Investigation of Lumped Element Equivalent Circuit for Distributed Microwave Circuit
for Distributed Microwave Circuit
Abstract
In this project the network synthesis of both one-port and symmetric two-port microwave
circuit is investigated. The network synthesis methods include Foster and Brune’s
synthesis. At the end, a graphic user interface window is created and it provides an easier
way for users to use. Obtaining the data is the starting point for the generation of the
lumped element equivalent circuit. By vector fitting and subsequent system
identification, we can get a positive rational function which represents of the Z
parameters. On the basis of the positive rational functions, Foster equivalent circuits
and Brune’s equivalent circuits are established. These equivalent circuits exhibit
lumped elements only and allow an accurate modeling of the circuits within a finite
frequency range. 4940
Keywords network synthesis foster I brune vector fitting
Contents
1. INTRODUCTION . 3
1.1. PROJECT DESCRIPTION 3
1.2. TOOLS . 3
1.2.1 SONNET ® 3
1.2.2 Spice 3 . 3
1.2.3 Matlab® R2012a . 4
1.3. PRELIMINARIES . 4
1.3.1 System 4
1.3.2 Positive Real function 6
1.4. NETWORK SYNTHESIS PROCEDURE 7
1.4.1 General Foster equivalent circuit 7
1.4.2 Brune’s equivalent circuit . 8
2. NETWORK DESIGN 9
2.1. FOSTER I . 9
2.2. BRUNE’S SYNTHESIS [1, 14] 9
2.2.1 Synthesis procedure . 9
2.2.2 Highlights 15
2.2.3 Tips in programming . 17
3. EXAMPLES . 19
3.1. LOW PASS FILTER USING TRANSMISSION LINE STUBS 19
3.1.1 Create the prototype circuit . 19
3.1.2 Design the filter by using stubs 19
3.1.3 Transfer the stubs to microstrip line 22
3.2. STEPPED-IMPEDANCE LOW PASS FILTER 24
3.2.1 Create the prototype circuit . 24
3.2.2 Stepped-impedance implementation 25
3.2.3 Transfer the stepped-impedance to microstrip line . 26
4. SIMULATIONS OF EXAMPLES 28
4.1. LOW PASS FILTER USING TRANSMISSION LINE STUBS . 29
4.1.1 Foster I synthesis . 30
4.1.2 Brune’s synthesis . 31
4.2. STEPPED-IMPEDANCE LOW PASS FILTER 33
4.2.1 Foster I synthesis . 33
4.2.2 Brune’s synthesis . 35
5. MULTIPORT NETWORK SYNTHESIS . 36
5.1. ANALYSIS OF THE TWO-PORT SYMMETRIC STRUCTURE . 36
5.2. APPLICATION IN TWO-PORT SYMMETRIC MICROWAVE CIRCUIT . 37
6. USER INTERFACE DESIGN 39
7. CONCLUSION 41
8. FUTURE WORK . 42
9. ACKNOWLEDGMENT . 43
REFERENCE . 44 1. Introduction
1.1. Project description
In this project lumped element equivalent circuit for distributed microwave circuits
will be investigated. The models will be established on the basis of data obtained by
numerical full-wave simulation of the distributed circuits with electromagnetic solvers (e.g.
SONNET®). The data is stored in a tabular form which contains the multiport matrix
characterization by Z-parameters. Obtaining the data is the starting point for the generation
of the lumped element equivalent circuit. By vector fitting and subsequent system
identification, we can get a positive rational function which represents the Z-parameters.
On the basis of the positive rational functions, Foster equivalent circuits and Brune’s
equivalent circuits are obtained. These equivalent circuits exhibit lumped elements only
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