Coaxial line versus two-wire open line — characteristic impedance and wave velocity In typical RF practice, how do a coaxial line and a two-wire open line compare?

Introduction / Context:Coaxial cables and two-wire open lines (ladder line) are common RF transmission media. Their characteristic impedance Z0 and phase velocity v_p follow from geometry and dielectric properties. Comparing them helps guide cable selection for matching and loss considerations.

Given Data / Assumptions:

• Typical two-wire open line in air (ε_r ≈ 1) with high Z0 (often hundreds of ohms).
• Typical coax uses a solid or foamed dielectric (ε_r > 1) and has Z0 around 50–75 Ω.
• Equal port impedances assumed for comparison.

Concept / Approach:Characteristic impedance: two-wire lines in air generally exhibit higher Z0 than common coaxes → Z0(coax) is less. Wave velocity: v_p = c / sqrt(ε_eff). For an air-line, ε_eff ≈ 1 → v_p ≈ c. For dielectric-filled coax, ε_eff ≈ ε_r > 1 → v_p < c. Therefore, both statements (a) and (b) are usually true in practical builds.

Step-by-Step Solution:

Verification / Alternative check:Vendor datasheets list velocity factor and Z0 values consistent with these trends for common products (RG-58, RG-59, ladder line, etc.).

Why Other Options Are Wrong:

• A or B alone omits the other true statement.
• D contradicts widely observed practice for typical materials and geometries.

Common Pitfalls:Assuming air-spaced coax (higher v_p) or dielectric-loaded two-wire; while exceptions exist, the general comparison stands.

Final Answer:both (a) and (b)