VIETNAM NATIONAL UNIVERSITY HOCHIMINH CITY INTERNATIONAL UNIVERSITY SCHOOL OF ELECTRICAL ENGINEERING

Transcription

1 VIETNAM NATIONAL UNIVERSITY HOCHIMINH CITY INTERNATIONAL UNIVERSITY SCHOOL OF ELECTRICAL ENGINEERING BUILD A METHOD TO MEASURE THE RELATIVE PERMITTIVITY OF THE SUBSTRATE OF A PCB USING VECTOR NETWORK ANALYZER By Le Duy Trinh A thesis submitted to the School of Electrical Engineering in partial fulfillment of the requirements for the degree of Bachelor of Electrical Engineering HoChiMinh City, Vietnam June 2012

2 BUILD A METHOD TO MEASURE THE RELATIVE PERMITTIVITY OF THE SUBSTRATE OF A PCB USING VECTOR NETWORK ANALYZER APPROVED BY: THESIS COMMITTEE

3 ACKNOWLEDGMENTS Foremost, I would like to express my sincere gratitude to my advisor, M.E. Tran Van Su, for his continuous support to my work. His guidance helped me in all the time of doing this thesis and writing this report. This thesis cannot be done smoothly without his instruction he gave me. I also thank to Mr. Vu Huy Long for his support in the work shop. Thank to Tran Trung Kien, Nhan Nhat Quang and Vo Truong Tien for technical support in the laboratory during the time doing thesis. iii

4 TABLE OF CONTENT ACKNOWLEDGMENTS... iii LIST OF FIGURE... v LIST OF TABLE... vi ABSTRACT... vii CHAPTER 1: INTRODUCTION Background and problems: Project objectives:... 4 CHAPTER 2: LITERATURE REVIEW Theory of Relative Permittivity Review measuring permittivity of PCB s substrate methods that exist Method that using VNA and XFDTD Parallel plate method Transmission line method CHAPTER 3: METHODOLOGY Fabricate the test board Measure S11 and S21 using Vector Network Analyzer Set up the Optimization controller and Goals Build the model of transmission line: Run the simulation Setup the Optimization controller and goals Evaluate the result: CHAPTER 4: RESULT CHAPTER 5: CONCLUSION AND RECOMMENDATION Conclusion: Recommendation: REFERENCES: iv

5 LIST OF FIGURE 1. Figure 1: Flowchart of the proposed method Figure 2: Algorithm to estimate the dielectric constant of a PCB substrate Figure 3: Parallel plate method probe Figure 4: Transmission line method coaxial probe Figure 5: Example of transmision line method waveguide probe Figure 6: Measurement using transmission method and coaxial probe Figure 7: 100mm long transmission line Figure 8: Data File Tool windows in ADS Figure 9: Schematic of a 100mm long transmission line, include SMA model Figure 10: Plot 2 different traces from 2 different datasets Figure 11: Measured S and Simulated S plot on a same rectangular Figure 12: The major point of measured S11 magnitude Figure 13: The goal of magnitude of S Figure 14: The goal of magnitude of S Figure 15: The goal of phase S Figure 16: Optimization Variable Setup Figure 17: Final schematic Figure 18: The Optimization window Figure 19: Result of trial # Figure 19: Result of trial # v

6 LIST OF TABLE 1. Table 1: Relative permittivity of some material at room temperature...6 vi

7 ABSTRACT This report presents a method for determining the relative permittivity (dielectric constant) of a PCB s substrates. In the presented method, a 100mm long transmission line on the PCB substrate with a userpredicted dielectric constant value is designed and fabricated. Then the Vector Network Analyzer is used to measure the magnitude and phase of S11 and S21 of the transmission line. The measured data then inputted to Optimization functionality in Advance Design System (ADS) software to compare with a simulated data. The Optimization functionality plays the role as an adaptive algorithm that used the measured data as a goal. It tries to match simulated data to the goal. If it is matched, the program will stop and give us the result. Key words: Relative permittivity (dielectric constant), Vector Network Analyzer, transmission line, Optimization functionality, ADS Software. vii

8 CHAPTER 1: INTRODUCTION 1. Background and problems: In recent years, the prosperous development of mobile cell phones and mobile communications has propelled the high speed and high frequency circuit developers to design low price products to promote their market competition. It has then become an important task for them to find a high efficiency and high frequency printed circuit board (PCB). FR4 has the advantages of low cost and favorable fabrication characteristics that make it as the current commonly selected dielectric material for the PCB. The dielectric characteristics of the dielectric material for the PCB may vary due to different fabrication processes and fabrication environment. The dielectric parameters such as the relative permittivity, also called dielectric constant (εr) and the attenuation constant (A) of the circuit board have great impact on the high frequency or high speed characteristics of the system performance. The dielectric constant affects the circuit characteristic impedance and the signal transmission speed while the attenuation constant is relating to the power loss when the signal is transmitting through the circuit. 1

9 The dielectric constant of microwave substrate is an important parameter to design the passive devices such as filters and antennas or microwave electronic packaging for microwave integrated circuit. However, the dielectric information of substrate is usually given at low frequencies by the manufacturer. In addition, due to manufacturing errors, the dielectric constant of microwave substrate is usually in a range. Therefore, we need to know the accurate dielectric constant of substrate at high frequencies to get the best frequency response of the circuit. In the utilization of the current network vector analyzer it can only measure the circuit Sparameter, it does not provide any measurement or operation that with only one simple touch to immediately measure the PCB s dielectric constant and attenuation loss. For every application frequency it has different measurement methods to measure the dielectric constant and coupling loss of the dielectric material. Figure 1 portrays the procedure of the proposed method to build a simple measurable equivalent module for a lossy transmission line by using Agilent s ADS software and Vector Network Analyzer (VNA). 2

10 Fabricate a 100mm long transmission line Using VNA measure S11 and S21 By utilizing optimized ADS s functionality, (include SMA model) Find out the dielectric constant by reading from schematic Figure 1: Flowchart of the proposed method. It is needed at the test point to include the equivalent circuit of an SMA connector into the equivalent transmission line module to make a complete equivalent circuit. We then used the optimization functionalities of the ADS to have the transmission line characteristic impedance, effective dielectric constant, attenuation coefficient, dielectric attention coefficient due to skin effect and by using proper formulas to calculate the impedance loss, dielectric loss, and dielectric coefficient. 3

11 2. Project objectives: The goals of this project are: To build a method to measure permittivity of PCB s substrate. To study how to apply Optimization functionalities of the ADS to measure permittivity of PCB s substrate. To estimate the error of the result. 4

12 CHAPTER 2: LITERATURE REVIEW 1. Theory of Relative Permittivity Relative permittivity, usually denote as εr. Definition: The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux [1]. Relative permittivity is defined as: r ( ) ( ) where ε(ω) is the complex 0 frequency which dependents on absolute permittivity of the material, and ε0 is the vacuum permittivity. Relative permittivity εr is equivalent to dielectric constant (which usually denoted by K). Effective dielectric constant εe of a microstip line defined by formula [2]: e r 1 r H W Where H is the thickness of substrate, W is the width of transmission line. 5

13 Measurement [1]: The relative static permittivity, ε r, can be measured for static electric fields as follows: First the capacitance of a test capacitor, C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates the capacitance, Cx, with a dielectric between the plates is measured. The relative dielectric constant can be calculated as: r Cx C0 Table 1 showed the relative permittivity of some material at room temperature. Material Freq. Εr Alumina 99.5% 10Ghz Ceramic A35 3Ghz 5.6 Glass (Pyrex) 3Ghz 4.82 Silicon 10Ghz 11.9 Teflon 10Ghz 2.08 Table 1: The Relative permittivity of some materials at room temperature. 6

14 2. Review measuring permittivity of PCB s substrate methods that exist. Several methods varying in accuracy and computational effort are available in the literature to determine the dielectric constant of microwave substrates. Some of them can be listed below: Coaxial probe Free space Transmission line [3] Resonant cavity [3], [4] Parallel plate One of these is the transmission line method in which the scattering parameters of a single transmission line on the substrate are measured and the dielectric constant is then determined. Another method is to use a cavity resonator formed by metallization of all faces of a substrate, and the microwave signal is injected via a small hole. Then, dielectric constant information can be extracted from the resonance frequency expression [3]. Alternatively, by using a ring resonator, the dielectric constant of substrate can be calculated from the resonance frequency [5]. The dielectric constant can also be determined by measuring the capacitance with a parallel plate capacitor. To do so, a piece of PCB substrate without metallization is inserted into a waveguide, and 7

15 the dielectric constant is calculated from scattering parameters using reflection of microwaves [5]. These methods with their relative merits and limitations can be used in microwave frequencies. The listed above methods can be understood deeply by seeing the references at the end of this report. In the some next pages of Literature review chapter, some typical method will be briefly presented Method that using VNA and XFDTD Description: In this method, a bandpass microstrip filter on the PCB substrate with a userpredicted dielectric constant value is designed for a given center frequency, and it is implemented. The simulation results of the designed bandpass filter are obtained by the help of electromagnetic analysis software; XFDTD. Experimental results regarding the filter frequency characteristic are accomplished by means of a vector network analyzer. The simulation results of the designed filter are modified to overlap with the experimental ones by varying the dielectric constant value. When the simulation and experimental 8

16 results are overlapped, the value of dielectric constant is accurately selected [6]. The block diagram that summarizes the method is shows in figure 2. A bandpass microstrip filter constructed on the PCB substrate with a userpredicted permittivity is designed and is implemented. The simulation results of the designed bandpass filter are obtained using XFDTD, (a Computer Aid Design by REMCOM Inc.). S21 of designed filter are measured using VNA and is acquired by a computer. Both the simulation and experimental frequency characteristic results of the filter are transferred to the same diagram. The simulation results of designed filter and the experimental ones are mapped by varying the dielectric constant value. The accurate value of dielectric constant is then selected by overlapping the simulation and experimental results. Advantages and disadvantages: The advantage of this method is that any microwave designer can use it practically without any background in sophisticated mathematical techniques. The proposed method is easy to understand the algorithm, the test circuit is easy to fabricate; most of calculations are done by computer. However, the accuracy of the proposed method is also affected by the numerical noise of the microwave design software used. 9

17 Design and implementation of the microstrip S21 parameter measurement of the filter by vector network analyzer (VNA) Transfer of S21 measurement data to PC environment Comparison of simulated and measured filter characteristics Adjustment of the unknown dielectric constant to its accurate value in the simulation to map simulated and measured characteristics Figure 2: Algorithm to estimate the dielectric constant of a PCB substrate. 10

18 2.2. Parallel plate method Description [7]: In the parallel plate method, the material under test (MUT) is sandwiched between two parallel metallic plates as shown in figure below: Figure 3: Parallel plate method probe. This structure creates a capacitor which capacity is measured by RLC meter. The capacity of the capacitor is expressed by the formula: C 0 r S d Where ε0 is dielectric constant of the vacuum, 11

19 εr is relative dielectric constant, S is surface of the plates, d is distance between plates. Therefore, r Cd 0S Advantages and disadvantages: This method is easy to process, take short time. However, this method has a disadvantage is small frequency range of the permittivity measurement simply limited to 1 GHz Transmission line method Description [7]: In the transmission line method, material under test (MUT) is inserted in to the coaxial, air cell as shown in figure 4 or in to the waveguide cell as shown in figure 5. The probe is connected to the Vector Network Analyzer (VNA) as shown in figure 6. 12

20 Assuming the four poles model of coaxial probe with MUT, the Vector Network Analyzer measures all parameters of matrix s from which we can calculate the complex permittivity of the MUT. There are various approaches for obtaining the permittivity from sparameters. In this method, the most popular method is NicholsonRossWeir (NRW) Method [8] was used. NRW said that permittivity can be computed from following equation: r r 2 1 c 2 c 2 2 Where 1 r μr is relative permeability, λ0 is free space wavelength, λc is cutoff wavelength. X X 2 1; and 1; X S112 S ; 2 S 21 13

21 Figure 4: Transmission line method coaxial probe. Figure 5: Example of transmision line method waveguide probe. 14

22 Figure 6: Measurement using transmission method and coaxial probe. Advantages and disadvantages: The main disadvantage of the transmission method using waveguide is cutoff frequency of the waveguide which determines the minimum frequency value where we can obtain the dielectric permittivity. The method is dedicated for high frequency measurements only. The other disadvantage is complicated sample preparation especially in case of textiles. In the coaxial probe, however, the material must also be prepared, but the tested textile material can be rolled into a roll around inner conductor. 15

23 CHAPTER 3: METHODOLOGY In order to achieve goals, the following steps must be done: Fabricate the test board. Measure S11 and S21 using Vector Network Analyzer. Setup the Optimization controller and goals. Evaluate the result. Some steps in this chapter will be described in detail. 1. Fabricate the test board In this thesis, FR4 printed circuit board was used, with εr=4.2~4.8. Two samples were fabricated. Sample #1: Microstripline s dimension: length=100mm, width=5mm, Z0 about 70ohm. Figure 7 shows the sample #1. Sample #2: Microstripline s dimension: length=100mm, width=7mm, Z0 about 80ohm. 16

24 Figure 7: 100mm long transmission line. 2. Measure S11 and S21 using Vector Network Analyzer. The Vector Network Analyzer equipment (ENCE5071C) of Agilent was used to measure S parameters, (includes magnitude and phase), of transmission line in the frequency range 1GHz to 4GHz. The data will be saved as data.s2p file, then copy to PC. Input the measured data to ADS: This step aims to read the data in.s2p file into a dataset. The dataset will contain the traces of S11 and S21. First we run Data File Tool in ADS, then choose mode Read data file into Dataset. Figure 8 shows the Data File Tool windows. 17

25 Figure 8: Data File Tool windows in ADS. Link the input file name to the location of file data.s2p. Names the dataset is MEASURED_DATA_5mm. Then click Read File to read the.s2p into dataset. 18

26 Until here the magnitude and phase of S parameter is contained in dataset file MEASURED_DATA_5mm.ds. 3. Setup the Optimization controller and Goals. In this step, a model of transmission line will be created in ADS, then simulated and compared to measured data of transmission line on test board. (Compare S parameter). The simulated is then optimizing until the S11 and S21 match to measured data Build the model of transmission line: Open a new schematic window, name s_optim_5mm. A Terminal Physical Transmission Line (TLINP) will be used. Pick TLINP up from TLinesIdeal group. L L1 L=L1 nh R= Term Term1 Num=1 Z=50 Ohm C C1 C=C1 pf C C2 C=C2 pf TLINP TL1 Z=40.0 Ohm L=100 mm K=2.1 A= F=2.5 GHz TanD=0.002 Mur=1 TanM=0 Sigma=0 L L2 L=L2 nh R= Term Term2 Num=2 Z=50 Ohm Figure 9: Schematic of a 100mm long transmission line, include SMA model. 19

27 L1, C1 and L2, C2 represent two SMA connectors. Four lumped components are define by Var: Var Eqn VAR VAR1 L1= opt{ 0 to 2 } L2= opt{ 0 to 2 } C1= opt{ 0 to 2 } C2= opt{ 0 to 2 } Place a simulation controller. Set frequency range from 1GHz to 4GHz Run the simulation. In this step, we place both simulate S11 and measured S11 in a same rectangular plot. In the Data Display Windows appear, place a Rectangular Plot. Displays simulated S11 from dataset s_optim_5mm and then pick measured S11 from dataset MEASURED_DATA_5mm. See figure and figure below. 20

28 Figure 10: Plot 2 different traces from 2 different datasets. End of this step, there are 4 Rectangular Plots, shown in figure 11, include: o S11 magnitude and phase. o S22 magnitude and phase. 21

29 phase(s(2,1)) phase(s(1,1)) phase(measured_dataset_5mm..s(2,1)) phase(measured_dataset_5mm..s(1,1)) mag(s(1,1)) mag(measured_dataset_5mm..s(1,1)) mag(s(2,1)) mag(measured_dataset_5mm..s(2,1)) freq, GHz freq, GHz freq, GHz freq, GHz Figure 11: Measured S and Simulated S plot on a same rectangular. 22

30 3.3. Setup the Optimization controller and goals. This step aim to tune (automatically) the simulated S11 and S21 match the measured. In schematic s_optim_5mm, place an Optimization Controller and two Goals, pick from the Optim/Stat/DOE group. OPTIM Optim Optim1 UseAllOptVars=yes UseAllGoals=yes GOAL Goal OptimGoal1 Expr="mag(S(1,1))" SimInstanceName="SP1" Weight=1 GOAL Goal OptimGoal2 Expr="mag(S(2,1))" SimInstanceName="SP1" Weight=1 23

31 Setup Optimization Controller: Final Analysis = SP1. Optimization type = Gradient. Number of iteration = 500. Setup Goals: This step aim to match simulated data and measured data. In the figure below, the red trace is measured S11 magnitude, while the blue trace is the simulated S11, so we try to force the blue trace to pass these major points of mag(s(1,1)) mag(measured_dataset_5mm..s(1,1)) the red trace freq, GHz Figure 12: The major point of measured S11 magnitude. 24

32 In order to do this step, the goal can be set as figure below. Figure 13: The goal of magnitude of S11. 25

33 Figure 14: The goal of magnitude of S21. 26

34 Figure 15: The goal of phase S21. 27

35 After setup the Controller and Goals, we must enable the components that under optimizing process, by running Simulation Variable Setup in Simulate menu. Figure below shows components which under optimizing: L1, C1, L2, C2, characteristic impedance (Z), effective dielectric constant (relative permittivity) (K), loss tangent (TanD) and Attenuation (A). Figure 16: Optimization Variable Setup. By doing that step, the Optimization is ready to run. Figure 17 shows the schematic at the final. 28

36 GOAL OPTIM Var Eqn VAR VAR1 L1=1 opt{ 0 to 2 } L2=1 opt{ 0 to 2 } C1=1 opt{ 0 to 2 } C2=1 opt{ 0 to 2 } L L1 L=L1 nh R= Term Term1 Num=1 Z=50 Ohm SPARAMETERS S_Param SP1 Start=1 GHz Stop=4 GHz Step=1 MHz Optim Optim1 UseAllOptVars=y es UseAllGoals=y es Goal OptimGoal1 Expr="mag(S(1,1))" SimInstanceName="SP1" Weight=1 GOAL C C C1 TLINP C2 C=C1 pf TL1 C=C2 pf Z=40 Ohm opt{ 0 Ohm to 100 Ohm } L=100 mm K=3 opt{ 2 to 5 } A=1 opt{ 0 to 2 } F=2.5 GHz TanD=0.01 opt{ 0 to 0.1 } Mur=1 TanM=0 Sigma=0 Goal OptimGoal2 Expr="mag(S(2,1))" SimInstanceName="SP1" Weight=1 L L2 L=L2 nh R= GOAL Term Term2 Num=2 Z=50 Ohm Goal OptimGoal3 Expr="phase(S(2,1))" SimInstanceName="SP1" Weight=1 Figure 17: Final schematic. Run the optimization by click the symbol of Optimization Cockpit. The Optimization window will show the changing of component s value and the corresponding traces of S11 and S21. 29

37 Figure below shows the Optimization window. Figure 18: The Optimization window. The Optimization run until the all the goals is match or the number of iteration is reached. 30

38 4. Evaluate the result: In this thesis, the Optimization methods were used is Gradient [9]. The error function (EF) of Gradient: EF Wi simulationi goali, where W is the weight, in our case is set 2 allgoals one. Hence, the smaller EF is, the less differences of two measured and simulated are. In the other word, we aim to reach the minimum EF. 31

39 CHAPTER 4: RESULT The samples are under tested by the same procedure. Result of trial #1: Figure 19 shows the magnitude and phase comparison between measured and simulated. Figure 19: Magnitude and phase comparison between measured and simulated in trial #1. 32

40 The error function is Effectivity dielectric constant (relative permittivity) Keff = Using the formula e r 1 r H 1 12 W, where in our case H=1.6mm and W=5mm, so by calculation: r 22 e = r Attenuation A = 1.8. Loss tangent TanD = Characteristic impedance Z = Ohm. 33

41 Result of trial #2: Figure 20 shows the magnitude and phase comparison between measured and simulated. Figure 20: Magnitude and phase comparison between measured and simulated in trial #2. The error function is Relative permittivity ε r= Attenuation A = Loss tangent TanD = Characteristic impedance Z = Ohm. 34

42 CHAPTER 5: CONCLUSION AND RECOMMENDATION 1. Conclusion: A new method of measument relative permittivity of PCB s substrate was proposed. This method use a sample of transmission line of under test PCB, Vector Network Analyzer, and Optimization functionality in ADS. At the final, all the goals have been achieved. The relative permittivity found in two trial are and These are comparable with the datashet of the PCB s manufactor. 2. Recommendation: Followings are some recommendation for this thesis: The figure of measured and simulated comparison shown that there is an unmatch between phase of S11 of measured one and simulated one. This different must be considered. This method can be applied on a different PCB type (e.g. duroid). 35

43 REFERENCES 1. visited on May D. M. Pozar, Microwave Engineering, 2nd edition, Wiley and Sons, S.H. Chang, H. Kuan, H.W. Wu, R.Y. Yang, M. Weng, Determination of microwave dielectric constant by two microstrip line method combined with EM simulation, Microwave and Optical Technology Letters, Vol: 48, pp , A. Namba, O. Wada, Y. Toyota, Y. Fukumoto, Z. L. Wang, R.Koga, T. Miyashita, A. Watanabe, A Simple Method for Measuring the Relative Permittivity of Printed Circuit Board Materials, IEEE Transactions on Electromagnetic Compatibility, Vol:43, No: 4, pp , A.H. Boughriet, C. Legrand, A. Chapoton, Noniterative Stable Transmission/Reflection Method for LowLoss Material Complex Permittivity Determination, IEEE Trans. Microwave Theory Tech., Vol. 45, pp , Serhan Yamacli, Ali Akdagli and Caner Ozdemir, A method to determine the dielectric constant value of microwave PCB substrates, an article, Jacek Leśnikowski, Dielectric permittivity measurement methods of textile substrate of textile transmission lines, visited May an article published on

44 8. Weir Winks, Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies, Proceedings of IEEE, Vol.62 page 3336, Advanced Design System 2009 Update 1 Documentation Tuning, Optimization, and Statistical Design. Agilent, Permittivity Measurement of PC Boards and Substrate Materials Using HP4291A and HP16453A, Hewlett Packard Application Note,