Physica C 479 (2012) 119–122

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Physica C

journal homepage: www.elsevier .com/locate /physc

Array designs for active electrically small superconductive antennas

Victor Kornev a,⇑, Igor Soloviev b, Nikolai Klenov a, Alexey Sharafiev a, Oleg Mukhanov c

a Physics Department, Moscow State University, 119991 Moscow, Russiab Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Moscow, Russiac HYPRES, Inc., 175 Clearbrook Road, Elmsford, NY 10523, USA

a r t i c l e i n f o a b s t r a c t

Article history:Accepted 29 December 2011Available online 17 January 2012

Keywords:Josephson junctionDc SQUIDArray structureDynamic rangeLinear voltage responseBi-SQUID

0921-4534/$ - see front matter � 2012 Elsevier B.V. Adoi:10.1016/j.physc.2011.12.038

⇑ Corresponding author. Tel.: +7 495 939 4351; faxE-mail address: kornev@phys.msu.ru (V. Kornev).

Active electrically small superconductive antennas based on serial arrays of the cells capable of providinghighly linear voltage response to magnetic signal were proposed and developed. Two different basic cellswere devised. The first one is bi-SQUID, and the second one is the cell consisting of two parallel SQIFsconnected in differential way. The antenna prototypes were designed, fabricated and evaluated. Themostly efficient antenna prototype occupied area of 3.3 mm � 3.3 mm was characterized by the transferfactor dV/dB of about 750 mV/mT and the transfer function linearity up to 70 dB.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

The electrically small antenna (ESA), i.e. antenna with a size thatis much less than one wavelength, is very attractive for many appli-cations due to the small antenna size and the wide bandwidth[1–4]. But in some cases (loop type antennas) the small size resultsalso in a low radiation resistance. As far as one tries to make theradiation resistance much more than the antenna conductor lossresistance to increase antenna sensitivity, the use of superconduc-tors instead of the metal conductors substantially improves the an-tenna characteristics [4–7], but usually requires thorough matchingwith load impedance [8,9].

Next critical step is the development and implementation of anactive ESA. This promises a substantial improvement of all charac-teristics of the antenna including solution of the matching problem.However, in contrast to a passive ESA which is a linear network, theperformance of an active ESA can be degraded by intermodulationdistortions. Thus the active antenna design must satisfy require-ments of the high linearity transfer function within sufficiently highdynamic range.

Such an active high-sensitive broadband superconductor antennais required for the superconductor digital rf receiver systems withdirect digitization [10–12]. The present-day superconductor ADCsdemonstrate outstanding linearity and dynamic range [13–15].However, the inferior linearity and dynamic range of antenna andlow noise amplifier compared to those of the ADC can constrainthe overall system performance. Therefore the development of an

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active wideband, high linearity superconductor antenna can over-come these limitations and lead to the improvement of the overallsystem performance.

2. Design approaches

Earlier theoretical and experimental studies [16–20] allow thedevelopment of the appropriate approaches to design multi ele-ment Josephson structures capable of providing a high linearitymagnetic field to voltage transfer function and high dynamic range.The approaches are as follows. High linearity transfer function ofthe multi element structure can be attained by devising ways tolinearize the response of the individual circuit elements. The ele-ments as basic cells must be connected in series to increase dynamicrange. This serial array can be generalized to a serial-parallel arraystructure to improve an output capacity and to decrease a load backaction. These array structures integrated with the properly de-signed superconducting magnetic flux transformers (concentrators)for magnetic component B of the incident electromagnetic wave,can be used as active electrically small antennas. Moreover, thearray structures can be used also for designing of the broadbandGHz-frequency-range amplifiers operating without any externalfeedback.

2.1. Basic cells

Two types of the basic cells capable of providing high linearityvoltage response were devised. The first one is bi-SQUID (Fig. 1a)[16], and the second one is the cell consisting of two parallelSQIFs (Superconducting Quantum Interference Filters) which are

Fig. 1. (a) Bi-SQUID, (b) the cell consisting of two parallel SQIFs which aredifferentially connected and oppositely frustrated by a magnetic flux dU.

Fig. 2. (a) Micro photograph of the fabricated prototype of active ESA based onserial array of 12 bi-SQUIDs with individual flux transformer loops and (b)schematic of the ESA; the gray-filled area is the circuit section formed with asuperconducting screen; the ‘‘magnetic’’ current IM is to set operation point incenter of linear range of the antenna voltage response.

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differentially connected and oppositely frustrated by some mag-netic fluxdU (see Fig. 1b) [20]. In fact, the serial connection ofthe last-named cells is similar to differential connection of twoserial arrays of the parallel SQIFs.

Fig. 3. Schematics of the active ESAs based on two differentially connected serialarrays of parallel SQIFs with one shared transformer loop for both arrays (a) andwith two shared loops each for one of the two arrays (b). The arrays are formed withsuperconducting screen (the gray-filled areas). ‘‘Magnetic’’ current IM is to producemagnetic biasing to the arrays with opposite signs. Inset shows micro photographof the array section.

2.1.1. Bi-SQUID cellTheoretical prediction gives a strict triangular voltage response

of bi-SQUID at the biasing current value equal to the bi-SQUID crit-ical current 2Ic. However, all the experimentally observed voltageresponses of serial arrays of bi-SQUIDs are characterized bysmoothed lower corners and imperfect linearity. As it was under-stood, such a shape of the responses results from fabrication pro-cess spread in Josephson junction critical currents. An adequatesolution of the problem is to use a higher current biasing Ib > 2Ic

of the serial arrays with the bi-SQUID parameters adjusted to thisbiasing. Really, if the bias current exceeds a nominal critical currentvalue 2Ic by the critical current spread |dIc|, it provides switching ofall bi-SQUIDs in resistive state, and the spread in critical currentsfirstly results in different amplitudes of the individual responsesat approximately same linearity.

2.1.2. SQIF-based cellVoltage response of parallel SQIF can approach parabolic law.

This is very significant since the subtraction of two parabolic re-sponses to magnetic signal oppositely frustrated by some constant

magnetic fluxdU results in absolute linear differential response. Toprovide the nearest approach of the response sides to the parabolicshape, we solved the minimization problem for the idealized SQIFwith vanishing inductances between Josephson junctions andfound the problem solution as follows:

dU=dxU=XR

¼ 1:2� 0:48 � ðsinðpxÞÞ3; ð1Þ

where dU/dx is the distribution of the applied magnetic fluxU alongparallel SQIF of length XR. Differential response of two such parallelSQIFs oppositely frustrated by some magnetic fluxdU approacheslinear law for all the dU-values providing subtraction of the para-bolic parts of the individual responses. At finite values of the cou-pling inductances and therefore at finite Josephson-junction

Fig. 5. Result of two-tone measurement of the voltage response of the antennaprototypes shown schematically in Fig. 3.

V. Kornev et al. / Physica C 479 (2012) 119–122 121

interaction radius, the obtained solution (1) can be implementedonly when the number of Josephson junctions is less than the onewithin the interaction radius [20]. This is the reason for the numberof Josephson junctions in parallel SQIF implemented in the fabri-cated and tested antenna circuits was restricted to N = 10.

2.2. Integration with flux transformer

The flux concentrator efficiency depends on both the concentra-tor area and the efficacy of coupling to the antenna cells. Thereforewe should (i) increase the transformer loop area and (ii) decreaseratio of the external loop inductance to the coupling inductancedown to the optimal ratio equal 1. Therefore, to maximize the an-tenna transfer factor, one should use the integrated circuit designsmostly satisfying these contradicting requirements.

One can use individual superconducting flux transformer loopsinductively coupled to the array cells as shown in Fig. 2 for ESAbased on array of bi-SQUIDs. The other way is to use a sharedtransformer loop as shown in Fig. 3 for the ESAs based on two dif-ferentially connected serial arrays of parallel SQIFs.

3. Experimental evaluation

The active electrically small antenna prototypes were designedand fabricated using HYPRES 4.5 kA/cm2 Nb process [21]. Theexperimentally evaluated factor dV/dI characterizing the effectivetransfer of the current I in the implemented control lines induc-tively coupled to the array cells to the cell voltage V was foundas high as about 130 . . .140 lV/mA for both the single bi-SQUIDand the differentially connected two parallel SQIFs.

To evaluate of the antenna prototypes as whole, an external rfmagnetic field was induced by thin film coils around the antennastructures. The antenna prototype based on a serial array of 12bi-SQUIDs (Fig. 2) each provided with individual transformer0.2 � 0.05 mm2 loop, was characterized by transfer factor dV/dBof about 50 mV/mT.

The antenna prototypes are schematically shown in Fig. 3. Thesewere composed of 80 and 84 differential SQIF-cells, correspond-ingly. This means that the total number of SQIFs in ESA is twotimes more. The integrated structures occupy area of about 3.3 �3.3 mm2 each. Fig. 4 shows a set of voltage responses of the firstESA prototype (Fig. 3a) with increase in the ‘‘magnetic’’ currentIM which is to produce some frustrating magnetic flux applied tothe antenna arrays with opposite signs. Inset shows a set of indi-vidual voltage responses of the arrays with bias current IB. Transfer

Fig. 4. The measured set of the antenna voltage responses with ‘‘magnetic’’ currentIM which produces magnetic biasing of the antenna arrays with opposite signs. Insetshows the measured set of the individual voltage responses of the differentiallyconnected arrays with bias current IB. Icoil is the coil current producing externalmagnetic field.

factor of the antenna prototype was measured as high as about750 mV/mT, whereas the second antenna prototype (Fig. 3b) wascharacterized by transfer factor only of about 500 mV/mT.

The voltage response linearity for the shown in Fig. 3 antennaprototypes was evaluated at frequency 300 kHz using a two-toneanalysis technique. The linearity was found as high as about70 dB (see Fig. 5). Depending on magnetic frustration of the anten-na arrays induced by current IM, this linearity was observed within30–80% of the voltage response swing.

4. Conclusion

Different prototypes of active electrically small antennas basedon the implementation of either the serial array of bi-SQUIDs or thedifferentially connected two serial arrays of parallel SQIFs were de-signed, fabricated and experimentally evaluated.

Voltage response linearity up to 70 dB and transfer factor dV/dBof about 750 mV/mT were obtained at low frequency 300 kHz forthe antenna prototype occupying area 3.3 mm � 3.3 mm. At thesame time, the antenna efficiency was found in strong dependenceon the flux transformer used and the integration design with thearray structures.

This work was supported in part by CRDF Grant RUP1-1493-MO-05, and by Grants of Russian Ministry of Science FTP GK14.740.11.0389, PGSS 5423.2010.2 and PGSS 3322.2010.2.

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