FDTD S A Study on FDTD Analysis based on S-Parameter 18 2 7 04GD168
FDTD FDTD S S FDTD S S S S FDTD FDTD i
1 1 1.1 FDTD.................................... 1 1.2 FDTD..................... 3 2 S 5 2.1 FDTD S.............. 5 2.2 FDTD S............... 10 2.2.1............................. 10 2.2.2.............. 11 2.2.3............... 13 2.2.4.............. 15 2.2.5............... 18 2.2.6..................... 19 2.3............................. 21 2.3.1.............. 21 2.3.2............. 24 2.3.3 S.... 26 2.3.4..... 30 2.3.5..................... 31 3 S FDTD 32 3.1 50ΩMSL S............... 32 3.1.1 S.................... 33 3.1.2.............................. 34 3.1.3.......................... 37 3.1.4........................ 39 3.2 S..................... 41 3.2.1 50ΩMSL.............. 41 ii
3.2.2 LPF................................... 42 3.2.3 BPF............................. 44 4 49 50 51 53 iii
1 1.1 FDTD (FDTD : Finite Difference Time Domain) [1],[2] FDTD FDTD FDTD 3 2 FDTD 1 FDTD 1
2
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
S S FDTD [8] S S FDTD 2 S S S 3 S FDTD 4 4
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
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
(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
R 2.3 S S FDTD Voltage [V] 0.4 0.3 0.2 0.1 Pulse wave Observe wave Unabsorbed Pulse wave 0 0 500 1000 1500 Timestep [Step] 2.3: S FDTD ( 2.4) Extended part S FDTD 8
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
2.2 FDTD S FDTD (Δt) (f max ) GHz 2.1 2.1 0 10[GHz] 10 500[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] 2.2.1 (a) (b) 1 (c) N+1 N (d) 10
3 1 ( 1 ) (e) 3 2 ( 1 2 ) 3 3 S 2.2.2 2.1 0 10[GHz] (Δf) 50[MHz] Δf 200[MHz] 4 3 3 (Δf=50[MHz]) 2.5 S (S11) real data 200 Δf=500[MHz] 20 2.6 11
1 0.8 S11 0.6 0.4 0.2 linear hermite spline real data 0 0 2 4 6 8 10 Frequency [GHz] 2.5: 0.001 0.0005 Error 0 linear hermite spline 0 2 4 6 8 10 Frequency [GHz] 2.6: 12
2.2: 2.19 10 4 3.55 10 5 1.09 10 6 2.2 3 2.2.3 f=0 10[GHz] Δf = 200[MHz] 50 2.3: (0 10GHz) data 1 data 2 data 3 200 10 20 50 Δf[MHz] 50 1000 500 200 3 2.2.2 2.7 S (S11) real data 200 Δf=500[MHz] 20 2.8 13
1 0.8 S11 0.6 0.4 0.2 0 data 1 data 2 data 3 real data 0 2 4 6 8 10 Frequency [GHz] 2.7: 0.0002 Error 0-0.0002 data 1 data 2 data 3-0.0004 0 2 4 6 8 10 Frequency [GHz] 2.8: 14
2.4: data 1(Δf=1000[MHz]) data 2(Δf=500[MHz]) data 3(Δf=200[MHz]) 1.05 10 4 4.35 10 5 1.09 10 6 2.4 3 data 1 20 2.2.4 2.1 10 500[GHz] 3 3 ( 0 500[GHz] Δf=50[MHz]) ( 2.9) (f max ) S S11 1 S21 0 15
1 1 0.8 0.8 S-parameter 0.6 0.4 0.2 S11 S21 S-parameter 0.6 0.4 0.2 S11 S21 0 0 100 200 300 400 500 Frequency [GHz] 0 0.01 0.1 1 10 100 1000 Frequency [GHz] (a) (b) 2.9: 1 S11 0.9 0.8 linear hermite spline real data 0.7 0 100 200 300 400 500 Frequency [GHz] 2.10: 16
2.10 S (S11) real data 20,000 Δf=1.25[GHz] 400 2.11 0.02 0 Error -0.02-0.04 linear hermite spline -0.06 0 100 200 300 400 500 Frequency [GHz] 2.11: 2.5: 0.0249 0.0103 0.0031 2.5 3 17
2.2.5 f=0 10[GHz] 2.6: data 1 data 2 data 3 f max [GHz] 500 5 10 20 3 2.2.2 1 S11 0.9 0.8 data 1 data 2 data 3 real data 0.7 0 20 40 60 80 100 Frequency [GHz] 2.12: 2.10 S (S11) real data 200 Δf=500[MHz] 20 18
0.02 0 Error -0.02-0.04 data 1 data 2 data 3-0.06 0 20 40 60 80 100 Frequency [GHz] 2.13: 2.13 2.7: data 1(f max =5[GHz]) data 2(f max =10[GHz]) data 3(f max =20[GHz]) 0.0076 0.0031 0.0011 2.7 S 2.2.6 S FDTD 3 19
FDTD S FDTD S LPF FDTD FDTD S FDTD S 20
2.3 S ( 2.3) [1] [9] S (2.6) (2.8) 20 20 20 4 40 [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) 2.3.1 2.2 50Ω 21
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) 4 1 4 V i L 0 =1/, V = L 0 L i i=1 i=1 L i ( 2.15 2.16) 50Ω MSL Feed V 1in (t) P 2 P 3 P1 1 P 4 2.15: 22
L I L -V V L N 2.16: 2.17 (Method 1) (Method 2) 2.14 (Ob1) 2.18 2.18 (Input Voltage) (Reflection Voltage) 0 S-parameter [db] -10-20 -30-40 Method 2 Method 1-50 0 2 4 6 8 10 Frequency [GHz] 2.17: 23
0.03 Input Voltage Voltage [V] 0.02 0.01 0 Method 1-0.01 Reflection Voltage Method 2 0 200 400 600 Timestep [Step] 2.18: 2.3.2 MSL 50Ω 50Ω [10] MSL MSL 48Ω 51Ω 2.19 (Method 1) (Method 2) 2.14 Ob1 2.20 48Ω [10] 24
S-parameter [db] -20-30 -40-50 -60 Method 2 Method 1 after before 0 2 4 6 8 10 Frequency [GHz] 2.19: 0.006 Voltage [V] 0.004 0.002 0-0.002-0.004 R=50 R=48 0 200 400 600 Timestep [Step] 2.20: 25
2.3.3 S MSL MSL [11] MSL via0 2.21 via-4 via4 MSL Current via -4-3 -2-1 0 1 2 3 4 2.21: 2.22 2.23 5GHz via0 5GHz 2 26
0 Current [A] -0.0002-0.0004-0.0006-0.0008 via0 via1, via-1 via2, via-2 via3, via-3 via4, via-4 100 200 300 400 Timestep[Time] 2.22: Normalization 2 1.5 1-4 -2 0 2 4 via 2.23: 5GHz 27
0 S-parameter [db] -20-40 -60 Frequency [GHz] via-4 - via4 via-3 - via3 via-2 - via2 via-1 - via1 via0 0 2 4 6 8 10 2.24: 2.24 (via-4 via4) 7 via-3 - via3 MSL 2.25 MSL 2.26 3 MSL MSL 28
MSL Feed V 1in (t) 2.25: S-parameter [db] 0-10 -20-30 -40 step nomal -50 0 2 4 6 8 10 Frequency [GHz] 2.26: 29
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] 0.05 0-0.05 before after 0 200 400 600 Timestep [Step] 2.27: 30
2.3.5 MSL S S 31
3 S FDTD S FDTD FDTD FDTD 3.1 50ΩMSL 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
MSL MSL PML 8layer Feed Ob1 z R y Ob2 GND PML 8layer x 3.2: 3.1.1 S S S S Anritsu 37347C 3680V ( 3.3) ( 3.4) S S FDTD S 33
3.3: 3.4: 3.1.2 50Ω MSL S ( 3.5) S 34
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 48 3 2 = 72Ω Δt 0.5ps 20000 S 500GHz (Δf) 50MHz Δf 50MHz 10GHz S 3.6 3.7 FDTD S 35
0 S11 S21[dB] -10-20 -30-40 S11 S21 FDTD Simulator -50 0 2 4 6 8 10 Frequency [GHz] 3.6: S11 S21[dB] 0-10 -20-30 -40-50 S21 S11 FDTD Simulator 0 2 4 6 8 10 Frequency [GHz] 3.7: 36
3.1.3 1SV280 S 50Ω MSL ( 3.8) 50Ω MSL Varactor diode 3.8: S FDTD S S FDTD [12] 0V 10V S FDTD FDTD S FDTD 3.1.2 3.9 3.10 FDTD S 37
0 S11 S21[dB] -10-20 -30-40 -50 S11 S21 FDTD Simulator 0 1 2 3 4 5 6 Frequency [GHz] 3.9: Bias=0V 0 S11 S21[dB] -10-20 -30-40 -50 S11 S21 FDTD Simulator 0 1 2 3 4 5 6 Frequency [GHz] 3.10: Bias=10V 38
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 3.1.2 3.12 FDTD S 39
0 S11 S21[dB] -10-20 -30-40 -50 S11 S21 FDTD Simulator 0 1 2 3 4 5 6 Frequency [GHz] 3.12: LC 40
3.2 S 50Ω MSL S FDTD S FDTD 3.2.1 50ΩMSL 50ΩMSL S 50ΩMSL ( 3.13) Capacitor 3.13: 50ΩMSL 50ΩMSL 2 2 S FDTD FDTD 50ΩMSL S FDTD 3.1.2 3.14 FDTD 50ΩMSL S 41
S11 S21[dB] 0-10 -20-30 -40-50 S11 S21 FDTD Simulator 0 2 4 6 8 10 Frequency [GHz] 3.14: 50ΩMSL 3.2.2 LPF S LPF(Low- Pass-Filter) FDTD FDTD 3.1 3.1: LPF FDTD 150*80*41cell Δx =0.5mm Δy =0.55mm Δz =0.32mm 40000steps Δt =0.5ps PML5 42
S (48 7 2 = 168Ω) FDTD Δt 0.5ps 40000 S 1000GHz (Δf) 50MHz HK1608 6GHz ɛ r =2.56 1.6[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
S FDTD 3.17 S FDTD FDTD S FDTD S11 S21[dB] 0-10 -20-30 -40 S21 S11 FDTD Simulator Meas. -50 0 1 2 3 4 5 6 Frequency [GHz] 3.17: LPF 3.2.3 BPF BPF(Band-Pass-Filter) FDTD [13] BPF 3 2 ( 3.18) C L 0V 15V C s 0V 3V 44
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 3.2 3.2: BPF FDTD 165*60*35cell Δx =0.5mm Δy =0.55mm Δz =0.32mm 40000steps Δt =0.5ps PML5 S (48 7 2 = 168Ω) FDTD Δt 0.5ps 40000 S 1000GHz (Δf) 50MHz UMK1608 1SV280 S 6GHz 45
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
S FDTD 3.21 3.22 S FDTD S FDTD S S11 S21[dB] 0-10 -20-30 -40-50 S21 S11 Frequency [GHz] FDTD Simulator Meas. 0.5 1 1.5 2 2.5 3.21: BPF 47
S11 S21[dB] 0-10 -20-30 S21 S11-40 -50 FDTD Simulator Meas. 0.5 1 1.5 2 2.5 Frequency [GHz] 3.22: BPF 48
4 S FDTD FDTD S GHz S MSL S FDTD FDTD 49
FDTD 50
[1], FDTD,, 1998. [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.724-730, 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.333-335, 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.1097-1104, 1998 [6],, FDTD,, EMCJ97-96, pp.29-35, Jan. 1998 [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.1526-1534, Sept. 2002 [9],,,, FDTD,, C-2-89, March 2004. [10],,,, FDTD,, EMCJ2003-4 51
[11],,,, FDTD,, EMCJ2003-8, pp.47-52, April 2003. [12],,,, FDTD,, B-1-111, Sept. 2005. [13],,,, λ/2 BPF,, MW2001-90, pp.125-132, Oct. 2001. [14],,, 1996 52
Takashi Hibino, Hiroyuki Arai, Frequency Tunable Dual-Band Filter with Fixed Attenuation Poles, 2004 Asia Pacific Microwave Conference, Delhi, India, Dec. 2004. 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. 2005. 2 C-2-76 Sept 2004. S FDTD B-1-110 Sept 2005. S FDTD B-1-190 March 2005. 53