# Magnetron

The magnetron is not a simple linear signal source. Its parameters (efficiency, internal impedance, generated power and frequency, etc.) are interrelated and depend on many factors, such as anode voltage, applied DC magnetic field intensity (or electromagnet current), filament current, and even microwave load impedance.

Nevertheless, for the purpose of this program, the magnetron is simulated as a conventional linear signal source, defined by the following parameters:

- Anode voltage Va

- Anode current Ia

- Efficiency, relating the input DC power to the RF power delivered to a matched load (see Power to Match below).

- Internal impedance, expressed in terms of source reflection coefficient magnitude and phase. For a system with a circulator, the source reflection coefficient GS is the one that would be seen when looking into the magnetron through the circulator.

The following program controls pertain to the magnetron:

Anode V

The Anode V edit box is used for entering the magnetron DC anode voltage in volts.

Anode I

The Anode I edit box is used for entering the magnetron DC anode current in amperes.

Efficiency

The Efficiency edit box is used for entering the magnetron efficiency as a percentage. The value can also be incremented by the attached up-down control. Efficiency relates the DC input power to the RF power delivered to a matched load.

The controls contained in the Source Reflection box are related to the magnetron reflection coefficient (or that of a magnetron-circulator combination):

Magnitude

The Magnitude edit box is used for defining the source reflection coefficient magnitude |GS|. Depending on the setting of the attached pull-down selection box (Mag, dB, SWR), the value can be typed in as follows:

Mag Linear reflection coefficient magnitude (0 to 1)

dB Reflection coefficient magnitude in dB (negative of return loss)

SWR Voltage Standing Wave Ratio VSWR of the source (values ³ 1)

Note that changing the format recalculates the current reflection coefficient to the new format, so this can also serve as a tool for converting reflection coefficient to return loss or to VSWR, or vice versa.

Phase

The Phase edit box is used for defining the source reflection coefficient phase angle in degrees (‑180 to 180). The value can also be stepped by the attached up-down control.

Mismatch

The Mismatch text box displays the computed source mismatch factor mS . The source mismatch factor is a figure representing the fraction of the power of an external wave incident on the source that is absorbed within the source. It is computed as

where GS is the source reflection coefficient.

The mismatch factor can be displayed as a linear dimensionless quantity, in dB, or in percent. To change the format, select it from the attached pull-down selection box.

Two characteristic powers that a source can deliver are displayed in the following text boxes:

Power to Match

Power to Match box displays the power that a source would deliver to a matched load (i.e., a load with zero reflection coefficient). Magnetron efficiency is related to this power, hence Power to Match is computed as the product of the DC input power and magnetron’s efficiency.

Available Power

Available Power box displays the maximum power a linear source is capable of delivering when varying its load impedance (load reflection coefficient). It is the power absorbed in the load with the reflection coefficient GL equal to the complex conjugate of the source reflection coefficient GS :

The available power ( Pav ) and the power delivered to a matched load ( Pm ) are related by source mismatch factor ( mS ) as

However, there is a catch when using the available power in connection with magnetrons (and, generally, high-power generators).

To achieve high magnetron efficiency, its internal reflection coefficient must be high (otherwise a large portion of the generated power would convert to heat within the magnetron itself). Magnetrons therefore act as very mismatched signal sources.

As a result of this excessive source mismatch, the available power turns out to be much higher than the power delivered to a load, even higher than the input DC power! The term available power therefore loses its physical meaning and becomes only a fictitious quantity: an extrapolation, useful only for mathematical analysis. Therefore, do not worry about the energy conservation law violation.

In order that high-power magnetrons appear matched, they are combined with circulators. For an ideal circulator, this has the following consequences:

- The magnetron always looks into a nearly-matched load. This is the load magnetrons have been optimized for.

- The power that the magnetron delivers is always equal to the power deliverable to a matched load (regardless of actual load reflection coefficient).

- Looking from outside, the magnetron-circulator combination appears well-matched (GS » 0).

- Any power reflected from the actual load is fully absorbed in the circulator (diverted to an auxiliary load).

Note: In practice, however, no circulator is perfectly matched, and therefore variations of the incident power with load will be experienced. Depending on conditions, it may be even ±10% or more.