Pulse propagation on nonlinear transmission lines (NLTLs), which are transmission lines with regularly spaced Schottky varactors, is investigated for the amplification of short pulses. We recently found that the soliton developed in an NLTL experiences an exponential amplitude growth, when it couples with an existing voltage edge. This paper clarifies how the pulse gain depends on the device parameters, including the line inductance, capacitance, and gradient of voltage edge, and describes the design criteria of an NLTL as a pulse amplifier, together with several results of calculations that examine the potential of the NLTL.