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  • Tutorial
  • Open Access

Synthesis of Parametrically Coupled Networks

Ofer Naaman1,* and José Aumentado2,†

  • 1Google Quantum AI, Santa Barbara, California 93117, USA
  • 2National Institute of Standards and Technology, Boulder, Colorado 80305, USA

  • *ofernaaman@google.com
  • †jose.aumentado@boulder.nist.gov
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PRX Quantum 3, 020201 – Published 16 May, 2022

DOI: https://doi.org/10.1103/PRXQuantum.3.020201

Abstract

We show that a common language can be used to unify the description of parametrically coupled circuits—parametric amplifiers, frequency converters, and parametric nonreciprocal devices—with that of band-pass filter and impedance matching networks. This enables one to readily adapt network synthesis methods from microwave engineering in the design of parametrically coupled devices having prescribed transfer characteristics, e.g., gain, bandwidth, return loss, and isolation. We review basic practical aspects of coupled-mode theory and filter synthesis, and then show how to apply both, on an equal footing, to the design of multipole, broadband parametric and nonreciprocal networks. We supplement the discussion with a range of examples and reference designs.

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The success of Josephson parametric amplifiers in enabling high-fidelity readout of superconducting qubits has led to a flurry of research into parametrically coupled networks, including amplifiers, frequency converters, and parametric nonreciprocal devices such as circulators. Despite significant progress, there is still a lack of design methodologies to enable deliberate engineering of these devices’ transfer characteristics—gain, ripple, bandwidth, return loss, and isolation. This tutorial shows how band-pass impedance matching and filter network synthesis techniques from microwave engineering can be applied to the design of parametric and nonreciprocal devices, and demonstrates practical examples that dramatically simplify the design of wideband Josephson parametric amplifiers, frequency converters, and circulators.

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PRX Quantum 3, 020201– Published 16 May, 2022
  • Received 17 September 2021
  • Revised 15 February 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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