外文翻譯--衡量由衰減常數(shù)和非線性相位常數(shù)引起的失真及其變化（英文）

1、A Measure Of Distortion And Its Variation Due To Attenuation Constant And Frequency Dependent Non-Linear Phase Constant Sultan Shoaib#1, Waqar Ali Shah#2, Muhammad Naeem#3, Muhammad Amin#4 #Department of Communication

2、Systems Engineering, Institute of Space Technology, Islamabad, Pakistan. 1sultan.shoaib@live.com 2waqar1130@hotmail.com 3muhammad_naeem265@yahoo.com 4mamughal.pk@gmail.com Abstract In this paper a measure of distorti

3、on in propagation of electromagnetic wave which results from frequency dependence of attenuation constant and non-linear phase constant in microwave transmission line is presented as correlation of the reference sign

4、al and the distorted signal. By taking the Fourier series of a particular pulse train and then taking the sum of first few dominant components that contain ? 90% of the energy, a reference input signal is obtained. Di

5、stortion due to variation in amplitude and phase characteristics of the transmission line is simulated by comparing the distorted signal with the reference signal. Amplitude variation is represented as percentage var

6、iation in energy of the reference signal whereas nonlinearity in phase constant is represented by degree of the polynomial of ? (in radians/second). Simulations show that distortion due to nonlinear phase is more pron

7、ounced (lower correlation coefficient) as compared to that which results because of frequency dependent attenuation constant (higher correlation coefficient). Simulations are validated by measured results. Furthermo

8、re a GUI has been developed in MATLAB® that can represent the signal distortion as correlation coefficient for desired amplitude distortion (in percentage of energy) and nonlinear phase constant (in terms of degr

9、ee of polynomial). Index Terms Distortionless transmission line, Distortion measurement, attenuation constant, nonlinear phase constant. I. INTRODUCTION A distortionless transmission line is defined as one that ha

10、s an attenuation constant ‘?’ which is independent of frequency (.i.e. the magnitude has no loss or a constant loss for all components.). The phase constant ‘?’ of distortionless transmission line is linearly depende

11、nt on frequency. The general expressions of ? and ? are given by [1, 2]: ? ? ??? (1) ? ? ???? (2) The characteristic impedance Zo of

12、transmission line in general is then given by: Zo = Ro + jXo (3) A microwave transmission line which would attenuate the electromagnetic signal travelling in it lossy line can preserve the shape of the input signal

13、 i.e. act as distortionless transmission line if Ro =? ?? ? ? ??? and Xo = 0 (4) Any time domain signal can be represented as sum of sinusoidal harmonics preserving the shape of the transmitted

14、 and signal requires that all frequency components be treated identically in the channel (transmission line) which technically means fulfilling the above two conditions. The phase velocity u is given by ?/? and will

15、be independent of ?, if ? is linearly dependent on frequency. However for nonlinear variation of ? with frequency, the velocity of all frequency components will not be identical resulting in fewer components reaching

16、 later than others, thus distorting the shape of the original signal. Similarly an attenuation constant that is frequency dependent will decrease the amplitude of certain frequency components more than others again no

17、t preserving the shape of the original signal. In order to quantify and measure the original distortion, correlation coefficient is obtained between the transmitted and the received signal. Amplitude distortion is re

18、presented as percentage increase or decrease in the total energy content of the signal. Phase distortion is given by the degree of the polynomial of ? which represents nonlinear dependence of ?. The proposed quantifi

19、cation can be used to grade the distortion of any microwave transmission line. II. FORMULATION OF THE PROBLEM A rectangular pulse is assumed on the transmission side. Its Fourier series contains infinite components and

20、 only first few components (first four dominant components in this case) are taken that account for at least 90% energy of the total signal. These four components are summed, and the resulting signal 978-1-4244-2721-5

21、/09/$25.00 ©2009 IEEE2009 Loughborough Antennas & Propagation Conference 16-17 November 2009, Loughborough, UK697Fig. 4 illustrates different cases of amplitude distortion of the referance signal where all or

22、some of the Fourier components are multiplied by a constant ( a = 2 ) and compared with the original signal. This is simulated using Graphical user interface (GUI). Fig. 4a. When all components are multiplied by same

23、constant Fig. 4b. When only first component is multiplied by constant Fig. 4c. When only third component is multiplied by constant Fig. 4d. When first and third components are multiplied by constant Fig. 4e. When second

24、and fourth components are multiplied by constant One can notice that in general distortion is greater when components with higher energy contents (Fig.4b) are multiplied by a scaling factor whereas the effect of compo

25、nents that contain less energy content is not significant. Fig.5 illustrates different cases of signal distortion of the microwave transmission line when phase constant is not linearly dependent on ?. Fig. 5a. When li

26、near phase is added Fig. 5b. When phase is nonlinear (Polynomial of degree 2). V. QUANTIFICATION OF DISTORTION The quantification of distortion is carried out by correlation coefficient, a built-in MATLAB® function

27、 which takes original signal and distorted signal as input parameters and carries out correlation. The results are given in Table II. Where percentage of energy distortion is given below, ?????????????????????? ? ????

28、????????????????????????????????????????????????????????????????????????????????????????? (8) The following results obtained using eq. (8) are tabulated in Table III. 2009 Loughborough Antennas &