Dielectric Loss in Integrated Microwave Circuits

Abstract

Dielectric loss is important in integrated microwave and millimeter wave circuits which require small attenuation. Such circuits are usually built with microstrip or suspended microstrip transmission lines. This paper shows that the dielectric loss, the filling factor of the microstrip, and the stored field energy in the dielectric substrate can be computed from the partial derivative ∂U/∂∊ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> where U is the total electric field energy and ∊ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> the relative dielectric constant of the substrate. It also shows that the effective loss tangent is determined by the partial derivative ∂∊ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</inf> /∂∊ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> where ∊ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</inf> is the effective dielectric constant of the microstrip. Useful design formulas for computing the dielectric loss are given for the most important cases.