the conductor

Examoogle · Answer

Option B: Conductivity of the conductor material

Examoogle · Answer

Option D: None of above

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)