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Applied Physics Letters

Microstrip superconducting quantum interference device radio-frequency amplifier: Scattering parameters and input coupling

D. Kinion, John L. Clarke

Published Apr 28, 2008• 27 citations
Publisher

Abstract

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.

DOI
10.1063/1.2902173

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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 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.
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.
The resonant frequency of an amplifier based on a low-temperature dc superconducting quantum interference device (SQUID) is tuned by varying the capacitance across the end of the input microstrip by means of a varactor diode. The resonant frequency can be reduced substantially, for example, from 190 to 110 MHz, while maintaining an on-resonance gain of 27–28 dB. Two microstrip SQUID amplifiers with the same resonant frequency are cascaded to achieve a gain of 33.5±1 dB at 386 MHz; with the SQUIDs tuned to different frequencies, the gain is 22 dB or higher from about 260 to 420 MHz.
A dc superconducting quantum interference device (SQUID) was used to amplify radio-frequency signals that were coupled to one end of the microstrip formed by the input coil and the SQUID washer. For one device, the resonant frequency of the microstrip was increased from about 200 to 620 MHz by progressively shortening the length of the coil. At an operating temperature of 4.2 K, the gain was typically 18 dB, and the system noise temperature ranged from 0.5±0.3 K at 80 MHz to 3.0±0.7 K at 500 MHz.
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.