The User Defined Functions of the Sonnet Lite free Electromagnetic Simulator. N.Ishitobi. Sonnet Giken Co. Ltd. Sonnet Lite S Sonnet Lite.

: Sonnet Lite The User Defined Functions of the Sonnet Lite free Electromagnetic Simulator N.Ishitobi Sonnet Giken Co. Ltd. Sonnet Lite S Sonnet Lite CRLH, KID : keywords : factor,, electromagnetic simulator, user-defined function, dielectric material, superconductor, phase constant, quality 1 Sonnet Lite Sonnet Lite Sonnet [1] Sonnet Lite ( 1) S Sonnet Lite 1 Sonnet Lite ( 90, LPF,BPF. ) S S Touchstone [2] Emgraph S L k[3] kq [4] [5] Z 0 γ[6] k[7] S Emgraph Sonnet Lite Emgraph Sonnet Lite Touchstone Emgraph S Touchstone CRLH KID

[8] Sonnet Lite Sonnet Lite Sonnet Lite KID CRLH *1. Sonnet Lite 3 S. S CRLH S β p = cos 1 1 S 11S 22 + S 21 S 12 2S 21 (1) Sonnet Emgraph 1 2 CRLH [9] [10] CRLH(Composite Right/Left-handed) β. 2 3 S S CRLH 2 CRLH Sonnet Lite 4 β p 1.6GHz β p = π 4.2GHz β p = 0 *1 [9] 3.3 REAL DISTRIBUTED 1D CRLH STRUC- TURES

* 2 *3. ACOS((1-(S11*S22)+(S21*S12))/(2*S21)) 4 β p 4.2GHz CRLH *4. 3 [11] ε r [12]. S r T i O 3 ε r 5 [13]. Cole-Cole ε r [14] Xgeom: Xgeom Sonnet Lite Xgeom *5 Xgeom 5 2 Erel MagEr ε r (ω) = ε r + (ε r 0 ε r ) 1 + (jωτ 0 ) 1 α (2) τ 0 ε r ω 0d ε r 0 ω 0d ε r ε r ω 0d ε r α 0 1 ω 0d ε r 1decade ε r, tan δ tan δ ω decade 5 S r T i O 3 2 ε r 0 = 12766, τ 0 = 9.048 10 11, ε r = 2972, α = 0.31 *2 Emgraph *3 [10] A Sonnet Emgraph β p *4 Emgraph cos 1 (x) 0 π β p 4.2GHz β p < 0 β p ω 6 fig6 50pF const Er.Tand freq.dependent material 10MHz 1GHz 1GHz *5

Dielectric Loss Tan tand *6 er0 12766 eri -2972 f0 1.759e9 alpha 0.31 ReEr ImEr MagEr tand real(eri+(er0-eri) /(1+(sqrt(-1)*freq/f0)ˆ(1-alpha))) -imag(eri+(er0-eri) /(1+(sqrt(-1)*freq/f0)ˆ(1-alpha))) sqrt(reerˆ2+imerˆ2) ImEr/ReEr 6 50pF 10MHz 1GHz 4 KID KID Kinetic Inductance Detector [15] KID KID [16]. KID Sonnet Lite KID KID S f 0 f Q = f 0 / f *6 [11] 4 f [17] Q = ω 0 2 z (ω 0 ) Q = ω 0 y (ω 0 ) (3) z(ω 0 ) 2 y(ω 0 ) S Z Y *7 Sonnet Emgraph 3. FREQ /2 /real(a[f]) *sqrt ( (real(a[f+1])-real(a[f-1]))ˆ2 + (imag(a[f+1])-imag(a[f-1]))ˆ2 ) /(FREQ[f+1]-FREQ[f-1]) Emgraph FREQ Hz FREQ[f] f A[f] f f-1 f+1 FREQ[f] A[f] A[f] Z Y KID Y *8 0 [19] R S = 1 2 ω2 µ 2 0 λ3 L (T)σ N( T T c ) 4 (4) L S = µ 0 λ L (T) (5) λ L (0) λ L (T) = (6) 1 ( TTc ) 4 T T c σ N µ 0 λ L *7 [18] *8 Z Y KID Z

R s L s KID T/T c L s Xgeom *9 General Rdc Rs Xdc Xs * 10 T = 4.2 T_c = 8.7 Lambda_L0 = 8.5e-008 sigma_n = 11690000 u0 = 4*pi*10ˆ(-7) omega = 2*pi*freq Lambda_LT = Lambda_L0/sqrt(1-(T/T_c)ˆ4) Rs = omegaˆ2*u0ˆ2/2*lambda_ltˆ3 *sigma_n*(t/t_c)ˆ4 Ls = u0*lambda_lt*1e12 Xs = omega*ls*1e-12 7 LEKID 300µm Si, 50Ω 4 5 4µm Sonnet Lite *11 4.1 7 * 12 LEKID * 13 8 f /60 f /6 8 LEKID 0.92 K 4.6 K 5 S 21 0.92 K 4.6 K f /60 5 [13] *9 [20] 2.5 *10 Sonnet Normal Rdc/Rrf General General Xdc Ls Sonnet Lite Ls Xs *11 T T c λ L (0) σ N Niobium *12 [21] 4. Lumped Element Kinetic Inductance Detectors LEKID *13 KID LEKID(Lumped Element KID) MKID(Microwave KID). [1] J.C. Rautio and R.F. Harrington, An electromagnetic time-harmonic analysis of shielded microstrip circuits, Microwave Theory and Techniques, IEEE Transactions on, vol.35, no.8, pp.726 730, aug 1987. http://www. sonnetsoftware.com/resources/ [2] I.O. Forum, Touchstone(r) file format

specification version 2.0, Apr. 24 2009. https://ibis.org/touchstone_ver2.0/ touchstone_ver2_0.pdf [3] Sonnet 2010 http://www.sonnetsoftware.co. jp/support/tips/magnetic_transformer. pdf [4] max, CEATEC2014 ES10,NW13,4J Oct. 2014 http://www.sonnetsoftware.co.jp/ product/seminar/ceatec2014/ [5], WPT2014-5 vol.114 no.9 pp.23 25 2014-04-17 [6] Sonnet crlh(composite right/left-handed), Sept. 2011 http://www.sonnetsoftware.co.jp/ support/tips/crlh/crlhline.pdf [7] S k, http://www.sonnetsoftware.co.jp/ support/tips/user_defined_equation/ [8] A.F. Horn, J.W. Reynolds, and J.C. Rautio, Conductor profile effects on the propagation constant of microstrip transmission lines, Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International, pp.868 871, may 2010. [9] C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley - IEEE, Wiley, 2005. [10] Sonnet crlh(composite right/left-handed) 2011 http://www.sonnetsoftware.co.jp/ product/seminar/tsy2012/tsy2012.pdf [11] 2012 http://www.sonnetsoftware.co. jp/support/tips/freq_dep_dielectric/ freq_dep_dielectric.pdf [12] 2003 [13] http://www.tecdia.com/jp/ [14] pp.8 12 1987 [15] A. Baryshev, J.J.A. Baselmans, A. Freni, G. Gerini, H. Hoevers, A. Iacono, and A. Neto, Progress in antenna coupled kinetic inductance detectors, Terahertz Science and Technology, IEEE Transactions on, vol.1, no.1, pp.112 123, Sept. 2011. [16] P.K. Day, H.G. Leduc, A. Goldin, T. Vayonakis, B.A. Mazin, S. Kumar, J. Gao, and J. Zmuidzinas, Antenna-coupled microwave kinetic inductance detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.559, no.2, pp.561 563, 2006. [17], MWE2011 TL2011 05a Dec. 2011 http://apmc-mwe. org/mwe2012/pdf/tut11/tl2011_05a.pdf [18] Emgraph touchstone, 2013 http://www.sonnetsoftware. co.jp/product/seminar/ceatec2016/ ceatec2016.pdf [19] 1995 [20] Sonnet, http://www.sonnetsoftware.co.jp/ [21] R. Markus J, Development of lumped element kinetic inductance detectors for mm-wave astronomy at the IRAM 30m telescope, Karlsruher Institut fur Technologie Scientific Publishing, 2013. 5-1-1-706 tovy@sonnetsoftware.co.jp