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Accurate design of partial-height ferrite resonators for waveguide circulators
Journal of Magnetism North-Holland
and Magnetic
Materials
ACCURATE DESIGN OF PARTIAL-HEIGHT FOR WAVEGUIDE CIRCULATORS
M.A. TSANKOV
435
83 (1990) 435-436
FERRITE RESONATORS
and L.G. MILENOVA
Institute of Electronics, Bulgarian Academy of Sciences, Boul. Lenin 72, Sofia 1784, Bulgaria A procedure for a precise dimensioning circulators is described. The experimental strongly reduces the cut-and-try procedure
of an HE,,-mode quarterwave-long demagnetized-ferrite resonator data presented prove the good practical accuracy of the design in circulator development.
1. Introduction The
partial-height
(air)
spacer
is widely
tion
circulators.
ferrite used
Although
resonator in H-plane a number
with
dielectric
waveguide of
papers
junchave
been published on the theory of waveguide circulators, it is always necessary to optimize experimentally the calculated dimensions in order to obtain a high-quality device. The design procedure consists of the dimensioning of the ferrite-dielectric insert and the matching elements, the machining of the ferrite cylinder or prism during the cut-and-try procedure being most difficult and time-consuming. Therefore, if the geometry of the ferrite insert is calculated with a good practical accuracy, the time for circulator development will be reduced substantially and only the dimensions of the metal matching transformer have to be optimized. This paper considers the easy-to-fabricate cylindrical ferrite resonator. The basic structure of the nonreciprocal junction is shown in fig. 1 and consists of a quarterwave-long ferrite cylinder loaded at one end by a metal or image wall and at the other by a short-circuited cut-off dielectric waveguide. Usually this structure is approximated by a demagnetized resonator with a magnetic lateral wall [l-3] which leads to a calculation error for the resonance frequency of more than ten percent. A more accurate treatment of a hybrid HE,, open dielectric resonator is considered in ref. [4], using the concept of effective permittivity. The present paper considers the calculation of the resonance conditions of the hybrid HE,, mode, using its characteristic equation.
Fig. 1. Basic structure 0304-8853/90/$03.50 (North-Holland)
0 Elsevier Science Publishers
The results are compared with many experiments and it is demonstrated that the increased accuracy in the calculation of the ferrite geometry is usually sufficient for the practice. If a symmetry image plane is introduced, a halfwave-long ferrite resonator terminated at both ends by dielectric spacers is dual to the structure on fig. 1 and can be designed by the same procedure.
2. Theory The characteristic equation of the HE,, mode in the demagnetized ferrite is used in the form given by Kajfez
[51
pdJlw + Jl~~ldG;Y' X
[
ow* ‘+’
=
B.V
J{(x) + Jl(X)G(Y) Ii
(k,,R)2qi x2
X
ErYK,(Y)
1
1’ *
Y2
x being the argument of the Bessel functions at the cylinder surface, y* = (k,R)*(~,p~ - 1) -x2, ke = 2~f/c, R is the ferrite insert radius, rr is the permittivity and pd = 0.33 + 0.67[1 - (yMS/~0w)2]1/2 is the demagnetized permeability, y is the gyromagnetic ratio, o = 2-nf, M, is the saturation magnetization. The propagation constant p is given by (j3R)2=
(k,,R)2efpd-~2.
(2)
The calculation of the ferrite-dielectric resonator for a given frequency f starts with a suitable choice of the radial wavenumber k,R in the interval 0.75-0.95 [6]. The value of x is then found from (1) with the aid of an iterative microcomputer program, and /3 is obtained from (2). Using a value of the filling factor k = h/( h + d) obtained from considerations concerning the in-phase mode adjustment [6,7], the ferrite cylinder height h and the spacer thickness d are found from [6] CYE~ cot( /3/r) = ,&
under consideration
for waveguide method which
coth( ad),
(3)
436
M.A. Tsankov, L. G. Milenova
/ Design of ferrite resonators for cwculators
2 where a 2_-(x/R) -k$,, td being the permittivity of the spacer. According to the weakly-magnetized model, the resonance frequency of the demagnetized-ferrite resonator appears as central operating frequency of the matched circulator.
3. Experiments
Table 1 Comparison between the calculated resonance frequency f, and the measured frequency f, in a normal-height or halfheight Y junction and the central operating frequency /a of a circulator with a ferrite insert of radius R and height h and dielectric spacer of height d Freq. band
Substantial experimental work was carried out to verify the proposed calculation procedure. The resonators realized after calculations were measured (a) in a reduced-height Y junction, (b) in a normal-height junction and (c) in a matched circulator. In the (a)-type measurements the ferrite-dielectric resonator is placed in the center of a Y junction between the top waveguide wall and a short metal post of the same diameter extending to the bottom wall. The resonance frequency of the resonator is determined at the minimum of the input VSWR (return loss) vs. frequency curve of one port, while the remaining two ports are terminated by matched loads. The agreement between the calculated and measured results is very close in this case. If a reduced-height Y junction and suitable tapers are not available, the measurements can be made with a normal-height junction. In this case, however, the additional metal post is rather long and its reactance substantially reduces the measured resonance frequency. If, in a first-order approximation, this reactance is considered to be connected parallel to the ferrite resonance circuit, the apparent resonance occurs when the reactance of the ferrite-dielectric resonator is equal and opposite to that of the post. If the post reactance is approximately frequency-independent, the true resonance frequency corresponds to the point of intersection (fig. 2) of the return loss vs. frequency curves: (a) of the resonator (the solid line) and (b) of the post without the resonator (the dotted line). The degree of
S Xl,: X K “l/Z K K*
Ferrite
Diel.
R (mm)
h (mm)
11.1 11.1 4.50 4.00 4.00 4.3 2.42 2.30 1.81 1.38 1.00
4.12 4.12 2.4 3.25 3.25 2.62 1.90 1.91 1.32 0.98 0.69
approximation
depends
the agreement
appears
d (mm)
f, (GHz)
f, (GHz)
0.45 0.26 1.33 1.40 1.40 0.94 0.79 0.87 0.59 0.23 0.31
3.69 3.40 9.697 9.66 9.66 9.47 15.x 16.23 21.12 27.78 35.9
3.65 3.38 9.70 9.78 9.77 9.44 16.0 16.5 20.51 29.0 35.8
on the diameter to be closest
/(I (GHz) 9.6 9.7 9.7 15.7 15.8 20.73 27.8 37.2
of the post
when
and
the diameter
is about 20% greater than that of the ferrite in the case of a dielectric spacer (usually Teflon) placed at the metal post. Some typical results of several calculations and measurements are given in table 1. The index l/2 denotes measurements in half-height waveguide junction. Most of the measurements were performed on structures of the type shown on fig. 1 with a Teflon spacer. while the results in the S band were for two quarterwave-long ferrite discs separated by an air gap. All the results obtained are in a reasonably good agreement. Most encouraging is the agreement between the calculated frequency and the central operating frequency of the developed circulators.
References [l] E.J. Denlinger, [2] [3] [4] [5] [6] [7] Fig. 2. Determination
of the actual resonance
frequency
IEEE Trans. on MTT 22 (1974) 810. Y. Akaiwa. IEEE Trans. on MTI 22 (1974) 954. J. Helszajn and F.C.C. Tan, Proc. IEE 122 (1975) 34. J. Helszajn and J. Sharp, Proc. IEE 133 (1986) 271. D. Kajfez, Microwave System News 13 (1983) 152. J. Helszajn. IEEE Trans. on M’IT 32 (1984) 908. M. Tsankov, in: Proc. 8th Intern. Conf. on Microwave Ferrites (Esztergom, Hungary, 1988) 377.
and Magnetic
Materials
ACCURATE DESIGN OF PARTIAL-HEIGHT FOR WAVEGUIDE CIRCULATORS
M.A. TSANKOV
435
83 (1990) 435-436
FERRITE RESONATORS
and L.G. MILENOVA
Institute of Electronics, Bulgarian Academy of Sciences, Boul. Lenin 72, Sofia 1784, Bulgaria A procedure for a precise dimensioning circulators is described. The experimental strongly reduces the cut-and-try procedure
of an HE,,-mode quarterwave-long demagnetized-ferrite resonator data presented prove the good practical accuracy of the design in circulator development.
1. Introduction The
partial-height
(air)
spacer
is widely
tion
circulators.
ferrite used
Although
resonator in H-plane a number
with
dielectric
waveguide of
papers
junchave
been published on the theory of waveguide circulators, it is always necessary to optimize experimentally the calculated dimensions in order to obtain a high-quality device. The design procedure consists of the dimensioning of the ferrite-dielectric insert and the matching elements, the machining of the ferrite cylinder or prism during the cut-and-try procedure being most difficult and time-consuming. Therefore, if the geometry of the ferrite insert is calculated with a good practical accuracy, the time for circulator development will be reduced substantially and only the dimensions of the metal matching transformer have to be optimized. This paper considers the easy-to-fabricate cylindrical ferrite resonator. The basic structure of the nonreciprocal junction is shown in fig. 1 and consists of a quarterwave-long ferrite cylinder loaded at one end by a metal or image wall and at the other by a short-circuited cut-off dielectric waveguide. Usually this structure is approximated by a demagnetized resonator with a magnetic lateral wall [l-3] which leads to a calculation error for the resonance frequency of more than ten percent. A more accurate treatment of a hybrid HE,, open dielectric resonator is considered in ref. [4], using the concept of effective permittivity. The present paper considers the calculation of the resonance conditions of the hybrid HE,, mode, using its characteristic equation.
Fig. 1. Basic structure 0304-8853/90/$03.50 (North-Holland)
0 Elsevier Science Publishers
The results are compared with many experiments and it is demonstrated that the increased accuracy in the calculation of the ferrite geometry is usually sufficient for the practice. If a symmetry image plane is introduced, a halfwave-long ferrite resonator terminated at both ends by dielectric spacers is dual to the structure on fig. 1 and can be designed by the same procedure.
2. Theory The characteristic equation of the HE,, mode in the demagnetized ferrite is used in the form given by Kajfez
[51
pdJlw + Jl~~ldG;Y' X
[
ow* ‘+’
=
B.V
J{(x) + Jl(X)G(Y) Ii
(k,,R)2qi x2
X
ErYK,(Y)
1
1’ *
Y2
x being the argument of the Bessel functions at the cylinder surface, y* = (k,R)*(~,p~ - 1) -x2, ke = 2~f/c, R is the ferrite insert radius, rr is the permittivity and pd = 0.33 + 0.67[1 - (yMS/~0w)2]1/2 is the demagnetized permeability, y is the gyromagnetic ratio, o = 2-nf, M, is the saturation magnetization. The propagation constant p is given by (j3R)2=
(k,,R)2efpd-~2.
(2)
The calculation of the ferrite-dielectric resonator for a given frequency f starts with a suitable choice of the radial wavenumber k,R in the interval 0.75-0.95 [6]. The value of x is then found from (1) with the aid of an iterative microcomputer program, and /3 is obtained from (2). Using a value of the filling factor k = h/( h + d) obtained from considerations concerning the in-phase mode adjustment [6,7], the ferrite cylinder height h and the spacer thickness d are found from [6] CYE~ cot( /3/r) = ,&
under consideration
for waveguide method which
coth( ad),
(3)
436
M.A. Tsankov, L. G. Milenova
/ Design of ferrite resonators for cwculators
2 where a 2_-(x/R) -k$,, td being the permittivity of the spacer. According to the weakly-magnetized model, the resonance frequency of the demagnetized-ferrite resonator appears as central operating frequency of the matched circulator.
3. Experiments
Table 1 Comparison between the calculated resonance frequency f, and the measured frequency f, in a normal-height or halfheight Y junction and the central operating frequency /a of a circulator with a ferrite insert of radius R and height h and dielectric spacer of height d Freq. band
Substantial experimental work was carried out to verify the proposed calculation procedure. The resonators realized after calculations were measured (a) in a reduced-height Y junction, (b) in a normal-height junction and (c) in a matched circulator. In the (a)-type measurements the ferrite-dielectric resonator is placed in the center of a Y junction between the top waveguide wall and a short metal post of the same diameter extending to the bottom wall. The resonance frequency of the resonator is determined at the minimum of the input VSWR (return loss) vs. frequency curve of one port, while the remaining two ports are terminated by matched loads. The agreement between the calculated and measured results is very close in this case. If a reduced-height Y junction and suitable tapers are not available, the measurements can be made with a normal-height junction. In this case, however, the additional metal post is rather long and its reactance substantially reduces the measured resonance frequency. If, in a first-order approximation, this reactance is considered to be connected parallel to the ferrite resonance circuit, the apparent resonance occurs when the reactance of the ferrite-dielectric resonator is equal and opposite to that of the post. If the post reactance is approximately frequency-independent, the true resonance frequency corresponds to the point of intersection (fig. 2) of the return loss vs. frequency curves: (a) of the resonator (the solid line) and (b) of the post without the resonator (the dotted line). The degree of
S Xl,: X K “l/Z K K*
Ferrite
Diel.
R (mm)
h (mm)
11.1 11.1 4.50 4.00 4.00 4.3 2.42 2.30 1.81 1.38 1.00
4.12 4.12 2.4 3.25 3.25 2.62 1.90 1.91 1.32 0.98 0.69
approximation
depends
the agreement
appears
d (mm)
f, (GHz)
f, (GHz)
0.45 0.26 1.33 1.40 1.40 0.94 0.79 0.87 0.59 0.23 0.31
3.69 3.40 9.697 9.66 9.66 9.47 15.x 16.23 21.12 27.78 35.9
3.65 3.38 9.70 9.78 9.77 9.44 16.0 16.5 20.51 29.0 35.8
on the diameter to be closest
/(I (GHz) 9.6 9.7 9.7 15.7 15.8 20.73 27.8 37.2
of the post
when
and
the diameter
is about 20% greater than that of the ferrite in the case of a dielectric spacer (usually Teflon) placed at the metal post. Some typical results of several calculations and measurements are given in table 1. The index l/2 denotes measurements in half-height waveguide junction. Most of the measurements were performed on structures of the type shown on fig. 1 with a Teflon spacer. while the results in the S band were for two quarterwave-long ferrite discs separated by an air gap. All the results obtained are in a reasonably good agreement. Most encouraging is the agreement between the calculated frequency and the central operating frequency of the developed circulators.
References [l] E.J. Denlinger, [2] [3] [4] [5] [6] [7] Fig. 2. Determination
of the actual resonance
frequency
IEEE Trans. on MTT 22 (1974) 810. Y. Akaiwa. IEEE Trans. on MTI 22 (1974) 954. J. Helszajn and F.C.C. Tan, Proc. IEE 122 (1975) 34. J. Helszajn and J. Sharp, Proc. IEE 133 (1986) 271. D. Kajfez, Microwave System News 13 (1983) 152. J. Helszajn. IEEE Trans. on M’IT 32 (1984) 908. M. Tsankov, in: Proc. 8th Intern. Conf. on Microwave Ferrites (Esztergom, Hungary, 1988) 377.