A measure of distortion and its variation due to attenuation constant and frequency dependent non-linear phase constant

In this paper a measure of distortion 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 signal 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. Distortion 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 variation in energy of the reference signal whereas nonlinearity in phase constant is represented by degree of the polynomial of to (in radians/second). Simulations show that distortion due to nonlinear phase is more pronounced (lower correlation coefficient) as compared to that which results because of frequency dependent attenuation constant (higher correlation coefficient). Simulations are validated by measured results. Furthermore 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 degree of polynomial).