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IEEE Transactions on Applied Superconductivity

Interactive graphics simulation program for the RF-SQUID

A. C. Bruno, James Edward Zimmerman

Published Mar 1, 1993• 1 citation
Publisher

Abstract

An interactive graphics simulation program for the RF-SQUID (superconducting quantum interference device) has been developed. The program allows the user to graphically observe fluxoid quantization, the amplitude-limiting effect of the tank circuit voltage due to the SQUID coupling, the periodic voltage response due to an external DC flux, the tank circuit and SQUID voltage versus time, and the tank circuit voltage versus current. Having a graphical user interface, the program also provides a means for changing circuit and SQUID parameters, namely, RF drive, DC bias, coupling, tuning, Q, and critical current.>

DOI
10.1109/77.233322

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An interactive graphics simulation program for the RF-SQUID (superconducting quantum interference device) has been developed. The program allows the user to graphically observe fluxoid quantization, the amplitude-limiting effect of the tank circuit voltage due to the SQUID coupling, the periodic voltage response due to an external DC flux, the tank circuit and SQUID voltage versus time, and the tank circuit voltage versus current. Having a graphical user interface, the program also provides a means for changing circuit and SQUID parameters, namely, RF drive, DC bias, coupling, tuning, Q, and critical current.>
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
We have measured with high accuracy (100 ppm) and high precision (5--10 ppm) the impedance of a rf-driven resistive superconducting quantum interference device (SQUID) as a function of the amplitude and frequency of the radio-frequency (rf) bias, as a function of the current bias, and as a function of several other circuit parameters. We have developed the coupled differential equations for the resistive SQUID and for the rf tank circuit. The fit of the solutions of these equations to the data for nonhysteretic junctions is excellent. We were unable to develop solutions for the hysteretic case and thus simply present examples of typical data obtained in order to illustrate the differences with the nonhysteretic case. The relationship of this study to noise thermometry using resistive SQUID's is indicated.
A method for determining the superconducting-quantum-interference-device (SQUID) parameter β = LsIc/Φo and the coupling coefficient K between the SQUID loop and tank circuit based on the general theory for the nonhysteretic rf SQUID is derived. Analysis of the periodic dependence of the amplitude of the tank-circuit voltage on applied dc flux leads to explicit expressions for β and K. Important advantages of the method are that, during measurements, the SQUID loop has neither to be opened nor decoupled from the tank circuit, and the temperature of the sample does not have to be changed. Measurements with a Nb-point-contact SQUID at 4.2 K to verify the method in practice are reported. Intrinsic errors were estimated to be less than 10%.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.
It is theoretically explained that a response of a superconducting quantum interference device (SQUID) is periodically dependent on total magnetic flux coupling to the SQUID ring (Φ) and its period is a flux quantum (Φ(o)=h/2e, where h and e, respectively, express Planck's constant and elementary charge). For example, the voltage of an electromagnetically oscillated rf-SQUID or a current biased dc-SQUID is thought to be periodically dependent on Φ with a period of Φ(o). In this paper, we propose an accurate method to check the periodicity of a SQUID response by using a set of sensing coils covered with a superconducting sheath. As a demonstration, we measured periodicity of a commercially available thin-film type rf-SQUID response in magnetic flux ranging up to approximately 4300Φ(o). Its flux dependence was periodic below about 3400Φ(o).
A number of applications of high-temperature superconductor radio frequency superconducting quantum interference devices (rf SQUIDs) require a certain immunity of these sensors against electromagnetic interference (EMI). We have investigated effects of electromagnetic radiation in the high-frequency and ultrahigh-frequency range on various types of rf SQUIDs. It has been found that EMI of sufficient field strength reduces the voltage versus flux transfer function, and thus increases the flux noise of the SQUIDs. SQUIDs with a wire wound tank circuit coil have been found to be more sensitive to EMI than SQUIDs integrated into a superconducting microstrip resonator.