# A linear magnetic flux-to-voltage transfer function of differential DC SQUID

## TL;DR

This paper demonstrates that a differential SQUID (DSQUID) provides a highly linear magnetic flux-to-voltage transfer function with high dynamic range and low distortion, suitable for precise magnetic measurements.

## Contribution

The study shows that DSQUID achieves a linear flux-to-voltage transfer function with high SFDR and low THD, enhancing magnetic sensing performance compared to traditional SQUIDs.

## Key findings

- SFDR > 100 dB for DSQUID
- THD < 10^{-3}% with a quarter flux quantum signal
- High linearity requires precise junction matching and current control

## Abstract

A superconducting quantum interference device with differential output or "DSQUID" was proposed earlier for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that Spur-Free Dynamic Range (SFDR) of DSQUID magnetic flux-to-voltage transfer function is higher than SFDR > 100 dB while Total Harmonic Distortion (THD) of a signal is less than THD < $10^{-3}\%$ with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, $2\Phi_a = \Phi_0/8$. Analysis of DSQUID voltage response stability to a variation of the circuit parameters shows that DSQUID implementation allows doing highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.