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Computer Aided Design and Optimization of Three-Port Ferrite Stripline and
Microstrip Circulators
Article in WSEAS Transactions on Information Science and Applications · September 2005
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Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp395-398)
Computer Aided Design and Optimization of Three-Port Ferrite
Stripline and Microstrip Circulators
E. J. SĘDEK*, A. T. MILEWSKI#
*Telecommunications Research Institute
30, Poligonowa Str. 04-051 Warsaw, Poland
http:/www.pit.edu.pl
#
Tele&Radioelectronics Institute & Agriculture Technical University
11, Ratuszowa Str. 03-450 Warsaw, Poland
http:/www.itr.org.pl
Abstract: - A new computer-aided method for designing stripline and microstrip circulators is being described. The
method may be used to design circulator and optimize its parameters over a given frequency bandwidth. Optimization
is implemented using the error function determined by eigenvalues of scattering matrix characterizing the ferrite junction. The error function is minimalized using the optimization procedure which is based on the Hook-Jeeves method
(direct search method). By applying this method a large degree of conformity between theoretical and experimental
results can be achieved.
Key-words: - microwave, ferrites, stripline circulators, microstrip circulators, optimization method
1 Introduction
The design of stripline and microstrip Y-junction circulators is generally based on the works of Bosma [1]
and Yildirim [2]. These methods allow to determine
dimensions and parameters of the designed circulator
only approximately [3]. In order to optimize these
parameters successive measurements of circulator
characteristics, the “cut and try” method should be
used. As a result, the cost of the circulator increases
substantially. This disadvantage is avoided applying
the CAD described in this paper.
2 Problem formulation
The presented method consist of three main parts:
- electromagnetic field analysis of a ferrite junction,
- computer modeling of input impedance of a ferrite
junction,
- synthesis of a junction circulator based on threedimension error function, which is determined by
scattering matrix elements.
Fig. 1. A stripline structure junction circulator
An analysis of electromagnetic fields existing in the
structure circulator - shown in Fig.1 – has been made
using the relation given by Bosma [1] and Lint [4],
Young [5]. They were used to calculate frequency
characteristics of ferrite junction and the results were
compared with measurement data. Serious discrepancies have been observed. Thus, a new method of computer-aided modeling was introduced to reduce these
discrepancies in this paper. This method takes into
account an influence of the magnetic filed appearing at
the ferrite edge, components µ and k of permeability
tensor and a suitable number of terms of a series describing the parameters of the circulator. The problem
of the edge field distribution at the ferrite disc boundary was simplified by calculation parameters of
equivalent resonator with ferrite material. The resonator is characterized by its effective radius Ref (larger
than the real radius), equivalent permeability µsub.
3 Problem solution
The proposed designing method is based on locations
of scattering matrix eigenvalues on a complex plane.
Generally, algorithm of calculation is realized as follows: firstly, the ferrite junction is analyzed using a
computer in result values of scattering matrix eigenvalues and than parameters of scattering matrix are
achieved. If the desired specifications are met, the
circulator parameters are printed out. If not, the junction parameters are modified automatically using the
Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp395-398)
optimizing procedure and a calculation process is repeated. The elements impedance matrix of junction
shown in Fig.1 is obtained by:
z11 = j
z12 = j
z13 = j
z ef
π
z ef
π
z ef
π
∞
∑K
−∞
Next, one can compute parameters of scattering matrix
characterizing a junction:
(1)
n
s11 =
∞
∑ K ne
j
2πn
3
(2)
−∞
∞
∑ K ne
−j
2πn
3
(3)
−∞
where:
sin 2 nψ
Kn =
n 2ψ
λ si - scattering matrix eigenvalues
J n (KR )
k nJ n (KR )
J n ' (KR ) −
µ KR
(4)
(
1
λ s + λ s 2 + λ s3
3 1
µ ef
µ 0 µ ef ε 0 ε ef
2πn
2πn
−j
j

1
s13 =  λ s1 + λ s2 e 3 + λ s3 e 3  (14)
3

Then, one can define the error function by the equation:
T = W1 ∑ [A(i ) − s11 ] + W2 ∑ [B(i ) − s12 ]
2
(5)
µ2 − k2
=
µ
z ef =
(6)
µ 0 µ ef
(7)
ε 0ε f
k, µ - tensor permeability components
εef - ferrite permeativity
ψ - angle shown in Fig.1
Jn(KR), Jn’(KR) - Bessel function and its derivative.
Impedance matrix of eigenvalues can be presented in
the form:
(8)
λ z1 = z11 + z12 + z13
λ z2 = z11 + z12 e
λ z3 = z11 + z12 e
j
−j
2πn
3
2πn
3
+ z13 e
+ z13 e
−j
j
2πn
3
2πn
3
(9)
(10)
The relation between impedance eigenvalues and scattering eigenvalues is given by:
λ si =
λ zi − 1
λ zi + 1
i = 1, 2, 3
(12)
2πn
2πn
j
−j

1
s12 =  λ s1 + λ s2 e 3 + λ s3 e 3  (13)
3

i
2πf
K=
c
)
(11)
+ W3 ∑ [C (i ) − s13 ]
2
2
i
(15)
i
where:
A(i) – requirement on reflection coefficient value for fi
frequency
B(i) - requirement on value of isolation between circulator ports
C(i) - requirement on value of insertion loss between
circulator ports
W1, W2,, W3 – weighting factors
When ideal circulation is achieved, the error function
T = 0. The error function is minimalized using the
optimization procedure which is based on the HookJeeves method (direct search method) [6]. The error
function determined as above, depends on ferrite parameters, internal polarizing magnetic field and all
significant dimensions of junction. To determine the
error function dimensionability (as needed), an eigenvalues sensitivity analysis was performed. It was assumed that a three-dimensional error function of the
type T1 = f (r , H in ,ψ ) is sufficient for analysis of
direct
coupling
circulators
and
of
type
T2 = f (r , H in , Z t ) for analysis of circulators with
quarter wavelenght transformers (r – being ferrite radius, Hin – internal polarizing magnetic field, 2ψ - the
angle determined by stripline or microstrip width, as
seen from the center of the junction, Zt – transformers
characteristic impedance.
The following input data are necessary to analyze a
junction including a given ferrite material:
Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp395-398)
♦ the designed circulator desired frequency
bandwidth determined by the lower fd and upper fg frequency
♦ the ferrite material parameters:
- saturation magnetization Ms
- resonance line-width ∆H
- ferrite permeativity εf
- ferrite material dielectric losses determined by tgδ ε ef
-
effective gyromagnetic ratio gsk
♦ parameters of dielectric surrounding the ferrite
- dielectric permeativity εd
- dielectric losses given by tgδ ε d
♦ initial geometrical dimensions of the junction
and the initial value of the internal polarizing
magnetic field. The relation between internal
and external polarizing magnetic field is as
follow: Hex = Hin – NzMs (Nz – demagnetizing factor).
The data given above allow to calculate the scattering
matrix eigenvalues and next the parameters of a
circulator. The eigenvalues are coded in the form of
field equations.
3.1 Experimental results
The experimental characteristics of circulators designed to operate in L, S and C frequency bands are
presented. The comparison between theoretical and
experimental data has been made for different types of
circulators. In practice, the microstrip and stripline
circulators were designed. For microstrip circulator,
the polycristalline stable-temperature magnetic material with garnet structure (Yttrium-Gadolinium-Ferrite)
G-84SK produced by PIT was used as a substrate. The
following parameters characterize this material:
♦ saturation magnetization Ms=67kA/m
♦ resonance linewidth ∆H=6.8kA/m
♦ dielectric constant εf = 13.5
♦ dielectric loss factor tgδ = 5x10-4
♦ Curie temperature TC = 285°C
♦ Lande g-factor geff = 2.02
♦ stability temperature range ∆T = -60°C÷
150°C
For L-Band application stripline circulators the polycristalline garnet material G32 with saturation magnetization Ms = 30kA/m and resonance linewidth ∆H =
4kA/m was used. The characteristics of narrow-band
microstrip circulator printed on the G-84SK garnet
substrate are shown in Fig. 2.
Fig. 2 The comparison of computed and measured
characteristics of microstrip circulator: material garnet
G-84SK, thickness of the garnet substrate h = 0.8mm,
radius R = 5.65mm, Zt = 30.8Ω, Hex = 87.5kA/m.
Circulator isolation is larger than 20dB from 4.0 to 4.4
GHz. The VSWR is lower than 1.25 in measured band
and an insertion loss is at the level of about 0.5dB. It
can be seen that computed insertion loss is much lower
than the measured. This is due to the fact that losses in
transformers (printed on the garnet substrate) are not
included in the computer program. The second reason
for this difference is an absence of a good model of
magnetic loss characterized by resonance linewidth.
The properties of a S-band circulator operated in wide
frequency band are shown in Fig.3.
Fig.3 The comparison of computed and measured
characteristics of microstrip circulator: material garnet
G-84SK, thickness of the garnet substrate h = 1.5mm,
R = 7.5mm, Zt = 32.5Ω, Hex = 61.6kA/m.
In this case, the difference between computed and
measured insertion loss also occurs. The reason for
this is equivalent to the described above. Isolation
between circulator ports is larger than 17dB in 2.7 to
Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp395-398)
3.9GHz. A considerable level of conformity between
measured and computed characteristics is achieved.
Similar results of the measured and computed
characteristics of L-band stripline circulator are given
in Fig.4.
parameters are pertain to the designer experience. It is necessary to find the error function
T global minimum
♦ the method may be applied in various frequency bands in microwave region
♦ an optimum solution is obtained and the time
required by PC computer with Pentium processor is low (an average time needed for circulator design is less than 5 min.)
The next works will be focused on the losses model in
microstrip transmission line printed on garnet substrate
taking into account magnetic losses characterized by
tgδ µ mag and dielectric losses characterized by tgδ ε f .
Moreover it is necessary to take into account the conducting loss appearing in stripline and microstrip lines.
Fig.4 The comparison of computed and measured
characteristics of stripline circulator: R=17.8mm, Hex
= 33.4 kA/m, dimensions of the stripline: w = 14.1mm,
t = 1.6mm, b = 12.6mm.
In a designed circulator the polycristalline yttriumgadolinium garnet was applied. This material characterizes a saturation magnetization Ms = 20 kA/m and
resonance linewidth ∆H = 2.0 kA/m. The matching
circuit in each port of the circulator was realized as a
quarter-wave transformer with polystyrene material
placed between center conductor and ground planes of
the line. Isolation between circulator ports is larger
than 20dB in 1.6 to 1.8GHz and a insertion loss is
lower than 0.3dB.
In this case, a large level of conformity between calculated and measured characteristics of insertion loss is
achieved. This is due to the fact that low-loss dielectric
is applied in transformers section in the circulator.
4
Conclusion
The proposed method of stripline and microstrip circulators design and optimizing offers some substantial
advantages, as compared to other methods, namely:
♦ circulators are designed in a whole frequency
band, and not only for one center (midband)
frequency
♦ obtained dimensions of circulator from optimization process are exact enough, thus no
correction afterwards is required
♦ it is very important to select an optimization
process starting point; the values of this point
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References:
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Microwaves, Academic Press, New York, 1971
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Circulator, International Microwave Symposium, Baltimor, USA, 1998, Conf. Digest, Vol. 2, 1998, pp. 629632
[3] S.A. Ivanov, Application of the Planar Model to
the Analysis on Design of the Y-Junction Stripline
Circulators, IEEE Trans. of MTT, Vol. 43, No. 6,
1995, pp.1253-1263
[4] Z. C. Lint, A. Delfour, A. Priou, Y-Junction Circulator Analysis, International Microwave Symposium,
USA, Conf. Digest Vol.1, 1975, pp.247-249
[5] J. L. Young, J. W. Sterbentz, The Circular Homogeneous-Ferrite Microwave Circulator – an Analysis
Green’s Function and Impedance Analysis, IEEE
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