Effect of loading a transmission line (e.g., with loading coils in telephony): what happens to Z0, the attenuation constant α, and the phase constant β? Select the correct combined qualitative effect.

Introduction / Context:
In classical telephony and low-RF practice, long cables were sometimes ‘‘loaded’’ by inserting series inductance (loading coils) to improve voice-band transmission. Understanding how loading alters the characteristic impedance (Z0), the attenuation constant (α), and the phase constant (β) helps explain why loading extends useful bandwidth and reduces distortion in the intended band.

Given Data / Assumptions:

• Loading means adding series inductance per unit length (effective L increases).
• Capacitance per unit length C is essentially unchanged.
• We consider qualitative, band-limited effects near the passband created by loading.

Concept / Approach:
For a low-loss line: Z0 ≈ sqrt(L/C). Adding inductive loading raises L, so Z0 increases. The attenuation constant α depends on R and G relative to the reactive terms jωL and jωC; by increasing L, the reactive impedance dominates more strongly over R in the voice band, which typically reduces α in the passband. The phase constant β ≈ ω * sqrt(L * C), so increasing L raises β for a given frequency. Hence, the combined effect is higher Z0, lower α in the designed band, and higher β.

Step-by-Step Solution:

Verification / Alternative check:
Frequency-response plots of loaded lines show flatter amplitude and phase characteristics across the design band with reduced attenuation compared to the same cable without loading coils.

Why Other Options Are Wrong:

• A: Claims α increases, contradicting the typical passband reduction.
• C: Predicts all three decrease; inconsistent with Z0 ≈ sqrt(L/C).
• D: Predicts Z0 and β decrease; both should increase when L increases.

Common Pitfalls:
Assuming loading always improves loss across all frequencies; in reality, loading shapes a passband and introduces cutoff behavior outside it.

Final Answer:
increase in Z0 and β but decrease in α