Microwave-harmonic generation in ferrites at high power

Journal of Magnetism and Magnetic Materials 45 (1984) 377-381 North-Holland, Amsterdam

377

MICROWAVE-HARMONIC GENERATION IN FERRITES AT HIGH POWER E. SCHIED and O. WEIS Abteilung ffir Festkbrperphysik, Universiti~t Ulm, Oberer Eselsberg, 7900 Ulm- Donau, Fed. Rep. Germany

A ferrite microwave harmonic generator is presented in the form of a rectangular cavity resonator. The ferrite-plate is attached to one wall and fills out the whole cross-sectionof the resonator which has a variable length. In the experiments a resonator length has been used at which the fundamental and the harmonic frequencies are resonant. Frequency doubling, tripling and quadruplinghas been performedat input power levelsup to the 10 kW range. Investigatingvarious polycrystalline ferrites, best results were obtained with a Mg-ferrite at a thickness of 2.0 ram. Highest achievedconversionefficiencieswere 40% with frequency doubling, 1.1% with tripling and 0.016% with quadrupling. A strong dependence of the efficiencieson ferrite thickness was observed.

1. Introduction Ferrite-frequency doublers described in the literature [1-3] have proved to be suitable for achieving high conversion efficiencies at input powers in the kW-range. Furthermore, these investigations have shown that, in using polycrystalline ferrites, their dimensions should be comparable to wavelengths in order to avoid losses due to the excitation of spin waves. Under these conditions propagation effects and displacement currents cannot be neglected. In order to evaluate the electromagnetic fields in such a frequency doubler, one has to solve the complete set of Maxwell equations by fulfilling all electromagnetic boundary conditions. Since the rf-field amplitudes are higher in a cavity resonator than in a guided wave (using the same input power), it is to be expected that a suitably designed cavity resonator will show a higher conversion. Having all these requirements in mind, we chose for our experiments the simplest geometry: a rectangular cavity resonator driven in a H10n-fundamental mode with a ferrite plate covering the whole cross-section at one side (compare fig. 2). If a sufficiently high static magnetic field H0 is appried in the plane of the ferrite plate, the evaluation of the corresponding resonator fields and resonance frequencies runs into difficulties: the

usual electromagnetic boundary conditions at the air/ferrite interface cannot be fulfilled rigorously within the usual treatment which uses the complex Polder tensor [4,5] for the magnetic permeability. Therefore, in the 'quasi-isotropic' approximation [6], the alr/ferrite-boundary is treated like the isotropic case by neglecting the effect of the off-diagonal elements of the Polder tensor. N o attempt is made in this paper to overcome these difficulties. A related theoretical treatment will be published elsewhere. The present work is concerned with experiments. Using the ferriteloaded rectangular cavity described, we achieved not only frequency doubling but also frequency tripling and frequency quadrupling.

2. Ferrite-loaded resonator for harmonic generation The physical reason for harmonic generation in ferrites is a nonlinearity in the phenomenological equation of motion for the magnetization vector M. In the case of uniform precession this equation is given by = yg0 M

x

H + damping term.

(1)

H denotes the internal magnetic field in the ferrite sample, 3' the magnetogyric ratio, go the permeability of vacuum and IMI--Mo the saturation magnetization. With the magnetic field de-

0304-8853/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

E. Schiea~ O. Weis / Microwave-harmonic generation in ferrites

378

h'-FIELD AT to1 Hm2-iESONANCE

TOP VIE

",,........~ E I z .~o

SIDE

H'o

VIEW

\

z.~,,

-

'

", ] / M

/

Hm3-RESONANCE CIRCULAR PRECESSION

h-FIELD AT 2w 1

ELLIPTICAL PRECESSION

Fig. 1. Precessional motion of the magnetization vector in the isotropic and the anisotropic case.

composed in the strong static field H 0 and the microwave field of frequency 6o with the complex field amplitude h 1 H = H o + h I e i~°t +

C.C.,

(2)

one obtains the magnetization in a form: M=

M o eHo + m a e i~°t + m 2 e 2i~°t + m 3 e 3i~°t

+...

+ c.c.

(3)

Explicit expressions for the complex components given by Jepsen [7] for instance. The first term Moeno corresponds to the alignment of the magnetization parallel to the static field. The amplitude m 1 in eq. (3) describes the precessional motion of the magnetization vector around the static field H 0. Magnetic resonance occurs at a certain field-strength, m I is linear related t o h a by the Polder susceptibility tensor. The following amplitudes m 2, m 3. . . . in (3) are, in general, small in comparison to ma, but they are the source of the generated harmonics. They are caused by an anisotropic precession of the magnetization vector M. Fig. 1 illustrates [1] the occurrence of m2 as a consequence of IMI = M0 = const. The anisotropic motion may either be caused by an excitation with a linearly polarized field hi or by demagnetizing fields in samples with non rotational symmetry or, especially in single crystals, by crystal anisotropy. These facts are common to all

m ] , m 2 , m 3 are

FERRITE

Fig. 2. Magnetic fields in the resonator during frequency doubling.

frequency doublers. Differences consist in the way the field h 1 is produced and how the power of the second harmonic is coupled out from the ferrite sample. The principle of our harmonic generator is shown in fig. 2. The exciting field hi is produced in a rectangular cavity resonator with the ferrite at one wall of the cavity. In order to achieve high exciting field amplitudes hi, it is necessary to work at a suitable resonance of the resonator at frequency 6or The static magnetic field is directed perpendicular to the broad side of the resonator and thus perpendicular to the field h 1. In this arrangement there exist magnetization components m 2, m 4 with frequencies 26oI and 46oI parallel to the static field H 0 and a magnetization component m 3 with frequency 3601 perpendicular to the static field H 0. These magnetization components may excite a resonator mode very strongly, if this resonator mode possesses a resonance frequency at the required harmonic frequency 26ol, 36o I o r 4601, respectively, and if this mode has components of its magnetic field parallel to the magnetization component of the harmonics. Obviously, efficient harmonic generation requires two conditions: 1) a resonance at the fundamental frequency to get high exciting field amplitudes and 2) a resonance of a suitable mode at the required harmonic frequency to maintain optimal power transfer from the ferrite to the cavity oscillation. The large polycrystalline ferrite samples, necessary

379

E. Schiea~ O. Weis / Microwave-harmonic generation in ferrites

1[GHz] 20i

'

'

/

'

t.U {:~ ILl

1104~//~ / // I103 ~ / ~ / //

oI-

1°I// / ~

~10 <~: Z O U') IJJ rY 0

102 /

. . . .

7"

'/

2/~

/ ,..-I ''~--

'

'

HIO4 HIO3

H101 RESONATOR: 22.9x10,2x 31.7mm3 Mg-FERRITE: 22.9x10.2x2.0 mm3 '. ' i ' '

0 05 T/IJ.o ] MAGNETIC FIELD H, Fig. 3. Dependence of the resonance frequency of the Hlo,-modes on the static magnetic field, calculated in quasiisotropic approximation. The circle indicates the point where frequencydoubling has been performed.

for an efficient harmonic generation, lead to a strong dependence of the resonance frequencies on the static magnetic field. The resonance frequencies, calculated within the quasi-isotropic approximation, are shown in fig. 3 as a function of the internal magnetic field for conditions explained in the inset. The dashed line indicates where magnetic resonance occurs. There are two classes of resonance frequencies: one at values of the magnetic field-strength below the magnetic resonance and one above. For harmonic generation the resonances at the higher field-strength are used. Thus it is possible to work below the spinwave spectrum [3,8] and hence to avoid saturation effects caused by spin waves. These field-strength values are relatively far from the field-strength at magnetic resonance. But nevertheless, it is possible to get sufficiently large magnetization components. Far from magnetic resonance, the ferrite absorbes only weakly and the resonator can build up high field amplitudes. Furthermore, the precessional motion of the magnetization vector M gets a higher ellipticity out of resonance which also contributes to larger magnetization components [8]. In contrast to the fundamental cavity-resonance frequency, which we call o~1, the resonance frequencies in the neighbourhood of o~ = 2tOl, 3601 and 4to] depend only weakly on H 0. The reason is twofold: Firstly, the resonator modes used at 2601 and 4to 1 show h-field components almost parallel

to the static magnetic field H 0, i.e., the interaction of these modes with the ferrite is rather small. Secondly, the magnetic resonance-field strength at 3¢ol, and 4~0] is so far away from the applied field-strength, that there remains only little field dependence.

3. Experimental The technical construction of the resonator is shown in fig. 4. It consists of an X-band waveguide which is closed on one side by a metal plate and on the other side by a shorting plunger. The ferrite is attached to the shorting plunger. The metal plate contains a coupling slit for the input power at the fundamental frequency. This plate can easily be replaced in order to get optimal coupling. There is a second window at the broadside of the resonator where the power at the harmonic frequencies is coupled out. The best location of this window depends on the required harmonic. To achieve a good coupling out a coupling loop has been used. The coupling out is influenced by the position of the shorting plunger of the K / Q - b a n d waveguide. The length of the resonator is variable continuously and can be measured by a displacement transducer. Fig. 5 shows the block diagram of our experimental set-up. At the fundamental frequency to1 we used a klystron to determine the properties of the resonator and a pulsed high-power magnetron for harmonic generation. The cavity resonances at the harmonic frequencies 2,o a 3t01 and 4o~1 were measured by means of a Gunn oscillator combined

PmIm~ I )

,I X-BAND

~

Ho

~K/Q-BAND

\ _ H ° V / / ~ RRI TE DRIVE Pl(tOl)~ F ~ , . . - , , . / ~ _ ~ _ z a ~ - T j _ . _ _ DISPLACEMENT~ TRANSDUCER RESONATOR

TUNING PLUNGER FOR THE RESONATOR

MATCHING PLUNGER

Fig. 4. Resonator used for harmonic generation.

380

E. Schied, O. Weis / Microwave-harmonic generation in ferrites TO

O S C I L L O S C O P E / XY-RECORDER

"- "~ DISPLAC!ENT # ITRANsDuCER

I

II

t t

X-BAND

]

K/O-BAND

Fig. 5. Block diagram of the harmonic generator.

with a diode-harmonic generator. In preparing an experiment for high-powerharmonic generation with a given ferrite plate, one has to find a resonator length at which the cavity possesses a resonance at the magnetron frequency to1 and simultaneously at the required harmonic frequency. This can be done in the following simple way. One measures the reflected klystron power from the resonator at the frequency to1 while changing the length of the resonator. At distinct 'resonance lengths' there appears a resonance absorption by the cavity. Carrying out these measurements with a varying static magnetic field, one gets a diagram with the resonance length of the cavity as a function of the applied static magnetic field. Thereafter, the same method is used to get the resonance lengths at the wanted harmonic frequencies. Of course, these measurements are done in the K- or Q-band waveguides from the

output side in reverse direction. Then, these resonance lengths for the harmonic frequency are plotted in the same diagram. Intersections of both plots indicate for which cavity length and magnetic field both resonances occur. If the magnetic field lies at the high field side in comparison to the magnetic resonance, we have a suitable cavity configuration for effective harmonic generation. The actual experiment of harmonic generation at high-power levels was performed in the following way: The known output power of the magnetron is damped by a variable calibrated attenuator to the required power P. A fraction of this power will then be reflected at the resonator window. The difference between incident power P and the reflected power is the power P1 entering the resonator. (Typically, we had a power reflection coefficient of 0.1 to 0.3 after matching was done.) The later quoted efficiency of harmonic generation is calculated as the ratio of the power Pm coupled out at the harmonic frequency tom i n t o I to the power P1- The power P,, is measured with the help of a calibrated attenuator and a calibrated diode. In the case of frequency quadrupling, a constricted waveguide was placed in the Q-band-output waveguide in order to prevent propagation of the third harmonic. These experiments were carried out with a magnetron frequency of 9.0 G H z and with four different ferrites, all polycrystalline. The main magnetic and dielectric properties of these ferrites are compiled in table 1. Our samples had a thickness between 1 and 3.5 =

mm.

Best results were obtained using a Mg-ferrite sample with a thickness of 2.0 mm. Already small deviations from this thickness reduced the efficiency considerably. Fig. 6 shows the measured

Table 1 Properties of ferrite samples used. All ferrites were supplied by Thomson CSF under the given names. Ferrite material

Mg-ferrite Li-ferrlte High-power garnet Narrow-linewidth garnet

U A D Y

21 50 1 220

Saturation magnetization Ho (mT/#o)

Linewidth AH (mT/# o)

Dielectric constant

240 500 140 195

29 17 11 1

13.0 15.3 15.5 15.5

E. Schied, O. Weis / Microwave-harmonicgeneration in ferrites

10a . • '" .... ' ......... ' G¢-'-~15.5 k~ 5.5 kW [W1103 ~112~X = 9.0 GHz . 1~&6kWl I 10~ / ~2.TkW] n- 10 W /" / ~ - - z3w o I 0_ P2(2W1~ ./ it/ ~(j~ " o 104 /ji/O/ P3(3(.01 ' 139kWI z 10_2 ~E rr <"1- 10-3

./

// /

10 10 2 10 3 10~' W] INPUT POWER P~(~o~) Fig. 6. Output power of the resonator at the second, third and fourth harmonic as function of the input power at the fundamental frequency (o/2~r = 9.0 GHGz. harmonic power Pm for the second (m = 2), third (m = 3) and fourth (m = 4) harmonic as a function of the input power P1 having the fundamental frequency (~1. The highest efficiency achieved in frequency doubling was 40%, in frequency tripling 1.1% and 1.6 × 10 - a in frequency quadrupling. In our experiments, the highest input power P1 was mainly limited by electrical flashovers. The static magnetic field had values of 0.40 T//~ 0 in frequency doubling, 0.43 T//~ 0 in tripling and 0.38 T / / % in quadrupling. The dependence of the harmonic output power Pm on input power /)1 can be taken from the slopes of the double-logarithmic plot of fig. 6. F r o m simple arguments one expects a relation Pm -- const. (P1)m',

m = 2, 3, 4 ....

(4)

where m ' = m. The slopes in fig. 6 reveal that a somewhat higher exponent occurs: frequency doubling ( m = 2) : m ' = 2.02, frequency tripling ( m = 3): m' = 3.4, frequency quadrupling(m = 4) : m ' = 4.7.

(5)

4. D i s c u s s i o n

F r o m conslaerations on small ferrite samples [9,10] one would expect that the efficiency is proportional to M o / A H . This would favour the narrow linewidth garnet and the Mg-ferrite should

381

have the lowest efficiency. But these considerations are not applicable to large ferrite samples. In theoretical considerations for small samples, the magnetization components are calculated at the center of magnetic resonance. In this case, the magnetization components are indeed (proportional to M o / A H . In the case of large samples, however, the harmonic generation is done at fieldstrength above that of the magnetic resonance. At these higher magnetic fields, the damping should have only minor influence on the magnetization components. Moreover, the spatial distribution of the magnetization components and its influence on the conversion efficiency must also be taken into account. The observed strong dependence of conversion efficiency of the ferrite thickness is also not yet understood, but we are confident that all these problems can be solved by looking for the exact magnetodynamic solutions for the vibrations in our simple cavity structure.

Acknowledgements

During the early stage of this investigation PD Dr. H. Bialas was also involved in this work. We wish to thank him for his valuable help and for m a n y fruitful discussions.

References

[1] J.L. Melchor, W.P. Ayres and P.H. Vartanian, Proc. IRE 45 (1957) 643. [2] M. Weiner, IEEE Trans. on Electr. Devices ED-14 (1967) 395. [3] A i . Lutsenko and G.A. Melkov, Radio Eng. and Electron. Phys. USA 18 (1973) 1668. [4] B. Lax and K.J. Button, Microwave Ferrites and Ferrimagnetics (McGraw Hill, New York, 1962). [5] D. Polder, Phil. Mag. 40 (1949) 99. [6] H. Brand, A.E.O. 18 (1964) 371. [7] R.L. Jepsen, J. Appl. Phys. 32 (1961) 2627 and Scientific Report no. 16, AFCRC-TN-58-150, Gordon McKay Laboratory of Applied Science, Harvard University, Cambridge, Massachusetts (May 25, 1958). ASTIA Document no. AD 152381. [8] G.A. Melkov, Izv. Vuz. Radioelektron. (USSR) 18 (1975) 74. [9] W.P. Ayres, IRE Transact. MTF 7 (1959) 62. [10] D.D. Douthett, I. Kaufman and A.S. Risley, J. Appl. Phys. 32 (1961) 1905,