Group paths and dispersion coefficients of pulsed radio signals reflected from model ionospheres

When pulsed electromagnetic signals propagate through a stratified, inhomogeneous, isotropic ionosphere, their shapes are usually distorted because of dispersion. To the first-order approximation, this distortion is determined by the dispersion coefficient ϕ”, the second derivative of the phase with respect to the angular frequency. In order to derive analytic expressions of the group path and the dispersion coefficient in model ionospheres for the spherical Earth-ionosphere geometry the quasi-linear and quasi-parabolic electron density models already in existence in the literature have been used. When generalized to an ionosphere with known virtual height, the secant law applicable to the plane geometry must be modified for application to the spherical geometry. In this regard, a correction factor can be introduced. This correction factor is computed, and a dispersion coefficient in terms of a correction factor is derived using a modified secant law and the geometry of a spherical Earth-ionosphere. All calculations are made under conditions which neglect the Earth's magnetic field, absorption, and horizontal gradients. The results show the dependence of the group path and the dispersion coefficient on propagation geometry and ionospheric parameters.