For a microstrip line printed on a substrate with relative permittivity ε_r, the effective dielectric constant ε_eff of the quasi-TEM mode (accounting for fringing fields in air) is typically

Introduction / Context:
Microstrip supports a quasi-TEM mode with fields partly in the substrate and partly in air. Designers use an effective dielectric constant ε_eff to model phase velocity, impedance, and dispersion of this mixed-media line.

Given Data / Assumptions:

• Microstrip conductor on a dielectric substrate (ε_r > 1) with air above.
• Operating in microwave region where quasi-TEM approximation is valid.
• Fringing fields extend significantly into air.

Concept / Approach:

Because a portion of the field lines pass through air (ε ≈ 1) and the rest through the substrate (ε_r), the modal effective permittivity satisfies 1 < ε_eff < ε_r. The exact value depends on geometry (conductor width, substrate thickness) and ε_r, and it approaches ε_r only for very wide traces or very thick/high-ε_r substrates that confine more field in the dielectric.

Step-by-Step Solution:

Verification / Alternative check:

EM solvers and closed-form models consistently produce ε_eff values between 1 and ε_r for practical microstrip geometries.

Why Other Options Are Wrong:

• ε_eff > ε_r or =1: Physically inconsistent for microstrip with finite substrate.
• Independent of ε_r: Contradicts the mixed-media nature.

Common Pitfalls:

Assuming ε_eff equals ε_r (that would be closer for stripline with full dielectric confinement).

Final Answer:

less than ε_r (but greater than 1)