In typical high-frequency transmission-line modeling (RLCG model), which primary distributed parameter is often negligible under many practical conditions?
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AG (shunt conductance)
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BR (series resistance)
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CL (series inductance)
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DC (shunt capacitance)
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EAll are always negligible
Answer
Correct Answer: G (shunt conductance)
Explanation
Introduction / Context:Distributed-parameter models describe lines using R, L, C, and G per unit length. Understanding which parameters dominate guides low-loss approximations and design choices across frequency bands.
Given Data / Assumptions:
- Dielectric is low-loss (tan δ small).
- Conductor losses and skin effect may be present but manageable.
- Typical RF/microwave coaxial, microstrip, or twin-lead environments.
Concept / Approach:At many RF frequencies with quality dielectrics, shunt conductance G (which models dielectric leakage) is very small compared to susceptance from C and reactance from L. Hence, the well-known 'low-loss line' approximation treats R and G as small compared to ωL and ωC, with G often the smallest of the four.
Step-by-Step Solution:
Telegrapher parameters: R (Ω/m), L (H/m), C (F/m), G (S/m).Dielectric loss modeled by G is minimal for high-quality, dry dielectrics; tan δ ≈ ωC/G is low.Thus, for many practical lines, G is negligible first; sometimes R is also small but not as negligible as G in many PCB and coax cases.Verification / Alternative check:Attenuation constant α ≈ (R/2)√(C/L) + (G/2)√(L/C); for low-loss lines, the G-term is frequently orders of magnitude smaller than the R-term.
Why Other Options Are Wrong:
L and C define the line's phase velocity and characteristic impedance and are never negligible.R can be small, but conductor loss is often significant compared with G, especially with skin effect.Common Pitfalls:
Assuming G is always zero; humidity or lossy dielectrics can increase G at low or very high frequencies.Final Answer:
G (shunt conductance)