It is well known that the parametric principle can give low noise amplification at microwave frequencies. The conventional parametric amplifier involves a single variable-element and one or more resonant cavities. Such an amplifier is extremely narrow band, it suffers from large changes in gain due to small changes in pump level, and it must be used with a circulator if unilateral gain is desired. These difficulties can be overcome by using a number of variable elements in a traveling-wave circuit. This paper presents the circuit considerations appropriate to wideband operation in a traveling-wave parametric amplifier. The model which is analyzed is a transmission line periodically loaded with parametric diodes. The diodes constitute the variable elements. Across each diode is fed a large pumping voltage which produces a time-varying capacitance. A Brillouin diagram for the structure (i.e., a plot of

vs

) can be computed from the analysis. The conditions for high gain, wide band, and other desirable characteristics are conveniently determined from this diagram.