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Superconducting traveling-wave parametric amplifiers are a promising amplification technology suitable for applications in submillimeter astronomy. Their implementation relies on the use of Floquet transmission lines in order to create strong stopbands to suppress undesired harmonics. In the design process, amplitude equations&#x00A0;are used to predict their gain, operation frequency, and bandwidth. However, usual amplitude equations&#x00A0;do not take into account the real and imaginary parts of the dispersion and characteristic impedance that results from the use of Floquet lines, hindering reliable design. In order to overcome this limitation, we have used the multiple-scales method to include those effects. We demonstrate that complex dispersion and characteristic impedance have a stark effect on the transmission line&#x0027;s gain, even suppressing it completely in certain cases. The equations&#x00A0;presented here can, thus, guide to a better design and understanding of the properties of this kind of amplifier.

The Effect of Complex Dispersion and Characteristic Impedance on the Gain of Superconducting Traveling-Wave Kinetic Inductance Parametric Amplifiers