1 - 宇宙線研究室 - 京都大学

1 http://www-cr.scphys.kyoto-u.ac.jp/member/tsuru/lecture/Ver 2008 02008/4∼2008/72008/(4/11), 4/19, 4/25, 5/2, 5/9, 5/16, 5/23, (5/30), 6/6, 6/13, 6/20, 6/27, 7/4, 7/11 7/18

51: (2)1.1 X Astro-D GIS X ??PMT /A/D Daq. (House Keeping ) X CCD CCD CCD CCDpn MOS 1.1: Astro-D GIS

6 1 : (2 )1.2 1.2.1 GNDCOMMON=GND GND COMMON 0V GNDCOMMON (Astro-E2 GND GND(COMMON) ) 1.2: GNDCOMMON GND(chassis) GND(Earth) GND(Common) 1.2.2 1.3: (1) (2) (3) (4) (4) 1.2.3 1.4: (1) (2) (3) (1) 1.2.4 AC DC DC AC DC 1.5V AC 100V 50Hz 60Hz

1.2. 71.2.5 R 1.5: V = R · I (1.1)R (1.2)R (1.3)() (1.4)Ω() (1.5)0.1Ω ∼ 1(10?)GΩ 1Ω ∼ 5.1MΩ1/4 ∼ 1/2W Ni-Cr 0.2Ω ∼ 10MΩ1/8 ∼ 1W 0.1Ω ∼ 100kΩ1/2 ∼ 5W 0.01Ω ∼ 75kΩ1 ∼ 40W 22Ω ∼ 10MΩ1/10 ∼ 1/2W4 8 MΩ GΩ 100kΩ ∼ 1GΩ1/4 ∼ 2W4 8 () () 2 3 (10 · a + b) × 10 d Ω(2 ) (1.6)(100 · a + 10 · b + c) × 10 d Ω(3 ) (1.7)(1.8)

8 1 : (2 )1.2.6 1.6: C ?? (??)Q = C · V (1.9)I = dQdt = C dV(1.10)dt V

1.2. 9 1.7: : (): a b dabcd C ω cos 1.8: V = V 0 cos(ωt) (1.11)I = C dVdt = −CωV 0 sin(ωt) = −I 0 sin(ωt) (1.12)V 0 = I 01ωC Z Z =1ωC(1.13)(1.14) V |V | V = V 0 e iωt (1.15)Re(V ) = V 0 cos(ωt) (1.16) 1.9:

I 1.10: V10 1 : (2 ) I |I| ω I = C dVdt = iωCV 0e iωt (1.17)Re(I) = −ωCV 0 sin(ωt) = −I 0 sin(ωt) (1.18)1V 0 = I 0ωC(1.19) ω ω I = C dVdt(1.20)V =IiωC(1.21)Z = 1/iωC (1.22) : () (1.23) : (1.24) F() pF µF nF 1pF ∼ 47000µF 1F ∼ 100F ?? () 1000pF ∼ 0.1µF 0.01µF ∼ 1µF 2 ∼ 3 PET0.001µF ∼ 10µF 1000pF ∼ 1µF 0.1µF ∼ 47000µFOS-CON () ()1µF ∼2200µF tan δ tan δ 0.1µF ∼ 100µF

1.2. 11 1.11: DC 1kV ∼ 10kV 500 ∼ 5000pF

12 1 : (2 ) 1.12: OS-CON () () () () 1 ∼ 10 6 F 3 abc (10 · a + b) × 10 c pF (1.25)”104” (10 · 1 + 0) × 10 4 pF = 1 × 10 −7 F = 0.1µF (1.26) 0 R C = 4πε 0 R (1.27) 6.4 × 10 6 m ε 0 = (4π) −1 c −2 × 10 7 = 8.85 × 10 −12 F · m −1 C = 7.1 × 10 −4 F 1F (2008/4/19 )

1.2. 131.2.7 L 1.13: (??)V = L dIdt(1.28)V = iωL · I (1.29)iωL (1.30)() (1.31) (1.32)H() (1.33)1µH ∼ V100µH 1.14: I () 3 abc (10 · a + b) × 10 c µH (1.34)”104” (10 · 1 + 0) × 10 4 µH = 0.1H (1.35)1.2.8 pn

14 1 : (2 ) 1.15: p n (carrier) p (positive) carrier n (negative) carrier n (As) (P) 5 p (B) 3 p n p 1.16: p n ()pn 1V 2 ∼ 5V ( ) ] eVI = I s[exp − 1k B T LED Si GaAs 2V - pn n(1.36)

1.2. 15 1.17: pn 1.18: 1.2.9 (FET) 1.2.10 pnp npn pnp n NPN n (n+) n -

16 1 : (2 ) 1.19: pn () 1.20: ON I C = βI B (1.37)β = 100 ∼ 500 (1.38)β h FE 1.21: 2SAxxxx, 2SBxxxxx, 2SCxxxxx, 2SDxxxx ( 2Nxxxx)2SAxxxx PNP 2SBxxxx PNP 2SCxxxx NPN

1.2. 172SDxxxx NPN NPN PNP () ()2SA1048/2SC2458() 2SA1015/2SC1815 2SA1428/2SC3668() (I C < 2(A))2SC3113() h F E = β = 600 ∼ 3600 2SC2668() 100MHz 2SC3605() 1GHz 1.22: 1.23:

18 1 : (2 )1.2.11 FET-FET MOS-FET 2 1.24: FET 1.25: FET

1.2. 191.2.12 ()( GND ) () () (2 ) 7 LM7171 ( 741 )10 µA741 = 2mVSR = 0.5V/µs4558 2 = 0.5mVGB = 3MHzSR = 1V/µsNJM4580 2 = 0.3mVGB = 15MHzSR = 5V/µsLF356 FET ()GB = 5MHzSR = 7.5V/µs = 10000pFTL071/TL072/TL074 JFET GB = 3MHzSR = 13V/µsTL071 1 TL072 2 TL074 4 TL081/TL082/TL084 JFET GB = 3MHzSR = 13V/µsTL081 1 TL082 2 TL084 4 LM6361 GB = 50MHzSR = 300V/µsA ≥ 1LM6364 GB = 175MHzSR = 300V/µsA ≥ 5LM6365 GB = 725MHzSR = 300V/µsA ≥ 25LM7171 GB = 200MHzSR = 4100V/µsA ≥ +2or−1 = 100mAAD829 GB = 750MHzSR = 230V/µs = 2nV/ √ Hz ( 10 ∼ 20nV/ √ Hz)OP-07 (DC ) = 60µV ( 0.5 ∼ 5mV)GB = 0.5MHzSR = 0.17V/µsOP-27 (DC ) = 30µV ( 0.5 ∼ 5mV)GB = 8MHzSR = 2.8V/µsOP-37 (DC ) = 30µV ( 0.5 ∼ 5mV)GB = 63MHzSR = 17V/µsA ≥ 25 1.26:

20 1 : (2 )+- 1.27: 1.3 1.28: 1.3.1 100V AC GND () () V r ∆V R r R I ∆W W (??)r ≪ R (1.39)∆W ≪ W (1.40)I =VR + r ≃ V R(1) (1.41)W = V · I = Const (2) (1.42)∆V = r · VR(3) (1.43)(1) (3) ∆W = ∆V · I = r V R· I = r(V I)2V IR = r W 2V 2 = r W 2V 2 (1.44)W r V ∆W

1.3. 21I+rV ∆V∆WRVW 1.29: AC-DC DC-DC DC AC DC 1.3.2 2 +V, -V COM GND COM +V, -V RefferenceGND GND COM, +V, -V +V, -V COM () ( 100V ) 500MHz GHz FFT 0.001Hz ∼ 500MHz ()sin 1ns ∼ 1sec () (AC, DC) (AC, DC) (500Ω ∼ 50MΩ)

22 1 : (2 ) 15W [dB] = G V = 20 log 10 A V = 20 log 10V outV in(1.45) = G I = 20 log 10 A I = 20 log 10I outI in(1.46) = G W = 10 log 10 A P = 10 log 10P outP in(1.47) () 2 10 = 10 log 10 A P = 10 log 10P outP in= 10 log 10 10 = 10 (1.48)10[dB] 10 √ 10 = 20 log 10 A V = 20 log 10V outV in= 20 log 10√10 = 10 (1.49) 10[dB] 1.4 LED 100V 100V 50Ω

232L, C, R (2)2.1 2.1.1 100V AC 100V AC 100V √ 2 × 100V 100V 2 V (t) = V 0 cos (ωt) (2.1)V 2eff = 1 T∫ T0V (t) 2 dt = 1 2 V 20 (2.2)V eff = 1 √2V 0 (2.3) θ V (t) = V 0 cos (ωt) (2.4)I(t) = I 0 cos (ωt + θ) (2.5)P (t) = V (t)I(t) (2.6)P = 1 T= 1 T∫ T0∫ T0V (t)I(t)dt (2.7)V 0 cos(ωt)I 0 cos(ωt − θ)dt (2.8)= 1 2 V 0I 0 cos θ = V eff I eff cos θ (2.9)2.1.2 e iα = cos α + i sin α (2.10)e iπ/2 = i (2.11)

24 2 L, C, R (2 )˜ã = a 0 + ia 1 (2.12)ã ∗ = a 0 − ia 1 (2.13)√ã = a 2 0 + a2 1 exp (i · atan(a 1/a 0 )) (2.14)√|ã| = a 2 0 + a2 1 (2.15)Re(ã) = a 0 = 1 2 (ã + ã∗ ) (2.16)2.1.3 V (t) = V 0 cos (ωt + φ) (2.17) () v(t) V (t) = Re(V 0 e i(ωt+φ) ) (2.18)= Re[(V 0 e iφ )e iωt ] (2.19)v(t) ≡ V 0 e i(ωt+φ) (2.20)V (t) = Re[v(t)] (2.21) Ṽ v(t) = V 0 e iφ e iωt = √ 1 V 0 e iφ · √2e iωt2(2.22)= Ṽ √ 2e iωt (2.23)Ṽ = √ 1 V 0 e iφ2(2.24) Ṽ phasoreiωt Ṽ v(t) V (t) () v a (t) = √ 2Ṽae iωt (2.25)v b (t) = √ 2Ṽbe iωt (2.26)v a (t) + v b (t) = √ 2(Ṽa + Ṽb)e iωt (2.27)v a (t) + v b (t) ←→ Ṽa + Ṽb (2.28)

2.1. 25ddt v(t) = d (√2 Ṽ e iωt) (2.29)dt= √ 2(iωṼ )eiωt (2.30)dv(t) ←→ iωṼ (2.31)dt∫v(t)dt =∫ √2Ṽ e iωt dt (2.32)= √ 2( 1iω Ṽ )eiωt (2.33)∫v(t)dt ←→ 1iω Ṽ (2.34)2.1.4 R,L,C v(t) i(t)( i ...) Z v(t) = Z · i(t) (2.35) v(t) i(t) Ṽ Ĩ Ṽ = Z · Ĩ (2.36)Z Re[Z] (Ω) : (2.37)Im[Z] (Ω) : (2.38) Z Y Y ≡ 1/Z (S) : (2.39)G ≡ Re[Y ] (S) : (2.40) Ω() S () G S V = ZI I = Y V

26 2 L, C, R (2 ) V (t) I(t) V (t) = R · I(t) (2.41)I(t) i(t) v(t) = R · i(t) (2.42)Ṽ = R · Ĩ (2.43)Z = R (2.44) R G ()G = 1/R (2.45) Ω() S() (2008/4/25 ) V (t) I(t) V (t) = 1 ∫I(t)dt (2.46)Cv(t) = 1 C∫i(t)dt (2.47)∫i(t)dt ←→ 1iω Ĩ (2.48)Ṽ =1iωC Ĩ (2.49)Z =1iωC ( DC) Ṽ =(2.50)1iωC Ĩ (2.51)= 1 C e−iπ/2 Ĩ (2.52) 90 −I 0 sin(ωt) V 0 cos(ωt) (??)

2.2. 271.5I1V0.5-2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2t-0.5-1-1.5 2.1: () V (t) I(t) V (t) = L d I(t) (2.53)dtL v(t) = L d i(t) (2.54)dtdi(t) ←→ iωĨ (2.55)dtṼ = iωL · Ĩ (2.56)Z = iωL (2.57) ( DC) Ṽ = iωLĨ (2.58)= Le iπ/2 Ĩ (2.59) 90 90 I 0 sin(ωt) V 0 cos(ωt) (??)2.2 R L ω V (t) = Re[V 0 · e iωt ] I(t) (??)

28 2 L, C, R (2 )1.51VI0.5t-2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2-0.5-1-1.5 2.2: () 2.2.1 2.3: R L ω V (t) = R · I(t) + L dI(t)dtv(t) = R · i(t) + L di(t)dt(2.60)(2.61)v(t) = V 0 e iωt (2.62)i(t) = I 0 e i(ωt+φ) (2.63)V 0 e iωt = (R + iωL)e iφ I 0 e iωt (2.64)V 0 = (R + iωL)e iφ I 0 (2.65)= √ R 2 + (ωL) 2 e i·atan(ωL/R) e iφ I 0 (2.66) φ I 0 V 0 φ = −atan(ωL/R) (2.67)I 0 =V 0√R2 + (ωL) 2 (2.68)i(t) =V 0√R2 + (ωL) 2 e−i·atan(ωL/R) · e iωt (2.69)I(t) = Re[i(t)] (2.70)

2.2. 29 R L V R = R · I(t) (2.71)V L = L dI(t)(2.72)dt2.2.2 V (t) = R · I(t) + L dI(t)dtv(t) = R · i(t) + L di(t)dt(2.73)(2.74)Ṽ = RĨ + iωLĨ = (R + iωL)Ĩ (2.75)= √ R 2 + (ωL) 2 e i·atan(ωL/R) Ĩ (2.76)Ĩ =1√ e−i·atan(ωL/R) ṼR2 + (ωL) 2 (2.77)=1√R2 + (ωL) 2 e−i·atan(ωL/R) V 0 e iφ (2.78)2.2.3 R, C, L R L C R, C, L V (t) = R · I(t) + L dI(t)dtv(t) = R · i(t) + L di(t)Ṽ =dt(R + iωL + 1iωC+ 1 ∫I(t)dt (2.79)C+ 1 ∫i(t)dt (2.80)C)Ĩ (2.81)V 0 I 0 2.2.4 R, C, L Ṽ = Z · Ĩ (2.82) Z Z = R + iωL + 1iωC(2.83)

30 2 L, C, R (2 ) 2.4: R L C ω R, C, L √(V 0 = R 2 + ωL − 1 ) 2· I 0 (2.84)ωCV 0 = |Z|I 0 (2.85)√(|Z| = R 2 + ωL − 1 ) 2(2.86)ωC(1) (2) R, C, L ω 0 L = 1/ω 0 C (2.87)ω 0 = 1/ √ LC (2.88) ω 0 (1) (2) (3) (4) 2.3 L, R, C 2.3.1 V in (t) 0() V out (t)

2.3. L, R, C 31 RC () 2.5: () ()RṼ out = Ṽin (1/iωC) + R = 1Ṽin (1/iωCR) + 1(2.89)ω 0 CR = 1, ω 0 = 1/CR (2.90)ω → 0 ω → 0 =⇒ Ṽout → Ṽin · iωCR = ωCR · e iπ/2 · Ṽin (2.91)Ṽin Ṽout 90 ()ω → 0 =⇒ |Ṽout/Ṽin| → ωCR (2.92) ω → ∞ ω → ∞ =⇒ Ṽout → Ṽin (2.93)(2008/5/2 )RC ()?? RC () 1/iωCṼ out = Ṽin (1/iωC) + R = 1Ṽin 1 + iωRC(2.94)ω 0 CR = 1, ω 0 = 1/CR (2.95)ω → 0 =⇒ |Ṽout/Ṽin| → 1 (2.96)ω → ∞ =⇒ |Ṽout/Ṽin| → 1/ωCR (2.97) ()

32 2 L, C, R (2 ) 2.6: () ()LR ?? LR RṼ out = Ṽin (iωL) + R = 1Ṽin 1 + iω(L/R)(2.98)ω 0 (L/R) = 1, ω 0 = R/L (2.99)ω → 0 =⇒ |Ṽout/Ṽin| → 1 (2.100)ω → ∞ =⇒ |Ṽout/Ṽin| → R/ωL (2.101) () 2.7: LR () (): RC RC () RC () RC RC ω 1 = 1/R 1 C 1 , ω 2 = 1/R 2 C 2 (2.102)ω 1 < ω 2 (2.103)?? RC C 1 V in (R 1 C 1 )

2.3. L, R, C 33 () 2.8: RC () ()2.3.2 LC LC (??) R L R C L Ciω/RCṼ out = Ṽin (1/LC) − ω 2 + (iω/RC) (??)(2.104)ω 0 = 1 √LC(2.105)Ṽ out = Ṽin (2.106)C L 90 (C)90 (L) L C C L Ṽ out = iωL · ĨL = 1iωC · ĨC (2.107)ω 0 =1√LC(2.108)iω 0 L · ĨL =1iω 0 C · ĨC (2.109)i√LC · ĨL = −i√LC · ĨC (2.110)Ĩ L + ĨC = 0 (2.111)

34 2 L, C, R (2 ) ω 0 = 1/ √ LC L C L, C 0 C ω 0 Ṽin R C L Ṽout = Ṽin R Ṽout = Ṽin R C L Ṽout = Ṽin 1 2.9: LC () ()(2007/5/18 )2.3.3 DC IC IC 0 ???? () IC DC AC ?? IC V CC GND () AC IC 0.1µF 2.4 ???? RC RC

2.4. 35 2.10: 2.11: R = 1.6kΩC = (103) = 0.01µF ω 0 = 2πf 0 = 1/CR (2.112)f 0 =12πCR = 12π · 1.6 × 10 3 Ω · 0.01 × 10 −6 = 10kHzF(2.113)?? LC R = 10kΩC = (104) = 0.1µF = 0.1 × 10 −6 FL = (104) = 10 × 10 4 µH = 10 × 10 −2 H ω 0 = 2πf 0 = 1/ √ LC (2.114)f 0 =12π √ LC = 12π · √10 = 1.6kHz× 10 −2 · 0.1 × 10−6 (2.115) 1.6kHz 1 L = (104) = 10 × 10 4 µH = 10 × 10 −2 H ∼ 100Ω (??)L R 2.12:

36 2 L, C, R (2 )1time10 11 12 13 14 15 msVIN+0.000 pV-VSIN+ SINR110E3Ω+ C11E-7F-VOUT+0.000 pV-V0L11E-1H-1VOUTVINtime10 11 12 13 14 15 ms1VIN+0.000 pV-VSIN+ SINR110E3Ω+ C11E-7F-RL100ΩVOUT+0.000 pV-V0L11E-1H-1 2.13: LC(R) 1.6kHz VOUTVIN

373 (1)3.1 V (t)I(t) v(t)i(t) Chapter v(t)i(t)V (s)I(s) 3.1.1 f(t) F (s) F (s)≡∫ ∞0f(t) · exp (−st) · dt (3.1)f(t) → F (s) (3.2)δ(t) 1 (3.3)⎧⎨0, t < 0 step(t) =1/s (3.4)⎩1, t > 0t1s 2 (3.5)t 2 2s 3 (3.6)11(n − 1)! tn−1 s n (3.7)exp(−at) 1/(s + a) (3.8)sin(at) a/(s 2 + a 2 ) (3.9)t · exp(−at) 1/(s + a) 2 (3.10)exp(−at) · sin(bt) b/ [ (s + a) 2 + b 2] (3.11)exp(−at) · f(t) F (s + a) (3.12)f(t/a) a · F (as) (3.13)df(t)dts · F (s) − f(0) (3.14)

38 3 (1 )∫ t0∫ t0d 2 f(t)dt 2 s 2 F (s) − sf(0) − f ′ (0) (3.15)f(t ′ ) · dt ′ F (s)/s (3.16)f(t − t ′ ) · g(t ′ ) · dt ′ F (s) · G(s) (3.17)3.1.2 d 2 f(t)dt 2+ 4 df(t) + 13f(t) = 0dt(3.18)f(0) = 0, f ′ (0) = 1 (3.19)s 2 F (s) − 1 + 4sF (s) + 13F (s) = 0 (3.20)1F (s) =s 2 + 4s + 13 = 1 33 (s + 2) 2 + 3 2 (3.21)f(t) = 1 3 e−2t sin(3t) (3.22)3.2 3.2.1 RC ?? RC t = 0 v out (t) = 1 C∫ tV out (s) = 1 C0I(s)sI(s) 1V out (s) = V in (s)1 + sRC1Ṽ out = Ṽin 1 + iωRC iω s i(t ′ )dt ′ = v in (t) − i(t)R (3.23)= V in (s) − I(s)R (3.24)(3.25)(3.26)

3.2. 39 RC v in (t) V in (s) ⎧⎨0 t < 0 v in = v 0 · step(t) =(3.27)⎩v 0 t > 0V in (s) = v 0 /s (3.28)V out (s) = V in11 + sRCV out (s) = v 0s11 + sRC= v 0( 1s − 1s + (1/RC))(3.29)(3.30)(3.31)v out (t) = v 0 · (step(t) − exp(−t/RC)) (3.32)exponential v 0 /RC v 03.2.2 LC ?? LC t = 0 ∫ tv out (t) = L di L(t)= 1 i C · dt = v in (t) − R · [i C (t) + i L (t)] (3.33)dt C 0i L (0) = 0 (3.34)V out (s) = L · s · I L (s) = 1 I CC s = V in(s) − R · [I C (s) + I L (s)] (3.35)s/RCV out (s) = V in (s)(1/LC) + s 2 + (s/RC)iω/RCṼ out = Ṽin (1/LC) − ω 2 + (iω/RC)(3.36)(3.37) iω s iω s

40 3 (1 ) v 0 · step(t) =⎧⎨0 t < 0⎩v 0 t > 0(3.38)V in (s) = v 0 /s (3.39)V out (s) =v 0 /RC(1/LC) + s 2 + (s/RC)(3.40)=v 0 bRCb (s + a) 2 + b 2 , a = 1√12RC , b = LC − 14R 2 C 2 (3.41)v 0v out (t) = · exp(−at) · sin(bt) (3.42)RCb3.2.3 1) ṼinṼout 2) iω s ṼinṼout V in (s)V out (s) s 3) v in (t) V in (s) 2) 4) V out (s) = (s ) v out (t) 3) 5) V out (s) = (s ) v out (t) 3.2.4 ???? R 1 C C R 1 11R + iωC = R 1(3.43)1 + iωCR 1 R 2 R 2R 1=1+iωCR 1+ R 2R 2 + iωCR 1 R 2R 1 + R 2 + iωCR 1 R 2(3.44)iω s F (s) F (s) =a≡R 2 + sCR 1 R 2R 1 + R 2 + sCR 1 R 2=1CR 1,b ≡ 1 C( 1R 1+ 1 R 2)s + 1CR 1s + 1CR 1+ 1CR 2=s + 1CR( 1) = s + as + 1 C+ 1 s + bR 2v in (t) v out (t) V in (s) V out (s) (v in (t) = v 0 exp −t )= v 0 exp (−at) (3.47)RC 1V in (s) = v 01s + a1R 1(3.45)(3.46)(3.48)

vinvoutCR1R20t vin=v0exp(-t/R1C)3.3. 41V out = F (s)V in (s) = s + as + b · v 10s + a = v 10(3.49)s + bv out = v 0 exp (−bt) (3.50) 3.1: 3.3 LC(R) ??R = 10kΩC = (104) = 0.1µF = 10 −7 FL = (104) = 10 × 10 4 µH =0.1H v out (t) =a =b =v 0· exp(−at) · sin(bt) (3.51)RCb12RC = 12 × 10 4 = 500 =⇒ τ ≡ 1/a = 2msec (3.52)× 10−7 √ √1LC − 14R 2 C 2 = 10.1 × 10 −7 − 14 × 10 8 × 10 −14 = 9987 ∼ 104 (3.53)ω ≡ b, f = ω = 1.59kHz =⇒ T = 628µsec (3.54)2π

42 3 (1 )VIN+0.000 pV-VPULSE+ PLSR110E3Ω+-C11E-7FL11E-1HVOUT+0.000 pV-Vtransient1time0 1 2 3 4 5 ms0V-1VOUTtransient0.1VINtime0 1 2 3 4 5 ms0.0-0.1VOUT 3.2: LC(R)

4344.1 4.1.1 AM FM 4.2 ()L C (1N60) () () 4.1: () ()4.3 4.4

455 (2)5.1 ( MHz ) 5.1.1 a b L = Φ I = µ ln (b/a)2π(5.1) b → ∞ log ln (b/a) ∼ 1 L ∼ µ 2π = 2 × 10−7 H/m = 0.2µH/m (5.2)f = 1MHz f = 1GHz 1m |Z| = |iωL| ∼ 1.3Ω/m f = 1MHz (5.3)∼ 1.3kΩ/m f = 1GHz (5.4)( ∼ 10nH/m http://www.miyazaki-gijutsu.jp f = 100kHz 1Ω/m = 1 × 10 −8 H/m ∼ 10 −6 H/m )5.1.2 a b C 2πεC =ln (b/a) b → ∞ log ln (b/a) ∼ 1 C ∼ 2πε = 56 × 10 −12 F/m = 56pF/m (5.6) pF R ∼ 0.01Ω R C () f = ω/2π = 1/2πRC f ∼ 280GHz (5.7)(5.5)

46 5 (2 )5.1.3 L C pFµH 104 pFµH 5.1.4 dl f I 0 exp(iωt), 2πf = ω dl θ r () ⃗P = 1 2 ⃗ E × ⃗ H (5.8)P (θ) =√µ0( ) 2 √ Idlsin 2 µ0θ =λr1ε 0 8√ (µ0 fIdlε 0 c( ) 21 fIdlsin 2 θ (5.9)ε 0 8 cr) 2(5.10)P tot = π 3√µ0= 120π = 377Ω (5.11)ε 0f = 1MHz f = 1GHz I = 1A dl = 1m P tot = 0.0044W/m f = 1MHz (5.12)= 4400W/m f = 1GHz (5.13)5.2 1kHz ∼ 1GHz (1) TEM (2) ( C L )5.2.1 ???? 2 3D2V JIS RG-58A/U MIL JIS MIL

5.2. 47 5.1:

48 5 (2 ) 5.2:

5.2. 495.2.2 ±Q r E r V E r =Q2πεrV = V a − V b = Q2πε ln b a C C = Q V = 2πεln (b/a)(5.14)(5.15)(5.16) () I B ϕ Φ B ϕ = µI2πrΦ =∫ baB ϕ dr = µI2π ln b a L (5.17)(5.18)L = Φ I = µ ln (b/a) (5.19)2π GND C L R C (≫ 1/iωC) R L (≪ iωL) ?? 5.3: ω I(z)e iωt V (z)e iωt Z L Z L = R L + iωL (5.20)→ iωL (for R L → 0) (5.21) ∆z Z L ∆z (5.22)

50 5 (2 ) I −∆V −∆V = Z L ∆z · I = (R L + iωL)∆z · I (5.23) Z C ∆z 1∆zR C+ iωC · ∆z=Z C =1 11R C+ iωC ∆z = Z C∆z11R C+ iωC ∆z Y C ( Z C ∆z Y C ∆z ) R C G C (G C = 1/R C )(5.24)(5.25)1Y C = = 1 + iωC = G C + iωC (5.26)Z C R C→ iωC (for R C → ∞) (5.27) ∆I ∆I = − VZ C /∆z = −Y C∆z · V (5.28)dVdzdIdz= −Z L · I = −(R L + iωL)I (5.29)= −Y C · V = −(G C + iωC)V (5.30)|R L | ≪ |iωL| (5.31)|R C | ≫ |1/iωC| → |G C | ≪ |iωC| (5.32) R L = 0G C = 0 Y C = iωCZ L = iωL d 2 Idz 2 = Y C Z L · I = −ω 2 LCI (5.33)d 2 Vdz 2 = Y C Z L · V = −ω 2 LCV (5.34)I(t, z) = I 0 exp [iω(t ∓ √ LCz)] (5.35)V (t, z) = V 0 exp [iω(t ∓ √ LCz)] (5.36)∓ − +z + −z v v =1√LC(5.37)ω

5.2. 51 |R L | ≪ |iωL| |G C | ≪ |iωC| I(t, z) = I exp (iωt) = I 0 exp (iωt ∓ γz) (5.38)= I 0 exp (iωt ∓ (iβ + α)z) = I 0 exp (i(ωt ∓ βz) ∓ αz) = I 0 exp (iω(t ∓ √ LCz) ∓ αz) (5.39)V (t, z) = V exp (iωt) = V 0 exp (iωt ∓ γz) (5.40)= V 0 exp (iωt ∓ (iβ + α)z) = V 0 exp (i(ωt ∓ βz) ∓ αz) = V 0 exp (iω(t ∓ √ LCz) ∓ αz) (5.41)γ = α + iβ = √ Y C Z L (5.42)β = ω √ LC (5.43)α = R √L C2 L + G √C L(5.44)2 C ()γ α β β ∓ − +z + −z v v = ω β = ωω √ LC = 1 √LC(5.45)ω α +z −z exp R C = ∞ → G C = 0R L = 0 α = 0 I V Z 0 ??????√ZLV= V 0= ± = ±Z 0 (5.46)I I 0 Y√ CZLZ 0 =(5.47)Y C Z L = iωLY C = iωC Z 0 =√LC(5.48) +z−z 2 +z () V + I + −z () V − I − I(z)e iωt (= I + e −(iβ+α)z + I − e (iβ+α)z) e iωt → ( I + e −iβz + I − e iβz) e iωt (for α → 0) (5.49)V (z)e iωt (= V + e −(iβ+α)z + V − e (iβ+α)z) e iωt → ( V + e −iβz + V − e iβz) e iωt (for α → 0) (5.50)??V +I += Z 0 , V −I −= −Z 0 (5.51)Z 0 α β (Advanced)Y C = G C + iωC (5.52)Z L = R L + iωL (5.53)

52 5 (2 ) γ γ = √ Y C Z L = √ G C R L + iω(G C L + R L C) − ω 2 LC = α + iβ (5.54)x + iy = √ x 2 + y 2 exp (i · atan(y/x)) (5.55) √ i |R L | ≪ |iωL| (5.56)|R C | ≫ |1/iωC| → |G C | ≪ |iωC| (5.57)iω √ LC γ = √ Y C Z L = √ G C R L + iω(G C L + R L C) − ω 2 LC (5.58)= (iω √ LC) ·√G [CR L GC(iω √ ) 2− iωC + R ]L+ 1 (5.59)ωLLC≃ (iω √ [LC) · 1 − i (GC2 ωC + R )]L= iω √ LC +ωL[G C2√LC + R √ ]L C= iβ + α (5.60)2 Lβ = ω √ LC (5.61)α = R L2√CL + G C2√LC(5.62)5.2.3 2πεC =(5.63)ln (b/a)L = µ ln (b/a) (5.64)2π Z 0 √LZ 0 =C = 1 √ µ2π ε ln b (5.65)av = 1 √LC= 1 √ εµ(5.66) ε = (2 ∼ 4)ε 0 µ = µ 0 a,b 50Ω 75Ω 50%∼75% 1m 5nsec 5.2.4 R L R C (??)3D-2V 10m 0.15dB(1/1.02) @ 1MHz0.4dB(1/1.05) @ 10MHz1.5dB(1/1.12) @ 100MHz5dB(1/1.8) @ 1GHz 1km 15dB(1/5.6) @ 1MHz40dB(1/100) @ 10MHz150dB @ 100MHz500dB @ 1GHz

5.2. 535.2.5 5.4: √µ0ε 0= 120π = 377Ω (5.67) z E x H y E x = Ẽ exp [i · (ωt − kz)], E y = E z = 0 (5.68)H y = ˜H exp [i · (ωt − kz)], H x = H z = 0 (5.69)c = ω k = 1 √µ0 ε 0(5.70)∇ × E ⃗ = − ∂ B ⃗ (5.71)∂t⃗B = µ 0H ⃗ (5.72)∂E x ∂H y= −µ 0 (5.73)∂z∂t−i · kẼei·(ωt−kz) = −i · µ 0 ω ˜He i·(ωt−kz) (5.74)Ẽ˜H = µ 0ωk = µ 0c = √ 1 √µ0=(5.75)µ0 ε 0 ε 0Ẽ/ ˜H Z = Ṽ /Ĩ Z = Ẽ/ ˜H Ṽ Ẽ Ĩ ˜H

54 5 (2 )5.2.6 ω ?? Z L = iωLY C = iωC Z 0 =√LC(5.76) 50Ω( 75Ω) 1V 20mA 5.5: 5.2.7 ??Z z = 0 Z 5.6: Z (??)(??)(??) V (z = 0)Z =I(z = 0) = Z V + + V −0(5.77)V + − V −

5.2. 55+z V + z = 0 −z V − r r = V −V += Z − Z 0Z + Z 0(5.78)z = 0 Z Z DC V + V − V − = V +Z − Z 0Z + Z 0(5.79) (z = 0) V V + V − (V = V + + V − = 1 + Z − Z )02= V +Z + Z 0 1 + (Z 0 /Z) = V 2+1 + (Z 0 /Z)(5.80) Z 0 Z = Z 0 V = V +21 + (Z 0 /Z 0 ) = V + (5.81) R V = 2V +11 + (Z 0 /R)(5.82) Z = 0 V = 0 (5.83) V + 0 −V + Z = ∞ V = 2V + (5.84)2V + Z = 1/iωC V = 2V +11 + iωZ 0 CL,R,C RC RC 1Ṽ out = Ṽin 1 + iωRC2 RC Z = iωL V = 2V +11 − i (Z 0 /ωL)(5.85)(5.86)(5.87)

56 5 (2 )LR 1Ṽ out = Ṽin 1 − i (R/ωL)(5.88) Z ?? 50Ω 50Ω

5.2. 57 5.7:

58 5 (2 )5.2.8 2 ??(A) FGZ 0 /2 (B) (C) 1/2 1/4 FanIn-FanOutFanIn-FanOut ( 1MΩ 10MΩ) T 5.8: 5.9:

5.2. 595.2.9 : TEM(Transverse Electric Magnetic) (Advanced)?? a b εµ 5.10: ∇ × E + ∂B∂t= 0 (5.89)1µ ∇ × B − ε∂E ∂t= 0 (5.90)∇ · E = 0 (5.91)∇ · B = 0 (5.92) exp (iωt) ∂(rE r )r∂r∂(rB r )r∂r∂E zr∂ϕ − ∂E ϕ∂z= −iωB r (5.93)∂E r∂z − ∂E z∂r= −iωB ϕ (5.94)∂(rE ϕ )− ∂E rr∂r r∂ϕ = −iωB z (5.95)∂B zr∂ϕ − ∂B ϕ∂z= iεµωE r (5.96)∂B r∂z − ∂B z∂r= iεµωE ϕ (5.97)∂(rB ϕ )− ∂B rr∂r r∂ϕ = iεµωE z (5.98)+ ∂E ϕr∂ϕ + ∂E z∂z+ ∂B ϕr∂ϕ + ∂B z∂z= 0 (5.99)= 0 (5.100)r = a r = b E t = 0()B n = 0() E r B ϕ E ϕ = E z = 0, B r = B z = 0 (5.101)

60 5 (2 )− ∂B ϕ∂z∂(rB ϕ )r∂r∂E r∂z= iεµωE r (5.102)= 0 (5.103)= −iωB ϕ (5.104)− ∂E rr∂ϕ = 0 (5.105)3 1 1 3 B ϕ E r ∂ 2 E r∂z 2 = −εµω 2 E r (5.106)∂ 2 B ϕ∂z 2 = −εµω 2 B ϕ (5.107)E r B ϕ exp [iωt ∓ i √ εµωz] (5.108) z B φ E r I √ µ I 1E r =ε 2π r exp [iωt ∓ i√ εµωz] (5.109)B ϕ = µ I 12π r exp [iωt ∓ i√ εµωz] (5.110)E ϕ = 0, E z = 0 (5.111)B r = 0, B z = 0 (5.112)5.2.10 (?) ± ()5.3 ()2

5.4. 615.3.1 ()2 XXX GND XXX 5.3.2 5.3.3 5.3.4 5.4

636 (2.5)6.1 6.1.1 IC DC 100MHz ??1) R i 2) R o 03) () 4) DC 5) CMRR 6) 0 0 0 6.1: 6.1.2 / A

64 6 (2.5 )V out = A(V + − V − ) = −AV − (6.1)I 1 = (V in − V − )/R 1 (6.2)I 2 = (V − − V out )/R 2 (6.3)V − I 1 = I 2 (6.4)I 1 = (V in − V − )/R 1 = I 2 = (V − − V out )/R 2 (6.5)V − = R 1V out + R 2 V inR 1 + R 2(6.6)A → ∞ V out = −A R 1V out + R 2 V in(6.7)R 1 + R 2AR 2R 2V out = −V in = −(1 + A)R 1 + R 2 ( 1 A + 1)R 1 + 1 A R V in → − R 2V in (6.8)2 R 1V − = R 1V out + R 2 V inR 1 + R 2→ 0 (6.9)V − → 0 V out = −A · V − A → ∞ V out V − → 0 V out = A(V + − V − ) A → ∞ V out V + − V − → 0 V − = V + (6.10)”Vertual Short”“Imaginary Short” () (: )

6.1. 65 R210E3ΩVSIN+ SINVIN+0.000 pV- R11E3Ω-+OPAMPVOUT+ -0.000 pV 6.2: transient5time0 1 2 3 4 5 msV31-1-3-5VOUTVIN 6.3:

66 6 (2.5 ) (??) AR 2R 2V out = −V in = −(1 + A)R 1 + R 2 ( 1 A + 1)R 1 + 1 A R V in (6.11)2 A −A (−A)R 2V out = −V in = −(1 + (−A))R 1 + R 2R 2(1(−A) + 1)R 1 + 1(−A) R 2V in → − R 2R 1V in (6.12) V out ∆V out V out V in R 1 R 2 V − V out = A(V + − V − )V out ()1) Imaginary Short 2) 3) 6.2 6.2.1 V − = V + = 0 (6.13)I = V in − V −R 1= −V in /R 1 (6.14)V out = V − + IR 2 = 0 + (−V in /R 1 )R 2 = − R 2R 1V in (6.15) − R2R 10V V − R 1 R 1

6.2. 67 R210E3ΩVSIN+ SINVIN+0.000 pV- R11E3Ω-+OPAMPVOUT+ -0.000 pV 6.4: transient5time0 1 2 3 4 5 msV31-1-3-5VOUTVIN 6.5:

68 6 (2.5 )6.2.2 OpAmp V out = R 1 + R 2R 1V − (6.16)Vertual Short V − = V + = V in (6.17)V out = R 1 + R 2R 1V in (6.18) R 1+R 2R 1> 1 OPAMPVSIN+ SINVIN+0.000 pV-+-R29E3ΩVOUT+ -0.000 pVR11E3Ω 6.6: transient5time0 1 2 3 4 5 msV31-1-3-5VOUTVIN 6.7:

6.2. 696.2.3 R 1 = ∞R 2 = 0 R 1+R 2R 1= 1 OpAmp () OpAmp IC( LH0033 ) OPAMPVSIN+ SINVIN+0.000 pV-+-VOUT+ -0.000 pV 6.8: transient0.5time0 1 2 3 4 5 msV0.30.1-0.1-0.3-0.5VOUTVIN 6.9:

70 6 (2.5 )6.2.4 /V 0 ≡ V − = V + (6.19)(V 1 − V 0 )/R 1 = (V 0 − V out )/R 2 (6.20)(V 2 − V 0 )/R 3 = (V 0 − 0)/R 4 (6.21)V out = R 4R 1R 1 + R 2R 3 + R 4V 2 − R 2R 1V 1 (6.22)R 1 = R 3 R 2 = R 4 V out = R 2R 1(V 2 − V 1 ) (6.23)AMMTR1R11E3ΩR25E3ΩVSIN1+ SINVIN1+0.000 pV-0.000 pAOPAMPVSIN2+ SINVIN2+0.000 pV-AMMTR20.000 pAR31E3Ω-+R410E3ΩVOUT+ -0.000 pV 6.10: /transient3time0 1 2 3 4 5 msV210-1-2-3VOUT VIN2 VIN1 6.11: /

6.2. 716.2.5 ??V − = V + = 0 (6.24)I = V in − V −= V in(6.25)R 1 R 1V out = V − − 1 ∫Idt = − 1 ∫Vindt (6.26)CC R 1 2 1) 2) CF1E-6F+ -VPIN+ PLSVIN+0.000 pV-R1E3ΩAMMTRIN0.000 pAOPAMP-+VOUT+ -0.000 pV 6.12: transient1time0 1 2 3 4 5 msV0-1VOUTVIN 6.13:

72 6 (2.5 )RF5E2ΩCF1E-6F+ -VPIN+ PLSVIN+0.000 pV-R1E3ΩAMMTRIN0.000 pAOPAMP-+VOUT+ -0.000 pV 6.14: transient0.5time0 1 2 3 4 5 msV0.40.30.20.10.0-0.1VOUTVIN 6.15: 6.16:

6.2. 736.2.6 (Advanced)RF5E2VPIN+ PLSVIN+0.000 pV-R1E3C1E-6F+ -AMMTRIN0.000 pAOPAMP-+VOUT0.000 pV 6.17: 6.18:

74 6 (2.5 )6.2.7 RC RC 2 2 1 1 R21E2C21E-7F+ -VPIN+ PLSVIN+0.000 pV-R11E3C11E-6F+ -AMMTRIN0.000 pAOPAMP-+VOUT0.000 pV 6.19: 6.20:

6.3. 756.3 6.3.1 741 6.21: LM741 (page1)

76 6 (2.5 ) 6.22: LM741 (page2)

6.3. 77 6.23: LM741 (page3)

78 6 (2.5 ) 6.24: LM741 (page4)

6.3. 796.3.2 −10 R 1 R 2 1) R 1 = 1Ω, R 2 = 10Ω2) R 1 = 1kΩ, R 2 = 10kΩ3) R 1 = 10kΩ, R 2 = 100kΩ4) R 1 = 10MΩ, R 2 = 100MΩ 4 1) 4) 1) 1Ω 100Ω R 0 = 100Ω R 2 4) () 741 2MΩR 1 FET LF356 10 12 Ω LF356 3pF R 2 = 100MΩ 2) 3) 6.3.3 GB 10Hz GB (MHz) GB 6.25: GB

80 6 (2.5 )6.3.4 (V/µsec) GB 6.26:

6.3. 816.3.5 (Advanced)RMS(1σ) ∆V in (f)[nV/ √ Hz] (6.27)?? AD797 AD797 30kHz ∼ 100kHz 10 ∆V 2out = A ×= 10 ×∫ f1∆Vin(f)df 2(6.28)f 0∫ 100[kHz]30[kHz](0.9[nV/ √ Hz]) 2 df (6.29)= 10 × (100 − 30)[kHz] × 0.81[nV 2 /Hz] = 5.67 × 10 5 [nV 2 ] (6.30)∆V out = 750[nV] (6.31) Rppt Mean Square 1σ 3σ 3 ( RMS )1) 2) AD797 Input Voltage Noise Spectral Density5INPUT VOLTAGE NOISE ñ nV/ Hz4321010 100 1k 10k 100k 1M 10MFREQUENCY ñ Hz 6.27: Ultralow Noise, Ultralow Distortion OpAmp AD797

82 6 (2.5 )6.3.6 (Advanced) 0 0 0 () 2 1) V BE V os 2) h FE I B I os ??V + = 0 V + = V os R 2 I os ∆V out (∆V out = 1 + R )2V os + R 2 I os (6.32)R 1R 2 GND ?? GND R 1 R 2 R C =R 1 R 2R 1 + R 2(6.33)?? 6.28:

6.3. 83R210E3ΩR11E3ΩOPAMP-+RC91E1ΩRVR10E3Ω+VCCM15V 6.29:

84 6 (2.5 )6.4 6.4.1 OpAmp FET OpAmp GND (CF) (eg. ∼ 0.1pC) (eg.∼ pF) (?? C CABLE pF C CABLE C FC F C F C F OpAmp A Q Q = Q cable + Q F (6.34)Q cable = V in C cable (6.35)V out = −A · V in (6.36)Q F = −(V out − V in )C F (6.37)Q F= (A + 1)C F(6.38)Q cable C cableQ cable =Q F =C cableQ(A + 1)C F + C cable(6.39)(A + 1)C FQ(A + 1)C F + C cable(6.40)OpAmp C F (A + 1) C F RF10E6ΩIPINPLSCCABLE+- AMMTRIN 0.000 pA1E-12F CF2E-12F+ - OPAMP-+VOUT+ -0.000 pV 6.30:

6.4. 856.4.2 (Advanced)V ref V in VIN+ SINVREF+ 5VRM10E3ΩRP10E3Ω+OPAMP-VOUT+ -0.000 pV 6.31:

86 6 (2.5 )6.4.3 ??[V1V out = −R f + V 2+ V 3+ V ]4R 1 R 2 R 3 R 4(6.41)R 2 = R 1 /2 (6.42)R 3 = R 1 /4 (6.43)R 4 = R 1 /8 (6.44) V 4 MSB 2 DAC(Digital Analog Converter) ??R-2R DACR18E3V1+ SINVIN1+0.000 pV-R24E3RF10E3V2+ SINVIN2+0.000 pV-R32E3OPAMP-+VOUT0.000 pVV3+ SINVIN3+0.000 pV-R41E3V4+ SINVIN4+0.000 pV- 6.32:

6.4. 87 6.33: R-2R DAC

88 6 (2.5 )6.4.4 R 1 () V ref = 0 V out = +V CC ← V in < 0 (6.45)V out = −V CC ← V in > 0 (6.46)V ref R 1 R 2 V out GND ??VSIN+ SINVIN+0.000 pV-RM10E3Ω-OPAMP+R140E3ΩVOUT+ -0.000 pVVREF+0.000 pV-R210E3Ω 6.34: 6.35:

6.4. 896.4.5 (Advanced)+V CC R F C in V ref +V CC −V CC C in V ref −V CC +V CC V ref (T = 2C in R F · ln 1 + 2R )2R 1RF100E3Ω(6.47)VIN+0.000 pV-+-CIN1000E-12F-OPAMP+R15E3ΩVOUT+ -0.000 pVVREF+0.000 pV-R250E3Ω 6.36:

90 6 (2.5 )6.4.6 RC (Advanced) RC C = C 1 = C 2 R = R 1 = R 2 f 0 =12πCR f 0 1/3 (6.48)R a + R bR a= 1 + R b> 3R a(6.49)R b> 2R a(6.50)R b /R a > 2 2 2.1 R21E3Ω+ C2159E-9F-R11E3ΩC1159E-9F- +VIN+0.000 pV-+OPAMP-RB21E2ΩVOUT+ -0.000 pVVREF+0.000 pV-RA1E3Ω 6.37: RC

6.5. 916.5

937 (2)7.1 AC ?? 2 DC AC DC V AC v AC 0DC AC 7.1.1 DC DC AC AC DC ??DC AC ??DC V out V CC R 1 R 2 R 2V out = V CC (7.1)R 1 + R 222K= 15 ·= 2.7V (7.2)100K + 22KR 1 R 2 DC V CC15=0.12mA (7.3)R 1 + R 2 100K + 22KAC C 1 ?? v v R 1 R 2 i 1 i 2 i 1 = − v R 1(7.4)i 2 = v R 2(7.5)( vi = i 2 − i 1 = + v ) ( 1= v + 1 )R 1 R 2 R 1 R 2(7.6)v =(i) (7.7)1R 1+ 1 R 21R = ( ) (7.8)1R 1+ 1 R 2 R 1 R 2 R 1 R 2 C 1 R =1= 18K(1/22K) + (1/100K)(7.9)f 0 = ω 0 /2π = 1/2π(18K × 10µ) = 0.88Hz (7.10)

iR2i1viR2i1R194 7 (2 )vR1 7.1: AC i2VCC15V- +i2R1100E3ΩC110E-6F- +VIN+0.000 pV-VSININ+ SINR222E3ΩVOUT+2.705 V- 7.2: Vtransient43time0 20 40 60 80 100e-4s210-1VINVOUT 7.3: ±2V 1kHz 7.1.2 AC DC

7.1. AC 95R122E3ΩVIN+0.000 pV-VSININ+ SINR2100E3Ω+-C110E-6FVOUT+0.000 pV- 7.4: AC DC

1. する.その 2. の 3. 新 エミッタの コレクタに たな 結 電 果 結 子 , 果 の 存 電 型 ,エミッタの 供 子 在 流 NPN 給 はベース していた 空 がないので,コレクタ 流 乏 れない.1. 層 側 電 ベースに 子 移 は,プラス の 動 移 し,ベースのホールと 動 コレクタ は 中 停 側 の 止 へ 電 する. 移 子 動 は する.ベース(エミッタ)から 停 止 結 合 . 空 乏 層 電 ホール を 子 形 成 型 トランジスタプレーナ に 2. 3. ことになり, 4. 向 ベースには 電 コレクタにはベースを コレクタ-エミッタ かって 子 の 中 一 引 再 の 部 き 結 大 全 新 はベースからのホールと NPN 寄 合 部 体 たにホールが せられる. する 分 としてコレクタ-エミッタ の 間 電 子 通 流 はコレクタへ じてエミッタから はベースに 流 れ 流 ホールが 込 れ むため,エミッタ 型 込 再 む流 トランジスタ(NPN)の 結 れ 合 間 込 するが,ベースは 新 に む む. たな 大 電 きな 流 電 に 中 子 電 比 の 供 流 例 電 給 が する. 子 流 薄 がベース 行 れる. いので われる構 造96 7 (2 )7.2 7.2.1 () 7.5: () µm 7.2.2 トランジスタPNP NPN 7.6: 7.2.3 ?????? () I 0[mA] R 0[V] V 0 (V, I) = (1.5[V], 0[mA]) 0[V] R = I = V 0 /R = 1.5[V]/250[Ω] = 6[mA] (V, I) = (0[V], 6[mA])

1.5VVV RI 250ΩI動 作 点 V07.2. 97 2 ?? (V, I) = (1.0[V], 2.0[mA]) V 0 = RI + V (7.11)I = V 0 − V(7.12)R 7.7: 7.2.4 ?? 1 I B I E I C ?? β 200 I B V CE I C I B ≪ I C , I E (7.13)I C ≃ I E (7.14)I C = βI B , β = 200 (7.15)- I C − V CE V 0 = R C I C + V CE + R E I E = R C I C + V CE + R E I C (7.16)V CE = V 0 − (R C + R E ) I C = 6.0[V] − 500[Ω]I C (7.17)V CE = 0 →V 0I C = =6[V] = 12[mA]R C + R E 500[Ω](7.18)I C = 0 → V CE = V 0 = 6[V] (7.19)??I C − V CE I B ?? I B − V BE

698 7 (2 )V 1 = R B I B + V BE + R E I C = R B I B + V BE + R E βI B = (R B + βR E ) I B + V BE (7.20)2.1[V] = (25[kΩ] + 200 · 100[Ω]) I B + V BE (7.21)V BE = 2.1[V] − 45[kΩ] · I B (7.22)??-??- 作 点 V1IC VBE REV0 RCVCEIB400¢IE 7.8: 動 RB2.0 6V 100¢2.1V 1.57.2.5 -2.1-0.7[V] − 0.7[V] 7.3 25k¢7.3.1 (?)1) 2) AC () DC 3) AC

7.3. 991) 0.6 ∼ 0.7V ON/OFF 0.6 ∼ 0.7V On 0.7V 2) 3) 4) 1) : 2) : 3) h F E = β : h F E 2SC2458 O:70-140Y:120-240GR:200-400BL:350-700 f fe h F E h fe 4) (Advanced) f T − I E : h F E = 1 5) (Advanced) C ob : () - C BC

100 7 (2 ) 7.9: 2SC2458 (page1)

7.3. 101 7.10: 2SC2458 (page2)

102 7 (2 ) 7.11: 2SC2458 (page3)

7.3. 1037.3.2 VCC+ 3VRL10E3ΩVIN+0.000 pV-VPIN+ PLSRB1E3ΩQ2SC2458CustomVOUT+2.999 V- 7.12: transient3time0 1 2 sV210VOUTVIN 7.13:

104 7 (2 )7.3.3 ( 1)RC10E3Ω+ C161E-7F-+ C1710E-6F-VCC+ 15VR1100E3ΩAC1.004 mAVIN+0.000 pV-VSIN+ SINC110E-6F- +AB1.908 µAR222E3ΩVB+2.671 V-Q2SC2458CustomAE1.006 mARE2E3ΩVOUT+4.957 V-VE+2.012 V- 7.14: 5 transient6time0 1 2 3 4 5 msV543210-1VOUT VIN VBVE 7.15: v pp = 0.5V 1kHz ??AC GND COM AC ??DC AC V B V CC R 1 R 2 R 222KΩV B = V CC = 15V= 2.7V (7.23)R 1 + R 2 22kΩ + 100kΩ ON () V BE = 0.7V V E = V B − V BE = 2.7 − 0.7 = 2.0V (7.24)

7.3. 105 I E V E R E I E = V E= 2.0V = 1.0mA (7.25)R E 2.0kΩ I B I C I C = βI B (7.26)β = 100 ∼ 500 (7.27)I C = I E = 1.0mA ≪ I B = 2 ∼ 10µA (7.28) R C V C V RC = I C · R C = 1.0mA · 10(kΩ) = 10.0V (7.29)V C = V CC − V RC = 15.0 − 10.0 = 5.0V (7.30)- V CE V CE = V C − V E = 5.0 − 2.0 = 3.0V (7.31)V CE > V BE = 0.7V (7.32) ON R 1 R 2 I bias I B I B I bias =V CC 15V=R 1 + R 2 100kΩ + 22kΩ = 0.12mA ≫ I B = 2 ∼ 10µA (7.33)AC AC v in AC v out v in 0.7V AC v in v B = v E = v in (7.34)R E i E = v ER E= v inR E(7.35)i C = i E = v inR E(7.36)R C v RC = i C · R C (7.37)v out = v C = −v RC = i C · R C (7.38)R C 10kΩ= −v in = −v inR E 2kΩ = −5 · v in (7.39)v out= −5 (7.40)v in-5 AC 5

106 7 (2 )7.3.4 ( 1) (Advanced)1) 5 0.2Vpp 1Vpp2) RC RE 5 (2SC2458 200mW) 3) () 40mA 0.1 − 5mA 1mA 4) 0.6V R E 1V 1) V C ()V C V C 5 V CC − V C ∼ 5 × V E 2) DC β 3) AC 7.3.5 PNP ( 1)(Advanced)NPN PNP RE2E3Ω+ C161E-7F-+ C1710E-6F-VCC+ 15VR222E3ΩAC1.006 mAVIN+0.000 pV-VSIN+ SINC110E-6F- +AB-1.908 µAR1100E3ΩVB+12.329 V-Q2SA1048CustomAE1.004 mARC10E3ΩVE+12.988 V-VOUT+10.043 V- 7.16: PNP 5

7.3. 107transient0.2time0 1 2 3 4 5 msV0.0-0.2VINtransient12time0 1 2 3 4 5 msV11109VOUT 7.17: PNP v pp = 0.5V 1kHz

108 7 (2 )7.3.6 ( 2) R E R C R E 1V V cc = 15V 10 DC AC AC DC DC R E = 2kΩ AC R E = 390Ω AC R C /R E = 10kΩ/390Ω = 26 AC GND AC AC RC10E3Ω+ C161E-7F-+ C1710E-6F-VCC+ 15VR1100E3ΩAC1.004 mAVIN+0.000 pV-VSIN+ SINC110E-6F- +AB1.908 µAR222E3ΩVB+2.671 V-Q2SC2458CustomAE1.006 mAR390ΩVOUT+4.957 V-VE+2.012 V-RE2E3Ω+ C100E-6F- 7.18: ( 2) 26

7.3. 109transient50time0 1 2 3 4 5 msmV3010-10-30-50VINtransient7time0 1 2 3 4 5 msV53VOUT 7.19: ( 2) v pp = 0.05V 1kHz 1.3V

110 7 (2 )7.3.7 ( 1) ( 1) () R OUT = 100kΩ RC10E3Ω+ C161E-7F-+ C1710E-6F-VCC+ 15VR1100E3ΩAC1.004 mAC2510E-6F- +VIN+0.000 pV-VSIN+ SINC110E-6F- +AB1.908 µAR222E3ΩVB+2.671 V-Q2SC2458CustomAE1.006 mAROUT100E3ΩVOUT+0.000 pV-RE2E3Ωtransient1time0 1 2 3 4 5 msV0-1VOUTVIN 7.20: ( 1) 100kΩ R OUT = 10kΩ 10kΩ AC 0 V CC GND R C R OUT R OUT = R C 10kΩ 100kΩ

7.3. 111RC10E3Ω+ C161E-7F-+ C1710E-6F-VCC+ 15VR1100E3ΩAC1.004 mAC2510E-6F- +VIN+0.000 pV-VSIN+ SINC110E-6F- +AB1.908 µAR222E3ΩVB+2.671 V-Q2SC2458CustomAE1.006 mAROUT10E3ΩVOUT+0.000 pV-RE2E3Ωtransient0.5time0 1 2 3 4 5 msV0.30.1-0.1-0.3-0.5VOUTVIN 7.21: ( 1) 10kΩ

112 7 (2 )7.3.8 + C161E-7F+ C1710E-6FVCC+ 15V--R110E3ΩAC9.824 mAVIN+0.000 pV-VSIN+ SINC110E-6F- +AB19.549 µAR210E3ΩVB+7.402 V-Q2SC2458CustomAE9.844 mARE680ΩVE+6.694 V-C210E-6F+ -ROUT680ΩVOUT+0.000 pV-transient1time0 1 2 3 4 5 msV0-1VINVOUT 7.22: 0.5V V E V B 0.6 ∼ 0.7(V) AC R E R OUT ??0A DC V E /R E V E 7.5V 0.7V DC I E = 6.8V/680Ω = 10mA V B V E 0V AC DC R E AC R E R OUT R E = R OUT 340Ω 5V i E = v E /340Ω = 14.7mADC 10mA I E − i E = −4.7mA -(- ) I E = i E = 0 0mA 1) AC AC 2) DC 3) AC DC R E 4) - V CE I C = I E V C = V CC V CE () 5) h F E = β AC+DC

7.3. 1136) AC transient20time0 1 2 3 4 5 msV100-10VIN VOUT VEtransient30time0 1 2 3 4 5 msmA20100AE 7.23: 5V

114 7 (2 )7.3.9 RC39E2Ω+ C161E-7F-+ C1710E-6F-VCC+ 5VR133E3ΩAC493.424 µAQ2SC2458BCustomVIN+0.000 pV-VSIN+ SINC110E-6F- +AB878.856 nAR216E3ΩVB+1.623 V-Q2SC2458ACustomAE490.407 µAAFE2.002 mAVOUT+2.402 V-RACE390ΩRE2E3Ω+ C47E-6F-RFE1200Ωtransient4time0 1 2 3 4 5 msV3210-1VINVOUT 7.24: 5V 7.3.10 h F E 2 1 0.6V 1.2V QD1CustomQD2Custom 7.25:

7.4. 1157.3.11 (Advanced) DC NPN PNP 0 -±0.6V ON R110E3Ω Q2SC2458Custom+ CP1P1E-7F-+ CP2P10E-6F-VCCP+ 5VD1DefaultVSIN+ SIND2Default Q2SA1428CustomVOUT+ -0.000 pVR210E3Ω+ CP1M1E-7F 7.26: -+ CP2M10E-6F-VCCM+ 5V7.4 7.4.1 : ????h fe = 1 f T 2CS2458 80MHz 1MHz ?? A v C bc (1 + A v ) – AC i be – AC i be AC v b AC v e v e = v b i be =11/iωC be(v b − v e ) = 0 (7.41) A v v b i bc =11/iωC bc(v b − (−A v v b )) = (A v + 1)iωC bc v b (7.42)–C bc (A v + 1)C bc r b C bc + C be r b (A v + 1)C bc + C be A v C A AC B GND C B Q = CV A-B C

116 7 (2 ) 7.27: (??RB10Ω+ CBC2E-12F-QIDEALDefault+ CBE2E-12F+ CCE2E-12F-VIN+0.000 pV-R2510ΩVSIN+ SIN+ CBC02E-12F-QIDEAL0Default+ CBE02E-12F+ CCE02E-12F-VOUT+0.000 pV--- 7.28:

7.4. 1177.4.2 MHz nsec () ??RC51E2Ω+ C31E-7F-+ C410E-6F-VCC+ 15VR1100E3ΩAC1.004 mA+ C5100E-6FQ2SC2458CustomVOUT+9.878 V--R222E3ΩRE1E3ΩVE+2.012 V-VIN+8.000 V-VSIN+ SINC110E-6F- +R31E3ΩVQ+1.006 V- 7.29: transienttime0.0 0.2 0.4 0.6 0.8 1.0 us11V97VOUTVIN 7.30: V in 8V DC 1) DC R 1 R 2 V B = 2.7V

118 7 (2 )C 5 AC v B = 02) DC V E = 2.0V AC AC v E = 03) R E R 3 DC V q = 1.0VAC v q = v in4) v E = 0 v q = v in R E i E = −v in /R E5) R C AC i C = i rmEv out = −R C · i C = −R C · i E = v in · (R C /R E )6) R C /R E = 5.1 AC () 7.31:

7.4. 119R C 5.1kΩ R E R 3 500Ω ∼ 100kΩ 10kΩ

120 7 (2 )7.4.3 1) DC 2) (??) RC2E3Ω+ C31E-7F-+ C410E-6F-VCC+ 15VR1100E3ΩR4100E3ΩQ2SC2458TR2CustomVOUT+11.162 V-R556E3Ω+ C71E-7F+ C810E-6F--VVIN+8.000-VSIN+ SINC110E-6F- +R222E3ΩQ2SC2458TR1CustomAE1.926 mARE200ΩR3820Ω+ C51E-7F-+ C6100E-6F- 7.32: Cascodetime0.0 0.2 0.4 0.6 0.8 1.0 us13V121110987VOUTVIN 7.33: V in 8V DC 1) Q2SC2458TR2 DC R 4 R 5 V B2 = 5.2V

7.4. 121C 7 C 8 AC v B2 = 02) Q2SC2458TR2 Q2SC2458TR1 DC V E2 = V C1 = 4.6VAC v E2 = v C1 = 0.0V3) Q2SC2458A DC V B1 = 2.7VAC v B1 = v in4) Q2SC2458A DC V E1 = 2.0VAC v E1 = v in5) R E R 3 C 5 C 6 DC R = R E + R 3 = 1.0kΩAC R = R E = 200Ω6) Q2SC2458A AC i E1 = v in /R E7) AC Q2SC2458B AC i C2 AC Rv out = −i C2 R C = −i E1 R C = −v C in R E8) A = R C /R E = 5Q2SC2458B R C Q2SC2458A Q2SC2458A AC Q2SC2458B f ch = 12.8MHz f ch = 18.0MHz 7.34: () ()

122 7 (2 )7.5 ()...7.6 (Advanced)AC DC () V BE 0.6V −2.5mV/ ◦ C DC DC 7.6.1 R322E2ΩR422E2Ω+ CP1P1E-7F-+ CP2P10E-6F-VCCP+ 5VQ2SC2458TR1CustomQ2SC2458TR2CustomVOUT+0.000 pV-VOUT1+ -2.869 VVOUT2+ -2.869 VVIN1+0.000 pV-VSIN1+ SINVIN+0.000 pV-RE1500ΩRE2500ΩR636E3ΩVIN2+0.000 pV-VSIN2+ SINVC+-1.142 V-Q2SC2458TR3CustomR51E3Ω 7.35: R713E3Ω+ CP1M1E-7F-+ CP2M10E-6F-VCCM+ 5V Tr1 Tr2 Tr1 Tr2 1) Tr3 DC R 6 R 7 V B3 = −2.4V 2) Tr3 DC V E3 = −3.0V3) R 5 Tr3 I E3 = I C3 = (−3.0 − (−5.0))/1kΩ = 2mAi E3 = i C3 = 04) Tr3 R E1 R E2 Tr1Tr2 I E1 = I E2 = 0.5I C3 = 1mAi E1 + i E2 = 0

7.6. (Advanced) 123transient3time0 1 2 3 4 5 msV210-1-2-3VINVOUT 7.36: v in = v 1 − v 2 = 0.5V 5) DC V out1 = V out2 = +5 − 2.2kΩ × 1mA = 2.8V6) AC i E1 + i E2 = 0v in1 − i E1 R E1 =v in2 − i E2 R E2v out1 = −i E1 R 3v out2 = −i E2 R 47) R E = R E1 = R E2 2 i E1 = (v in1 − v in2 )/2R Ei E2 = (v in2 − v in1 )/2R E8) R = R 3 = R 4 2 v out1 = −(v in1 − v in2 ) R2R Ev out2 = −(v in2 − v in1 ) R2R E9) v in = v in1 − v in2 v out = v out1 − v out2 Rv out = −v in1 R E10) A = −R/R ETr3 Tr1 Tr2 DC V out1 V out2 V out Tr1 Tr2 V BE R E1 R E2 V out1 V out2 Tr1 Tr2 V out1 V out2 V out Tr1 Tr2 2 1

124 7 (2 ) OP DC () DC R = R E1 = R E2 = 0 (??) (??)R322E2ΩR422E2Ω+ CP1P1E-7F-+ CP2P10E-6F-VCCP+ 5VQ2SC2458TR1CustomQ2SC2458TR2CustomVOUT+0.000 pV-VOUT1+ -2.869 VVOUT2+ -2.869 VVIN1+0.000 pV-VSIN1+ SINVIN+0.000 pV-VIN2+0.000 pV-VSIN2+ SINQ2SC2458TR3CustomR636E3ΩR51E3Ω 7.37: R713E3Ω+ CP1M1E-7F-+ CP2M10E-6F-VCCM+ 5VR347E2ΩR447E2Ω+ CP1P1E-7F-+ CP2P10E-6F-VCCP+ 15VQ2SA1428TR3CustomQ2SA1428TR4CustomQ2SC2458TR1CustomQ2SC2458TR2CustomVOUT+9.839 V-VOUT1+ -9.651 VVOUT2+ --187.955 mVVIN1+0.000 pV-VSIN1+ SINVIN+0.000 pV-VIN2+0.000 pV-VSIN2+ SINQ2SC2458TR5CustomR6130E3ΩR51E3ΩR713E3Ω 7.38: + + CP1M1E-7F-+ CP2M10E-6F-VCCM+ 15V

7.7. 1257.7

1278

12999.1 9.1.1 9.1.2 9.1.3 9.2 9.2.1 9.3 pn 9.4 9.4.1 9.4.2 9.4.3 9.5 MOS 9.6 9.6.1 PIN 9.6.2 9.6.3 9.6.4 9.6.5 CCD9.6.6 CMOS

1311010.1 10.2 10.2.1 NOT, AND, NAND, OR, NOR, XOR10.2.2 JK D 10.2.3 10.2.4 10.2.5 ROM RAMEPROMEEPROMDRAMSRAM10.2.6 IC10.3 PALPLDFPGA10.4 LED

13311ADDA11.1 ADC 11.1.1 11.1.2 11.1.3 11.2 AD 11.2.1 11.2.2 11.2.3 FIFO11.3 DAC11.4

1351212.1 12.2 12.3 VME 12.4 12.4.1 I/O 12.4.2 RS232C GPIB12.4.3 SCSIUSBFireWire

1371313.1 13.2 13.3 13.3.1 13.3.2 13.3.3 13.3.4 13.4 13.4.1 13.4.2 13.5 13.5.1 13.5.2 13.5.3 13.5.4

1391414.1 14.2 14.2.1 ()14.2.2 LAC14.2.3 GIS14.2.4 Astro-E XIS14.3

141 6. II, , , 2001 4 , () , CQ 2000 10 , () , CQ 1997 6 , () , CQ , 11, , CQ SPECIAL No. 22, () , CQ , ISBN4-7898-3194-9 SPECIAL No. 50, () , CQ [] , , CQ , ISBN4-7898-3948-9, , , , ISBN4-7853-2316-7, , , , ISBN4-7853-2318-3, , , ISBN4-06-154504-3, , , ISBN4-563-03553-X, , , ISBN4-254-13585-8The Art of Electronics, Horowitz, Hill Cambridge University Press, ISBN 0-521-37095-7, , , ISBN4-339-00631-9