1 SK00500M10A6 S (0.25 ± 0.025) 2 mm ± mm 50 ± 20% pf ε r S r T i O Sonnet ε r, tan δ Sonnet [2] [3] : 2 : 3 : 4

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1 Sonnet [1] L ε r Sonnet [1] 1GHz 1 : 2 : 3 : 4 : 1

2 1 SK00500M10A6 S (0.25 ± 0.025) 2 mm ± mm 50 ± 20% pf ε r S r T i O Sonnet ε r, tan δ Sonnet [2] [3] : 2 : 3 : 4 : S c 0 c 0 2 2ε r S 2.3 ε r (1) ε r = ε r jε r (2) tan δ D D = tan δ (3) G ω = ε r (4) ε r 2

3 = ε 0ε rs (5) 4 G G = ω ε 0ε r S (6) 1 G 5 6 G + jω = ω ε 0ε r S + jω ε 0ε rs = ω ε 0(ε r + jε r)s = jω ε 0ε r S Z = j ω L + 1 G + j ω G + jω 9 Z = j(ω L (7) (8) (9) (10) ωε 0 ε r S ) (11) ε r ε r = 1 ωε 0 S (ωl + jz) (12) ε r = ωl Im(Z) ωε 0 S (ωl Im(Z)) 2 + Re(Z) 2 (13) ε r = ωε 0 S Re(Z) (ωl Im(Z)) 2 + Re(Z) 2 (14) 2.5 L Z 1 L. ω 0 Im(Z) = 0 ω , ω ω 0 ω 0 ω 0 0 = ω 0 L G 2 + ω0 2 (15) 2 L ω 0 = ± G2 (16) ω 0 Re(Z) Re(Z) = 10 G G 2 + ω 2 2 (17) ω 16 ω 0 Re(Z) = GL ω 0 Re(Z) ω Re(Z) (18) 10 = 2 ω 2 G (G 2 + ω 2 2 ) 2 (19) ω 16 ω 0 Re(Z) = 2 G L G2 L 2 ω 0 Im(Z) ω (20) 10 = L G 2 + ω ω 2 3 (G 2 + ω 2 2 ) 2 (21) ω 16 ω 0 L = 2 ( L G2) L 2 (22) 18, 20, 22 L 18 G G = Re(Z) L (23) 22 G 23 = = 2L 2(Re(Z)) 2 (24) 2L 2Re(Z) 2 (25) 20 G 23 ( Re(Z) )2 = 4(Re(Z)) 2 L 4(Re(Z)) 4 2 3

4 25 = 2L(2L ( L ( Re(Z) )2 )) (2L ( ))2 = 2( )L ( )2 L L = ( ) 2 + ( Re(Z) ) 2 2 (26) 12 L SK00500M10A6 Agilent 16196A/B//D SMD [4] 3GHz 7mm GHz 2 3GHz *1 3.2 ε r 26 L 2 * L f MHz Re(Z 1 ) 2.26 Ω Im(Z 1 ) Ω f MHz Re(Z 2 ) 2.18 Ω Im(Z 2 ) 0.10 Ω Re(Z) 2.20 Ω Re(Z) p Ω ra/sec p Ω ra/sec L 81.0 ph 12 ε r (ω) = ε r + (ε r 0 ε r ) 1 + (jωτ 0 ) 1 α (27) τ 0 ε r ω 0 ε r 0 ω 0 ε r ε r ω 0 ε r α 0 1 ω 0 ε r * 2 ε r *2 ole-ole [5] 4

5 3 ole-ole ε r τ ε r α 0.31 Sonnet ielectric layer * 5 ε r tan δ Sonnet csv *6 extructe er table.csv 4 3 csv ω 0 ε r = ε r + (ε r 0 ε r )/2 ε r * Sonnet * 7, 1, 2, 3... (Hz), ε r ε r Hz Hz Sonnet * 4 3 *3 ε r 3 ε r ω 0 ε r *4 *5 Sonnet ielectric layer( ) Sonnet ielectric layer *6 csv csv *7 csv OK, csv 5

6 4 csv, 1, e3, 12766, e6, 12766, e6, 12761, e6, 12747, 191 : : : e6, 3898, e6, 3437, e6, 3032, e9, 3032, ReEr table2("extructe_er_table.csv", freq,1) ImEr table2("extructe_er_table.csv", freq,2) MagEr sqrt(reer^2+imer^2) tan ImEr/ReEr 3. New Name ReEr 5. Value or Equation table2("extructe_er_table.csv",freq,1) *9 * OK OK 4 * Sonnet Sonnet extructe er table.csv Sonnet 1. ( 4) 2. extructe er.csv Xgeom 2. ircuit - Variable List... * MagEr tan 1. ircuit - Brick Materials... * 11 *9 table2 csv Sonnet extructe er table.csv freq freq Hz freq Sonnet online help (manual ) *10 Evaluates to an t rea extructe_er_table.csv *11 Brick Materials... ircuite Dielectric Layers... 6

7 6 er eri f e9 alpha 0.31 ReEr real(eri+(er0-eri) /(1+(sqrt(-1)*freq/f0)^(1-alpha))) ImEr -imag(eri+(er0-eri) /(1+(sqrt(-1)*freq/f0)^(1-alpha))) MagEr sqrt(reer^2+imer^2) tan ImEr/ReEr Erel MagEr Dielectric Loss Tan tan ( 6) 4. OK GHz 6 Sonnet 3GHz [1]. DEI, vol.2006 no.77 pp [2] [3] 2003 [4] Agilent Technologies, Agilent 16196A/B//D SMD / 4, [5], 7

8 pp [2] 8

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