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Applied Physics Letters

Microstrip superconducting quantum interference device amplifier: Conditional stability

D. Kinion, John L. Clarke

Published Apr 26, 2010• 6 citations
Publisher

Abstract

The scattering parameters of an amplifier based on a dc superconducting quantum interference device are directly measured at 4.2 K as functions of the bias current and applied magnetic flux. These parameters are used to determine the stability of the amplifier with arbitrary source and output load impedances. It was found that the amplifier is conditionally stable, and that the stability is improved by decreasing the gain or adding negative feedback. With suitable bias selection, the amplifier is shown to be sufficiently stable to allow operation with a resonant source impedance.

DOI
10.1063/1.3377898

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Applied Physics Letters•Jul 8, 2013•14 citations
The scattering parameters of an amplifier based on a dc superconducting quantum interference device are directly measured at 4.2 K as functions of the bias current and applied magnetic flux. These parameters are used to determine the stability of the amplifier with arbitrary source and output load impedances. It was found that the amplifier is conditionally stable, and that the stability is improved by decreasing the gain or adding negative feedback. With suitable bias selection, the amplifier is shown to be sufficiently stable to allow operation with a resonant source impedance.
The forward scattering parameters of an amplifier based on a dc superconducting quantum interference device are directly measured at 4.2K as functions of the applied magnetic flux. These parameters are equivalent to the real and imaginary components of the input impedance and forward gain of the amplifier. The results can be described using an equivalent circuit model of the fundamental resonance of the microstrip resonator which forms the input of the amplifier. The circuit model is used to determine the series capacitance required for critical coupling of the microstrip to the input circuit.
We present the results of measurements of the scattering parameters of microstrip amplifiers (MSAs) based on the dc superconducting quantum interference device. The amplifier input impedance is poorly matched to typical transmission line impedances, resulting in high input return loss around −2 dB. We show that negative feedback can lower the MSA input impedance to achieve a robust match to 50 Ω. In the presence of capacitive and inductive feedback, the input return loss of the MSA can be reduced below −10 dB, opening the door to the practical use of the MSA for a variety of demanding applications.
The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.
A series of about twenty superconducting quantum interference devices (SQUIDs) has been operated as microstrip-SQUID amplifiers (MSAs) at frequencies ranging from 100 MHz to 2 GHz to study the dependence of their gain and noise temperature on bias current and flux. The measured values were in good agreement with theory. The observed dependence of MSA gain and noise temperature on bias current and flux resembled the static transfer function of the SQUIDs. The gains are relatively insensitive to changes in bias current and bias flux; the noise temperature is strongly dependent on the bias flux.
Computer models are presented for a microstrip amplifier based on a dc superconducting quantum interference device (SQUID). In this device, the signal is applied between one end of the spiral input coil and the square washer on which it is deposited. The amplifier exhibits substantial power gain when the signal frequency is such that a half wavelength is approximately equal to the length of the microstrip formed by the coil and the groundplane. The resonant frequency is lowered significantly by the inductance of the square washer transformed into the input coil; this reduction is consistent with predictions of a simple model and with analog simulations. With the washer grounded, the gain of the amplifier peaks at a frequency that is lowered from the unloaded resonant frequency by the damping of the resistance associated with the source. The position and magnitude of the peak are in good agreement with both a lumped circuit model and with a model representing the microstrip as a transmission line. When the counter electrode of the SQUID is grounded and the washer floats, feedback from the output of the SQUID to the input via the capacitance of the microstrip plays a major role and is well described by simulations using the transmission line model. Measurements of the input impedance of the microstrip amplifier show that the return loss can be positive or negative, depending on the sign of the feedback and whether the frequency is above or below the resonant frequency. This behavior is in good accord with simulations.
In this work, we characterize the 2-port scattering parameters of a superconducting quantum interference device amplifier at ∼20 mK over several gigahertz of bandwidth. The measurement reference plane is positioned on a 6.25 Ω microstrip line situated directly at the input and output of the device by means of a thru-reflect-line cryogenic calibration procedure. From the scattering parameters, we derive the device available power gain, isolation, and input impedance over the 2–8 GHz range. This measurement methodology provides a path towards designing wide-band matching circuits for low impedance superconducting amplifiers operating at dilution refrigerator temperatures.