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Applied Physics Letters

Broadband calibrated scattering parameters characterization of a superconducting quantum interference device amplifier

Leonardo Ranzani, Lafe Spietz, José Aumentado

Published Jul 8, 2013• 14 citations
Publisher

Abstract

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.

DOI
10.1063/1.4813549

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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.
We present a 4 : 1 superconducting transmission-line impedance transformer for cryogenic applications. The device transforms 25 Ω in the coplanar waveguide to 6.25 Ω in the microstrip and is designed to operate at 20 mK. Calibrated measurements in a dilution refrigerator demonstrate a -3 dB bandwidth from 1.6 to 13 GHz. In a modified Ruthroff design, a small capacitor is integrated at the input as a direct-current block, making it suitable for biasing and matching to low-impedance active circuits, such as superconducting quantum interference device (SQUID) amplifiers.
Due to their superior noise performance, superconducting quantum interference devices (SQUIDs) are an attractive alternative to high electron mobility transistors for constructing ultra-low-noise microwave amplifiers for cryogenic use. We describe the use of a lumped element SQUID inductively coupled to a quarter wave resonator. The resonator acts as an impedance transformer and also makes it possible to accurately measure the input impedance and intrinsic microwave characteristics of the SQUID. We present a model for input impedance and gain, compare it to the measured scattering parameters, and describe how to use the model for the systematic design of low-noise microwave amplifiers with a wide range of performance characteristics.
Abstract High-performance cryogenic amplifiers are essential components for quantum information technology and astronomical observation. In this work, we report the design and characterization of a microwave amplifier based on a superconducting quantum interference device (SQUID). The design incorporates input and output impedance transformers to center the operating frequency at approximately 5.5 GHz for specific applications. Preliminary characterization at a bath temperature of 4.2 K demonstrates a peak gain of 10.79 dB at 5.39 GHz and a saturation power of approximately −115 dBm.
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.
Accurate knowledge of the microwave power delivered to a cryogenic device under test (DUT) is essential for the characterization and operation of superconducting quantum circuits. However, this information is difficult to obtain inside dilution refrigerators because of distributed attenuation, impedance mismatch, switch-path repeatability, and temperature-dependent microwave components. This paper presents an in situ measurement method for RF power at the cryogenic device plane. The method uses a custom variable temperature stage (VTS) as a cryogenic thermal-transfer element. The TVS is alternately heated by a four-wire DC heater and by microwave power dissipated in a 20 dB pass-through attenuator. By fitting the thermal transients and comparing the corresponding steady-state temperatures, the absorbed microwave power is inferred from a directly measured DC electrical power through an AC/DC substitution procedure. The finite reflection and transmission of the attenuator are then accounted for by cryogenic two-port scattering-parameter measurements based on a switch-assisted Short--Open--Load--Reciprocal calibration, so that the result is referred to the DUT reference plane. The system is demonstrated in a dilution refrigerator with powers between -43 and -58 dBm at the DUT input plane. The demonstrated relative standard uncertainty ranges from about 2% at -43.9 dBm to about 40% at -57.6 dBm. The proposed approach combines thermal RF power transfer, cryogenic S-parameter correction, and uncertainty evaluation in a measurement architecture compatible with quantum-device experiments, providing a practical route toward traceable microwave-power calibration at millikelvin stages.