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- あいね みやのじょう
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1 FDTD S A Study on FDTD Analysis based on S-Parameter GD168
2 FDTD FDTD S S FDTD S S S S FDTD FDTD i
3 FDTD FDTD S FDTD S FDTD S S S FDTD ΩMSL S S S ΩMSL ii
4 3.2.2 LPF BPF iii
5 1 1.1 FDTD (FDTD : Finite Difference Time Domain) [1],[2] FDTD FDTD FDTD 3 2 FDTD 1 FDTD 1
6 2
7 1.2 FDTD FDTD FDTD FDTD [3] [4] [3] [4] FDTD SPICE(Simulation Program with Integrated Circuit Emphasis) SPICE FDTD [5] TDCM(Time-Domain Characteristic Models) TDCM [6],[7],[8] [8] (a)s (b) (c) 3
8 S S FDTD [8] S S FDTD 2 S S S 3 S FDTD 4 4
9 2 S FDTD S S S 2.1 FDTD S 2.1 S S Z 0 (MSL : Microstrip Line) V 1in V 2in S V 11 V 22 V 21 V 12 V 1view V 2view R MSL (Z 0 ) V 1in V 11 +V 12 V 21 +V 22 V 2in MSL(Z 0 =R) MSL V 1view R R V 2view GND 2.1: S 5
10 S FDTD FDTD S (S t ) S (S f ) (2.1) S t (k) = 1 N N 1 i=0 S f (i)e j 2πik N (2.1) FDTD (Δt) (Δt) (2.2) Courant Δt c 1 ( 1 Δx )2 +( 1 Δy )2 +( 1 Δz )2 (2.2) c Δx Δy Δz (2.3) FDTD (Δt) (f max ) GHz S FDTD Δt=1.0[ps] 20,000 (2.3) (2.4) S f=0 500[GHz] Δf=50[MHz] f=0 500[GHz] S Δt = 1 2 f max (2.3) Δf = 1 T (2.4) FDTD S S FDTD (2.5) S 1 (V 1in ) S 1 (V 11 ) 2 (V 21 ) V i1 [n] = S i1 [n] V 1in [n] (i =1, 2) n = S i1 [n k +1]V 1in [k] (2.5) k=1 6
11 (2.6) (V 1in ) 1 1 (V 1view ) V 11 V 12 V 1in [n] V 1view [n 1] V 11 [n 1] V 12 [n 1] (2.6) 2 V 12 V 22 V i2 [n] = S i2 [n] V 2in [n] (i =1, 2) n = S i2 [n k +1]V 2in [k] (2.7) k=1 V 2in [n] V 2view [n 1] V 21 [n 1] V 22 [n 1] (2.8) 50Ω 2.2 MSL MSL (Z 0 ) V 11 + V 12 MSL V 1in (t) R V 1view 2.2: S 7
12 R 2.3 S S FDTD Voltage [V] Pulse wave Observe wave Unabsorbed Pulse wave Timestep [Step] 2.3: S FDTD ( 2.4) Extended part S FDTD 8
13 FDTD Initialize E, H Update E S-parameter Calculation of an incident wave Convolution Generation of the reflection wave and the transmission wave Extended part Calculation of the observing wave Update H 2.4: S 9
14 2.2 FDTD S FDTD (Δt) (f max ) GHz [GHz] [GHz] 2.1: f=0 10[GHz] f=0 500[GHz] Δt = 1.0[ps] Δf = 200[MHz] Δf = 50[MHz] idft N = 20000[Steps] N = 50[Steps] N = 20000[Steps] T = 20000[ps] (a) (b) 1 (c) N+1 N (d) 10
15 3 1 ( 1 ) (e) 3 2 ( 1 2 ) 3 3 S [GHz] (Δf) 50[MHz] Δf 200[MHz] (Δf=50[MHz]) 2.5 S (S11) real data 200 Δf=500[MHz]
16 1 0.8 S linear hermite spline real data Frequency [GHz] 2.5: Error 0 linear hermite spline Frequency [GHz] 2.6: 12
17 2.2: f=0 10[GHz] Δf = 200[MHz] : (0 10GHz) data 1 data 2 data Δf[MHz] S (S11) real data 200 Δf=500[MHz]
18 1 0.8 S data 1 data 2 data 3 real data Frequency [GHz] 2.7: Error data 1 data 2 data Frequency [GHz] 2.8: 14
19 2.4: data 1(Δf=1000[MHz]) data 2(Δf=500[MHz]) data 3(Δf=200[MHz]) data [GHz] 3 3 ( 0 500[GHz] Δf=50[MHz]) ( 2.9) (f max ) S S11 1 S
20 S-parameter S11 S21 S-parameter S11 S Frequency [GHz] Frequency [GHz] (a) (b) 2.9: 1 S linear hermite spline real data Frequency [GHz] 2.10: 16
21 2.10 S (S11) real data 20,000 Δf=1.25[GHz] Error linear hermite spline Frequency [GHz] 2.11: 2.5:
22 2.2.5 f=0 10[GHz] 2.6: data 1 data 2 data 3 f max [GHz] S data 1 data 2 data 3 real data Frequency [GHz] 2.12: 2.10 S (S11) real data 200 Δf=500[MHz] 20 18
23 Error data 1 data 2 data Frequency [GHz] 2.13: : data 1(f max =5[GHz]) data 2(f max =10[GHz]) data 3(f max =20[GHz]) S S FDTD 3 19
24 FDTD S FDTD S LPF FDTD FDTD S FDTD S 20
25 2.3 S ( 2.3) [1] [9] S (2.6) (2.8) [cell] MSL MSL PML 8layer Feed Ob1 R z y GND PML 8layer x 2.14: 2.14 (Δx Δy Δz) = (0.5mm 0.55mm 0.533mm) Δt (2.2) Courant 1.0ps 8Δy 3Δz MSL 0mm 30GHz 8 PML(Perfectly Matched Layer) Ω 21
26 E n Z = 1 ΔtΔz 2RɛΔxΔy 1+ ΔtΔz 2RɛΔxΔy E n 1 Z + Δt ɛ 1+ ΔtΔz ( H n 1 2 ) (2.9) 2RɛΔxΔy (2.9) 4 ( (2.10) (2.11)) V L = E Z Δz (2.10) di V L = L 0 dt V (2.11) V i L 0 =1/, V = L 0 L i i=1 i=1 L i ( ) 50Ω MSL Feed V 1in (t) P 2 P 3 P1 1 P : 22
27 L I L -V V L N 2.16: 2.17 (Method 1) (Method 2) 2.14 (Ob1) (Input Voltage) (Reflection Voltage) 0 S-parameter [db] Method 2 Method Frequency [GHz] 2.17: 23
28 0.03 Input Voltage Voltage [V] Method Reflection Voltage Method Timestep [Step] 2.18: MSL 50Ω 50Ω [10] MSL MSL 48Ω 51Ω 2.19 (Method 1) (Method 2) 2.14 Ob Ω [10] 24
29 S-parameter [db] Method 2 Method 1 after before Frequency [GHz] 2.19: Voltage [V] R=50 R= Timestep [Step] 2.20: 25
30 2.3.3 S MSL MSL [11] MSL via via-4 via4 MSL Current via : GHz via0 5GHz 2 26
31 0 Current [A] via0 via1, via-1 via2, via-2 via3, via-3 via4, via Timestep[Time] 2.22: Normalization via 2.23: 5GHz 27
32 0 S-parameter [db] Frequency [GHz] via-4 - via4 via-3 - via3 via-2 - via2 via-1 - via1 via : 2.24 (via-4 via4) 7 via-3 - via3 MSL 2.25 MSL MSL MSL 28
33 MSL Feed V 1in (t) 2.25: S-parameter [db] step nomal Frequency [GHz] 2.26: 29
34 2.3.4 S S V 11 + V 12 V 21 + V 22 V 1view + V 2view 4 (2.6) (2.8) V 1in [n] V 1view [n 1] V 11 [n 5] V 12 [n 5] (2.12) V 2in [n] V 2view [n 1] V 21 [n 5] V 22 [n 5] (2.13) ( 2.27) S 0.1 Voltage [V] before after Timestep [Step] 2.27: 30
35 2.3.5 MSL S S 31
36 3 S FDTD S FDTD FDTD FDTD ΩMSL S 50Ω MSL S FDTD Ob1 Ob2 ( 3.1) FDTD Ob1 ( 3.2) Ob1 1 Ob2 MSL MSL PML 8layer Feed Ob1 z y Ob2 GND PML 8layer x 3.1: 32
37 MSL MSL PML 8layer Feed Ob1 z R y Ob2 GND PML 8layer x 3.2: S S S S Anritsu 37347C 3680V ( 3.3) ( 3.4) S S FDTD S 33
38 3.3: 3.4: Ω MSL S ( 3.5) S 34
39 FDTD (AWR MicroWave-Office) FDTD S 50Ω MSL Inductor or Capacitor 3.5: (Δx Δy Δz) = (1.0mm 1.05mm 0.533mm) Δt (2.2) Courant 1.0ps 50Ω 4Δy 3Δz MSL 0mm 30GHz 5 PML(Perfectly Matched Layer) 1 2 MSL = 72Ω Δt 0.5ps S 500GHz (Δf) 50MHz Δf 50MHz 10GHz S FDTD S 35
40 0 S11 S21[dB] S11 S21 FDTD Simulator Frequency [GHz] 3.6: S11 S21[dB] S21 S11 FDTD Simulator Frequency [GHz] 3.7: 36
41 SV280 S 50Ω MSL ( 3.8) 50Ω MSL Varactor diode 3.8: S FDTD S S FDTD [12] 0V 10V S FDTD FDTD S FDTD FDTD S 37
42 0 S11 S21[dB] S11 S21 FDTD Simulator Frequency [GHz] 3.9: Bias=0V 0 S11 S21[dB] S11 S21 FDTD Simulator Frequency [GHz] 3.10: Bias=10V 38
43 3.1.4 FDTD S 50Ω MSL 2 LC ( 3.11) 50Ω MSL Capacitor Inductor 3.11: LC S 2.1 S S FDTD S 2 FDTD FDTD S FDTD FDTD S 39
44 0 S11 S21[dB] S11 S21 FDTD Simulator Frequency [GHz] 3.12: LC 40
45 3.2 S 50Ω MSL S FDTD S FDTD ΩMSL 50ΩMSL S 50ΩMSL ( 3.13) Capacitor 3.13: 50ΩMSL 50ΩMSL 2 2 S FDTD FDTD 50ΩMSL S FDTD FDTD 50ΩMSL S 41
46 S11 S21[dB] S11 S21 FDTD Simulator Frequency [GHz] 3.14: 50ΩMSL LPF S LPF(Low- Pass-Filter) FDTD FDTD : LPF FDTD 150*80*41cell Δx =0.5mm Δy =0.55mm Δz =0.32mm 40000steps Δt =0.5ps PML5 42
47 S ( = 168Ω) FDTD Δt 0.5ps S 1000GHz (Δf) 50MHz HK1608 6GHz ɛ r = [mm] tanδ =0.001 R4737 LPF 3.15 LPF 3.16 Chip Inductor 20.9mm Port1 Port2 51.4mm 3.15: LPF 3.16: LPF 43
48 S FDTD 3.17 S FDTD FDTD S FDTD S11 S21[dB] S21 S11 FDTD Simulator Meas Frequency [GHz] 3.17: LPF BPF BPF(Band-Pass-Filter) FDTD [13] BPF 3 2 ( 3.18) C L 0V 15V C s 0V 3V 44
49 Port1 Cin Cout Port2 C s MSL C MSL 1 l1 l2 CL l 1 =4.4[mm], l 2 =34.1[mm], C 1 =5.0[pF ], C in = C out =1.0[pF ] 3.18: BPF FDTD : BPF FDTD 165*60*35cell Δx =0.5mm Δy =0.55mm Δz =0.32mm 40000steps Δt =0.5ps PML5 S ( = 168Ω) FDTD Δt 0.5ps S 1000GHz (Δf) 50MHz UMK1608 1SV280 S 6GHz 45
50 10GHz R4737 BPF 3.19 BPF 3.20 Chip Capacitor (S-parameter) Port1 Port2 16.5mm Varactor Diode (S-parameter) Through-hole Through-hole 87.3mm 3.19: BPF 3.20: BPF 46
51 S FDTD S FDTD S FDTD S S11 S21[dB] S21 S11 Frequency [GHz] FDTD Simulator Meas : BPF 47
52 S11 S21[dB] S21 S FDTD Simulator Meas Frequency [GHz] 3.22: BPF 48
53 4 S FDTD FDTD S GHz S MSL S FDTD FDTD 49
54 FDTD 50
55 [1], FDTD,, [2], FD-TD, ( 17/18 ). [3] W.Sui, D.A.Christensen and C.H.Durney, Extending the Two-Dimensional FDTD Method to Hybrid Electromagnetic Systems with Active and Passive Lumped Elements, IEEE Trans. Microwave Theo. Tech., vol.40, no.4, pp , 1992 [4] V.A.Thomas, M.E.Jones, M.J.Picket-May, A.Taflove and E.Harrigan, The Use of SPICE Lumped Circuits as Sub-grid Models for FDTD Analysis, IEEE Microwave Guided Wave Lett., vol.3, pp , 1993 [5] Q.Chu, Y.Lau and F.Chang, Transient Analysis of Microwave Active Circuits Based on Time-Domain Characteristic Models, IEEE Trans. Microwave Theo. Tech., vol.46, no.8, pp , 1998 [6],, FDTD,, EMCJ97-96, pp.29-35, Jan [7] X. Ye, and J. L. Drewniak, Incorporating Two-Port Networks with S-Parameters into FDTD, IEEE Microwave and Wireless Components Lett., vol.11, pp.77-79, 2001 [8],,, S FDTD, Trans.IEICE, Vol.J85-B, No.9, pp , Sept [9],,,, FDTD,, C-2-89, March [10],,,, FDTD,, EMCJ
56 [11],,,, FDTD,, EMCJ2003-8, pp.47-52, April [12],,,, FDTD,, B-1-111, Sept [13],,,, λ/2 BPF,, MW , pp , Oct [14],,,
57 Takashi Hibino, Hiroyuki Arai, Frequency Tunable Dual-Band Filter with Fixed Attenuation Poles, 2004 Asia Pacific Microwave Conference, Delhi, India, Dec Takashi Hibino, Naobumi Michishita, Hiroyuki Arai, Improved Implement of S- Parameter for the FDTD Method, 2005 International Symposium on Antennas and Propagation, Seoul, Korea, Aug C-2-76 Sept S FDTD B Sept S FDTD B March
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