Download Equivalent Circuit Parameter Extraction Techniques for a PCS

Equivalent Circuit Parameter Extraction Techniques for a PCS
Ceramic Filter, Using Commercial Electromagnetic Software
P. Kyriazidis1, S. Tsitsos1, A. Kouiroukidis1, and A.A.P. Gibson2
1
Department of Informatics and Communications, Technological Educational Institute (T.E.I.) of Serres,
GR-62124, Serres, Greece, Tel: +30-23210-49177, e-mail: [email protected]
2
School of Electrical Engineering and Electronics, University of Manchester, Manchester M60 1QD, U.K.
Abstract — A computer-aided parameter extraction technique
for a microwave PCS ceramic filter is presented in this work. The
technique is based on first electromagnetic principles and exploits
the capabilities of the “field calculator” integrated in the
commercial software package HFSS. The main advantage of this
technique is its suitability for analysing structures of arbitrary
geometry and materials.
Index terms — Ceramic filter, electromagnetics, equivalent
circuit, parameter extraction, HFSS.
I. INTRODUCTION
In recent years, low loss and high dielectric constant ceramic
materials have resulted in very small sized microwave filters
suitable for GSM, DCS, PCS and other technologies.
Commercial electromagnetic simulators employing welldeveloped numerical techniques are nowadays routinely used by
the microwave industry to assist in the analysis, design and
performance prediction of such components [1]. Optimisation
techniques have also been integrated into electromagnetic
simulators, but the required optimisation time is rather large,
since ceramic monoblock filters usually employ highly irregular
geometries. This is especially true during prototyping, when
changes in the geometry are required in order to meet a new set
of specifications. To circumvent this problem, microwave
design engineers often make use of an equivalent circuit model
which enables the optimisation process to be performed by a
circuit simulator in significantly less CPU time. The optimised
equivalent circuit response is then matched to that of the actual
3D filter. The extraction of the equivalent parameters is usually
performed using experimental and electromagnetic simulation
data fitted to a basic topology equivalent model found in the
literature with arbitrary initial values. This basic model is often
limited and optimisation may result in unrealistic parameter
values.
In recent years new equivalent parameter extraction methods
have been presented [2]-[3] which employ canonical Foster subcircuits and Tellegen’s theorem or finite integration theory. In
this work a new computer-aided equivalent circuit parameter
extraction technique is presented. This technique is based on
first electromagnetic principles and exploits the capabilities of
the “field calculator” facility of the commercial software
package HFSS (High Frequency Structure Simulator). By
performing electromagnetic field calculations using Maxwell’s
equations in numerical form, accurate equivalent circuit
parameters can be extracted from 3D microwave structures
using first electro-magnetic principles, thus providing a physical
insight into the extraction process. This technique has already
been applied to the extraction of equivalent circuit parameters
for a GSM ceramic filter [4] and is expanded here to a more
complicated PCS structure. Its main advantage is its generality
and versatility, since any type of material structure can be
analysed.
II. PARAMETER EXTRACTION TECHNIQUE
One of the most important features of HFSS is the “field
calculator” and its ability to compute derived quantities of
interest from the general field solution. In particular, the field
calculator can be used to integrate, differentiate, curl, smooth,
multiply, add, subtract or divide field quantities over lines,
planes and three-dimensional regions. The exploitation of these
capabilities enables the extraction of equivalent circuit
parameters for a PCS ceramic filter. This structure is presented
in Fig. 1 [5]. It consists of three quarter-wavelength metallised
resonators and appropriate loading metallised cups to achieve
the desired frequency response characteristics. The inductances
and capacitances associated with the filter’s cups and the
impedances associated with the filter’s resonators were
determined by numerically solving well established
electromagnetic equations in the “field calculator” menu of
HFSS.
The capacitance per unit length of a transmission line is
given by C=q/V, where the electric charge q is calculated from
the electric flux density D over a closed surface A:
q = ∫ D ⋅ dA = ∫ ε E ⋅ dA
A
(1)
A
and the voltage V is evaluated by integrating the electric field E
along a line integral in the r direction:
V = − ∫ Ε ⋅ dr .
(2)
The inductance per unit length of a transmission line is given
by L=Φ/Ι. The magnetic flux Φ is calculated by integrating the
magnetic flux density B normal to an open surface S in a radial
direction:
Φ = ∫ B ⋅ dS = ∫ µ H ⋅ dS
S
arrangements of Figs. 2 and 3 are excited at the bottom of the
resonators (instead of probing to the cup side) to avoid
interfering with the sensitive fields around the cups.
(3)
S
and the current I is calculated by integrating the magnetic field
H around a closed contour:
I =
∫ H ⋅ dl
(4)
C
Fig. 3.
Fig. 1.
3D structure of a PCS ceramic monoblock filter.
Fig. 2 illustrates the geometry used to extract the filter’s cup
capacitances to ground (loading capacitances). Although there is
no middle cup in the filter, a small piece on the top of the
middle resonator is considered as “cup” to account for the
electromagnetic coupling with the end cups.
Extraction of inductances associated with the filter’s cups.
The coupling capacitance between adjacent cups was
extracted by calculating the electric charges of cups #1 and #2
and the voltage between these cups. In this case, both resonators
were excited individually at their bottom ends by stripline
probes to avoid interfering with the sensitive fields around the
cups and to establish the odd-mode field pattern between the
cups.
A load coaxial line of length λg/16 (at the centre frequency of
1960 MHz) and characteristic impedance of 50 Ohms
terminated in a short circuit was attached to the I/O ports, in
order to extract the end cups capacitances to these ports.
The discontinuity associated with the resonator to cup
interface was examined by simulating two quarter-wave lines
with the same cross section as the resonator and the cup (Fig. 4).
From the Z-parameter calculation by HFSS, the ABCD
parameters were obtained using the following equations:
A=
( Z ⋅ Z − Z 122 ) ,
Z
1 ,
Z 11 ,
B = 11 22
D = 22
C =
Z 12
Z 12
Z 12
Z 12
(5)
The behaviour of the ABCD parameters over the desired
frequency range (Fig. 5) indicates an inductive component
associated with the resonator to cup discontinuity.
The impedance of each individual resonator of the PCS filter,
was calculated directly by HFSS by performing a ports-only
analysis for the cross section of interest. The even- and oddmode impedances for two adjacent coupled resonators were
extracted by producing the even- and odd-mode field patterns in
HFSS (Fig. 6). Subsequently the two impedances were
calculated using the formula:
Fig. 2.
Extraction of filter’s cup capacitance to ground.
Fig. 3 presents the geometry used for the extraction of the
inductance associated with cup #1. It is noted that the
Z even / odd = V 2 / P
(6)
where V = − ∫ E ⋅ dl is the voltage of each resonator to ground
corresponding to the even- and odd-mode field patterns
respectively and P = 1 ( E × H * ) ⋅ dS is the power flow
2∫
calculated at the port’s surface.
Even-mode
Odd-mode
Fig. 6. Even- and odd-mode electric field distribution at the cross
section of two adjacent coupled resonators.
Fig. 4.
Resonator to cup discontinuity.
III. EQUIVALENT CIRCUIT
The equivalent parameters extracted using the techniques
described above were combined to produce the equivalent
circuit presented in Fig. 7 for the PCS filter of Fig. 1. This
equivalent circuit was subsequently simulated and optimised by
the microwave circuit simulator ADS [7] and its response is
compared against the 3D structural response produced by HFSS
(Fig. 8).
III. CONCLUSION
Fig. 5.
ABCD parameter variation vs. frequency.
Grayzel’s transform [6] was subsequently applied to obtain
transformed impedance values necessary to represent resonator
coupling in a circuit simulator.
A new computer-aided technique for the extraction of
equivalent circuit parameters for a microwave PCS ceramic
filter has been presented in this work. In particular, the field
solutions obtained from the commercial electromagnetic
software package HFSS were used in the “field calculator”
where field operations performed and lines and planes of
integration were specified in order to extract equivalent circuit
parameters. The main advantage of this technique - which is
based on first electromagnetic principles - is its generality and
versatility.
ACKNOWLEDGMENTS
The authors would like to acknowledge the financial support
provided by the European Social Fund and National Resources
under the “E.P.E.A.E.K. II – Archimedes” project.
TDK Corporation, Japan, are also acknowledged for
providing technical data for microwave ceramic filters.
Cup #1 (#3) capacitance to ground: C1=C3
Cup #1 (#3) inductance: L1=L3
Cup #2 capacitance to ground: C2
Coupling capacitance between cups # 1 and #2 (# 2 and #3): C12= C 23
Equivalent circuit parameters
Extracted values
1.8065 pF
0.1138 nH
0.4833 pF
0.6533 pF
Optimised values
1.5217 pF
0.0839 nH
0.2503 pF
0.6457 pF
Cup #1 (#3) capacitance to port: Cport
Resonator #1 (#3) to cup #1 (#3) discontinuity inductance: L1disc= L3disc
1.3454 pF
0.05115 nH
0.5933 pF
0.0640 nH
5.9680 Ohms
6.7980 Ohms
6.9705 Ohms
5.2680 Ohms
11.9360 Ohms
7.3994 Ohms
7.9880 Ohms
9.0909 Ohms
6.7338 Ohms
14.7987 Ohms
15.3543 Ohms
22.2189 Ohms
8.9692 Ohms
11.9740 Ohms
Resonator #1 (#3) characteristic impedance: Z01 =Z03
Resonator #2 characteristic impedance: Z02
Even-mode characteristic impedance of resonators #1 and #2 (#2 and #3): Z0e
Odd-mode characteristic impedance of resonators #1 and #2 (#2 and #3): Z0o
Transformed resonator #1 (or #3) characteristic impedance: Z´0
Transformed even-mode characteristic impedance of resonators #1 and #2
(#2 and #3): Z´0e
Transformed odd-mode characteristic impedance of resonators #1 and #2
(#2 and #3): Z´0ο
Fig. 7.
Equivalent circuit for the PCS ceramic filter of Fig. 1.
REFERENCES
Fig. 8.
PCS filter structural and equivalent circuit response.
[1] Ansoft HFSS, Ver. 9.0, 2003, Ansoft Corporation.
[2] P. Russer, “Network methods in electromagnetic field modelling
I: global modelling”, Int. Journal of Applied Electromagnetics and
Mechanics, 17 (1-3): 5-17 2003.
[3] P. Russer, M. Mongiardo, and L.B. Felsen, “Electromagnetic field
representations and computations in complex structures III:
network representations of the connection and subdomain
circuits”, Int. Journal of Numerical modelling - Electronic
Networks Devices and Fields, 15 (1): 127-145 Jan-Feb 2002.
[4] S. Tsitsos, A.A.P. Gibson, L.E. Davis, "A new technique for the
extraction of equivalent circuit parameters from 3-D monoblock
filters", Int. Journal of RF and Microwave Computer-Aided
Engineering, Vol. 15/ No 2, J. Wiley & Sons, Mar. 2005.
[5] Applied Products Development Division, TDK Corporation, Japan
(private communication).
[6] A.I. Grayzel, “A useful identity for the analysis of a class of
coupled transmission line structures”, IEEE Trans. Microwave
Theory and Techniques, pp. 904-907, Oct. 1974.
[7] Advanced Design System, Ver. 2003A, Agilent Technologies.