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THEORY AND DESIGN OF LOW LOSS ANALOGUE
MS-MODE PHASE CORRECTOR
E. Sawado, T. Inui
To cite this version:
JOURNAL DE PHYSIQUE Colloque C l , ~upplkment au no 4, Tome 38, Avril 1977, page Cl-281
THEORY AND DESIGN OF LOW LOSS ANALOGUE
MS-MODE PHASE CORRECTOR
E. SAWADO
Tokyo Metropolitan University, Setagaya, Tokyo, Japan and T. INUI
Central Research Laboratories, Nippon Electric Company Ltd., Kawasaki, Japan
Rksumk. - On presente une theorie pour le dkveloppement d'un correcteur de phase analogique a mode magnetostatique de volume, qui utilise des echantillons polycrystallins de grenat CaV substituk au Sn
a
faible largeur de raie (infkrieure a 3 Oe en bande X). L'etude theorique et expe- rimentale des modes magnktostatiques de volume se propageant dans des cylindresa
section rectangulaire transversalement aimantts ont montrk que des caracteristiques utilisables peuvent etre obtenue sur une largeur de bande de 100 MHz centrke sur 3,l GHz, avec une perte d'insertion inferieurea
13,5 dB et un taux d'ondes stationnaires a I'entrCe de 1,2 a 1,5.Abstract.
-
This paper describes the theory for designing of magnetostatic volume wave ana- logue phase corrector based on polycrystalline Sn-substituted calcium vanadium garnets with narrow resonance linewidth (AN 3 Oe at X-band). Theoretical and experimental studies of magnetostatic volume waves, propagating in a rectangular rod magnetized transversely, have shown that useful delay characteristics may be realized over 100 MHz bandwidth, for an insertion loss held as low as 13.5 dB centered on 3.1 GHz, and with an input VSWR of 1.2-
1.5.1. Introduction. - It is the purpose of this paper to present a theory for designing the low loss analogue phase corrector at microwave frequencies, and also search for the realistic possibilities of the polycrystal- Iine Sn-substituted Ca-V-Garnet materials [l] to the applications in the microwave devices. From initial experiment, a great deal of research has gone into the axially magnetized rod. However, the emphasis of this paper is on microwave phase corrector utilizing a square ferrite rod transversely magnetized to its axis. We wish to point out in this paper that the trans- versely magnetized rods are much promissible to gain high coupling efficiencies. This prognosis of remarkably high coupling efficiencies are mainly ascribed to the coupling degree enhanced by a pair of coupling loops specifically available on the MS-modes propagated along the ferrite rod. In interpreting the high conversion efficiency, the present authors resorted to a heuristic model of the MS-mode delay line. In this model the delay line of interest is represented by an equivalent transformer of a unit turn ratio, provided with a magnetic core having a retarded permeability
(without any magnetic relaxation in the sense of magnetostatic mode propagation) which interme- diates a signal source having a finite internal impe- dance, say, 50 Q, and a resistive load, say, 50 Q.
The potential bandwidths of magnetostatic volume waves are given by the limits of
o = ~ ( H , ( H ,
+
4 K M , ) ) ' / ~ and o = yHi((l+
q)/2) 'l2,where o is the signal frequency,
4 .nM, is the saturation magnetization and Hi is the internal magnetic field. Narrow linewidth polycrys- talline Sn-substituted Ca-V-Garnets are now available with a saturation magnetization in the range of 200
--
1900 gauss. At 2.6 GHz bandwidths of 666 MHz are possible for q = 4.56 with Hi = 500 Oe. The phase corrector to be presented showed a midband insertion loss of 13.5 dB with an input VSWR of 1.2--
1.5 and also demonstrated with a delay of 8--
10 ns/cm over a 100 MHz bandwidth centeredon 3.1 GHz.
2. Theory. - The electromagnetic boundary value problem to be solved for the transversely magnetized
waveguide filled with ferrimagnetic materials is shown in figure 1. The transcendental equation for electroma- gnetic wave propagation in the waveguide is given by [2]
(cosh (a,
-
6,) U ) ('-
(y-
+
(CO& (a,+
a,) U ) (a-
?)(B-
6) -(01
-
P)(Y-4
(a-B>
(Y-
6)-
Cl-282
where
E. SAWADO AND T. INUI
and the (+ 6,) for n = 1 , 2 are the roots of the following equation
(a4
C'+
d2(0'+
BC' - C )+
BD' - B' D ) = 0where
and ,U and K: are the diagonal and the nondiagonal elements of the tensor permeability, respectively, and in usual
2
notations kf = oe,po~,, k, wave number.
Modal solutions have been obtained from transcen- dental equation (l), and for the purpose of comparison are presented graphically using the same coordinate that is commonly used in magnetostatic analysis. Calculations are made for the case of q = 4.56 and the relative permittivity E, = 15, for the rectangular rods with the sectional area 3 X 3 mm2 and
10 X 10 mm2. For a small rod the results are shown in
figures 2 and 4 ; there is no significant distinction between exact solutions and the approximation. Figures 3 and 5 are the volume modes and surface modes for large samples. As we shall mention in the next section the agreements between the MS approxi- mation and the present theory, particularly in the low k region, is poor.
3. Experimental. - In order to obtain a uniform dc magnetic field within a sample, the rod are placed between the two iron sheets as illustrated in figure 1.
SOFT IRON SHEET
FIG. 1. - Coordinate system and two iron sheets.
Consequently, the MS-mode propagated on the rod is resonated at discrete frequencies subject to the rela- tionship
PE,
= nrr, whereP,
E, and n denote the phase constant of waves, the effective length of the rod and integers exclusive of null, respectively. The experimen- tal results are presented with cross signs in figures 2, 3, 4, and 5. Their accuracy is estimated to be+
1%.
As the sectional area is increased, the need for the exact formula becomes more and more eminent, because of ever-widening departure of the purely MS-mode formula from the exact dynamic version.O l c m
-
1
EXACT ANALYSIS
l c m MAGNETO STATIC ANALYSIS.
MODE; m= 1 , n = l m = l , n = 4 -.--
m = l , n = 1
THEORY AND DESIGN O F LOW LOSS ANALOGUE Cl-283
FIG. 3. - Dispersion curves for volume modes, large rod. Variation of 62 with k?, are also plotted.
FIG. 4. - Dispersion curves for surface modes, small rod.
EXACT ANALYSIS
FIG. 5. - Dispersion curves for surface modes, large rod.
4. Design and fabrication of phase correctors comprising square polycrystalline Sn-substituted Ca-V- garnet rod.
-
When some modification are made to the coupling scheme for a tigher coupling, the reso- nant MS-mode results in a class of an analogue phase corrector with, needless to mention, a pair of appro- priate matching sections incorporated at the input and output ports. One of the experimental analogue phase correctors designed and fabricated is of such aconfiguration as shown in figure 6. As illustrated this experimental unit comprises the rectangular rod of a polycrystalline Ca-V-Garnet with 4 n M , = 1 730 G
and measuring 3 X 3 X 10 mm3, input and output
; Surface metallized sector of CaVG square r o d
'; I]nmetallized e d g e of CaVG square rod
; One or t w o turnsof coil ; Semi-fixed m a t c h i n g capacitive probe ; M i c r o s t r i p l i n e ; Teflon s u b s t r a t e ; Partitioning ground block
FIG. 6. - A schematic sketch showing physical configuration of the MS-mode phase corrector.
coupling coils, each wounded in two turn and half snuggly around the rod with the pitch of 1 mm inward from each of a semi-fixed slide reactance tuner design.
Using the fact that a phase difference between the nodes of the interference pattern is 2 .n radian, delay time is calculated by
where the denominator is the phase difference corres- ponding to the frequency difference o, - m,. Figure 7
H , =670(0e) H,;Magnetic field ~ = 1 4 . 5 (dB) C-5 A ; I n s e r t i o n l o s s Hi=720(0e) U 4 A=
13.5(d
B) Workablerange 5-
I 1 IFIG. 7. - Group delay vs. frequency characteristics for various values of internal magnetic field.
Cl -284 E. SAWADO AND T. INUI
of the internal magnetic field, the theoretical delay
5
= bk/x. This class of analogue phase correctortime is given by demonstrated to have a loss low enough to held the
L/2 d
Y insertion loss below 15 dB and with inband VSWR's
7g=210
( 6 ) averaged below 1.2-
1.5 and a VSWR ripple held towithin f 0.2. These results are in good agreement where v,b) = do(y)/dy. The dispersion relation for with the values obtained from curve ( A = 40) in the rectangular rod is given below [3] figure 8. The fairly agreement between experimental and calculated results is one of the most remarkable
= y H
{
(qS2 + n 2 + + n2 +) l f 2 (7) bits of evidence of the volume modes of the magnetos-
where
5,
the normalized wavenumber, is defined by tatic character of the phenomenon.References
5. Conclusions. - It has been shown that the
analogue phase corrector described above, utilizing the volume MS-mode propagated through the polycrystal- line Sn-substituted Ca-V-Garnet, was measured to feature a group delay vs. frequency characteristics for an insertion loss held as low as 15 dB, for insertion losses nearly of the same values as those of single- cystalline versions.
Ackno.cvledgments. - The authors wish to thank Mr. H. Shimizu and T. Kamijo for help in the expe- rimental work, and T. Ohta for his invaluable advice and helpful discussions. We are greatly indebted to
[l] INUI, T., TAKAMIZAWA, H., OOASAWAKA, N. and FUSE, T.,
AIP Conf: Proc., No. 24 (1975) 483. 121 SAWADO, E., J. Appl. Phys. 46 (1975) 4946.
131 AULD, B. A. and MEHTA, K. B., J. Appl. Phys. 38 (1967)
4081.
10
2.8 3.0 f Nippon Electric Co. Ltd., for his continued interest 3'2 (GHz 1 on this work. One of us (E. S.) wish to thank FIG. 8. - Theoretical plot for variation of group delay with M. Sat0 Metropolitan University for helpful
frequency. discussions and for numerical calculations.
Volume m o d e
m - l , n = l
-
I
