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ASC'98, Palm Desert. Report EQB-04

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Flux Flow Oscillators for Sub-mm Wave Integrated Receivers
Valery P. Koshelets, Sergey V. Shitov, Alexey V. Shchukin, Lyudmila V. Filippenko, Pavel N. Dmitriev, Vladimir L. Vaks*
Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Mokhovaya 11, 103907 Moscow, Russia *Institute for Physics of Microstructure, Russian Academy of Sciences, GSP-105, 603600 Nizhny Novgorod, Russia

Jesper Mygind
Department of Physics, Technical University of Denmark, B309, DK-2800 Lyngby, Denmark

Andrey M. Baryshev, Willem Luinge, Hans Golstein
SRON-Groningen, P.O.Box 800, 9747 AV Groningen, the Netherlands

Abstract - The results of a detailed study of the microwave linewidth of Nb-AlOx-Nb flux flow oscillators (FFO) are presented. The dependence of the FFO linewidth on the junctions parameters has been measured by using an improved technique based on harmonic mixing in the frequency range 250 - 600 GHz. Experimental data are compared with theoretical estimates to evaluate the influence of the possible mechanisms responsible for the broadening of the FFO linewidth. The origins of the increased linewidth at the transition from the resonant to the "pure" flux-flow regime are discussed. The results of the linewidth measurements for the FFO locked via a wideband feedback loop are presented. The possibility of real phase locking of the Josephson oscillator has been demonstrated experimentally. A FFO linewidth as low as 3.3 kHz (determined by resolution bandwidth of spectrum analyzer) has been measured at 310 GHz; it is far below the fundamental level given by shot and thermal noise of the free-running tunnel junction.

I. I

NTRODUCTION

The FFO [1] has proven to be a reliable wideband and easy tunable local oscillator suitable for integration with a SISmixer in a single-chip sub-mm wave receiver [2]. A DSB noise temperature below 100 K has been achieved for an integrated receiver with the FFO operating near 500 GHz [3]. For spectral radio-astronomy applications the frequency resolution of the receiver, which is determined by both the instant linewidth of the local oscillator and its long-time stability, should be better than 1 PPM of the center frequency. Recently a new simple and reliable technique for linewidth measurements has been developed [4] and a FFO linewidth of only few hundred kHz was measured. It was found [5] that the FFO linewidth appears to be about one magnitude larger than predicted by the theory for a lumped Josephson tunnel junction even at the resonant Fiske steps. Furthermore, an abrupt increase of the FFO linewidth at the voltages higher than the boundary voltage has been found experimentally [5]; this broadening accompanies the change in the damping in a
Manuscript received September 14, 1998 The work was supported in parts by the Russian Program for Basic Research, the Russian SSP "Superconductivity", the Danish Research Academy, the Danish Natural Science Foundation, the Netherlandse Organisatie voor Wetenshappelijk Onderzoek (NWO) grant and ESA TRP contract 11/653/95/NL/PB/SC. E-mail: valery@hitech.cplire.ru

tunnel junction. This boundary voltage Vb is about 1/3 of the gap voltage, 950 µV for Nb-AlOx-Nb tunnel junctions. A simplified model based on Josephson radiation self-coupling [6] was introduced [5] to explain the experimentally measured FFO I-V curves. The effect of Josephson selfcoupling (JSC) basically is absorption of ac Josephson radiation by the quasiparticles. This leads to the well-known phenomenon of photon assisted tunneling. The JSC results in current bumps at VJSC = Vg/(2n + 1), which gives VJSC = Vg/3 for n = 1. The effect of self-pumping explains not only the FFO current bumps observed in the I-V curve, but also the abrupt transition of the Fiske steps (FS) at V Vg/3 caused by the increase of the damping [5]. The geometric resonances (or FSs) exist for low normalized damping l < 1, where l = L/J is the junction length normalized to the Josephson penetration length J. If the damping is sufficiently low (say, 0.01), this condition can be satisfied even for large normalized junction lengths, l = L/J 60. The FSs smear out (transition into the so-called Eck peak) when the damping increases to a value of about l 2. This happens at Vg/3 V > 950 µV where the FFO enters the "real" flux-flow regime. In this report a numerical model of the FFO taking into account all known noise sources (both internal and external) has been developed and used for explanations of the FFO linewidth broadening. The decrease of the intrinsic FFO linewidth (determined by wide band thermal fluctuations) by using an electronic phase locked loop (PLL) has been demonstrated experimentally. II. FFO
LINEWIDTH

The oscillation linewidth f of a Josephson junction is mainly determined by low frequency current fluctuations. For white noise it can be written (see e.g. [7] ) as:
f = (2/02) Rd2 Si(0),

(1)

where 0 is the magnetic flux quantum, Si(0) is the density of the low frequency current fluctuations, and Rd is the dc differential resistance which transforms the current fluctuations to voltage (and phase) noise. For a lumped tunnel junction [8] Si(0) = (e/2) Idc(Vdc) coth(v), v = (eVdc)/(2 kB Teff), (2)


where e is the electron charge, kB is the Boltzmann's constant. Idc and Vdc are the averaged normal current and voltage, and Teff is the effective temperature of the quasiparticles in the junction electrodes. This formula describes a nonlinear superposition of thermal and shot noise. Expression (2) is modified for a distributed Josephson junction placed in a real experimental environment. First the supercurrent should be taken into account along with the normal current IN. The power produced by the oscillating supercurrent is adsorbed both in the external circuitry and in the tunnel junction itself. The random absorption of the emitted photons leads to variations of the averaged supercurrent IS. Consequently an additional term appears [7] in the spectral density (2): Si(0)
FFO

= (e/2) {IN coth(v) +2 IS coth(2v)}.

(3)

The supercurrent itself can not be the source of fluctuations because of its reactive character; the additional term proportional to IS appears due to the interaction of the supercurrent with the embedding circuit. It should be noted that the overall linewidth does not depend strongly on the used ratio between the super and normal current, especially at an increase of Teff above 4.2 K. Expression (1) should be modified to include the thermal noise in the biasing resistors, and external low frequency interference. The linewidth f has been calculated numerically taking into account all noise components including noise contributions from the bias and control line circuitry. The low frequency components of the current density Si(f) should be considered in this calculation. The cut-off frequency is determined by a resulting linewidth [7], this means that the linewidth has to be calculated self-consistently. The results of the calculations are shown in Fig. 1 for different experimental parameters. A superposition of shot and thermal noise of a tunnel junction (f Rd2) mainly determines the value of f at high Rd. The level of the external interference becomes dominant (f Rd) at small Rd (below 0.01 in our
100 FFO Linewidth f (MHz)
(1) TJM, Teff=4.2 K (2) TJM, Teff=25 K (3) Ext.; Rd =0.002
CL CL

10

(4) Ext.; Rd =0.11 (5) Total; Rd =0.002 (6) Total; Rd =0.11
CL CL

6 5 4 3

1

Data at V < Vb Data at V > Vb Ifl=0.08 µA

1 2 0.001 0,01 Differential Resistance Rd () 0,1

Fig. 1 Numerically calculated dependencies of FFO linewidth on differ resistance Rd: (1), (2) ­ Tunnel Junction Model for Teff = 4.2 and correspondingly; (3), (5) ­ external interference and (4), (6) ­ resulting linewidth at Ifl = 0.08 µA and RdCL = 0.002 and 0.11 . Experimental data < Vb and V > Vb are shown by diamonds and triangular.

ential 25 K FFO for V

experiments). Furthermore the linewidth depends also on fluctuations in the external magnetic field described by the differential regulation resistance of the control line RdCL = dVFFO/dICL. The integrated control line in the base or counter electrode is used for the adjustment of the magnetic field in the FFO. The value of RdCL determines f at RdCL > Rd, and a plateau appears in the f(Rd) dependence. The RdCL value is very low when biased on Fiske steps (about 0.005 ) and increases considerably between steps. At V > Vb in the "pure" flux-flow regime RdCL is about 0.1 and does not depend noticeably on voltage. The noise contribution caused by RdCL becomes dominant at V > Vb even at large Rd, see Fig. 1. The calculated FFO linewidth versus Rd is shown in Fig. 1 for two values of RdCL above and below Vb. The value of the external low frequency interference corresponding to a current fluctuation Ifl = 0.08 µA is used in the calculations. The experimental data from Ref. [5] measured in different regimes are also shown in Fig. 1 for comparison. One can see that the experimental data taken below Vb agree well with calculations at Teff = 25 K. This large effective temperature may be due to absorption of the FFO Josephson radiation by quasiparticles in the Niobium electrodes. The quasiparticles could be heated above the bath temperature ("hot electrons") due to the finite electron-phonon interaction time. The data for V > Vb deviate noticeably from the calculated. A fit is only possible with a 5 times increase of the calculated linewidth. This large linewidth broadening corresponds to Teff = 60 K. According to our numerical calculations the level of self-pumping eVrf/hf is decreasing with the FFO voltage, so we can not attribute this additional increase of the linewidth to further rise of the electron temperature. The linewidth increase in the non-resonant regime may be explained by a model recently proposed by Golubov et al. [9]. This model accounts for the fluctuations in the inter-fluxon spacing in the moving fluxon chain under the influence of noncorrelated spatially distributed thermal noise in the junction. According to the theory [9] the broadening is significant at large fluxon velocities and small normalized magnetic fields where the fluxon chain is "soft". The experimental broadening of the FFO linewidth, however, is much smaller than predicted by [9]. Probably on the FS in the resonant regime the standing electromagnetic waves "regulate" the fluxon motion and reduce their degree of freedom. Even at V > Vb it is possible to suppress this broadening by additional resonant elements externally connected to the FFO [10]. According to [7] the radiation linewidth could be affected by changing the spectral density or differential resistance at considerably low frequencies f < f. This can be done by: i) appropriate shunting at low frequencies (provided that the impedance of the shunt Zsh(f) >> ZFFO at high Josephson oscillation frequency); ii) modification of the high frequency imbedding impedance in such a way that Rd is decreased [10], [11]; iii) suppression of the current fluctuation by an external phase locking (PLL) system with bandwidth > f.


averaged with a sufficiently small video bandwidth (~ 10 kHz). Due to the high tuning coefficient even a An integrated circuit comprising FFO, SIS mixer and relatively small low frequency drift of the control line and/or matching elements is used to measure the FFO linewidth. dc bias currents results in a significant shift of the FFO Overlap Nb-AlOx-Nb junctions (length L 500 µm, width W frequency leading to a smearing of the averaged linewidth. 2 about 3 µm, current density 5-8 kA/cm ) are used for the The PLL system with a relatively narrow bandwidth setting FFO. The details of the circuit design are published elsewhere (< 10 kHz) was used for frequency locking of the FFO to the [4], [5]. A block diagram of the set-up for linewidth 10 GHz synthesizer in order to measure the autonomous FFO measurements is shown in Fig. 2. In order to measure the linewidth fAUT. In this case the shape of the measured FFO linewidth in a wide frequency range up to 600 GHz a linewidth is unchanged, but the signal is stable in frequency. new experimental technique [4] was used. The mm-wave The measured FFO linewidth spectra in different operational signal coming from the FFO is mixed in the harmonic SIS regimes are shown in the Fig. 3. mixer with the n-th harmonic of the external reference synthesizer. In order to prevent the external oscillator signal a) (as well as its harmonics) from reaching the FFO a high-pass -28 RBW = 1 MHz VBW = 30 kHz 10 MHz/div 3 dB/div microstrip filter with cut-off frequency of about 200 GHz is f = 415 GHz -34 employed. The intermediate frequency (IF) signal, fIF = ±(fFFO ­ n fSYN) is amplified in a cooled amplifier (Tn of about 20 K, f = 7.3 MHz -40 gain 27 dB). After additional room temperature amplification -46 the signal enters the PLL system. In this unit the signal frequency is divided by four and in a Frequency-Phase -52 Discriminator compared with a 100 MHz reference signal. 360 380 400 420 440 Via the Loop Bandwidth Regulator (maximum bandwidth 10 MHz) the output signal proportional to the phase -38 b) RBW = 0.3 MHz VBW = 10 kHz difference is applied back to the FFO through the coaxial 5 MHz/div 2 dB/div -42 f = 270 GHz cable and the cold 50 resistor mounted on the bias plate. The same coaxial cable entering the cryostat is used both for the -46 10 GHz synthesizer signal and the PLL control output. The -50 f = 6.7 MHz couplers with microstrip filter are used to combine and split these signals. The PLL output signal can be connected both to the FFO -54 bias and the magnetic field control line. In order to perform accurate linewidth measurement, the IF spectra have to be -58
XPERIMENTAL DETAILS AND RESULTS
FFO Power (dBm)
FFO

III. E

AUT FFO

FFO Power (dBm)

FFO

AUT FFO

380

390

400

410

420

-20

c)

P L L w i t h L oop B a ndw i d t h R e g ula t i o n ( m ax B = 1 0 M H z ) PL L feed b a ck s i gn al 20 d B D i recti o n a l Co u p l e r ( 7 -12 G H z )

FE T

1 0 t o 10 0 M H z M u lt ip lie r 10 MH z Rf S p ectru m A n a l y z er 10 G H z Sy nthe s i z e r 10 G H z HE M T A m p lif ie r

FFO Power (dBm)

-30 -40
fFF
AUT O

RBW = 0.1 MHz VBW = 30 kHz 2 MHz/div 5 dB/div fFFO = 310 GHz

A d ju s t a ble A t t e nua to r Po w e r S p lit te r FE T

= 2.4 MHz

-50 -60

390
-30

395

400

405
RBW = 3 kHz VBW = 10 kHz 20 kHz/ div 2 dB/div fFFO = 310 GHz

410

d)
f
FF O

FFO Power (dBm)

-34 -38 -42 -46 -50

1 0 GHz

Ha r m o n i c SI S - M i x e r

= 3.3 kHz

C o uple r Hi - p a s s F ilte r FFO PL L i n LH e c r y o s t a t

3 99,9 2

3 99,9 6

400 ,00

40 0,04

4 00,0 8

Down-conve rted FFO Frequency (M Hz)

Fig. 2 Block-diagram of the set-up for linewidth measurements.

Fig. 3 IF power spectra of the FFO operating at different regimes.


It was experimentally found that the PLL system can considerably decrease the FFO linewidth if the fAUT at the 3 dB level is initially lower than the PLL regulation bandwidth BPLL. In the opposite case where fAUT > BPLL only frequency locking without a noticeable linewidth change was possible. The FFO spectra are shown in Fig. 3a-c for the minimal and the optimal BPLL at different initial fAUT (FFO frequency 270 - 420 GHz). At a fAUT of about BPLL (Fig. 3a, fAUT 7.5 MHz) there is a 10 dB increase of the FFO power at the central frequency while the 3 dB FFO linewidth is reduced by 3 times. A sharp peak appears at the central frequency (Fig. 3b) with further decreasing of the fAUT (different values of Rd and RdCL were used). The real phase locking takes place at fAUT 2.5 MHz (Fig. 3b, c), in this case 99% of FFO power initially present in a band of 25 MHz. A FFO linewidth as low as 3.3 kHz is presented in Fig. 3d. This value actually is determined by the resolution bandwidth of the spectrum analyzer. It means that the FFO linewidth can be reduced below the value determined by fundamental shot and thermal fluctuations of a tunnel junction. It should be noted that a vertical step appears in the FFO IVC (Rd = 0) with the FFO locked. The position of this step is insensitive to small changes in the control line current, so that RdCL = 0 as well. A regulation range in the FFO bias voltage as large as 1.5 µV has been experimentally measured. This corresponds to a PLL regulation band of about 750 MHz.

The developed technique for FFO phase locking could be used in the Integrated Receiver, a possible block diagram of such receiver is shown in Fig. 4. In this concept two separate SIS mixers are connected to the same FFO and placed on one chip-receiver. For operation at all FFO voltages including V > Vb an additional shunt should be used to decrease the initial FFO linewidth. Also an ultra-wide band PLL system with sufficiently small phase noise is needed. IV. CONCLUSI
ON

A numerical model taking into account all known noise components of the FFO integrated in the real experimental circuit has been developed. This model was used for quantitative analysis of the FFO linewidth measurements. All the results listed above demonstrate our ability to decrease the intrinsic linewidth of a Josephson oscillator by an external electronic PLL system, provided that the PLL bandwidth is larger than the initial oscillator linewidth. Authors thank Th. de Graauw and N. D. Whyborn for fruitful discussions. REFEREN
[1 ]

CES

[2 ]

HEMT 1

IF Output (1.5 GHz); SIS DC Bias, SIS CL

[3 ] [4 ]

RF Filters Antenna & SIS mixer 1 Directional Coupler & DC Break IF2 Output & 10 GHz Input; SIS DC Bias, SIS CL Si or Quartz chip of about 5 x 5 mm2

[5 ] [6 ] [7 ] [8 ] [9 ]

FFO & Impedance Transformer

High-pass Filters & DC Break Harmonic SIS Mixer 2 FFO Bias & FFO CL

T. Nagatsuma, K. Enpuku, F. Irie, and K. Yoshida, "Flux-Flow type Josephson oscillator for millimeter and submillimeter wave region", J. Appl. Phys. vol. 54, pp. 3302-3309, 1983; see also Pt. II, J. Appl. Phys,. vol. 56, pp. 3284, 1984; Pt. III, J. Appl. Phys., vol. 58, pp. 441, 1985; Pt. IV, J. Appl. Phys., vol. 63, pp. 1130, 1988. V.P. Koshelets, S.V. Shitov, L.V. Filippenko, A.M. Baryshev, W. Luinge, H. Golstein, H. van de Stadt, J.-R. Gao, T. de Graauw, "An Integrated 500 GHz Receiver with Superconducting Local Oscillator", IEEE Trans. on Appl. Supercond., vol. 7, pp. 3589-3592, 1997. S.V. Shitov, A.B. Ermakov, L.V. Filippenko, V.P. Koshelets, A.B. Baryshev, W. Luinge, Jian-Rong Gao, "Superconducting chip receiver for imaging applications", this conference, report EMA-09. V.P. Koshelets, S.V. Shitov, A.V. Shchukin, L.V. Filippenko, and J. Mygind, "Linewidth of submillimeter wave flux-flow oscillators," Appl. Phys. Lett., vol. 69, pp. 699-701, July 1996. V.P. Koshelets, S.V. Shitov, A.V. Shchukin, L.V. Filippenko, J. Mygind and A.V. Ustinov, "Self-pumping effects and radiation linewidth of FFO," Phys. Rev. B, vol. 56, pp. 5572- 5577, Sept. 1997. L.-E. Hasselberg, M.T. Levinsen, M.R. Samuelsen, "Theories of subharmonic gap structures in superconducting junctions," Phys. Rev. B, vol. 9, pp. 3757-3765, 1974. K.K. Likharev, Dynamics of Josephson junctions and circuits, Gordon and Brench Science Publichers, 1986. M.J. Stephen, "Noise in the ac Josephson effect," Phys. Rev., vol. 182, pp.

10 GHz 10 MHz reference

Phase Detector (bandwidth B > linewidth f of free-running FFO)

Directional Coupler

HEMT 2

10 GHz Synthesizer

531-538, 1969. A.A. Golubov, B.A. Malomed, and A.V. Ustinov, "Radiation linewidth of a long Josephson junction in the flux-flow regime," Phys. Rev. B, vol. 54, pp. 3047-3050, 1996. [10] V.P. Koshelets, S.V. Shitov, S.V. Shchukin, I.V. Abramova, J. Mygind, A.V. Ustinov. "Self-Pumping Effects and Radiation Linewidth of FFO", Proceedings of the ISEC'97, Berlin, Germany, June 26-29, vol 3, pp 210212, 1997. [11] A.B. Baryshev, A.V. Yulin, V.V. Kurin, V.P. Koshelets, S.V. Shitov, A.V. Shchukin, P.N. Dmitriev, L.V. Filippenko, "Cherenkov Flux-Flow Oscillators: Output Power and Linewidth", this conference, report ELD-05.

Fig. 4 Proposed block-diagram of the phase locked Integrated Receiver.