A mathematical treatment is given of the wave phenomena in a traveling wave parametric amplifier. The waves are described by two coupled differential equations of the 2nd order. By the elimination of one of the unknowns a 4th order differential equation arises. There are 4 waves of the signal frequency and 4 waves of the idler frequency, in contrast to linear transmission lines, where there are only 2 waves on a single frequency. The influence of the reflected waves on the stability of the amplifier is investigated, and oscillation criteria are given. Some methods to prevent oscillation are suggested. (Author.

The theoretical investigation includes derivations of expressions for gain and noise figure. Phase conditions necessary for maximum gain (synchronism) are included. Both iterative and distribution amplifiers are analyzed and the expressions for gain, synchronism and noise figure are shown to converge to the same results. For comparison purposes, the shunt connected iterative and distributed amplifiers are also analyzed. Computer programs are written comparing iterative series and shunt amplifiers with respect to gain and noise figure. Results are shown in graphical form over the passband of the amplifiers. (Author).