We show that the lightning return stroke model by Master, Uman, Lin, and Standler (MULS), a modification of the Lin, Uman, Standler (LUS) model, can be viewed mathematically as having a specified channel-base current, although in the original formulation it was the channel current sources that were specified. The specification of the MULS channel-base current is independent of the time dependence of the corona current sources which characterize the MULS model. Further, we show that, when starting from the same channel-base current, the MULS return stroke model, except for the uniform current component, is mathematically equivalent to the Modified Transmission Line (MTL) model. For both the MULS and the MTL models we present a single analytical expression relating the far fields and the channel-base current. This formulation provides for a simpler procedure to infer MULS channel-base currents from remote electric and magnetic field measurements than was previously available and hence to test experimentally the MULS model. ¿ American Geophysical Union 1990