A dispersion formula satisfying recent requirements in microstrip CAD

A dispersion formula ε^*_eff(f)=ε^* -{ε^*-ε^*_eff(0)}/{1+( f/f₅₀)^m}, for the effective relative permittivity ε^*_eff(f) of an open microstrip line is derived for computer-aided design (CAD) use. The 50% dispersion point (the frequency f₅₀ at which ε^*_eff(f₅₀)={ε ^*+ε^*_eff(0)}/2}) is used a normalizing frequency in the proposed formula, and an expression for f₅₀ is derived. To obtain the best fit of ε ^*_eff(f) to the theoretical numerical model, the power m of the normalized frequency in the proposed formula is expressed as a function of width-to-height ratio w/ h for w/h⩾0.7 and as a function of w /h, f₅₀, and f for w/h⩽0.7. The present formula has a high degree of accuracy, better than 0.6% in the range 0.1<w/h⩽10, 1<ε^*⩽128, and any height-to-wavelength ratio h/λ₀