A novel model for determining the reflection and transmission characteristics of RO-4350B materials by microstrip line technique

A NOVEL MODEL FOR DETERMINING THE REFLECTION AND TRANSMISSION CHARACTERISTICS OF RO-4350B MATERIALS BY MICROSTRIP LINE TECHNIQUE Ho Manh Cuong1, Vu Van Yem2 1Electric Power University, 2Hanoi University of Science and Technology 1. INTRODUCTION5 achieved by using the transmission/ The measurement of complex permittivity reflection method developed by Weir [1]. and permeability of material can be The basic concept of this method is to measure the S-parameters of a sample 5 placed in a transmission line. The transmission lines have been used as sample holders and can be coaxial, determined with the Computer Simulation waveguide or free-space [2-8]. For Technology (CST) software. Results of S- general transmission lines, Enders [9] parameters were calculated with adaptive presented a method for determining all mesh refinement. The calculation of properties of an unknown line and their complex permittivity based on the junctions to the line using three different frequency dependent value of the lengths of the unknown line. On the other complex effective permittivity. hand, Das [10] developed a two-line The paper is organized as follows. The method to measure substrate permittivity. second section describes the theory of This method is based on the use of proposed method a microstrip line transmission lines having the same technique. The results and discussions geometry with different lengths, and the follow in the next section. aim is to determine the complex propagation constant. Although the 2. THEORY method is simple, quick and reliable to * The complex effective permittivity ( eff ) use, it still has several drawbacks. One is and the complex permittivity or complex that the technique works well on the relative permittivity ( * ) are defined as condition that the transition effect of r coax-to-microstrip is relatively small. * , ,, , 1 (1) eff eff eff eff eff This means that the approximate substrate permittivity must be known before the * , ,, , 1 (2) r r r r r measurement, so that the characteristic impedance of the test section can be Where: -18]. , ,, eff and eff are the real and imaginary The other is that the method gives us an parts of complex effective permittivity. accurate result only if the electrical length , ,, of lines is long. r and r are the real and imaginary parts of complex permittivity (complex relative In this paper, we propose a new method permittivity). for determining complex permittivity of tan and tan are the effective material. This method uses a microstrip eff r line technique, which based on the dielectric and dielectric loss tangent. concepts of the reflection and Figure 1 shows a microstrip line with transmission coefficients of a material characteristic impedance (unnecessary to sample. Therefore, our method is different L. The measured from conventional methods. Our method two ports parameters expressed in relies solely on the measurement of only scattering matrix S form can be one microstrip line complex propagation considered as a product of the reflection constant, and the characteristic impedance and transmission coefficients S11, S22 and unnecessary to be designed in the vicinity S21, S12 (S-parameter). It can be shown that the S-parameters are related to the parameters and T by the following calculated based on the frequency equations: dependent value of the complex effective permittivity [19], as follows: 1 2 ,, S11 = S 22 = 2 2 (3) 1- ,, r s (10) eff r 1+ P(f) T(1 - 2 S21 = S 12 = 2 2 (4) P(f) is the frequency-dependent term and 1- it is given by (11). (11) PORT 1 PORT 2 with 0.525 P =0.6315 + * 1 (1+ 0.157 fh)20 (12) w Figure 1. Schematic diagram -8.7513 w h of a microstrip line * -0.065683 e + 0.27488 h , From (3) and (4), and T can be written -0.03442 r P2 =0.33622 1- e (13) as 4.97 w fh -4.6 - (5) h 4.87 P3 =0.363 e 1 - e (14) Where 2 2 , 8 S11 - S 21 +1 - r K = (6) 15.916 2S21 P4 =1+ 2.751 1 - e (15) S + S - T = 11 21 (7) 1-(S11 + S 21 ) where is static dielectric constant The complex propagation constant of , ( eff (f = 0)) and it can be written as the microstrip line can be written as * ,, log (1 / T) eff 1 1 1 e (8) , r r L c s 2 2 h 1+12 The complex effective permittivity of w (16) material is found from (8) t c.log (1 / T) 2 , 1 * e (9) - r h eff 4.6 w where c is the light velocity, is the h signal angular frequency and L is the where w is the width of track, t is the length of the microstrip line. thickness of track and h is the thickness of The complex relative permittivity is material. 3. RESULTS AND DISCUSSIONS technique in figure 2. The S-parameters 3.1. A brief introduction to RO-4350B obtained from CST software are shown in material figure 3. The RO-4350B nonmagnetic material (a type of roger) is widely used in communication devices, electronics devices, aerospace and military equipments. In these devices and equipments, this material plays a vital role in many components, such as power divider, combiner, power amplifier, line Figure 3. The S-parameters of material amplifier, base station, RF antenna, etc. The proposed method is used to The calculated values of S11 and S21 by determine the complex permittivity of equation (8), (9) and (10) in section 2 are RO-4350B nonmagnetic material in determined the complex permittivity of the frequency range of 0.5-12.5 GHz RO-4350B material. ( from data 4 sheet). 3 ' - Theory ' (simulation) ' (theory) r r r ' - Simulation 2 r '' - Theory 3.2. Simulations and Results r 1 " (simulation) '' - Simulation r r We use the Computer Simulation 0 " (theory) r -1 Technology (CST) software to determine 0.5 2.0 4.0 6.0 8.0 10.0 12.5 the S-parameters. The structure Frequency [GHz] dimensions are: height h = 0.254 mm, Figure 4. The complex permittivity thickness t = 18 µm, width w = 0.5 mm, of RO-4350B material length L = 6.5 mm and copper is the conductor being used. The following Figure 4 shows the data obtained using figure shows what it looks line. the proposed method. The real part of the complex permittivity is stable and the mean error difference of 1.7% in the entire frequency band. The imaginary part of the complex permittivity is acceptably stable and this error is small for simulation in the entire frequency band. The error of complex permittivity for Figure 2. A microstrip line determining material with dielectric constant and loss the S-parameters of material by CST tangent as shown in figure 5. Figure 5 shows that the error of simulated The reflection and transmission results compared to the theory is small. coefficients (S11 and S21) of material are Those results show that the dielectric measured using a microstrip line constant and loss tangent of RO-4350B materials are nearly identical with the determining the parameters of theoretical values. nonmagnetic material using a microstrip line technique. The usage of only one microstrip line is proposed to accurately determine the complex permittivity of wideband, nonmagnetic materials. Our proposed method can be used for a microstrip line with arbitrary width. The Figure 5. The root mean squared error of method has some benefits for determining dielectric constant and loss tangent RO-4350B the parameters of materials. It is simple, material quick, and reliable to use. This method could be used in many scientific fields 4. CONCLUSION such as: electronics, communications, We proposed a new method for metrology, etc.