Performance of Inhomogeneous Distributed Junction Arrays

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1 Performance of Inhomogeneous Distributed Junction Arrays M Takeda and T Noguchi The Graduate University for Advanced Studies, Nobeyama, Minamisaku, Nagano , Japan Nobeyama Radio Observatory, Nobeyama, Minamisaku, Nagano , Japan ABSTRACT: Mixing properties of a new type of distributed SIS junction arrays, which consists of different dimensions of junctions and lengths between every two junctions, has been theoretically investigated using quantum theory of mixing. A set of dimensions of junctions and lengths between every two junctions have been determined so as to minimize a reflection coefficient of an S-parameter, S11, at the input port in the array using microwave CAD. We report on the performance of an SIS mixer with distributed junction array designed to cover the frequency range from 90 GHz to 180 GHz. 1. INTRODUCTION Tuneless or fixed tuned SIS mixers are highly desirable for complex systems such as multibeam receivers and interferometer arrays at millimeter and submillimeter wavelengths. The bandwidth of such tuned SIS mixers is mainly governed by the ω R C n product, which is approximately equal to the Q-factor of the j resonance circuit, and is strongly dependent on the critical current density of a junction, J c. In order to achieve a broader bandwidth higher value of J c is generally required. Unfortunately, high J c may bring various disadvantages such as large sub-gap leakage current and reduction of yields of junctions in the fabrication (Kleinsasser et al. 1993). Recently, Shi et al. (1997) proposed an interesting SIS mixer composed of distributed junction arrays, which has a number of identical junctions equally separated by superconducting micro-striplines that act as tuning inductances. It has been shown that the critical current density required to achieve a reasonable bandwidth can be lowered in the mixer with the distributed junction arrays in contrast to the conventional single-junction SIS mixers. This type of distributed junction arrays, however, shows large periodic increase of noise at certain frequencies. These increase of noise will become an obstacle for the broad band operation. In this paper, we propose a new type of distributed junction arrays, or inhomogeneous distributed junction arrays, which has different dimensions of junctions and lengths between every two junctions, to reduce amplitude of the increase of noise discovered in the conventional distributed junction arrays, or homogeneous distributed junction arrays. 2. THEORY AND OPTIMIZATION OF DISTRIBUTED JUNCTION ARRAYS The inhomogeneous distributed junction array proposed here consists of a number of junctions with

2 Thin-film TRL 1st 2nd 3rd k-th N-th SIS (a) L (k) L (1) L (2) L (k) L (N-1) (1) C j (1) (2) C j (2) (k) C j (k) (N) C j (N) S 11 SIS-1 SIS-2 SIS-k SIS-N (b) Fig.1 (a) Schematic representation and (b) simplified equivalent circuit of an inhomogeneous arrays different dimensions distributed on a transmission line as illustrated in Fig.1. In the inhomogeneous distributed junction array the dimensions of junctions and the lengths between every two junctions must be determined for a given current density prior to the calculation of mixing properties. A simplified equivalent circuit of the inhomogeneous array, which consists of N-junctions represented by a combination of linear resistance and geometrical capacitance C j connected in parallel, is shown in Fig.2. The specific capacitance of an SIS junction is assumed to be 90.0fF/ µ m The reflection coefficient of S-parameter, S 11 2, seen from the input port of the inhomogeneous distributed junction array is not only minimized over the given frequency band but also as independent on frequency as possible, using a commercial microwave software (HP-MDS). Once a set of optimized dimensions of junctions and spacing between every two junctions, we established an equivalent large and small signal model for the inhomogeneous arrays following the method derived by Shi et al. (1997) for homogeneous arrays and then calculated mixing properties of the inhomogeneous arrays using Tucker s quantum theory of mixing (Tucker et al. 1985). In the analysis, we have adopted the quasi-five port approximation in which five sidebands are allowed, but the LO voltage is assumed to be sinusoidal (Kerr et al. 1993). Only the difference in the analysis for the inhomogeneous arrays from the homogeneous ones is that the conversion admittance and correlation matrices must be derived to every junction, since they depend on I-V curve of individual SIS junction. 3. SIMULATION RESULTS Using the quantum theory of mixing together with the equivalent circuit model established in the previous section we have calculated the mixing properties of the inhomogeneous distributed junction array with an optimized set of dimensions of junctions and lengths between every two junctions in the frequency range from 90 GHz to 180 GHz, which corresponds to a full band of the WR-8 waveguide. IF frequency was assumed to be 1.5 GHz. The number of junctions in the array was set to five so that the array has a moderate input impedance which makes it easy to match the source well. The RF termination normalized to the equivalent normal-state resistance of a junction array, R RF /, has been assumed to be unity over the frequency band. The conversion gain is strongly dependent on the magnitude of the IF termination, which is

3 Table 1. Simulation parameters A (1) A (2) A (3) A (4) A (5) L (1) L (2) L (3) L (4) Units of junction area and length of stripline are 2 µ m and µ m, respectively. approximately equal to the dynamic resistance of the pumped junction. We have selected IF termination of 10 Ω, since the large IF termination, for example 50 Ω which is typical IF termination, seriously degrades the conversion gain in the band. In the calculations, all the junctions were assumed to have the same critical current density of 2.0 ka/ cm 2 for both the homogeneous and inhomogeneous arrays. The dimensions of junctions and the lengths between every two junctions in the inhomogeneous array used in the calculation are listed in Table 1. In the 2 homogeneous array, the area of 2.0 µ m of a junction was adopted, which is a typical area of SIS junctions used in the conventional SIS mixers in the same frequency band. The lengths between every two junctions was determined so as to minimize the receiver noise temperature in the frequency band in the homogeneous array and we adopted the length of 90.0 µ m in the calculation for the homogeneous array. The width of stripline was assumed to be 8.6 Ω. 8.0 µ m for both arrays, which corresponds to the characteristic impedance of Figure 2 shows a reflection coefficient of S-parameter, S 11, and input coupling efficiency seen from the input port for the homogeneous and inhomogeneous arrays. In the homogeneous array, it is found that S 11 degrades at certain frequencies. On the contrary, such degradations of S 11 are considerably improved in the well-optimized inhomogeneous array. The improvement of S 11 at input port results in the improvement of input coupling efficiency. From this result excellent mixing properties can be expected in the inhomogeneous array.

4 Figure 3 shows the calculated mixer noise temperature and conversion gain for the homogeneous and inhomogeneous arrays. Note here that the dc bias and LO voltage across the last junction were optimized with respect to the receiver noise temperature at each frequency. As shown in Fig.3, broad-band operation has been accomplished in both arrays in spite of fairly low critical current density of 2.0 ka/cm 2. In the homogeneous array with five junctions, however, very large increase of noise are observed at several frequencies and the conversion gain is considerably decreased near those frequencies. If the number of junction is increased, for example, the number is set to ten as shown in Fig.3, amplitude of the increase of noise can be significantly suppressed in the homogeneous array. In the inhomogeneous array with five junctions, it is found that amplitude of the increase of noise at those frequencies are considerably suppressed in contrast to the homogeneous ones. The fluctuation of the conversion gain over the frequency band is also very much reduced in the inhomogeneous ones. Degradation of the conversion gain at lower frequency in the inhomogeneous array is caused by degradation of output coupling. If it is possible to make smaller IF termination, or if IF termination normalized to normal-state resistance, R 1, the conversion gain at IF lower frequency will be significantly improved. From the viewpoint of noise as a function of frequency, it is obvious that the inhomogeneous array with five junctions is nearly competitive with the homogeneous array with ten junctions. The reduction of number of junctions in the array will bring the following advantages. At first, it is easy to achieve good impedance match to the source, since effective normal-state resistance increases. Secondly, the dimensions of junctions can be larger in the array with a small number of junctions, if the impedance match at the input port can be allowed to be sacrificed to a little extent. This brings a great benefit for the fabrication of junctions and makes the fabrication of the inhomogeneous arrays easier than those of the homogeneous arrays. In spite of the restricted optimization, however, it is found that amplitude of the increase of noise has been extremely suppressed in the inhomogeneous array. It is noted here that the SSB (Single Side Band) mixer noise temperature and conversion gain of the inhomogeneous array are less than 30 K and larger than 5.0 db over the frequency range from 90 GHz to 180 GHz, respectively, which is competitive with those in conventional single-junction SIS mixers.

5 4. CONCLUSION We have investigated mixing properties of distributed junction arrays with different dimensions of junctions and lengths between every two junctions. If the dimensions of junctions and lengths between every two junctions in an array are well optimized in term of the reflection coefficient of S-parameter, S 11, seen from the input port of an array, it is demonstrated that the inhomogeneous distributed junction arrays can achieve low-noise SIS mixers in the frequency range from 90 GHz to 180 GHz. It is also found that critical current density for the inhomogeneous arrays can be very low compared with conventional single-junction SIS mixers as far as same frequency band is concerned. REFERENCES A W Kleinsasser, F M Rammo and M Bhushan 1993 Appl. Phys. Lett. 62, 1017 S C Shi, T Noghuchi and J Inatani 1997 Proc. 8th Int. Symp. on Space Terahertz Tech. pp 81 J R Tucker and M J Feldman 1985 Rev. Mod. Phys. 57, 1055 A R Kerr, S K Pan and S Withington 1993 IEEE Trans. Microwave Theory Tech. 41, 590

6 Predicted Performance of Superconductor-Insulator-Superconductor Mixers With Inhomogeneous Distributed Junction Arrays Masanori Takeda 1, Takashi Noguchi 2 and Sheng-Cai Shi 3 1 Department of Astronomical Science, The Graduate University for Advanced Studies, Nobeyama, Minamimaki, Minamisaku, Nagano , Japan 2 Nobeyama Radio Observatory, Nobeyama, Minamimaki, Minamisaku, Nagano , Japan 3 Purple Mountain Observatory, 2 West Beijing Road, Nanjing, JiangSu , China The mixing Properties of a new type of distributed superconductor-insulator-superconductor (SIS) junction array, which consists of different dimensions of junctions and spacings between every two junctions, have been theoretically investigated using quantum theory of mixing. A set of dimensions of junctions and spacings between every two junctions of the distributed junction array have been determined so as to minimize the reflection coefficient of an S-parameter, S 11, at the input port in the array using microwave computer-aided design, assuming that each SIS junction is represented by a parallel combination of linear normal-state resistance and geometrical capacitance. When the array is composed of well optimized set of dimensions of junctions and spacings between every two junctions, it is demonstrated that excellent mixing properties are attained over a broad-band in spite of the low critical current density of an SIS junction. It is also found that the degradation of mixing properties, which is always observed at certain frequencies in a conventional array with the equal dimensions of junctions and spacings, can be considerably suppressed in the array with a well optimized set of dimensions and spacings of junctions. KEYWORDS: millimeter wave, submillimeter wave, SIS mixer, distributed junction array 1. Introduction Supercondutor-insulator-superconductor (SIS) tunnel junctions have been well employed in astronomical observations as they are the most sensitive heterodyne mixers at millimeter and submillimeter wavelengths. In such receivers, excellent results have been obtained by adding an appropriate tuning circuit to the junctions in order to resonate out the geometrical capacitance of SIS junctions which usually prevents the signal from coupling with the junction efficiently. The bandwidth of such tuned SIS mixers is mainly governed by the ω C j product, which is approximately equal to Q-factor of the resonance circuit, and is strongly dependent on the critical current density of a junction, J c, as J c IcRn = ωcs ω R C n j, (1) where ω, and C j are the angular frequency of signal, normal-state resistance and geometrical capacitance of a junction, respectively. I c and C s are the critical current and specific capacitance of an SIS junction, respectively. This relation implies that the broader bandwidth of a conventional SIS mixer requires a higher critical current density of a junction. Unfortunately, high critical current density may cause various disadvantages such as large sub-gap leakage current and reduction of yields of junctions in the fabrication. 1,2) Recently, Shi et al. proposed an interesting SIS mixer composed of distributed junction arrays, which have a number of identical junctions equally separated by superconduting micro-striplines that act as tuning inductances. 3,4) It has been shown that the critical current density required to achieve a reasonable bandwidth in the mixer with the distributed junction array can be lowered in contrast with the conventional single-junction SIS mixers. This type of distributed junction array, however, shows a large increase in noise at certain frequencies. Since there will be serious degradation of efficiency in observation time in astronomical observations at these frequencies, the increase in noise should be suppressed to improve the observation efficiency at all the frequencies in the band. In this paper, we propose a new type of distributed junction array, or inhomogeneous distributed junction array, which has different dimensions of junctions and spaceings between every two junctions, to reduce the amplitude of the noise increase discovered in the conventional distributed

7 V junction array. The mixing properties of the inhomogeneous distributed junction array will be discussed in detail. S11 (1) Rn (1) Cj SIS-1 (2) (2) Cj SIS-2 (k) (k) Cj SIS-k (N) (N) Cj SIS-N Fig.2. Simplified equivalent circuit of an inhomogeneous distributed junction array. Array Inhomogeneous (Array A) Inhomogeneous (Array B) Homogeneous Array Inhomogeneous (Array A) Inhomogeneous (Array B) Homogeneous Thin-film TRL 1st 2nd 3rd k-th Table I. Simulation parameters. a) A (1) A (2) A (3) A (4) A (5) N-th SIS Fig.1. Schematic representation of an inhomogeneous distributed junction array with N junctions L (1) L (2) L (3) L (4) a) Units of junction area, A (i), and length of the stripline, L (i),areum 2 and um, respectively. Here, i is the number of junctions in the array. 2. Analysis The inhomogeneous distributed junction array proposed here consists of a number of junctions with different dimensions located on a transmission line, as illustrated in Fig.1. In the inhomogeneous distributed junction array, the dimensions of junctions and spacings between every two junctions must be determined for a given current density prior to the calculation of mixing properties. The specific capacitance of an SIS junction is assumed to be 90.0fF/um 2. The dimensions of junctions and spacings between every two junctions have been determined so that the reflection coefficient of an S-parameter, S 11, which is seen from the input port of the inhomogeneous distributed junction array, is not only minimized but also as independent of frequency as possible over the given frequency band using commercial microwave software (MDS). 5) To simplify the calculation in the determination of a set of dimensions and spacings of junctions in the array, we assume that every SIS junction can be represented by a combination of linear resistance and geometrical capacitance C j connected in parallel. The simplified equivalent circuit is shown in Fig.2. We have designed a mixer with the operating frequency in the range from 190GHz to 300GHz as an example. All the junctions were assumed to have the same critical current density of 3.0kA/cm 2, which is less than half of the values of those used in conventional SIS mixers in the same frequency range. 6) The number of junctions in the array was set as five to give the array a moderate input impedance which enables it to match the source well. The width of the stripline was assumed to be 6.0um, which corresponds to the characteristic impedance of 10.9 Ω. 7) The dimensions of junctions and spacings between every two junctions in the inhomogeneous array with five junctions determined using the above mentioned model are listed in Table I. For comparison, the dimensions of junctions and spacings between every two junctions in the homogeneous array with five junctions are also presented in Table I. In Table I, A (k) and L (k) express the dimension of the k-th junction and the spacing between k-th and (k+1)-th junctions, respectively. The frequency dependence of S 11 s for the inhomogeneous and homogeneous arrays is shown in Fig.3. As shown in Fig.3, S 11 is considerably improved over the given frequency band in the inhomogeneous arrays in comparison with the homogeneous array. Because the improvement of S 11 means the improvement of the input coupling efficiency, which is indirectly related to the improvement of the mixer con-

8 S-parameter S 11 [db] Inhomogeneous (Array A, N=5) Inhomogeneous (Array B, N=5) Homogeneous (N=5) LO frequency [GHz] Fig.3. S-parameter, S11, for inhomogeneous and homogeneous arrays with five junctions. N is the number of junctions in the array. version gain, it is predicted that the inhomogeneous array behaves as a more excellent SIS mixer than the homogeneous array. As shown in the homogeneous case, S 11 becomes less dependent on frequency as the critical current density or the number of junctions is increased. 3,4) We established an equivalent large and small signal model for the inhomogeneous arrays, following the method derived by Shi et al. for homogeneous arrays, and then calculated the mixing properties of the inhomogeneous arrays using Tucker s quantum theory of mixing. 8) In the analysis, we have adopted the quasi-five-port approximation in which five sidebands are allowed, but the local oscillator (LO) voltage is assumed to be sinusoidal. 9) The only difference between the analysis for the inhomogeneous arrays and that for the homogeneous ones is that the conversion admittance and correlation matrices must be derived for each junction, since they depend on the I-V curves of individual SIS junctions. 3. Results and Discussion Using the quantum theory of mixing together with the equivalent circuit model described in the previous section we have calculated the mixing properties of the inhomogeneous distributed junction arrays in the frequency band from 190GHz to 300GHz. An intermediate frequency (IF) is set to be 1.5GHz. The RF termination normalized to the equivalent normal-state resistance of junction arrays, R RF /,e, was assumed to be unity over the frequency band. The value of the IF termination, which is approximately equal to the dynamic resistance of the pumped I-V curve of the array, normalized to the equivalent normal-state resistance of junction arrays, R IF /,e, was assumed to be ten, since the high conversion gain can be achieved with a large IF termination. 10) In the determination of the dimensions of junctions and spacings between every two junctions, there are many possible sets of dimensions and spacings which could satisfy the condition of the optimization for S 11. We have compared the input resistance, R in (real part of input impedance), of the inhomogeneous arrays with five junctions obtained in the same way. The input resistance normalized to the equivalent normal-state resistnce of the junction array and the mixer noise temperature calculated for the two inhomogeneous arrays shown in Table I are plotted as a function of frequency in Fig.4. The imaginary parts of input impedance are nearly zero for both arrays. As shown in Fig.4, the correlation between input resistance and mixer noise temperature evidently differs in the two arrays. In array B with poor mixer performance, the mixer noise temperature exhibits minima at frequencies where the input resistance matches the equivalent normal-state resistance of junction array well (and vice versa). In contrast, in array A with good mixer performance, the mixer noise temperature exhibits maxima at frequencies where the input resistance matches the equivalent normal- Mixer noise temperature [K,SSB] Inhomogeneous (Array A) Inhomogeneous (Array B) Best matching LO frequency [GHz] Normalized input impedance Fig.4. Calculated input resistance and mixer noise temperature for array A (solid lines) and array B (dashed lines) with inhomogeneous distributed junction array with five junctions. RF termination normalized to normal-state resistance of junction array, RRF/Rn,e, is assumed to be 1. -1

9 state resistance of the junction array well. From these comparisons we have found that the amplitude of the noise increase can be suppressed by achieving the latter relationship between the input resistance and mixer noise temperature. Finally, among the obtained sets of dimensions of junctions and spacings between every two junctions we have selected the array with the set of dimensions corresponding to array A in order to achieve the latter situation. Although this situation can be achieved in the homogeneous arrays with either a small R RF /,e or a higher J c, a small ratio of R RF /,e may cause various disadvantages such as necessity of impedance transformers with a large transformation ratio and the fabrication of smaller dimensions of junctions in the array. These problems can be solved in the inhomogeneous arrays, since the latter situation can be achieved by changing the set of dimensions of junctions and spacings between every two junctions in the arrays for a given ratio of R RF /,e and a given critical current density. Figure 5 shows the calculated mixer noise temperature and conversion gain for the homogeneous and inhomogeneous arrays. Note here that the dc bias and LO voltages across the last junction were optimized with respect to the receiver noise temperature at each frequency by assuming a noise temperature of an IF amplifier of 10K. As shown in Fig.5, broadband operation has been accomplished in both arrays despite the low critical current density. In the homogeneous array with five junctions, however, a very large increase in noise is observed at several frequencies and the conversion gain is considerably decreased near those frequencies. If the number of junctions is increased, for example, if the number of junctions is set as ten as shown in Fig.5, the amplitude of the noise increase can be significantly suppressed in the homogeneous array. In the inhomogeneous array with five junctions, it is found that the amplitude of the noise increase at those frequencies is considerably suppressed in contrast with the homogeneous array. The fluctuation of the conversion gain over the frequency band is also very much reduced in the inhomogeneous array. Mixer noise temperature [K,SSB] Inhomogeneous (N=5) Homogeneous (N=5) Homogeneous (N=10) LO frequency [GHz] It is possible to reduce the distributed junction array to an equivalent single-junction as in the case of series array and it has been demonstrated that the limitation of noise temperature in the distributed junction array is given by ω k in the same way as in a single-junction mixer, where and k B express the Dirac constant and Boltzmann constant, respectively. Although the single-junction mixer has only one resonance frequency determined by its capacitance and inductance, the distributed junction array can have many resonance frequencies, whose number depends on the number of junctions. Consequently, a broadband operation can be achieved in the distributed junction array. It is possible to design the inhomogeneous distributed junction array so that the resonances continuously occur over the bandwidth. Then the fluctuations of noise temperature and conversion gain can be successfully reduced and the minimum noise temperature can be competitive with that of a single-junction mixer. From the viewpoint of noise as a function of frequency, it is clear that the inhomogeneous array with five junctions is nearly competitive with the homogeneous array with ten junctions. The reduction of the number of junctions in the array give the following advantages. At first, it becomes easy to achieve a good impedance match with the source because the B Conversion gain [db] Fig.5. Calculated mixer noise temperature and conversion gain for inhomogeneous and homogeneous arrays with five junctions and homogeneous arrays with ten junctions as a function of frequency in the range from 190GHz to 300GHz. N is the number of junctions in the array. Junction critical current density, RF and IF termination normalized to normal-state resistance of junction array are assumed to be 3.0kA/cm2, RRF/Rn,e=1 and RIF/Rn,e=10, respectively.

10 equivalent normal-state resistance of the junction array increases with the reduction of the number of junctions as /N, where N is the number of junctions. Secondly, the dimensions of junctions can be larger in the array with a smaller number of junctions. This is a significant benefit with respect to the fabrication of junctions. In the optimization of the dimensions of junctions, we have included a constraint that the size of each junction in the inhomogeneous array must be the same as or larger than that in the homogeneous array. This constraint makes the fabrication of the inhomogeneous array easier than that of the homogeneous array. In spite of the restricted optimization, however, it is found that the amplitude of the noise increase has been extremely suppressed in the inhomogeneous array. It is also noted here that the single sideband (SSB) mixer noise temperature and SSB conversion gain of the inhomogeneous array were expected to be less than 40K and larger than 5.0dB, respectively, over the frequency range from 190GHz to 300GHz, which is competitive with those in the conventional single-junction SIS mixers. 4. Conclusions We have investigated the mixing properties of distributed junction arrays with different dimensions of junctions and spacings between every two junctions. The dimensions of junctions and spacings between every two junctions in an array have been optimized in terms of the S-parameter, S 11, seen from the input port of an array, and then have been determined with attention paid to the relation between input resistance and mixer noise temperature. In an inhomogeneous distributed junction array with dimensions of junctions and spacings between every two junctions with well optimized S 11, it has been demonstrated that the amplitude of the noise increase, which always occurs at certain frequencies in a homogeneous distributed junction array, can be extremely suppressed and that critical current density can be lowered compared with those of conventional single-junction SIS mixers as far as the same frequency band in concerned. The number of junctions can be further reduced in the inhomogeneous array than that of a homogeneous array in order to achieve nearly the same mixing properties. 1) A.W. Kleinasser, F.M. Rammo and M. Bhushan: Appl. Phys. Lett. 62 (1993) ) G. de Lange, J.J. Kuipers, T.M. Klapwijk, R.A. Panhuyzen, H. van de Stadt and M.W.M de Graauw: J. Appl. Phys. 77 (1995) ) S.C. Shi, T. Noguchi and J. Inatani: Proc. 8th Int. Symp. Space Terahertz Technology, Boston, USA, March 1997, p.81. 4) S.C. Shi, T. Noguchi, J. Inatani, Y. Irimajiri and T. Saito: Proc. 9th Int. Symp. Space Terahertz Technorgy, Pasadena, USA, March 1998, p ) Microwave Design System, Hewlett-Packard Co., Palo Alto, CA 94303, USA. 6) R. Blundell, C.Y. Tong, D.C. Papa, R.L. Leombruno, X. Zhang, S. Paine, A. Stern, H.G. LeDuc and B. Bumble: IEEE Trans. Microwave Theory Tech. 4 (1995) ) W.H. Chang: J. Appl. Phys. 50 (1979) ) J.R. Tucker and M.J. Feldman: Rev. Mod. Phys. 57 (1985) ) A.R. Kerr, S.K. Pan and S. Withington: IEEE Trans. Microwave Theory Tech. 41 (1993) ) S.C. Shi: Dr. Thesis, Graduate University for Advanced Studies, 1996.