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Journal of Applied Physics

Analysis of effective coupling strength in high-frequency SQUIDs

M. Gottschlich, Erik Sodtke, Y. Zhang, Alan M. Portis

Published Nov 15, 1995• 1 citation
Publisher

Abstract

Understanding the coupling mechanism between SQUID (superconducting quantum interference device) loop and resonator in high-frequency SQUIDs is essential for the application of these devices in sensitive magnetometers or controllable microwave devices. We have investigated, therefore, two kinds of planar microstrip tank circuit resonators: (1) S-shaped λ/2-resonators with direct or indirect coupling to the SQUID loop with optional flux-focussing pads and (2) conventional rf-washer-SQUID structures for which we have found resonant modes of the washer providing a coupling to the SQUID loop. A lumped element representation of SQUID loop and resonator is presented in order to describe the effective SQUID-resonator coupling in case of direct or indirect coupling. According to this approach, the square of the effective coupling constant k in both cases is equal to the ratio of the magnetic energy stored in the SQUID loop to that stored in the resonator. For the indirect coupled S-shaped λ/2-resonators, k can be described in terms of a geometry-defined mutual inductance. The predictions of the lumped element description are compared with simulations using a standard full-wave analysis computer program in order to quantify the effect of the different layouts on microwave current distribution and on k. A method for the determination of k by simulation is described, leading to useful design rules for the optimization of high-frequency SQUIDs. The simulation results will also be compared with experimental data.

DOI
10.1063/1.360508

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Understanding the coupling mechanism between SQUID (superconducting quantum interference device) loop and resonator in high-frequency SQUIDs is essential for the application of these devices in sensitive magnetometers or controllable microwave devices. We have investigated, therefore, two kinds of planar microstrip tank circuit resonators: (1) S-shaped λ/2-resonators with direct or indirect coupling to the SQUID loop with optional flux-focussing pads and (2) conventional rf-washer-SQUID structures for which we have found resonant modes of the washer providing a coupling to the SQUID loop. A lumped element representation of SQUID loop and resonator is presented in order to describe the effective SQUID-resonator coupling in case of direct or indirect coupling. According to this approach, the square of the effective coupling constant k in both cases is equal to the ratio of the magnetic energy stored in the SQUID loop to that stored in the resonator. For the indirect coupled S-shaped λ/2-resonators, k can be described in terms of a geometry-defined mutual inductance. The predictions of the lumped element description are compared with simulations using a standard full-wave analysis computer program in order to quantify the effect of the different layouts on microwave current distribution and on k. A method for the determination of k by simulation is described, leading to useful design rules for the optimization of high-frequency SQUIDs. The simulation results will also be compared with experimental data.
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.
DC Superconducting Quantum Interference Devices (SQUIDs) are widely used to amplify low-level, radio frequency (rf) electrical signals. SQUID amplifiers offer low noise, high gain, and low power dissipation. One method of implementing a SQUID rf amplifier for frequencies from a few hundred megahertz to several gigahertz is to operate the integrated input coil on top of the SQUID washer as a microstrip resonator. This is achieved by applying the input signal between one end of the coil and the SQUID washer, which acts as a groundplane; the other end of the coil is left open. Substantial levels of gain can be achieved from the microstrip SQUID amplifier for a signal frequency at the fundamental resonant frequency of the microstrip, at which the length of the microstrip is equal to one-half wavelength, λ/2. Since the length of the microstrip has to be made shorter for higher frequencies, however, the mutual inductance between a SQUID with a given geometry and the microstrip—and thus the gain—decreases with increasing frequency. We show that a significantly enhanced gain can be achieved by operating the microstrip resonator in higher-order modes, for example, with a microstrip length of 3λ/2 or 5λ/2, provided the winding sense of the microstrip for each consecutive λ/2 section is reversed. For a 4λ/2 resonator, we demonstrate a gain of 24 dB at 2.6 GHz, an increase in gain of about 10 dB compared to a λ/2 resonator on a SQUID of the same geometry and characteristics.
Characteristics of a lumped element L-C tank circuit resonator of high-Tc rf-SQUIDs, which plays an important role in the device operation, have been experimentally investigated, according to the corresponding simulations obtained by COMSOL Multiphysics. We experimentally investigated the characteristics of the resonators by measuring their scattering parameters, as well as evaluating the rf-SQUID signal. Our SQUIDs are made of sputtered YBCO thin films with 3-mm-diameter washer areas. Different configurations of the resonator are investigated, and it is observed that, by increasing the thickness of the dielectric in a specific range, the reflection coefficient (S11) increases. For the experimental verifications, we constructed resonators with different dielectric thicknesses and different configurations. The resonators are made of a dielectric board with a hole in its middle to hold the inductors for close coupling to the SQUID mounted on the backside. An increase in the thickness of the dielectric board confines the RF field distribution close to the SQUID, while also making further distance between the contact pads and the SQUID reducing their parasitic effects on the device signal. This is observed to improve the stability of the operating point of the SQUIDs, while also reducing the noise for measured frequency range of 0.1 to 100 Hz.
The operation of YBa2Cu3O7 rf superconducting quantum interference devices (SQUIDs) using a dielectric SrTiO3 resonator as tank circuit was tested. At 77 K, we attained for such resonators unloaded quality factors Q0 up to 7000 at resonant frequencies near 1 GHz, when measuring without electromagnetic shielding. For a washer SQUID with an area of 4×4 mm2 and an inductance of ≂100 pH, which was properly coupled to the resonator, we measured an approximately 60 μV peak-to-peak SQUID signal and a white flux noise spectral density of SΦ1/2=1×10−5Φ0/√Hz, corresponding to a field sensitivity of BN=105 fT/√Hz. With an additional single-layer flux transformer with a diameter of the pickup loop of 22 mm in flip-chip arrangement, the field sensitivity was improved to 30 fT/√Hz.
We have succeeded in the first demonstration of a simple and accurate resonator-superconducting quantum interference device (SQUID) coupling for microwave SQUID multiplexers. A simple theory shows our direct coupling with adjustable fractional inductance in the SQUID loop can decrease the deviation of resonance frequencies from designed values in contrast to a conventional inductive coupling. Our direct coupling provides the individual coupling that can be optimized with keeping identical structure, shape, and dimension of the SQUID among all pixels on the same chip. It covers experimentally three or potentially more factors of a frequency band that is larger than that of cryogenic high electron mobility transistor amplifiers. The deviation of experimental fractional inductance from the designed one is less than −3/+10%.
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.