MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA

SAINT PETERSBURG STATE ELECTROTECHNICAL UNIVERSITY

«LETI» N.A. V.I. ULYANOVA (LENINA)

DEPARTAMENT ME

5,75 +1а=6,75 балл

REPORT

on individual homework №2

in the discipline «Microwave electronics»

Topic: VACUUM DEVICES

Student №8 gr. 3206 __________

Teacher __________ Ivanov V. A.

Saint Petersburg

2026

Content

Task 1 3

Task 2 4

Task 3 8

Task 4 11

Task 5 15

Task 6 18

Sources 21

Task 1

1. For the selected device - Mitron, describe:

   1. Operating principle using: hydrodynamic approach and formula , quantum approach.

   2. What are the main similarities and differences between the devices?

   3. Estimate the typical size of one of the devices if it operates at a frequency

Power, gain, and other parameters - choose yourself, based on the typical parameters of this type of device at istokmw.ru

2. Solving:

   1. Principle using: [2], [3]

A mitron is a type of magnetron in which frequency adjustment is achieved by varying the anode voltage.

For a mitron (and other M-type devices), the power formula is:

An electron beam from a cold cathode is fed into the interaction region—between the interdigital slow-wave structure and the cold cathode. The beam drifts in the crossed fields E and B; when the drift velocity coincides with the phase velocity, phase matching occurs. The longitudinal high-frequency field модулирует modulates the longitudinal velocity of the electrons , forming charge bunches – spokes. Entering the decelerating phase of the field, the electrons transfer their power through a coaxial terminal.

In the quantum approach, discrete Landau levels exist in the crossed fields. The high-frequency field induces transitions between them, either emitting or absorbing. If phase matching conditions are met, induced emission—coherent amplification of the wave—occurs.

2. Similarities and differences:

All proposed devices operate in the microwave range, use a flow of electrons, and the interaction occurs between the electron and the field.

The difference between the devices is in the way the electrons interact with the field:

• Grid-controlled field control: These work poorly at high frequencies. These include the triode and tetrode.

• Electron velocity modulation: These have a narrow frequency band. These include the klystron and the reflection klystron.

• Wave slowing through a slow-wave structure: broadband. These include TWT and BWT.

• Movement in crossed E and B fields: high power. These include the magnetron and mitron.

• Cyclotron propulsion of electrons: very high operating frequencies. These include the gyrotron.

• Electron bremsstrahlung. This includes ubitron.

• Passage through an undulator: large dimensions, wide frequency range. These include a free-electron laser.

3. Estimation of typical size:

Let's choose a magnetron for calculating the characteristic size. The characteristic size is the resonator size. For a magnetron, the characteristic size is proportional to half the wavelength. [4]

Then the characteristic size:

1 Балл. Странно: ни конструкции,ни параметров… Task 2

1. Devices with quasi-static control. Triode.

Calculate the range of static carrier flight angles in the cathode-to-grid gap of a triode operating in one of the modes A, B, or C (choose your own). Specify the cathode phases from 0 to 360. (The number of phases is up to you. Assume the voltage on the electrodes remains constant during the flight time). Operate frequency 100*N_student [MHz], cathode-to-grid distance 0.2*N_group [mm], constant voltage on the anode 50*N_group [V], mesh permeability 0.01*(N_student + N_group).

Calculate the interaction coefficient for these angles. Using the results obtained, explain why triodes are inefficient at high frequencies.

Given:

Operate frequency:

Cathode-to-grid distance:

Constant voltage on the anode

Mesh permeability

Operating mode: A

Number op phases: φ₁ = 0, φ₂ = π/2, φ₃ = 3π/2

2. Solving:

Current voltage: [4]

Where the accelerating voltage consists of constant and variable components:

The angle of electron flight:[6]

From the law of conservation of energy:

Then:

Interaction coefficient: [6]

Selected phases:

-) φ₁ = 0

-) φ₂ = π/2

-) φ₂ = 3π/2

Increasing the wave frequency increases the electron flight angle, but the interaction coefficient decreases. Therefore, at high frequencies, there will be very little interaction between the flying electrons and the system's surfaces, and energy extraction will be very weak.

Answers:

The range of static angles of flight of electrons at a selected frequency:

[0.906; 1.57] rad

Interaction coefficients for angles in this range:

M(0) = 0.949

M(π/2) = 0.966

M(3π/2) = 0.9

0,5 Балл Task 3