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.
