A Non-Foster Superconducting Broadband Matching Network

Abstract

The nonlinear inductance of the Josephson junction has enabled the development of a wide range of continuous-variable amplifiers and qubit-based devices with unprecedented sensitivity. We present an alternative use of the Josephson junction in the context of broadband impedance matching. The idea poses a potential solution to a longstanding problem in the field of high energy particle physics. The axion, a compelling candidate for the dark matter, converts to a weak electromagnetic signal at an as-yet unknown frequency. As such, the ideal axion detector does not compromise bandwidth for sensitivity, a trade-off intrinsic to all linear, time-invariant and passive circuits. We propose a circuit that uses a Josephson junction in an impedance matching network to overcome these gain-bandwidth constraints and increase the scan rate of axion searches. The Josephson junction can be biased to exhibit negative inductance capable of canceling geometric inductance similar to a capacitor but across a wider frequency range.

Figures (12)

• Figure 1: Left: In a classical, single-pole resonant matching network, the reactive impedance is canceled at a single value, indicated by the zero crossing of the total reactive inductance. Right: In a non-Foster network with idealized negative inductance instead of capacitance, the reactive impedance is instead canceled across all frequencies, resulting in a technically infinite bandwidth network.
• Figure 2: Load receiver model for a signal with a complex source impedance. For a detector to achieve a perfect match, the real impedance of the 'load' (the readout) must match the real component of the source impedance, while the complex load impedance must equal the complex conjugate of the complex source impedance.
• Figure 3: A superconducting circuit loop with a geometric inductance, whose value is denoted by $L_{G}$, and Josephson junction with inductance $L_{J}$.
• Figure 4: Proposed non-Foster junction device with its equivalent circuit representation. The Thevenin equivalent look-back impedance at that port is $Z_\mathrm{in}$, with a corresponding voltage $V_\mathrm{in}$ across the terminals. The inductor that weakly couples in the magnetic flux from the DC current bias has an inductance much smaller than other sources of inductance.
• Figure 5: Full signal model and matching network. Simulations are performed to compare three different impedance matching networks in a $pi$-network configuration: (a) classical capacitor match, (b) negative inductance match with the device proposed in Fig. \ref{['fig_expanded_bfe']}, and (c) no match. The output voltage and subsequent power is measured across a 50 $\Omega$ load resistor $R_L$.