Characteristic Impedance of High-Frequency Coaxial Line In a high-frequency coaxial transmission line, the characteristic impedance Z0 depends on which physical properties?
-
Aproperties of insulating material only
-
Binner and outer conductor radius only
-
Cboth (a) and (b)
-
Dneither (a) nor (b)
-
Eshield braid angle only
Answer
Correct Answer: both (a) and (b)
Explanation
Introduction / Context:Coaxial lines are ubiquitous in RF systems. Their characteristic impedance Z0 determines matching, loss, and bandwidth performance.
Given Data / Assumptions:
- Lossless approximation to reveal first-order dependencies.
- Coax defined by inner radius a and outer radius b, filled with dielectric of relative permittivity εr and permeability close to μr ≈ 1.
Concept / Approach:
For a lossless coax, Z0 = (60 / sqrt(εr)) * ln(b / a) (with μr ≈ 1). Thus Z0 depends on geometry (ratio b/a) and material permittivity εr. Both the insulating material and conductor radii matter.
Step-by-Step Solution:
1) Recognize formula: Z0 ∝ ln(b/a) / sqrt(εr).2) Changing dielectric (εr) changes Z0 via 1/sqrt(εr).3) Changing geometry (b/a) alters the logarithmic factor and Z0.Verification / Alternative check:
Design calculators for coax dimensions ask for εr and the two radii because both determine Z0.
Why Other Options Are Wrong:
Only-dielectric or only-geometry cannot fully determine Z0; braid angle affects shielding but not the first-order Z0 relation.
Common Pitfalls:
Assuming copper thickness or plating dominates Z0; those affect loss, not the primary impedance.
Final Answer:
both (a) and (b)