It is shown, using three specific examples—a series fed patch (SFP) array, a phase reversal (PR) array and a composite right/left-handed (CRLH) antenna—that one-dimensional periodic leaky-wave antennas scanning through broadside build a class of leaky-wave antennas sharing qualitatively similar and quantitatively distinct dispersion and radiation characteristics. Based on an equivalent transmission line (TL) model using linearized series and shunt immittances to approximate the periodic (Bloch) antenna structure, asymptotic TL formulas for the characteristic propagation constant, impedance, energy, power and quality factor are derived for two fundamentally different nearand off-broadside radiation regimes. Based on these formulas, it is established that the total powers in the series and shunt elements are always equal at broadside, which constitutes one of the central results of this contribution. This equal power splitting implies a severe degradation of broadside radiation when only one of the two elements series or shunt efficiently contributes to radiation and the other is mainly dissipative. A condition for optimum broadside radiation is subsequently established and shown to be identical to the Heaviside condition for distortionless propagation in TL theory. Closed-form expressions are derived for the constitutive (LCRG) parameters of the TL model for the specific SFP, PR and CRLH antenna circuit models, and quantitative information on the validity range of the TL model is subsequently provided. Finally, full-wave simulation and measurement LCRG parameter extraction methods are proposed and validated.