In a traveling-wave tube (TWT) amplifier, how does the amplitude of the resultant RF wave along the helix vary under small-signal operation?
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AIt increases exponentially along the interaction region
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BIt increases linearly with distance
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CIt decreases exponentially due to loss
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DIt is almost constant from input to output
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EIt oscillates periodically between two levels
Answer
Correct Answer: It increases exponentially along the interaction region
Explanation
Introduction / Context:Traveling-wave tubes (TWTs) are broadband linear amplifiers. An electron beam interacts continuously with an RF wave on a slow-wave structure (e.g., helix), transferring kinetic energy to the wave and producing gain.
Given Data / Assumptions:
- Small-signal regime (no saturation).
- Proper synchronism between electron beam and RF wave phase velocity.
- Neglecting distributed loss for the conceptual answer.
Concept / Approach:
In the linear region, the coupled-mode equations predict an exponential growth of the RF amplitude with distance along the helix, characterized by a spatial gain constant dependent on beam current, voltage, and circuit parameters.
Step-by-Step Solution:
Electron beam is velocity-modulated by the RF field on the helix.Bunching forms and exchanges energy with the wave.The wave amplitude grows approximately as exp(g * z), where g is the gain per unit length.Verification / Alternative check:
Measured TWT gain (in dB) scales with length in small-signal operation, consistent with exponential growth until saturation effects limit further increase.
Why Other Options Are Wrong:
- Linear increase: An oversimplification; the correct dependence is exponential in the small-signal model.
- Decrease constant: Contradicts amplification mechanism.
- Constant or oscillatory amplitude: Not true for an amplifying device in linear regime.
Common Pitfalls:
Confusing TWT amplifiers with oscillators; assuming uniform amplitude due to misinterpreting the helix as a passive line.
Final Answer:
It increases exponentially along the interaction region