In the standing wave pattern formed on a transmission line due to impedance mismatch, how are the positions of voltage nodes and current antinodes, as well as current nodes and voltage antinodes, related?

Introduction / Context:
Standing waves form on a transmission line when the line is not properly matched with its load, causing reflections. Understanding the relationship between voltage and current standing wave patterns is essential in RF engineering and impedance matching applications.

Given Data / Assumptions:

• Transmission line with forward and reflected waves.
• Lossless line assumption.

Concept / Approach:

Voltage and current distributions on a standing wave pattern are spatially shifted by 90 degrees. Where voltage reaches minimum (node), current reaches maximum (antinodes). Where voltage reaches maximum (antinodes), current is at minimum (node). Hence, voltage nodes always coincide with current antinodes and vice versa.

Step-by-Step Solution:

Verification / Alternative check:

Microwave textbooks confirm that voltage and current standing wave patterns are spatially offset by λ/4, supporting this relationship.

Why Other Options Are Wrong:

• Option A: Nodes do not coincide; one is maximum when the other is minimum.
• Option B: Antinodes also do not coincide; they are shifted.
• Option D: Both statements are incorrect together.
• Option E: Not applicable as option C is correct.

Common Pitfalls:

Confusing optical interference patterns with RF standing waves; assuming voltage and current behave identically along the line.

Final Answer:

Voltage nodes coincide with current antinodes, and current nodes coincide with voltage antinodes