Read the paragraph and answer the questions : Microwave tubes are used as microwave amplifiers and oscillators. Three general type of microwave tubes in which third type tubes are important because in these tubes there is an interaction between an electron and an RF field is continuous. The Travelling Wave Tube (TWT) is the prime example of this interaction. It is an amplifier, whose oscillator counter part is called Backward Wave Oscillator (BWO). The second sub-group consists of tubes in which a magnetic field ensures a constant electron beam – RF field interaction, and this is complemented by the Cross-Field Amplifier (CFA). Multicavity Klystron is used as high and very high power amplifiers in the UHF and microwave ranges. The frequency range covered is from about 250 MHz to over 95 GHz. The reflex-Klystron is a low power microwave oscillator. It is assumed that oscillations are started by switching transients. For oscillations to be maintained the transient time in the repeller space cycle is given as \(T=\left(n+\dfrac{3}{4}\right)\) where n is an integer, each value of n is said to correspond to different reflex klystron mode. Reflex Klystrons with integral cavities are available in the frequency range 4 to 200 GHz.
One of the reasons why vacuum tubes eventually fail at microwave frequencies is that their
noise figure increases
Three of the four options state a real limitation with its direction reversed, and the fourth states it correctly — so the answer is option 4.
| Option | What actually happens | Verdict |
|---|---|---|
| Transit time too short | It becomes too long relative to the period | ✗ Reversed |
| Shunt capacitance too large | Its reactance becomes too small | ✗ Reversed |
| Series inductive reactance too small | It becomes too large | ✗ Reversed |
| Noise figure increases | ✓ | Correct |
The three limitations, stated properly.
Transit time. Electrons take a finite time to cross the grid-cathode gap. At low frequencies this is a negligible fraction of a cycle, but as the period shrinks the transit time becomes comparable with it, and the grid voltage reverses before the electrons have arrived. Control is lost, and the input conductance the effect creates loads the driving circuit:
\(\tau=\dfrac{d}{v}\qquad\text{must satisfy}\qquad\tau\ll T=\dfrac{1}{f}\)
Interelectrode capacitance. The electrodes form small capacitors of a few picofarads. Their reactance \(1/\omega C\) falls as frequency rises, until at microwave frequencies it is low enough to short-circuit the signal from grid to cathode.
Lead inductance. The connecting leads have an inductance of a few nanohenries, whose reactance \(\omega L\) rises with frequency, until it inserts a significant impedance in series with each electrode — degenerating the cathode circuit and detuning the input.
Why the noise figure rises is a consequence of the first of these: the transit-time effect produces a random loading of the input circuit, and the reduced gain of the first stage means later stages contribute more of the total noise. By Friis's formula the overall noise figure is dominated by the first stage's gain, and when that gain collapses the noise figure climbs.
The remedy is the whole subject of the passage : abandon the attempt to keep transit time short, and build tubes whose operation depends on it — klystrons, TWTs and magnetrons, in which the electron transit is deliberately used to modulate the beam.
Hence, the correct statement is that the noise figure increases.
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(A) The cyclotron angular frequency ωc = 5.91 × 106 rad
(B) ωc = 5.91 × 1010 rad
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