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Origin of Sideband and Spurious Noisesin Microwave Oven Magnetron

In-Keun Baek, Matlabjon Sattorov, Ranajoy Bhattacharya, Seontae Kim, Dongpyo Hong,Sun-Hong Min, and Gun-Sik Park, Member, IEEE

Abstract— The 3-D particle-in-cell (PIC) simulations areperformed to determine the origin of sideband and spuriousnoises generated in a cooker magnetron. A novel simula-tion technique is used, which introduces cathode emissioncurrent nonuniformities. These nonuniformities are due tononuniform distributions of electric field on a thermionicemission surface, which result from cathode geometry. It isshown that cathode end-caps shape and magnetic pole-piece geometries are the causes of sideband and spuriousnoises in conventionalmicrowave ovens.The 3-D simulationresults are in satisfactory agreement with the spectrum of atypical cooker magnetron.

Index Terms— Cathodes, magnetrons, oscillator noise.

I. INTRODUCTION

A MAGNETRON oscillator is primarily used to generatehigh-power microwaves for heating systems, radars, and

microwave ovens in homes [1]. A magnetron is a cross-fielddevice with high efficiency (∼70%), low weight/power ratio,and low cost, which makes it suitable for use in microwavepower transmission [2] and solar power satellites [3].

The drawbacks of widely used commercially availablemagnetrons used in microwave cooking, which operate at2.45 GHz, are wideband operation and spurious noise leaks

Manuscript received February 10, 2017; revised April 14, 2017 andMay 18, 2017; accepted May 30, 2017. This work was supportedby the National Research Foundation of Korea (NRF) through theKorea government (MSIP) under Grant 2016R1A3B1908336. The reviewof this paper was arranged by Editor M. Thumm. (Corresponding author:Gun-Sik Park.)

I.-K. Baek is with the Center for THz-driven Biological Systems,Department of Physics and Astronomy, Seoul National University,Seoul 151-747, South Korea, and also with Seoul-Teracom, Inc.,Seoul 151-747, South Korea (e-mail: 100inbun@gmail.com).

M. Sattorov is with Seoul-Teracom, Inc., Seoul 151-747, South Korea,and also with the Advanced Institutes of Convergence Technology,Seoul National University, Suwon 443-270, South Korea (e-mail:sattorovmatlabjon@gmail.com).

R. Bhattacharya is with the Center for THz-driven Biological Systems,Department of Electrical and Computer Engineering, Seoul NationalUniversity, Seoul 151-747, South Korea (e-mail: joy_trm@yahoo.com).

S. Kim and D. Hong are with the Center for THz-driven BiologicalSystems, Department of Physics and Astronomy, Seoul National Uni-versity, Seoul 151-747, South Korea (e-mail: kimseonta@gmail.com;dove9245594@snu.ac.kr).

S.-H. Min is with Korea Heavy Ion Medical Accelerator Project,Korea Institute of Radiological and Medical Science, Seoul 01812,South Korea (e-mail: msh103@kirams.re.kr).

G.-S. Park is with the Center for THz-driven Biological Systems,Department of Physics and Astronomy, Department of Electrical andComputer Engineering, Seoul National University, Seoul 151-747,South Korea, and also with Seoul-Teracom, Inc., Seoul 151-747,South Korea (e-mail: gunsik@snu.ac.kr).

Digital Object Identifier 10.1109/TED.2017.2714339

Fig. 1. Spectrum of origin of cooker magnetron noises.

that can interfere with other communication signals. It hasbeen determined by several researchers [4]–[6] that there aremultiple causes of these spurious noises (Fig. 1), which are asfollows: line noise below 1 GHz, which is typically suppressedby additional circuits and elements to prevent interferencewith radio, TV, and other electronic systems, noises dueto ion-plasma oscillation and rotational motion of electronbeams used in an interaction space, and noises due to higherharmonic components of resonance modes. Other source ofnoises is internal reflections from magnetron parts, such ashigh-voltage cathode leads [4] and nonuniform emission dueto cathode temperature distribution [5]. Yamamoto et al. [6]experimentally demonstrated that noises below 1 GHz, whichare caused by ions trapped in the vicinity of a cathode, can beeffectively reduced using an ion-drain electrode. By employingan internal feedback mechanism, Mitani et al. [7] achievednarrowband oscillation and the reduction of sideband noisesup to 60 dB, spurious noise reduction up to 50 dB inhigh frequency bands (4–10 GHz), and line conductive noisereduction up to 40 dB in low frequency bands (∼1 GHz).The internal feedback mechanism can be applied using adc stabilized power supply and turning OFF filament currentduring oscillation.

Intermodulation noises close to operating frequency are con-sidered as sources of interference in wireless communicationowing to their high amplitude. There are alternative methodsto reduce these noises, such as “electric priming” [8] and“magnetic priming” [9], [10], which reduce startup noisesthrough effective selection of the operating π-mode.

A time-domain analysis of an experimentally measuredmagnetron spectrum was performed by Mitani et al. [11], whopredicted the origin of noises. However, the mechanism ofnoise generation in cross-field devices is not fully understood,

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Fig. 2. Typical cooker magnetron noise spectra at normal operatingcondition (experiment).

and currently, there are no exact predictive computationalcalculations.

In this paper, we used 3-D simulation to determine andpredict the origin of sideband and spurious noises generatedby conventional cooker magnetrons as shown in measuredspectrum in Fig. 2. Line noises below 1 GHz were notconsidered. Using a novel simulation technique, we intro-duced emission current nonuniformities on a cathode surfaceand determined that the primary cause of sideband noisesis cathode geometry, which leads to non-uniform surfacetemperature on the filament, resulting in nonuniform electronbeam emission. In addition, this paper confirms the results ofMitani et al. [5], who studied cathode geometry experimentallyby shielding it at different locations to obtain uniform cathodetemperature. They shielded a cathode on the high-voltageinput side of the filament. Kohsaka et al. [12] suggested thata cathode should be shielded on the radio frequency (RF)output side and the high-voltage input side, which limits theemission of electrons from the ends of the filament. However,Mitani et al. [5] suggested using only high-voltage sideshielding, which is more effective than shielding both sides.

Our 3-D simulation analysis shows that the cathode geom-etry of a conventional cooker magnetron allows the filamentto emit electrons close to its ends, with nonuniform cathodeemission, which interacts with non-uniform electric field closeto the edge of anode vanes (cavities). Moreover, this is affectedby the shape and position of pole pieces.

II. SIMULATION MODEL AND ASSUMPTIONS

A commercialized ten-vane magnetron oscillator model isused for 3-D simulation, which is shown in Fig. 3. Theoscillator consists of a resonator with the double straps, anantenna, a cathode, the pole pieces, and a permanent magnet.The antenna is connected to one of the anode vanes toextract RF power, as shown in Fig. 3(b). The anode vanes arealternately connected to both sides of the straps to efficientlyexcite the operating π-mode, which reduces the oscillationstartup of the magnetron. The locations of the connections

Fig. 3. Schematics of a 10-vane strapped oven magnetron oscillatorin (a) xy plane and (b) xz plane. Electric priming is achieved by strapsconnected alternately to both sides of the anode vanes; locations ofconnections are indicated by dots. The antenna is connected to the anodeto extract microwave power.

between the anode vanes and straps are indicated by dots.The cathode is located at the center of the resonator withendcaps at both sides to prevent leakage current. The operatingfrequency of this magnetron is 2.45 GHz at a nominal voltageof 4.4 kV and an anode current of 330 mA with an outputpower of ∼1 kW. The measured frequency spectrum is shownin Fig. 2.

The following effects are analyzed to determine the originof noises in the cooker magnetron: 1) electron emissionnonuniformities on the cathode surface; 2) effect of emissioncurrent; and 3) effect of pole pieces and cathode end caps.

The MAGIC-3D code [13] with the particles has beenused to benchmark the magnetron performance successfully asshown in our previous works [8]. The measured output powerand operating frequency of commercial magnetron were ina good agreement with those by MAGIC-3D code. It is ourintention to use the same particle in cell (PIC) code, MAGIC-3D for the noise analysis. However, CST code [14] was usedin this paper to accommodate the geometries in such as thecathode and output section where the tetrahedral mesh hasan advantage over the hexahedral mesh. MAGIC-3D employsthe hexahedral meshes. So, all the works in this paper used

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Fig. 4. Cooker magnetron cathode; (a) original and (b) simplified model.

Fig. 5. Cooker magnetron geometry simulated in MAGIC-3D. Left: actualcathode. Right: simplified cooker magnetron model, cylindrical cathode.

MAGIC-3D code when the particle simulation is needed, whileCST is used without the particles.

Conventional cooker magnetrons use thermionic cathodesand temperature distribution in the cathodes depends on thecathode end-caps design. Nonuniform temperature distributionproduces nonuniform emission current, and this nonuniformitywas introduced in the simulation using explosive emissioninstead. Using explosive emission has many advantages com-pare to other emission mechanisms in simulations. Explosiveemission is totally geometry dependent phenomena, whereonly dc voltage is applied between cathode and anode andminimum E-field threshold provided. While for the thermionicemission model we have to provide exact work function ofmaterial and operation temperature, which can be taken fromexperimental data. For the field emission case, in additionto work function, we have to provide Fowler–Nordheim con-stants too, which is difficult to find exact numbers. Explosiveemission has a threshold electric field, at which the cathodestarts emitting electrons, and emission current depends oncathode geometry, i.e., the electric field close to cathodeendcaps is lower than that at its center, which produces currentnonuniformity. More electrons are emitted at the center, andthus, it carries more current.

The radius of the cylindrical cathode was optimized throughCST eigenmode simulations (Fig. 4) using tetrahedral meshes,to obtain a frequency shift of 0.0066% at the operatingπ-mode. When simplified cathode adopted, the CST eigen-mode simulation time was reduced from 35 to 1 h using aworkstation with 256-GB RAM and two processors of 3.5 GHzeach.

Fig. 6. Electron motion under the electromagnetic field in the interactionregion between the cathode and anode in the magnetron.

The emission area was estimated by calculating the totalemission area of the spiral filament and assigning it as a fixedcylindrical surface in the MAGIC-3D code (Fig. 5).

III. THEORETICAL CALCULATIONS

Before running simulations, we theoretically analyzed theorigin of measured sideband noises, which were shifted by65 MHz from the operating frequency. It is assumed that thisfrequency shift would be due to multiple reflections in themagnetron inner parts as suggested in [4]. In order to analyzethis, the propagation velocity of electromagnetic wave inmagnetron is needed to be estimated. In oscillation conditionof magnetron, the velocity of the electron beam must matchthe phase velocity of the oscillation mode formed near theanodes, so that the propagation velocity of the electromagneticwave can be approximated by the velocity of the electrons. Theelectron velocity in the interaction region between the cathodeand anode can be determined using the following equation:

va = ra θ̇a = raωc

2

(1 − r2

c

r2a

)(1)

where ωc = (e/m) · B is the electron cyclotron frequency,and ra and rc are the radii of the anode and cathode,respectively (see Fig. 6). The frequency of the electromagneticwave propagating between multiple reflections in the internalstructure of magnetron (i.e., cathode ends) can be determinedby considering half of the wave traveling time. Using thefrequency shift of experimental sideband noises (65 MHz),we calculated the wave traveling time to be τ ∼7.7 ns andthe distance propagated by this wave to be τ · va ∼46.2 cm,where va is given by (1).

The possible spots of the multireflection in the internalparts of the magnetron might be the pole pieces and cathodeend caps. The slight change of the distances between thepole pieces and cathode endcaps is made to see if thereexists the frequency change of the sideband noise usingMAGIC-3D simulation. The detailed result is described in thelatter part of this paper.

IV. SIMULATION RESULTS

A. Nonuniformities in Electron EmissionFrom the Cathode

As stated earlier, explosive emission was used in thisanalysis using MAGIC-3D. To determine the effect of current

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Fig. 7. MAGIC-3D: Emission area is shifted (a) to (b) to obtainnonuniform field interaction, i.e., to introduce the temperature effect onthe cathode surface.

nonuniformities due to nonuniform electric field distribution,which is affected by the end caps of the cathode, we shift theemission area to obtain nonuniform interaction of electronswith the RF field, as shown in Fig. 7. The electric fielddistribution on the cathode surface close to the endcaps isnot uniform owing to cooker magnetron geometry. Thus,when the emission area is not located at the center of theresonator [Fig. 7(b)], the emission from different positions onthe cathode is different. We used a nominal emission currentof 1 A.

First-order sideband noises were excited even when uniformcurrent emission [Fig. 7(a)] was used; their spectrum is shownin Fig. 8(a). Minor current nonuniformities produced othersideband noises, which are summarized in Table I.

When we moved the emission area close to the cathodeend caps, the emission current was not sufficient owing tolower electric field, which is required to emit electrons, andthis introduced the emission nonuniformity effect. From theTable I, one can see that the number of sideband noisesincreased for the case of nonuniform emission, which isconsisted with measured data. Based on this, we concludedthat more frequency components of sideband noises could beoriginated owing to cathode geometry, which allows emissioncurrent to be nonuniform, and these noises can be reducedusing a suitable cathode geometry design or by shielding thecathode close to its ends [5], [12].

TABLE IEFFECT OF CURRENT NONUNIFORMITIES ON SIDEBAND NOISES

Fig. 8. MAGIC-3D: Frequency spectrum of sideband noises, for sim-ulated geometries; (a) uniform emission and (b) non-uniform emissionshown in Fig. 7.

Fig. 9. MAGIC-3D: Spurious noises from 4 to 18 GHz, for simulatedgeometries shown in Fig. 7.

From Fig. 9, we can see that current nonuniformity has anegligible effect on higher harmonic noises. The frequencyand intensity of these noises are similar, as shown in Table II.Thus, we can conclude that current nonuniformity does notcause higher frequency spurious noises.

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TABLE IIEFFECT OF CURRENT NONUNIFORMITIES ON SPURIOUS NOISES

Fig. 10. MAGIC-3D: Emission current versus time, for the geometryshown in Fig. 7(a).

TABLE IIIEFFECT OF CURRENT ON SIDEBAND NOISES

B. Effect of Emission CurrentThe effect of current intensity was studied by changing the

emission current in the cathode in MAGIC-3D. Emission cur-rent is controlled by changing emission area and each emissionarea is assigned in the center of cathode with different areato rule out the nonuniform emission effect. Transition fromstationary state (below the space charge limit) to nonstationarystate (beyond the space charge limit) occurred as referredin [15] when emission current Ie was ∼3 times higher thanstart oscillation current Is (Fig. 10).

As seen from Fig. 11 and Table III, sideband noisesincrease (as expected) at higher emission currents, and their

Fig. 11. MAGIC-3D: Effect of emission current on sideband noises; solidline: Ie/Is = 1.7; dotted line: Ie/Is = 3.25.

Fig. 12. MAGIC-3D: Effect of emission current on spurious noises; solidline: nominal current, Ie/Is = 1.7; dotted line: Ie/Is = 3.25.

amplitude increases by ∼10 dBμV, while the amplitude ofthe operating mode does not change. A comparison withTable I and Fig. 8(b) shows that where current is nonuniform,spurious noises increase close to 4 GHz. The other resonancemodes shown Fig. 1 are not excited for analysis owing toeffective selection of the π-mode by the straps. In addition,the amplitude of spurious noises from 4 to 18 GHz increasesby ∼10 dBμV; however, the frequencies of these noises donot change (Fig. 12). Thus, similar to current nonuniformity,high emission current does not cause spurious noises.

C. Effect of Pole Pieces and Cathode Endcaps

The effect of pole pieces on noises was studied by removingthe pole pieces in the geometry shown in Fig. 7(a). Material ofpole pieces was assigned as nonmagnetic and magnetic fieldassigned as constant, to rule out the B-field effect. We obtaineda mode spectrum using CST code without the particles withand without the pole pieces (Fig. 13).

The power of the spurious noise near 4 GHz is increasedwhen the pole pieces is added. This is expected becauseadding pole pieces changes the geometry of the magnetroncavity. MAGIC-3D simulations with the particles show that

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Fig. 13. Mode spectrum in time domain; solid line: without pole pieces;dotted line: with pole pieces.

Fig. 14. MAGIC-3D: Full spectrum, including operating mode andspurious noises, with (dotted line) and without (solid line) pole pieces.

Fig. 15. MAGIC-3D: Spectrum of sideband noises at 1–4 GHz.

the amplitude of the second and third harmonics (Fig. 14)increased by approximately 15 dBμV; these can be suppressedby chokes, which were not included in these simulations todetermine the origin of these noises.

TABLE IVEFFECT OF POLE PIECES ON SIDEBAND NOISES

TABLE VEFFECT OF CATHODE END CAP ON SIDEBAND NOISES

Fig. 16. MAGIC-3D: |E| field plot at the xz plane. Top: without pole pieces.Bottom: with pole pieces.

To see the effects of the multiple reflections between internalstructures such as pole pieces and cathode end caps, a slight

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Fig. 17. Geometry of output section of cooker magnetron: chokes forharmonics noises suppression are marked.

Fig. 18. CST transient analysis of output section: operating modeefficiently propagated.

change of distance between the pole pieces and cathodeendcaps is made. MAGIC-3D simulation shows the shift of thesideband is occurred when the distance is slightly changed asshown in Table V and Fig. 15 for the pole pieces and Table VIfor the cathode end caps. The electric field distribution withand without the pole pieces are shown in Fig. 16. Thefrequency deviation of the sideband noise from the operatingfrequency is shifted from 50 to 40 MHz by increase of thedistance between the pole pieces from 12.8 to 13.8 mm.In Section III, using a simple model these frequency shifts arecalculated to be about 23 and 27 multiple reflection numbers.When the distance between the cathode endcaps is increasedby 1 mm but the noise power was decreased by 8.6 dBμV.Changed multiple reflection number shows us the evidencethat the multireflection between pole pieces contributes to thesources of the sideband noise. Multiple reflection numbershaving high value not being an integer suggest that the originof the sideband noise is not simply the multireflection of polepieces but the combination of multireflections from the wholeinternal structure of magnetron. On the other hand, geometryof the cathode end caps plays a role on the value of frequencyand power of the sideband noise as shown in Table V.

V. TIME-DOMAIN ANALYSIS OF OUTPUT

SECTION OF MAGNETRON

To determine whether the output section of the mag-netron efficiently suppress higher harmonics, which are shown

in Fig. 14, we performed transient time-domain analysisusing CST. The calculation of the length of each chockshows that it is equal to the half wavelength of the givenharmonics (Fig. 17).

We designed a special rectangular waveguide geometrythat converts radiation from the magnetron to a transverseelectric (TE) waveguide mode. A transverse electromagneticcoaxial mode was injected from the antenna side of the outputsection and a TE rectangular waveguide mode was detectedat the waveguide output. Frequency ranged from 0 to 20 GHzfor 20 injected modes. Electric field monitors were assignedfor visualizing wave propagation in the operating mode and itshigher harmonics at 2.45, 4.9, 7.35, 9.8, and 12.25 GHz. It wasconfirmed that the operating mode is efficiently transmittedthrough the waveguide (Fig. 18) while higher harmonics wereeffectively suppressed by chokes.

VI. CONCLUSION

We analyzed a conventional cooker magnetron using3-D simulation. A novel simulation technique was developedusing a PIC code for introducing different emission areas toobtain current nonuniformities. In addition, the effect of polepieces and different emission current values was studied forsideband noises close to the operating mode and spuriousnoises at higher frequencies ranging from 4 to 18 GHz. It wasdetermined that the primary cause of noises is cathode geom-etry design. Cathode end-cap geometry leads to nonuniformdistribution of electric field in the cathode filament and theemission of electrons with different energies and densities.Interaction of these nonuniform electrons with the RF fieldproduces noises. Pole pieces dominate the frequency deviationof the sideband noises and the cathode end caps affect to thenoise power of the sideband noises; therefore, they shouldbe appropriately designed to reduce this effect as much aspossible. Thus, a combination of nonuniform emission andpole pieces and end cap geometries produces sideband andspurious noises. High harmonic noises are suppressed effec-tively by chokes and other resonant modes through strapping.In this paper, we determined the origin of noises and predictedtheir behavior for suppression. Therefore, it is suggested todesign cathode geometry appropriately by the modification ofendcaps, the length of the cathode, and the pole pieces.

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[6] K. Yamamoto, H. Kuronuma, T. Koinuma, and N. Tashiro, “A studyof magnetron noise,” IEEE Trans. Electron Devices, vol. 34, no. 5,pp. 1223–1226, May 1987.

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[7] T. Mitani, N. Shinohara, and K. Hashimoto, “A fundamental study onspectral purity of a CW magnetron for microwave power transmission,”presented at the 29th URSI General Assembly, Chicago, IL, USA,Aug. 2008.

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In-Keun Baek received the B.S. degree inphysics from Seoul National University, Seoul,South Korea, in 2009, where he is currentlypursuing the Ph.D. degree with the Departmentof Physics and Astronomy.

Matlabjon Sattorov received the Ph.D. degreein physics from Seoul National University, Seoul,South Korea, in 2012.

He is currently a Senior Research Engineerwith Seoul-Teracom, Inc., Seoul, and a Vis-iting Research Scientist with Seoul NationalUniversity.

Ranajoy Bhattacharya received theM.Tech. (E&CE) degree from The Universityof Burdwan, Bardhaman, India, in 2011. Heis currently pursuing the Ph.D. degree withthe Department of Electrical and ComputerEngineering, Seoul National University, Seoul,South Korea.

He was a Research Student with CEERI-CSIR,Pilani, India, until 2013.

Seontae Kim received the B.S. degree in physicsfrom the Hankuk University of Foreign Studies,Seoul, South Korea, in 2009. He is currentlypursuing the Ph.D. degree with the Departmentof Physics and Astronomy, Seoul National Uni-versity, Seoul.

Dongpyo Hong is currently pursuing the Ph.D.degree with the Department of Physics andAstronomy, Seoul National University, Seoul,South Korea.

Sun-Hong Min received the B.S., M.S., andPh.D. degrees in physics from the Departmentof Physics and Astronomy, Seoul National Uni-versity, Seoul, South Korea, in 2003, 2006, and2012, respectively.

He is currently with Korea Heavy Ion MedicalAccelerator Project, Korea Institute of Radiolog-ical and Medical Science, Seoul.

Gun-Sik Park (M’00) received the Ph.D. degreein physics from the University of Maryland, Col-lege Park, MD, USA, in 1989.

He is currently a Professor and the Directorwith the Center for THz-Bio Application Systems,Department of Physics and Astronomy, SeoulNational University, Seoul, South Korea, and alsothe CEO of Seoul-Teracom, Inc., Seoul.