We investigate the peripheral circuits required to enable ideal performance for a high-gain traveling-wave parametric amplifier (TWPA) based on three-wave mixing . By embedding the TWPA in a network of superconducting diplexers, hybrid couplers, and impedance matching networks, the amplifier can deliver a high stable gain with near-quantum-limited noise performance, with suppressed gain ripples, while eliminating the reflections of the signal, the idler and the pump as well as the transmission of all unwanted tones. We also demonstrate a configuration where the amplifier can isolate. We call this technique (WIF). The theory is supported by simulations that predict over 20 dB gain in the 4–8 GHz band with 10 dB isolation for a single amplifier and 30 dB isolation for two cascaded amplifiers. We demonstrate how the WIF-TWPAs can be used to construct controllable isolators with over 40 dB isolation over the full 4–8 GHz band. Finally, we look at nonidealities and show how certain nonidealities can be devastating for both the gain and the idler filtering, especially a cutoff imbalance or a flux imbalance, and discuss how to compensate for them. Published by the American Physical Society 2024