8 cavity cylindrical travelling wave magnetron

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Microwave Engineering - Magnetrons

Unlike the tubes discussed so far, Magnetrons are the cross-field tubes in which the electric and magnetic fields cross, i.e. run perpendicular to each other. In TWT, it was observed that electrons when made to interact with RF, for a longer time, than in Klystron, resulted in higher efficiency. The same technique is followed in Magnetrons.

Types of Magnetrons

There are three main types of Magnetrons.

Negative Resistance Type

• The negative resistance between two anode segments, is used.
• They have low efficiency.
• They are used at low frequencies (< 500 MHz).

Cyclotron Frequency Magnetrons

The synchronism between the electric component and oscillating electrons is considered.

Useful for frequencies higher than 100MHz.

Travelling Wave or Cavity Type

The interaction between electrons and rotating EM field is taken into account.

High peak power oscillations are provided.

Useful in radar applications.

Cavity Magnetron

The Magnetron is called as Cavity Magnetron because the anode is made into resonant cavities and a permanent magnet is used to produce a strong magnetic field, where the action of both of these make the device work.

Construction of Cavity Magnetron

A thick cylindrical cathode is present at the center and a cylindrical block of copper, is fixed axially, which acts as an anode. This anode block is made of a number of slots that acts as resonant anode cavities.

The space present between the anode and cathode is called as Interaction space . The electric field is present radially while the magnetic field is present axially in the cavity magnetron. This magnetic field is produced by a permanent magnet, which is placed such that the magnetic lines are parallel to cathode and perpendicular to the electric field present between the anode and the cathode.

The following figures show the constructional details of a cavity magnetron and the magnetic lines of flux present, axially.

This Cavity Magnetron has 8 cavities tightly coupled to each other. An N-cavity magnetron has $N$ modes of operations. These operations depend upon the frequency and the phase of oscillations. The total phase shift around the ring of this cavity resonators should be $2n\pi$ where $n$ is an integer.

If $\phi_v$ represents the relative phase change of the AC electric field across adjacent cavities, then

$$\phi_v = \frac{2 \pi n}{N}$$

Where $n = 0, \: \pm1,\: \pm2,\: \pm \: (\frac{N}{2} -1), \: \pm \frac{N}{2}$

Which means that $\frac{N}{2}$ mode of resonance can exist if $N$ is an even number.

$$n = \frac{N}{2} \quad then \quad \phi_v = \pi$$

This mode of resonance is called as $\pi-mode$.

$$n = 0 \quad then \quad \phi_v = 0$$

This is called as the Zero mode , because there will be no RF electric field between the anode and the cathode. This is also called as Fringing Field and this mode is not used in magnetrons.

Operation of Cavity Magnetron

When the Cavity Klystron is under operation, we have different cases to consider. Let us go through them in detail.

If the magnetic field is absent, i.e. B = 0, then the behavior of electrons can be observed in the following figure. Considering an example, where electron a directly goes to anode under radial electric force.

If there is an increase in the magnetic field, a lateral force acts on the electrons. This can be observed in the following figure, considering electron b which takes a curved path, while both forces are acting on it.

Radius of this path is calculated as

$$R = \frac{mv}{eB}$$

It varies proportionally with the velocity of the electron and it is inversely proportional to the magnetic field strength.

If the magnetic field B is further increased, the electron follows a path such as the electron c , just grazing the anode surface and making the anode current zero. This is called as " Critical magnetic field " $(B_c)$, which is the cut-off magnetic field. Refer the following figure for better understanding.

If the magnetic field is made greater than the critical field,

$$B > B_c$$

Then the electrons follow a path as electron d , where the electron jumps back to the cathode, without going to the anode. This causes " back heating " of the cathode. Refer the following figure.

This is achieved by cutting off the electric supply once the oscillation begins. If this is continued, the emitting efficiency of the cathode gets affected.

Operation of Cavity Magnetron with Active RF Field

We have discussed so far the operation of cavity magnetron where the RF field is absent in the cavities of the magnetron (static case). Let us now discuss its operation when we have an active RF field.

As in TWT, let us assume that initial RF oscillations are present, due to some noise transient. The oscillations are sustained by the operation of the device. There are three kinds of electrons emitted in this process, whose actions are understood as electrons a , b and c , in three different cases.

When oscillations are present, an electron a , slows down transferring energy to oscillate. Such electrons that transfer their energy to the oscillations are called as favored electrons . These electrons are responsible for bunching effect .

In this case, another electron, say b , takes energy from the oscillations and increases its velocity. As and when this is done,

• It bends more sharply.
• It spends little time in interaction space.
• It returns to the cathode.

These electrons are called as unfavored electrons . They don't participate in the bunching effect. Also, these electrons are harmful as they cause "back heating".

In this case, electron c , which is emitted a little later, moves faster. It tries to catch up with electron a . The next emitted electron d , tries to step with a . As a result, the favored electrons a , c and d form electron bunches or electron clouds. It called as "Phase focusing effect".

This whole process is understood better by taking a look at the following figure.

Figure A shows the electron movements in different cases while figure B shows the electron clouds formed. These electron clouds occur while the device is in operation. The charges present on the internal surface of these anode segments, follow the oscillations in the cavities. This creates an electric field rotating clockwise, which can be actually seen while performing a practical experiment.

While the electric field is rotating, the magnetic flux lines are formed in parallel to the cathode, under whose combined effect, the electron bunches are formed with four spokes, directed in regular intervals, to the nearest positive anode segment, in spiral trajectories.

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Definition : A magnetron is a device that generates high power electromagnetic wave. It is basically considered as a self-excited microwave oscillator. And is also known as a crossed-field device .

The reason behind calling it so is that the electric and magnetic field produced inside the tube are mutually perpendicular to each other thus the two crosses each other.

Content: Magnetron

Operating principle.

• Construction

Frequency Pushing and Pulling

Disadvantages.

• Applications

A magnetron is basically a vacuum tube of high power having multiple cavities. It is also known as cavity magnetron because of the presence of anode in the resonant cavity of the tube.

The operating principle of a magnetron is such that when electrons interact with electric and magnetic field in the cavity then high power oscillations get generated.

Magnetrons are majorly used in radar as being the only high power source of RF signal as a power oscillator despite a power amplifier. It was invented in the year 1921 by Albert Hull. However, an improved high power cavity magnetron was invented in 1940 by John Randall and Harry Boot.

Here in this article, we will discuss how a cavity magnetron works. But before that, we must know how a magnetron is constructed.

Construction of Magnetrons

A cylindrical magnetron has a cylindrical cathode of a certain length and radius present at the centre around which a cylindrical anode is present. The cavities are present at the circumference of the anode at equal spacing.

Also, the area existing between anode and cathode of the tube is known as interaction space/region .

It is to be noted here that there exists a phase difference of 180⁰ between adjacent cavities. Therefore, cavities will transfer their excitation from one cavity to another with a phase shift of 180⁰.

Thus we can say that if one plate is positive then automatically its adjacent plate will be negative. And this is clearly shown in the figure given above.

More specifically we can say that edges and cavities show180⁰ phase apart relationship.

As we have already discussed that here the electric and magnetic field are perpendicular to each other. And the magnetic field is generated by using a permanent magnet.

Working of Magnetron

The excitation to the cathode of the magnetron is provided by a dc supply which causes the emergence of electrons from it.

Here in this section, we will discuss the working of magnetron under two categories. First without applying the RF input to the anode and the second one with the application of RF input.

1. When RF input is not present

Case I : When the magnetic field is 0 or absent

When the magnetic field is absent then the electron emerging from the cathode radially moves towards the anode. This is shown in the figure below:

This is so because the moving electron does not experience the effect of the magnetic field and moves in a straight path.

Case II : When a small magnetic field is present

The reaching of the emitted electrons from the cathode back to it is known as back heating . So to avoid this the electric supply provided to the cathode must be cut-off after oscillations have been set up in the tube.

2. When the RF field is present

Case I : In case an active RF input is provided to the anode of the magnetron then oscillations are set up in the interaction space of the magnetron. So, when an electron is emitted from the cathode to anode then it transfers its energy in order to oscillate.

Such electrons are called favoured electrons . In this condition, the electrons will have a low velocity and thus will take a considerably high amount of time to reach from cathode to anode.

Case II : Another condition arises in the presence of RF input. In this case, the emitted electron from the cathode while travelling takes energy from the oscillations thereby resultantly increasing its velocity.

So despite reaching the anode, the electrons will bounce back to the cathode and these electrons are known as unfavoured electrons .

Case III : When the RF input is further increased then the electron emitted while travelling increases its velocity in order to catch up the electron emitted earlier with comparatively lower velocity.

So, all those electrons that do not take energy from the oscillations for their movement are known as favoured electrons. And these favoured electrons form electron bunch or electron cloud and reaches anode from the cathode.

The formation of electron bunch inside the tube is known as phase focusing effect .

Due to this, the orbit of the electron gets confined into spokes. These spokes rotate according to some fractional value of electron emitted by the cathode until it reaches anode while delivering their energy to oscillations.

However, the electrons released from the region of cathode between spokes, will take the energy of the field and get back to the cathode very quickly. But this energy is very small in comparison to the energy delivered to the oscillations. This is shown in the figure below:

The movement of these favoured electrons inside the tube enhances the field existing between the gaps in the cavity. This leads to sustained oscillations inside the magnetron thereby providing high power at the output.

The variation in the oscillating frequency of the magnetron give rise to the term frequency pushing and pulling .

When the voltage applied at the anode of the magnetron is varied then this causes the variation in the velocity of the electrons moving from cathode to anode. This resultantly changes the frequency of oscillations.

Therefore, we can say when the resonant frequency of the magnetron shows variation due to the change in the anode voltage then it is known as frequency pushing .

The change in resonant frequency is sometimes a result of the change in the load impedance of the magnetron. The load impedance varies when the change is purely resistive or reactive. This frequency variation is known as frequency pulling . A steady power supply can provide a reduction in this frequency variation.

• Magnetrons are a highly efficient device used for generation of the high power microwave signal.
• The use of magnetrons in radar can produce radar system of better quality for tracking purpose.
• It is usually small in size thus less bulky.
• It is quite expensive.
• Despite producing a wide range of frequency, there exists a drawback in controllability of the generated frequency.
• It offers average power of around 1 to 2 kilowatts.
• Magnetrons are quite noisy.

Applications of Magnetron

• A major application of magnetron is present in a pulsed radar system in order to produce a high-power microwave signal.
• Magnetrons are also used in heating appliances likes microwave ovens so as to produce fixed frequency oscillations.
• Tunable magnetrons find their applications in sweep oscillators.

It is noteworthy here that this mode of operation of the magnetron is also known as π mode. This is so because a proper phase shift of 180⁰ is maintained between two adjacent plates. Also, it is to be noted that oscillations are only built-up in π mode.

Related Terms:

• Transmission Lines
• IMPATT Diode
• Backward Wave Oscillator

4 thoughts on “Magnetron”

Very very helpful

This is soo easy to understand Thank you

Very helpful thanks

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Cylindrical Magnetron Derivation

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Microwave Sources, Sensors, and Devices

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Part of the book series: Developments in Electromagnetic Theory and Applications ((DETA,volume 10))

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The generation of microwaves has been the main impediment to the development of microwave systems until the late 1930’s, when the first practical microwave sources were developed. Naturally, these were essentially vacuum tubes but the principles involved had to be different than those used for low frequency vacuum tubes. The limitations of interelement capacitance, for example, was one of the major problems in extending the operation of vacuum tubes to higher frequencies. The transit time of the electrons was of such orders of magnitude that it was not practical to operate beyond the lowest ranges of microwaves. The specially developed microwave tubes operate on velocity modulation of the electron beam and transition time does not play a role in these devices.

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Ida, N. (1992). Microwave Sources, Sensors, and Devices. In: Microwave NDT. Developments in Electromagnetic Theory and Applications, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2739-4_6

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