ユーザーズガイド LUXMAN LV-105U SERVICE MANUAL

[. . . ] 13 17 3 13 17 22 1 2 3 Circuit: Common plate voltage amplifier (cathode follower) with 12AU7 (fixed bias 1) 18 4 5 6 7 8 9 v(a1:4, a1:3) = 1. 000000e+02 v(a1:2, a1:3) = -3. 64683e+00 v:a1:bb#branch = -3. 03030e-03 abs(v(2)/v(1)) = 9. 278865e-01 abs(v(1)/i(vi)) = 1. 386594e+06 abs(v(4)/i(vo)) = 6. 089417e+02 2. 3. 2 1 2— 2 ( ??) (??) RC COMP2 CI 1 3 IN 1 µF 2 X1 12AU7 4 VBB CO 3 1000 µF 200 V VI RG 100 kΩ VG 1 96. 35 V OUT 2 4 RL 33 kΩ 0 RL 100 MΩ 2. 11: ( 2) (??) Zi Rg =∞ = Rg A Zi Zo 17. 18064 × 33 = 0. 9274518 + 17. 18064)33 + 11. 34946 = 100 [kΩ] = (1 = 1 1+17. 18064 11. 34946 + 1 33 = 0. 6126705 [kΩ] 100% |Ao | | Ao | = µ Af rp RL + RL (2. 24) β=1 = Ao 1 Af + Ao = 1 µr R +R L p L + µr RL p = +RL rp µRL + (1 + µ)RL (2. 25) (??) Rg =∞ com_p_2. cir 1 2 3 Common plate voltage amplifier (cathode follower) with 12AU7 (fixed bias 2) . INCLUDE 12AU7. lib . SUBCKT COMP2 IN OUT 19 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 X1 4 2 3 12AU7 RL 3 0 33k VBB 4 0 200V RG 2 1 100k VG 1 0 96. 35317V CI 2 IN 1u CO 3 OUT 1000u . ENDS XA1 1 2 COMP2 VI 1 0 DC 0V AC 1V RL 2 0 100Meg XA2 3 4 COMP2 VS 3 0 DC 0V VO 4 0 DC 0V AC 1V . control op print v(a1:4, a1:3) v(a1:2, a1:3) v:a1:bb#branch ac dec 1 1k 1k print abs(v(2)/v(1)) abs(v(1)/i(vi)) abs(v(4)/i(vo)) . endc . END 1 2 3 4 5 6 7 8 9 Circuit: Common plate voltage amplifier (cathode follower) with 12AU7 (fixed bias 2) v(a1:4, a1:3) = 1. 000000e+02 v(a1:2, a1:3) = -3. 64683e+00 v:a1:bb#branch = -3. 03030e-03 abs(v(2)/v(1)) = 9. 274435e-01 abs(v(1)/i(vi)) = 1. 000002e+05 abs(v(4)/i(vo)) = 6. 126713e+02 2. 3. 3 ?? 3— 1 RC 1 COMP3 CI 1 µF X1 12AU7 4 1 3 IN 2 CO 1000 µF 3 VBB 203. 65 V OUT 2 4 RG 100 kΩ VI RK 1203 Ω 5 CK 1000 µF RL 100 MΩ RL 33 kΩ 0 2. 12: ( 1) 20 com_p_3. cir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Common plate voltage amplifier (cathode follower) with 12AU7 (self bias 1) . INCLUDE 12AU7. lib . SUBCKT COMP3 IN OUT X1 4 2 3 12AU7 RK 3 5 1203. 454 CK 3 5 1000u RL 5 0 33k VBB 4 0 203. 64683V RG 2 5 100k CI 2 IN 1u CO 3 OUT 1000u . ENDS XA1 1 2 COMP3 VI 1 0 DC 0V AC 1V RL 2 0 100Meg XA2 3 4 COMP3 VS 3 0 DC 0V VO 4 0 DC 0V AC 1V . control op print v(a1:4, a1:3) v(a1:2, a1:3) v:a1:bb#branch ac dec 1 1k 1k print abs(v(2)/v(1)) abs(v(1)/i(vi)) abs(v(4)/i(vo)) . endc . END 1 2 3 4 5 6 7 8 9 Circuit: Common plate voltage amplifier (cathode follower) with 12AU7 (self bias 1) v(a1:4, a1:3) = 1. 000000e+02 v(a1:2, a1:3) = -3. 64683e+00 v:a1:bb#branch = -3. 03030e-03 abs(v(2)/v(1)) = 9. 278865e-01 abs(v(1)/i(vi)) = 1. 386595e+06 abs(v(4)/i(vo)) = 6. 089417e+02 2. 3. 4 4— 2 CK 33 kΩ ( ) eo RL RK ?? = = = = (i1 (i1 (i1 eg + i2 )RL + i2 Rk + i2 )RL + i2 (r p + Rk ) + i2 )RL + i1 Rg + (i1 + i2 )RL (2. 26) (2. 27) (2. 28) (2. 29) µeg ei ei eg = = = ei (1 (1 − eo = ei − (i1 + i2 )RL − i2 Rk + µ)(i1 + i2 )RL + {(1 + µ)Rk + r p }i2 + µ)RL i1 + {r p + (1 + µ)RL + (1 + µ)Rk }i2 21 µei COMP4 CI 1 µF X1 12AU7 4 1 3 IN 2 VBB CO 1000 µF 3 200 V OUT 2 4 RG 100 kΩ RK 1203 Ω 5 VI RL 100 MΩ RL 31. 8 kΩ 0 2. 13: ( 2) ei i1 = = = = = (RL i2 eo + Rg )i1 + RL i2 r p + RL + (1 + µ)Rk ei (1 + µ)(RL Rg + Rk Rg + Rk RL ) + r p (RL + Rg ) µRg − RL ei (1 + µ)(RL Rg + Rk Rg + Rk RL ) + r p (RL + Rg ) r p RL + µ(Rk RL + Rg RL + Rg Rk ) ei (1 + µ)(RL Rg + Rk Rg + Rk RL ) + r p (RL + Rg ) µ(RL + Rk + Rk RL /Rg ) + RL r p /Rg ei (1 + µ)(RL + Rk + Rk RL /Rg ) + (RL + Rg )r p /Rg Zi Zo A A = = = Zi µ(RL + Rk + Rk RL /Rg ) + RL r p /Rg (1 + µ)(RL + Rk + Rk RL /Rg ) + (RL + Rg )r p /Rg (1 + µ)(RL Rg + Rk Rg + Rk RL ) + r p (RL + Rg ) ei = i1 r p + RL + (1 + µ)Rk 1 1+µ rp (2. 30) (2. 31) Zo + Rk +Rg //RL 1 (2. 32) R A = = = = RL Zi Zo + Rk + Rk RL /Rg = 31. 79655 + 1. 203454 + 1. 203454 × 31. 79655/100 = 33. 38266 [kΩ] 17. 18064 × 33. 38266 + 31. 79655 × 11. 34946/100 = 0. 9280691 (1 + 17. 18064)33. 38266 + (31. 79655 + 100)11. 34946/100 (1 + 17. 18064)33. 38266 × 100 + (31. 79655 + 100)11. 34946 = 956. 357 [kΩ] 11. 34946 + 31. 79655 + (1 + 17. 18064)1. 203454 1 1+17. 18064 11. 34946 + 1. 203454+24. 12548 1 = 0. 6092449 [kΩ] com_p_4. cir 1 2 3 4 5 6 7 Common plate voltage amplifier (cathode follower) with 12AU7 (self bias 2) . INCLUDE 12AU7. lib . SUBCKT COMP4 IN OUT X1 4 2 3 12AU7 RK 3 5 1203. 454 RL 5 0 31. 79655k VBB 4 0 200V 22 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 RG 2 5 100k CI 2 IN 1u CO 3 OUT 1000u . ENDS XA1 1 2 COMP4 VI 1 0 DC 0V AC 1V RL 2 0 100Meg XA2 3 4 COMP4 VS 3 0 DC 0V VO 4 0 DC 0V AC 1V . control op print v(a1:4, a1:3) v(a1:2, a1:3) v:a1:bb#branch ac dec 1 1k 1k print abs(v(2)/v(1)) abs(v(1)/i(vi)) abs(v(4)/i(vo)) . endc . END 1 2 3 4 5 6 7 8 9 Circuit: Common plate voltage amplifier (cathode follower) with 12AU7 (self bias 2) v(a1:4, a1:3) = 1. 000000e+02 v(a1:2, a1:3) = -3. 64683e+00 v:a1:bb#branch = -3. 03030e-03 abs(v(2)/v(1)) = 9. 280620e-01 abs(v(1)/i(vi)) = 9. 562632e+05 abs(v(4)/i(vo)) = 6. 092468e+02 2. 4 ?? ( ?? Co ) RL Ci E bb ei Rk eo 2. 14: ( ) 23 K i1 ei Rk eg − −µeg + rp P RL G eo 2. 15: ??eo = = = = = (ei − µeg ) + µ) rp RL rp RL + RL = (1 + µ)ei RL rp + RL (2. 33) A (1 (1 + RL ii + µ)ei r p + RL ei Zi Zo i1 + ei Rk = 1 1+µ r p +RL + 1 Rk (2. 34) (2. 35) r p //RL 0 Rs ?? − Rs Rk eg −µeg + rp io eo 2. 16: io eg + µeg r p + R s //Rk = −io (R s //Rk ) = eo (2. 36) (2. 37) io eo Zo = − µio (R s //Rk ) r p + R s //Rk = {r p + (1 + µ)(R s //Rk )}io eo = eo io = r p + (1 + µ)(R s //Rk ) Zo (2. 38) 2. 4. 1 12AU7 RL = 33 kΩ, Rk = 1. 203454 kΩ 24 Ep = 203. 64683 V, = 100 V, Eg = −3. 646829 V, E bb Ip = 3. 0303 mA gm = 1513. 786 µS, r p = 11. 34946 kΩ, µ = 17. 18064 33 A Zi1 Zi = = = = (1 + 17. 18064) + 33 + 17. 18064 1 1 11. 34946 + 33 = 13. 52804 11. 34946 1 = 2. 439378 [kΩ] = 805. 8782 [Ω] 2439. 378 + + 1203. 454 1 Zo 1 11. 34946 1 1 33 = 8. 445022 [kΩ] 2. 4. 2 ?? COMG CO X1 12AU7 1 1000 µF OUT 2 4 RL CI 1 3 IN 1000 µF 3 33 kΩ 4 RL 100 MΩ EBB 200 V EI RK 1203 Ω 0 2. 17: ( ) com_g. cir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Common grid voltage amplifier with 12AU7 . INCLUDE 12AU7. lib . SUBCKT COMG IN OUT X1 1 0 3 12AU7 RK 3 0 1203. 454 RL 1 4 33k VBB 4 0 203. 64683V CI IN 3 1000u CO 1 OUT 1000u . ENDS XA1 1 2 COMG VIN 1 0 DC 0V AC 1V RL 2 0 100Meg XA2 3 4 COMG VS 3 0 DC 0V VO 4 0 DC 0V AC 1V . control op print v(a1:1, a1:3) v(a1:3)*-1 v:a1:bb#branch ac dec 1 1k 1k print abs(v(2)/v(1)) abs(v(1)/i(vin)) abs(v(4)/i(vo)) . endc . END 25 1 2 3 4 5 6 7 8 9 Circuit: Common grid voltage amplifier with 12AU7 v(a1:1, a1:3) = 1. 000000e+02 v(a1:3)*-1 = -3. 64683e+00 v:a1:bb#branch = -3. 03030e-03 abs(v(2)/v(1)) = 1. 352690e+01 abs(v(1)/i(vin)) = 8. 058129e+02 abs(v(4)/i(vo)) = 8. 445020e+03 2. 5 2. 5. 1 E p -I p 100 kΩ 25 kΩ Eg > −0. 7 V + 0. 7 V E g0 E g0 = −( + 0. 7) [V] (2. 39) E p -I p Eg =0 E p min E p min ep ≥ 2r p E p = (2/3) E bb √ ≈ Ebb /3 2 ≈ Ebb /5 RL E bb E p min ≈ E bb /3 12AU7 = 250 V 3 RL Ep = 80 V(≈ E bb /3), E g =0 rp ( ??) ≈ 7. 3 kΩ E p = E bb = 22 kΩ E g0 E g0 −18 V = −9 V = −6 V 26 15 Eg=0V −2 −4 10 −6 A −8 −10 −12 5 −14 Ip0=4. 36 O −16 B Epmin= 74. 0 0 50 100 Ep0=154. 1 150 Ep (V) Epmax=212. 5 200 250 300 Ip (mA) Ipmax=8. 00 Ipmin=1. 70 −18 0 2. 18: 12AU7 22 kΩ √ 6 I p0 Eg ≈ 4. 24 V I p max 1/2 = 0 2 E p0 ( E p max A) E p min = 74. 0 V, I p max = 8. 00 mA = 212. 5 V, I p min = 1. 70 mA E p min − E p0 = 74. 0 − 154. 1 = −80. 1 V (58. 4 + 80. 1)/2/6 = 11. 54167 10. 4295 kΩ, µ = 16. 61322, A = 11. 27032 Eg ?? = 154. 1 V, I p0 = 4. 36 mA +6 V −6 V E p max − E p0 = 212. 5 − 154. 1 = 58. 4 V rp = Ip I p0 = 4. 36 mA, Eg0 = −6 V (2. 40) Rk = −Eg0 I p0 Rk = 6 4. 36 = 1. 376147 [kΩ] E12 E bb = 1. 5 kΩ E bb = 256 V = 250 V ?? 2 I p0 < 1/2I p max 27 15 RL=10k 10 Ip (mA) RL=22k RL=33k 5 RL=47k RL=100k 0 −20 −18 −16 −14 −12 −10 Eg (V) −8 −6 −4 −2 0 2. 19: 12AU7 Ci Co Rg 1. 5 kΩ Ck 22 kΩ 256 V 2. 20: 28 2. 5. 2 R E p -I p FFT R ( ) trans. vol trans_vol. r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 "trans. vol" <function(p, ei, Ebb, Eg0, Rp, Rk=0) { # # p: # ei: # Ebb: # Eg0: # Rp: # Rk: RL <- Rp + Rk # f <- function(ep) { # ep: ip2 <- (Ebb - ep)/RL # ek <- ip2 * Rk # ip1 <- Ip(p, ep, eg-ek) # ip1 - ip2 # 0 } Eg <- ei + Eg0 # ep <- rep(0, length(Eg)) for (i in seq(along=Eg)) { # eg <- Eg[i] ep[i] <- if (Ip(p, Ebb, eg) == 0) Ebb # else uniroot(f, c(0, Ebb))$root } ip <- (Ebb - ep)/RL # ek <- ip * Rk # eo <- ep + ek list(Ip=ip, Eo=eo, Ep=ep, Ek=ek, Eg=Eg) ( ) } 3 9 Rk 0 11 12 f uniroot (24 0 P-K ) uniroot f f P-K ep ep 0 29 ip2 Rk G-K ( ) ek ip1 ip1 ip2 trans. vol ( ) ei 1 21 uniroot 23 0 uniroot Ebb > trans. vol(t12AU7, ei=0, Ebb=250, Eg=-6, Rp=22e3) $Ip [1] 0. 00435906 # $Eo [1] 154. 1007 # $Ep [1] 154. 1007 # $Ek [1] 0 # $Eg [1] -6 # ( ei= ) ei +6 V, 0 V, −6 V 3 > trans. vol(t12AU7, ei=c(6, 0, -6), Ebb=250, Eg=-6, Rp=22e3) $Ip [1] 0. 007998548 0. 004359060 0. 001703476 $Eo [1] 74. 03194 154. 10068 212. 52353 $Ep [1] 74. 03194 154. 10068 212. 52353 $Ek [1] 0 0 0 $Eg [1] 0 -6 -12 E p min , I p max ( ) > Eg <- seq(-19, 0, by=0. 5) > Eg [1] -19. 0 -18. 5 -18. 0 -17. 5 -17. 0 -16. 5 -16. 0 -15. 5 -15. 0 -14. 5 -14. 0 -13. 5 . . . [37] -1. 0 -0. 5 0. 0 > ip <- trans. vol(t12AU7, ei=0, Ebb=250, Eg=Eg, Rp=22e3)$Ip > ip [1] 1. 689226e-05 5. 087075e-05 1. 032984e-04 1. 727899e-04 2. 577371e-04 . . . [36] 6. 957745e-03 7. 295647e-03 7. 645951e-03 7. 998548e-03 > plot(Eg, ip, type="l") 30 ?? > trans. vol(t12AU7, ei=0, Ebb=256, Eg0=0, Rp=22e3, Rk=1. 5e3)$Ek [1] 6. 297733 2. 5. 3 E p -I p ?? [. . . ] [46] 0. 0073996938 0. 0075497245 0. 0076997719 0. 0078498346 0. 0079999121 > plot(eg, ip, type="l") 31 ?? 10 Ip (mA) 0 −20 2 4 6 8 0 20 40 60 80 Eg (V) 100 120 140 160 2. 22: 2. 5. 4 ?? ??(= P-K −Eg ) −Eg (B–O–A) E g0 I p0 = −6 V +6 V E p max E p0 = 152. 2 V E g min I p min = 4. 17 mA = −12 V ( A) ( O) = 207. 0 V I p max = 1. 41 mA E g max = 0 V ( B) −6 V E p min = 74. 0 V = 8. 00 mA R trans. comg 32 15 Eg=0V −2 −4 10 −6 B −8 −10 −12 5 −14 Ip0=4. 17 O −16 Ip (mA) Ipmax=8. 00 Ipmin=1. 41 0 Epmin= 74. 0 0 50 100 Ep0=152. 2 150 Ep (V) A Epmax=207. 0 200 250 −18 300 2. 23: trans_comg. r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 "trans. comg" <function(p, ei, Ebb, Eg0, Ek0, RL) { # # p: # ei: # Ebb: # Eg0: # Ek0: # RL: f <- function(ep) { # ep: ip2 <- (Ebb - ep)/RL # ip1 <- Ip(p, ep-ek, Eg0-ek) # ip1 - ip2 # 0 } Ek <- ei + Ek0 # ep <- rep(0, length(Ek)) for (i in seq(along=Ek)) { # ek <- Ek[i] ep[i] <- if (Ip(p, Ebb-ek, Eg0-ek) == 0) Ebb else uniroot(f, c(ek, Ebb))$root } ip <- (Ebb - ep)/RL # list(Ip=ip, Eo=ep, Ep=ep-Ek, Ip=ip, Ek=Ek) ( ) # } (14 ) > ek <- seq(0, 12, by=0. 5) > ip <- trans. comg(t12AU7, ei=0, Ebb=250, Eg0=0, Ek0=ek, 22e3)$Ip > ip 33 [1] 0. 007998548 0. 007629136 0. 007262160 0. 006907778 0. 006566853 0. 006237492 . . . [25] 0. 001410539 > plot(ek, ip, type="l") ?? 10 Ip (mA) 0 0 2 4 6 8 2 4 6 8 10 Ek (V) 12 14 16 18 2. 24: 2. 6 SRPP ??Rk1 Rk1 SRPP (Shunt Regulated Push Pull) ?? = 0 i eg2 eo ei = = r p1 −µ1 eg1 − µ2 eg2 + Rk1 + r p2 + Rk2 (2. 41) (2. 42) (2. 43) (2. 44) iRk2 = −µ1 eg1 − i(r p1 + Rk1 + Rk2 ) = eg1 − iRk1 eg1 (r p1 = ei + iRki + Rk1 + r p2 + Rk2 )i = −µ1 ei − (µ1 Rk1 + µ2 Rk2 )i {r p1 + (1 + µ1 )Rk1 + r p2 + (1 + µ2 )Rk2 }i = −µ1 ei 34 V2 Co Rk2 Ci V1 E bb Rg eo ei Eg 2. 25: SRPP r p2 + −µ2 eg2 − eg2 Rk2 i r p1 + −µ1 eg1 eg1 ei Rg ek1 eo − rK 1 2. 26: SRPP 35 i eo A −µ1 ei r p1 + (1 + µ1 )Rk1 + r p2 + (1 + µ2 )Rk2 r p2 + µ2 Rk2 = −µ1 ei r p1 + (1 + µ1 )Rk1 + r p2 + (1 + µ2 )Rk2 r p2 + µ2 Rk2 = −µ1 r p1 + (1 + µ1 )Rk1 + r p2 + (1 + µ2 )Rk2 = ?? (2. 45) r p2 + −µ2 eg2 iu id eg2 Rk2 − i r p1 + −µ1 eg1 − eg1 Rk1 eo 2. 27: SRPP id ( r p1 + Rk1 + Rk2 )id id + µ1 eg1 = + Rk1 + Rk2 = eo − µ1 id Rk1 = eo r p1 eo r p1 − µ1 id Rk1 + Rk1 + Rk2 = = = = = eo iu + (1 + µ1 )Rk1 + Rk2 eo − µ2 eg2 eo + µ2 id Rk2 = r p1 r p2 r p2 eo + µ2 r p1 +(1+µ1 )Rk1 +Rk2 Rk2 r p2 eo eo r p2 eo r p1 r p1 + (1 + µ1 )Rk1 + Rk2 + (1 + µ1 )Rk1 + (1 + µ2 )Rk2 r p2 {r p1 + (1 + µ1 )Rk1 + Rk2 } 1 + µ2 Rk2 Zo Zo = = eo iu + id = 1 r p1 +(1+µ1 )Rk1 +(1+µ2 )Rk2 r p2 {r p1 +(1+µ1 )Rk1 +Rk2 } + r p1 +(1+µ1 )Rk1 +Rk2 1 r p1 r p2 {r p1 + (1 + µ1 )Rk1 + Rk2 } + (1 + µ1 )Rk1 + r p2 + (1 + µ2 )Rk2 (2. 46) 2. 6. 1 1— 12AU7 SRPP E bb SPICE = 196. 4884 V, 36 Rk2 = 1. 2 kΩ, Rg = 470 kΩ gm = 96. 4884 V, Eg = −3. 5116 V, I p = 2. 92632 mA = 1503. 186 µS, r p = 11. 45684 kΩ, µ = 17. 22177 Ep 11. 45684 A Zi Zo = −17. 22177 = = 470 [kΩ] 11. 45684 + 17. 22177 × 1. 2 = −12. 3541 + 11. 45684 + (1 + 17. 22177) × 1. 2 + 1. 2) = 3. 238234 [kΩ] 11. 45684 + 11. 45684 + (1 + 17. 22177) × 1. 2 (−12. 78 (16. 6 kΩ 11. 45684(11. 45684 → −12. 35) → 3. 24 kΩ) ?? X2 12AU7 4 3 RK2 1. 2 kΩ 1 2 VBB 196. 5 V X1 12AU7 EI 3. 51 V RG 470 kΩ 0 2. 28: SRPP ( ) srpp. cir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 SRPP voltage amplifier with 12AU7 . OPTIONS ITL1=200 ITL2=200 . INCLUDE 12AU7. lib X1 1 2 0 12AU7 X2 4 1 3 12AU7 RK 1 3 1. 2k VBB 4 0 196. 4884V RG 2 0 470k VIN 2 0 DC -3. 511599V AC 1V . NODESET V(3)=100V . control op print v(1) v(2) v(4, 3) v(1, 3) i(vbb) tf v(3) vin print all . endc . END 1 2 3 4 5 Circuit: SRPP voltage amplifier with 12AU7 v(1) = 9. 648839e+01 v(2) = -3. 51160e+00 37 6 7 8 9 10 11 v(4, 3) = 9. 648841e+01 v(1, 3) = -3. 51160e+00 i(vbb) = -2. 92633e-03 transfer_function = -1. 23541e+01 output_impedance_at_v(3) = 3. 238233e+03 vin#input_impedance = 4. 700000e+05 2. 6. 2 2— V1 E bb Rk1 = 1. 2 kΩ V1 = 200 V 11. 45684 A Zi Zo = −17. 22177 = = 470 [kΩ] + 17. 22177 × 1. 2 = −8. 300797 11. 45684 + (1 + 17. 22177) × 1. 2 + 11. 45684 + (1 + 17. 22177) × 1. 2 11. 45684(11. 45684 11. 45684 + (1 + 17. 22177) × 1. 2 + 1. 2) = 5. 93471 [kΩ] + (1 + 17. 22177) × 1. 2 + 11. 45684 + (1 + 17. 22177) × 1. 2 ?? tf SRPPCF X2 12AU7 SPICE ac 4 CO 1000 µ 3 OUT 2 4 RK2 1. 2 kΩ 1 VBB 200 V 1 3 IN CI 1µ RG 470 kΩ 2 X1 12AU7 RL 100 MΩ EI 5 RK1 1. 2 kΩ 0 2. 29: SRPP ( ) srpp_cf. cir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 SRPP voltage amplifier with 12AU7 . OPTIONS ITL1=200 ITL2=200 . INCLUDE 12AU7. lib . SUBCKT SRPPCF IN OUT X1 1 2 5 12AU7 X2 4 1 3 12AU7 RK1 5 0 1. 2k RK2 1 3 1. 2k VBB 4 0 200V RG 2 0 470k CI IN 2 1u CO 3 OUT 1000u . ENDS XA1 1 2 SRPPCF VI 1 0 DC 0V AC 1V RL 2 0 100Meg 38 18 19 20 21 22 23 24 25 26 27 28 29 30 31 . NODESET V(A1:1)=100V XA2 3 4 SRPPCF VS 3 0 DC 0V VO 4 0 DC 0V AC 1V . NODESET V(A2:1)=100V . control op print v(a1:1, a1:5) v(a1:2, a1:5) v(a1:4, a1:3) v(a1:1, a1:3) v(a1:1) v:a1:bb#branch ac dec 1 1k 1k print abs(v(2)/v(1)) abs(v(1)/i(vi)) abs(v(4)/i(vo)) . endc . END 1 2 3 4 5 6 7 8 9 10 11 12 Circuit: SRPP voltage amplifier with 12AU7 v(a1:1, a1:5) = 9. 648840e+01 v(a1:2, a1:5) = -3. 51160e+00 v(a1:4, a1:3) = 9. 648840e+01 v(a1:1, a1:3) = -3. 51160e+00 v(a1:1) = 1. 000000e+02 v:a1:bb#branch = -2. 92633e-03 abs(v(2)/v(1)) = 8. 300174e+00 abs(v(1)/i(vi)) = 4. 694988e+05 abs(v(4)/i(vo)) = 5. 934634e+03 2. 6. 3 SRPP Ip (V2) E bb Rk2 I p Rk2 = 5 mA E g2 = 250 V Rk2 = 1. 2 kΩ = 5 · 1. 2 = 6 V V2 = −6 V > uniroot(function(ep) Ip(t12AU7, ep, -6) - 5e-3, c(0, 250))$root [1] 160. 5975 E p2 = 160. 6 V ?? ?? X Ip V2 160. 6/5 Ep ≈ 32 kΩ V1 ( r p2 + (1 + µ2 )Rk2 V1 ) Rk2 E bb V1 Rk − E p2 − I p Rk2 32 kΩ V1 V1 Rk2 V2 O A I p0 E g2 E g1 V1 E p1 E g1 = 0 ( E g1 = −0. 7 V) = −6 V E p1 = − Eg2 = 145. 0 V 141. 2 V, V2 = 3. 19 mA = −I p0 Rk2 = −3. 83 V, V2 39 15 Eg=0V −2 −4 10 −6 −8 Ip (mA) −10 Ipmax=5. 86 5 A X −12 −14 Ip0=3. 19 O −16 Ipmin=1. 34 0 Eomin= 63. 9 0 50 100 Eo0=145. 0 150 Ep (V) B Eomax=207. 1 200 250 −18 300 2. 30: SRPP +6 V E p1 min = 56. 9 V, V2 E p1 min − E g2 min = 63. 9 V I p min = 1. 34 mA, E g2 max = − I p min Rk2 = −1. 60 V, V2 V1 SRPP ( V1 = 5. 86 mA, E g2 min = − I p max Rk2 = −7. 03 V, V2 A) V1 −6 V E p1 max = 205. 5 V, V2 E p1 max − E g2 max = 207. 1 V I p max SRPP V1 ( E p1 B) = E p2 E p1 > E p2 2 V1 R E p1 < E p2 SRPP trans. srpp trans_srpp. r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 "trans. srpp" <function(p1, ei, Ebb, Eg1, Rk1=0, Rk2, p2=p1) { # SRPP # p1: V1 # p2: V2 # ei: # Ebb: # Eg1: V1 ( ) # Rk1: V1 # Rk2: V2 # # $Ip: # $Eg1: V1 # $Ep1: V1 # $Eg2: V2 # $Ep2: V2 40 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 # $Eo: ( V2 ) get. ep2 <- function(ip) { # ip V2 if (ip == 0) # return(0) eg2 <- -ip * Rk2 uniroot(function(ep2) Ip(p2, ep2, eg2) - ip, c(0, Ebb))$root } f <- function(ip) { ep2 <- get. ep2(ip) # V2 eg1 <- eg - ip * Rk1 # V1 ep1 <- Ebb - ip * (Rk1 + Rk2) - ep2 ip1 <- Ip(p1, ep1, eg1) ip - ip1 } # V2 Ipmax <- uniroot(function(ip) Ip(p2, Ebb-ip*(Rk1+Rk2), -ip*Rk2) - ip, c(0, Ip(p2, Ebb, 0)))$root Eg <- ei + Eg1 ip <- ep2 <- rep(0, length(Eg)) for (i in seq(along=Eg)) { eg <- Eg[i] cat(eg, "") ip[i] <- if (Ip(p1, Ebb, eg) == 0) 0 else uniroot(f, c(0, Ipmax*0. 99), tol=1e-8)$root ep2[i] <- get. ep2(ip[i]) # } cat("\n") eg2 <- -ip * Rk2 # eg1 <- Eg - ip * Rk1 # ep1 <- Ebb - ip * (Rk1 + Rk2) - ep2 # eo <- ip * (Rk1 + Rk2) + ep1 # V2 list(Ip=ip, Eo=eo, Eg1=eg1, Ep1=ep1, Eg2=eg2, Ep2=ep2) } SRPP > trans. srpp(t12AU7, ei=0, Ebb=250, Eg1=-6, Rk2=1. 2e3) -6 $Ip # [1] 0. 003193013 $Eo # [1] 144. 9966 $Eg1 # [1] -6 $Ep1 # [1] 141. 165 $Eg2 # [1] -3. 831616 $Ep2 # [1] 105. 0034 > ei <- c(0, 6, -6) > z <- trans. srpp(t12AU7, ei=ei, Ebb=250, Eg1=-6, Rk2=1. 2e3) -6 0 -12 > z$Ip [1] 0. 003193013 0. 005858398 0. 001339306 > z$Eo [1] 144. 99661 63. 93202 207. 14122 41 > eg <- seq(-20, 0, by=0. 5) > ip <- trans. srpp(t12AU7, ei=0, Ebb=250, Eg1=eg, Rk2=1. 2e3)$Ip -20 -19. 5 -19 . . . -2. 5 -2 -1. 5 -1 -0. 5 0 > plot(eg, ip, type="l") ?? Ip (mA) 0 −20 1 2 3 4 5 6 −18 −16 −14 −12 −10 Eg (V) −8 −6 −4 −2 0 2. 31: SRPP 2. 7 ??V1 (cascode) V2 (V1 ) V2 V2 V1 V2 ( ) ?? eo e p1 eg2 = (−µ1 eg1 − µ2 eg2 ) RL r p1 + r p2 + RL r p1 r p1 (2. 47) = −µ1 eg1 + (µ1 eg1 + µ2 eg2 ) = −e p1 42 + r p2 + RL (2. 48) (2. 49) RL Co V2 Ci V1 eo E g2 Rg E bb ei Eg 2. 32: r p1 −µ2 eg2 − + r p2 + ei Rg eg1 −µ1 eg1 − e p1 RL eo 2. 33: eg2 (r p1 = µ1 eg1 − (µ1 eg1 + µ2 eg2 ) r p1 r p1 + r p2 + RL )eg2 + r p2 + RL = µ1 (r p1 + r p2 + RL )eg1 − (µ1 eg1 + µ2 eg2 )r p1 = µ1 (r p2 + RL )eg1 µ1 (r p2 + RL ) = eg1 (1 + µ2 )r p1 + r p2 + RL = r p2 + RL RL eg1 + µ2 )r p1 + r p2 + RL r p1 + r p2 + RL r p2 + RL RL = −µ1 eg1 1 + µ2 (1 + µ2 )r p1 + r p2 + RL r p1 + r p2 + RL (1 + µ2 )(r p1 + r p2 + RL ) RL = −µ1 eg1 · (1 + µ2 )r p1 + r p2 + RL r p1 + r p2 + RL (1 + µ2 )RL = −µ1 eg1 (1 + µ2 )r p1 + r p2 + RL {(1 + µ2 )r p1 + r p2 + RL }eg2 eg2 eo −µ1 eg1 − µ2 µ1 (1 A = −µ1 (1 + µ2 ) RL (1 + µ2 )r p1 + r p2 + RL (2. 50) 2 Zi2 Zo1 = r p1 = (r p2 + RL )/(1 + µ2 ) r p2 +RL A1 Zi2 r p1 1+µ2 A1 = −µ1 + Zi2 = −µ1 r p1 + r p2 +R L 1+µ2 = −µ1 + RL (1 + µ2 )r p1 + r p2 + RL r p2 (2. 51) 43 A2 (??) A2 = (1 + µ2 ) RL r p2 + RL (2. 52) A A = A1 A2 = −µ1 (??) + RL RL RL (1 + µ2 ) = −µ1 (1 + µ2 ) (1 + µ2 )r p1 + r p2 + RL r p2 + RL (1 + µ2 )r p1 + r p2 + RL r p2 (2. 53) Zo ( (??)) Zo Zi = {r p2 + (1 + µ2 )r p1 }//RL = Rg (2. 54) (2. 55) 2. 7. 1 12AU7 SPICE E bb = 250 V, Rg = 470 kΩ, RL = 22 kΩ, V1 E g1 = −3 V, V2 E g2 = 72 V = 77. 89354 V, Eg1 = −3 V, E p2 = 125. 5693 V, Eg2 = −5. 893544 V, I p = 2. 115324 mA gm1 = 1347. 921 µS, r p1 = 12. 77094 kΩ, µ1 = 17. 21421, gm2 = 1129. 799 µS, r p2 = 14. 11705 kΩ, µ2 = 15. 94943 E p1 A Zi Zo = −17. 21421(1 + 15. 94943) = = 470 [kΩ] 1 14. 11705+(1+15. 94943)12. 77094 1 22 (1 + 15. 94943)12. 77094 + 14. 11705 + 22 = 20. 08375 [kΩ] = −25. 41387 + 1 22 2. 7. 2 ?? cascode. cir 1 2 3 4 5 6 7 8 9 10 11 12 Cascode voltage amplifier with 12AU7 . INCLUDE 12AU7. lib X1 1 2 0 12AU7 X2 3 4 1 12AU7 RL 3 5 22k VBB 5 0 250V VG2 4 0 72V RG 2 0 470k VI 2 0 DC -3V AC 1V . NODESET V(1)=78V . control op 44 5 RL 22 kΩ 3 4 X2 12AU7 X1 12AU7 2 1 VG2 72 V VBB 250 V VI 3V RG 470 kΩ 0 2. 34: ( ) 13 14 15 16 17 print v(1) v(2) v(3, 1) v(4, 1) v(3) i(vbb) tf v(3) vi print all . endc . END 1 2 3 4 5 6 7 8 9 10 11 12 Circuit: Cascode voltage amplifier with 12AU7 v(1) = 7. 789318e+01 v(2) = -3. 00000e+00 v(3, 1) = 1. 255705e+02 v(4, 1) = -5. 89318e+00 v(3) = 2. 034636e+02 i(vbb) = -2. 11529e-03 transfer_function = -2. 54139e+01 output_impedance_at_v(3) = 2. 008375e+04 vi#input_impedance = 4. 700000e+05 2. 7. 3 V2 0V E g2 V2 V2 E g2 V1 V1 V1 V2 ( ??) E bb − Eg2 (A2–O2–B2) (A1–O1–B1) µ gm gm V2 E g2 E g2 45 15 Eg=0V −1 −2 −3 −4 10 −5 −6 −8 Ip (mA) −10 −12 5 Ipmax=5. 24 A2 A1 A3 −14 −16 Ip0=2. 12 Ipmin=0. 49 0 0 50 O1 B1 100 O2 B2 O3 −18 Eomin=134. 6 150 Ep (V) B3 Eo0=203. 5 Eomax=239. 3 200 250 300 2. 35: V2 (V1 V1 ) E g0 E g0 =0 y = 1V V2 E g0 =0 0. 6 V1 gm ei gm V1 E g0 = 1V E g2 V1 E g1 O Eg V2 ( O3 ) 203. 5 V A1) V2 I p min B3 E o max 4 Vp−p = −3 V = −3 V O1 O1 2. 12 mA O2 I p max +2 V A3 E o min ( = 5. 24 mA ( = 134. 6 V −2 V V2 R = 0. 49 mA B1) = 239. 3 V trans. cascode trans_cascode. r 1 2 3 4 5 6 7 8 "trans. cascode" <function(p1, ei, Ebb, Eg1, Eg2, RL, Rk=0, p2=p1) { # # p1: V1 # p2: V2 # ei: # Ebb: 46 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 # # # # # # # # # # # Eg1: V1 Eg2: V2 RL: Rk: V1 $Ip: $Eo: $Eg1: $Ep1: $Eg2: $Ep2: ( ( ) V1 V1 V2 V2 V2 ) get. ek2 <- function(ip) { # ip # V2 if (ip == 0) # V2 return(Ek2max) # ep2 <- Ebb - ip * RL # V2 if (ep2 <= 0) return(0) uniroot(function(ek) Ip(p2, ep2-ek, Eg2-ek) - ip, c(0, Ek2max), tol=1e-8)$root } f <- function(ip) { ep1 <- get. ek2(ip) # ek1 <- ip * Rk # ip1 <- Ip(p1, ep1-ek1, eg-ek1) ip - ip1 } V1 V1 ? } # V2 (Ip=1nA) Ek2max <- uniroot(function(ek) Ip(p2, Ebb-ek, Eg2-ek) - 1e-9, c(Eg2, Ebb))$root cat("Ek2max=", Ek2max, "\n", sep="") Eg <- ei + Eg1 ip <- ek2 <- rep(0, length(Eg)) for (i in seq(along=Eg)) { eg <- Eg[i] cat(eg, "") ip[i] <- if(Ip(p1, Ek2max, eg) <= 1e-9) 0 else uniroot(f, c(0, (Ebb-Eg2)/RL), tol=1e-8)$root ek2[i] <- get. ek2(ip[i]) } cat("\n") eo <- Ebb - ip * RL ep2 <- eo - ek2 eg2 <- Eg2 - ek2 ep1 <- ek2 - ip * Rk eg1 <- Eg - ip * Rk list(Ip=ip, Eo=eo, Ep1=ep1, Eg1=eg1, Ep2=ep2, Eg2=eg2) > trans. cascode(t12AU7, ei=c(0, 2, -2), Ebb=250, Eg1=-3, Eg2=72, RL=22e3) Ek2max=85. 30461 -3 -1 -5 $Ip [1] 0. 0021153245 0. 0052434383 0. 0004876885 $Eo # (V2 ) [1] 203. 4629 134. 6444 239. 2709 $Ep1 [1] 77. 89354 72. 50324 82. 12975 $Eg1 [1] -3 -1 -5 $Ep2 47 [1] 125. 56932 62. 14111 157. 14110 $Eg2 [1] -5. 8935443 -0. 5032431 -10. 1297507 > eg <- seq(-7, 0, by=0. 25) > ip <- trans. cascode(t12AU7, ei=0, Ebb=250, Eg1=eg, Eg2=72, RL=22e3)$Ip Ek2max=85. 30461 -7 -6. 75 . . . -0. 75 -0. 5 -0. 25 0 > plot(eg, ip, type="l") ??gm ( 0. 6 gm ) Ip (mA) 0 −7 2 4 6 8 −6 −5 −4 Eg (V) −3 −2 −1 0 2. 36: 2. 8 Rg2 ??Rg2 = 100 kΩ RL 2 48 15 Eg=0V −2 −4 10 −6 Ipmax=8. 56 Ip (mA) A −8 −10 −12 5 −14 Ip0=4. 36 O −16 Ipmin=1. 42 0 Epmin= 78. 3 0 50 100 Ep0=154. 1 150 Ep (V) B Epmax=207. 1 200 250 −18 300 2. 37: ( RLac 2 ) Rg2 RL = RL //Rg2 trans. vol E bbac E bbac RLac = E p0 + I p0 RLac (2. 56) ?? > z0 <- trans. vol(t12AU7, ei=0, Ebb=250, Eg0=-6, 22e3) > RLac <- 22e3 %p% 100e3 # %p% > RLac # [1] 18032. 79 > Ebbac <- z0$Ep + z0$Ip * RLac # > Ebbac [1] 232. 7067 > ei <- c(0, 6, -6) > trans. vol(t12AU7, ei=ei, Ebb=Ebbac, Eg0=-6, Rp=RLac) $Ip [1] 0. 004359060 0. 008563391 0. 001418526 $Eo [1] 154. 10068 78. 28488 207. 12670 $Ep [1] 154. 10068 78. 28488 207. 12670 $Ek [1] 0 0 0 $Eg [1] -6 0 -12 49 2. 9 ( ) 50 3 P-K ( ) 3. 1 P-K P-K ( ??(2) ) E bb E bb Rp Rp Rg ei Rk ep ek E bb Rk (1) (2) 3. 1: P-K 1 2 1/2 (gm ) 3. 1. 1 P-K Zk , Z p ?? ek ep = −iZk = = iZ p i(r p (3. 1) (3. 2) −µeg + Zk + Z p ) (3. 3) 51 − ek Zk −µeg + rp i Zp ep 3. 2: P-K ei = eg + ek (3. 4) eg = ei − ek = ei + iZk + Zk + Z p ) −µ(ei + iZk ) = −µei i i(r p = {r p + (1 + µ)Zk + Z p }i −µei = r p + (1 + µ)Zk + Z p = −µei = µei Zp rp ep + (1 + µ)Zk + Z p Zk (3. 5) ek rp + (1 + µ)Zk + Z p (3. 6) Ap = −µ = µ Z Zp rp + (1 + µ)Zk + Z p Zk (3. 7) Ak rp + (1 + µ)Zk + Z p ( Z (3. 8) Zk = Zp ) |A| = µ rp + (2 + µ)Z (3. 9) 3. 1. 2 ?? − ek Zk −µeg + rp i2 i1 Zp eo 3. 3: P-K i1 = eo Zp (3. 10) 52 i2 (r p + Zk ) = µeg + eo = −µek + eo = −µi2 Zk + eo = = = = eo eo rp {r p + (1 + µ)Zk }i2 i2 + (1 + µ)Zk eo Zo p i1 + i2 = 1 1 Zp + r p +(1+µ)Zk 1 Z p //{r p + (1 + µ)Zk } (3. 11) ?? i1 − i2 eo Zk Zp −µeg + rp 3. 4: P-K i1 (r p + Zp) i2 i1 = = = = eo eo Zk − µeg = (1 + µ)eo (3. 12) (3. 13) +µ eo rp + Zp 1 eo i1 Zok + i2 = 1 1 Zk + 1+µ r p +Z p (3. 14) 3. 1. 3 12AU7 P-K Eg E bb = 250 V, Rk = Rp = 22 kΩ, = −6 V E p = 134. 2252 V, I p = 2. 63125 mA gm = 1250. 989 µS, r p = 12. 88682 kΩ, µ = 16. 12127 22 12. 88682 | A| = Zo p Zok = 0. 8617758 + (2 + 16. 12127)22 = 22//{12. 88682 + (1 + 16. 12127)22} = 20. 82397 [kΩ] = 1 1 22 16. 12127 + 12. 88682+22 1+16. 12127 = 1. 864904 [kΩ] 3. 1. 4 SPICE ?? 53 4 RP X1 12AU7 22 kΩ 1 2 VBB 250 V VI 42. 7 V RG 470 kΩ 3 RK 22 kΩ 0 3. 5: P-K ( ) pk. cir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 P-K phase inverter with 12AU7 . INCLUDE 12AU7. lib X1 1 2 3 12AU7 RP 1 4 22k RK 3 0 22k *CP 1 0 0. 01u *CK 3 0 0. 01u *CP 1 0 220p *CK 3 0 200p VBB 4 0 250V RG 2 0 470k VI 2 0 DC 51. 88741V AC 1V . control op print v(1, 3) v(2, 3) i(vbb) tf v(1) vi print all tf v(3) vi print all *ac dec 10 1 1meg *plot db(v(1)) db(v(3)) ylimit -5 0 . endc . END 1 2 3 4 5 6 7 8 9 10 11 12 Circuit: P-K phase inverter with 12AU7 v(1, 3) = 1. 342252e+02 v(2, 3) = -6. 00000e+00 i(vbb) = -2. 63125e-03 transfer_function = -8. 61776e-01 output_impedance_at_v(1) = 2. 082397e+04 vi#input_impedance = 4. 700000e+05 transfer_function = 8. 617758e-01 output_impedance_at_v(3) = 1. 864904e+03 vi#input_impedance = 4. 700000e+05 3. 1. 5 P-K 54 R, Z (??) C P-K = R//C Z = 1/(1/R + jωC ) = R/(1 + jωCR) 1 r p /Z |A| = µ Z rp + (2 + µ)Z 1 rp =µ + (2 + µ) R rp = µ 1+ jωCR R + (2 + µ) R =µ + (2 + µ)R + jωCr p R +(2+µ)R ) (3. 15) rp R = µ = {r p + (2 + µ)R}(1 + jωC r µR · + (2 + µ)R 1 1 p rp + jωC r rp R p +(2+µ)R Zo Zo = rpR rp + (2 + µ)R Zo (3. 16) = 688. 8756 [Ω] ?? 100 pF 0. 01 µF 100 pF 0. 01 µF, 0. 01 µF 100 pF 100 pF, 0. 01 µF 220 pF, ??4. ( ( ( ( ) Pd ) E g min ) E p max ) I p max ?? Ip I p max I p max Pd E p max E gmin E p max Ep 5. 24: C 2 B OTL 5. 8. 1 ?? 100 Ci Zp RL Ci Zp RL Rg ei Eg E bb ei Rg Rk Ck E bb (1) (2) 5. 25: ??Zp 1 6EM7 2 E p0 Zp = 2. 5 kΩ ?? = 200 V, I p0 = 50 mA r = 146. 8 Ω 150 Eg=0V −10 −20 DC load line (146. 8ohm) AC load line (2. 5kohm) −30 Ipmax=104. 5 100 A( 63. 8, 104. 5) −40 −50 Ip (mA) −60 −70 50 O(200. 0, 50. 0) −80 −90 Ipmin= 14. 5 D 0 Epmin= 63. 8 0 50 100 150 C(207. 3, 0) 200 Ep (V) 250 Epmax=288. 8 300 350 400 450 B(288. 8, 14. 5) −100 5. 26: 6EM7 E p0 = 200 V 0. 05 × 146. 8 = 7. 34 [V] = 207. 3 V “C” E bb E p0 = 200 V, I p0 = 50 mA E g0 = −29. 5 V 0V −29. 5 × 2 = −59 V 101 E p max = 0V = 289. 9 V, I p min = 14. 0 mA Eg ?? E p min = 64. 5 V, I p max = 104. 2 mA Eg = −59 V ?? Eg (V) Ep (V) Ip (mA) 20 40 60 80 100 100 150 200 250 −60 −40 −20 0 5. 27: 6EM7 Ip (mA) 0 20 40 60 80 100 120 −50 −40 −30 Eg (V) −20 −10 0 5. 28: 6EM7 ( ? ) 102 5. 8. 2 ( ??i(t) i(t) (ω f e(t) ) = I sin ωt (5. 61) ω = 2π f ) = i(t)R = IR sin ωt p(t) (5. 62) p(t) sin 2 = e(t)i(t) = i2 (t)R = I R sin 2 2 ωt (5. 63) α = (1 − cos 2α)/2 p(t) = I R ?? 2 1 − cos 2ωt 2 (5. 64) 2 i(t) e(t) R 5. 29: ( ) e, i, p p(t) e(t) P i(t) O π ω 2π ω t 5. 30: ( ) 2π/ω P p(t) 1 2π ω P = 2π ω 0 ω 2 p(t) dt = I R 2π 2π ω 1 − cos 2ωt 2 0 dt (5. 65) 0 P = ω 2 I R 2π 2π ω 1 2 dt = I R 2 2 (5. 66) 0 103 Irms P = Irms R 2 (5. 67) Irms R Irms 1/ 2 = = I R 2 I 2 √ 2 (5. 68) √ 2 I E 1/ √ 2 1/ 2 I2 √ 2 I1 i(t) 2 i(t) = I1 sin ωt + I2 sin(2ωt + θ) ) (5. 69) θ 2 ( P = = R ω 2π ω 2π 2π ω i (t) dt 0 2π 2 ω R {I1 sin ωt + I2 sin(2ωt + θ)}2 dt 2π 0 2 I1 ω = R 2π 1 ω 2π sin 0 2 ωt dt + I1 I2 0 ω 2π sin ωt sin(2ωt + θ) dt + 2 I2 ω sin (2ωt 2 + θ) dt 0 3 π/ω sin α 2 + sin β = cos(α − β) − cos(α + β) 2 2π ω 2π sin ωt sin(2ωt + θ) dt = 0 ω cos(−ωt − θ) − cos(3ωt + θ) 2 dt (5. 70) 0 cos(α + β) = cos α cos β − sin α sin β 2π ω cos(−ωt 2π − θ) − cos(3ωt + θ) 2 dt 2π 0 = 0 ω cos −ωt cos −θ − sin −ωt sin −θ dt − 0 ω cos 3ωt cos θ − sin 3ωt sin θ dt 0 (5. 71) cos nωt P P 2 sin nωt 2 2 2 =R I1 2 + I2 2 = I1 R 2 + I2 R 2 (5. 72) 104 2 5. 8. 3 2 2 ( ?? ) f, 2 h2 2 Ip 2 0) ±90 2 ( ◦ ) I pavg I pavg ( − h2 I p0 Ip I p max I p max + I p min 2 f h2 I pavg I p0 I p min t 5. 31: 2 I p max I p max I p min I p min (??) (??) I p max = I p0 + f + 2h2 (5. 73) = I p0 − f + 2h2 (5. 74) − I p min f = = 2f I p max − I p min 2 (5. 75) (??) (??) I p max + I p min h2 = = 2 I p0 I p max + 4h2 + I p min − 2I p0 4 (5. 76) 105 Po Po = (f 2 + h2 )R 2 2 (5. 77) 6EM7 f h2 = = 104. 2 104. 2 − 14. 0 2 = 45. 1 [mA] = 4. 55 [mA] + 14. 0 − 2 × 50. 0 4 Po 2 1% 2 = (0. 0451 2 + 0. 004552 ) × 2500 2 ( ) 10% = 2. 57 [W] Po = f R 2 2 = ( I p max − I p min )2 Z p 8 (5. 78) 6EM7 Po 1% = 0. 0451 2 × 2500 2 = 2. 54 [W] ( I p max − I p min )Z p = E p max − E p min Po ?? = ( E p max − E p min )(I p max − I p min ) 8 1/4 (5. 79) ABD 5. 8. 4 f D h2 f I p max + I p min −2 I p0 , 2 h2 D = = 4 I p max − I p min 2 = I p max + I p min − 2I p0 = 2( I p max − I p min ) I p max + I p min 2 − I p0 I p max − I p min (5. 80) I p max + I p min 2 I p max I p min I pavg 2 h2 + I p0 peak-peak p-p I p max h2 2 − I p min I pavg I p0 2 h2 106 6EM7 D = 4. 55 45. 1 = 10. 1 [%] 5. 8. 5 ( ??) G rp P + ei Rg eg −µeg − K Zp eo 5. 32: 1 Zo A 2 A = −µ = rp Zp rp + Zp + r2 1 2 (5. 81) Zo + r1 n2 (5. 82) 2 DF 2 DF ≡ Zo (5. 83) 6EM7 µ = 5. 0255, rp = 931. 21 Ω, gm = 5397 m§ A Zo = −5. 0255 = 931. 21 2546 931. 21 + 2546 = −3. 680 (5. 84) (5. 85) + 146. 8 16. 71322 + 0. 66 = 4. 519 [Ω] 2 107 5. 8. 6 5. 8. 7 5. 8. 8 5. 8. 9 5. 8. 10 2 NFB 5. 9 5. 9. 1 1 ??1 I11 P1 E 11 5 kΩ 1 = 40 mA I2 = 100 V B E2 E 12 = 100 V P2 I12 = 40 mA 5. 33: B 1 Z1 5 kΩ 2 I1 (mA) 200 1 Z1 = 100 + 100 0. 04 = 5000 Ω ( I1 (5. 86) E 11 - I1 200 × 0. 04 = I11 + I12 ) ?? A = 8W ( ) 100 80 mA 0 A −100 −200 −300 −200 −100 0 100 200 300 E 11 (V) 5. 34: 100 0. 08 = 1250 Ω (5. 87) 108 E 11 - I1 Z1 1 /4 E 11 - I1 (2 ) P1 - P2 1 Z1 = E 11 + E12 I1 /2 =4 E 11 I1 = 4Z s I1 (5. 88) Zs E 11 - I1 I1 I1 E 11 1 Zs = I11 + I12 = = = I11 I11 + I12 + + I12 E 11 1 Z12 1 (5. 89) E 11 1 Z11 ( 1 1 Z2 2 1 (??) E 11 2 I11 I12 1/4) I11 Po E2 I1 2 n E2 2 E 11 2 E 11 I1 I1 I2 2 = I12 2 2 E2 = I11 + I12 I1 1 I1 I11 , I12 5. 10 5. 11 SEPP 109 6 ( ) 6. 1 AM , 1 TL, TH A = = = AM 1 1 + − + jωT L 1 · · 1 1 + jωT H 1 (6. 1) AM 1 1 j ωT L TH TL 1 1 + jωT H ωT L ) 1 AM 1 (1 ) + j(ωT H − TL TH T H /T L ≈0 A ≈ AM 1 1 + j(ωT H − ωT L ) A 1 F A = ≈ = = ≈ = A 1 + Aβ AM 1 + j(ωT H − ωT L ) 1 + AM β ωT L ) 1 1 AM 1 + A M β + j(ωT H − · · 1 1 1 = AM F + j(ωT H − ωT L ) 1 AM F AM F AM F + j(ωT H /F − 1 ωFT L ) 1 + − TH F2TL + j(ωT H /F − · TL 1 1 ωFT L ) (6. 2) · 1 1 j ωFT L 1 + jωT L /F FT L F F TH A M /F , 1/ F AM = = T H /F ?? = 1000 (60 dB), F = 10 (20 dB) 6. 2 AM , 2 T L1 , T L2 AL AL 1 1 = AM + jωT L1 1 · 1 1 + jωT L2 1 110 Gain (dB) 20 1 30 40 50 60 10 100 1k Frequency (Hz) 10k 100k 1M 6. 1: = x AM 1 1 − j ωT L1 1 · 1 1 − j ωT L2 1 = 1/ωT L1 , n = T L2 /T L1 AL = = AM 1 1 − − jx · 1 1 − j x n (6. 3) AM 1 (1 x2 n ) − jx(1 + 1 n (6. 4) ) β AL AL = = AL 1 + AL β AM (6. 5) (1 − x2 n ) − jx(1 AM + − 1 n ) + AM β + 1 n (6. 6) = (1 1 + AM β − x2 n (6. 7) ) ) jx(1 + AM β = FM AL = (F M AM − x2 n ) − jx(1 + 1 n (6. 8) ) AM ( ) | AL | = = 2 AM (F M 1 (6. 9) − x 2 n ) 2 +x 2 (1 + 1 2 ) n X x (??) FM − X n 2 +X 1 + 1 n 2 (6. 10) 111 = = = = 1 n2 1 n2 1 n 2 X 2 + 1 + 1 n 2 − 2F M n X + F2 M (6. 11) (6. 12) X 2 + (n2 + 2n + 1 − 2nF M )X + n2 F 2 M − 2nF M X − (n + 1)2 2 2 2 + n2 F 2 − M (n 2nF M − (n + 1)2 2 2 (6. 13) 1 n2 X − 2nF M − (n + 1)2 2 + + 1)2 n FM − (n + 1)4 4n2 (6. 14) ( x | AL | ) 1 T L1 x p 1 T L1 nF M ) X = xp ≡ nF M − (n + 1) /2 2 = nF M − (n + 1)2 /2 ωp ( ωp = = (6. 15) − (n+1)2 2 | AL p | | AL p | = = A M /F M FM (n+1)2 n AM 1 (n+1)2 n FM − (n+1)4 4n2 (6. 16) AM P 1 (n+1) nF M 2 P = | AL p | AM = = − (n+1)4 4n2 FM − (n+1)4 4n 2 2 F M (6. 17) 1 N = (n + 1)2 /n N FM − N 2 2 4F M ≥ ≥ ≤ 1 (6. 18) N FM FM 2 − N 2 4 N 2 FM 0 0 N 2 2 (6. 19) − N FM + FM 4 2 (6. 20) (6. 21) − N 2 ≤ = FM (??) ??1 = (n + 1)2 2n (6. 22) n (??) 1 P2 FM P FM 2 − n (n + 1)2 n FM + (1 (n + 1)4 4n2 = = 0 (6. 23) (n+1) 2 FM = ± (n+1)4 n2 − 1/P2 ) P (n 2 + 1)2 2/ P 2 2n (1 ± 1 − 1/ P2 ) (6. 24) 112 F=0dB 6dB −10 0 12dB 15dB 20dB 26dB 30dB Gain (dB) −50 0. 05 −40 −30 −20 0. 1 1 f/fc 10 20 Phase (deg) 100 150 0 50 30dB 26dB 20dB 15dB 12dB 6dB F=0dB 0. 05 0. 1 1 f/fc 10 20 6. 2: 1 113 35 11dB 10dB 30 9dB 8dB 7dB 25 6dB 5dB Feedback (dB) 4dB 3dB 20 15 2dB 1dB 10 P=0dB 5 0 0. 01 0. 1 1 Stagger ratio 10 100 6. 3: 12 xp 2 4 6 8 10 20 n=1 2 0 5 4 10 Feedback (dB) 8 10 15 20 25 25 0 15 6. 4: (n ≥ 1) 114 n=1 4 0. 8 3 0. 4 xp 2 0. 2 1 0. 1 0. 067 0. 05 0. 04 0 0 5 10 Feedback (dB) 15 20 25 6. 5: (n ≤ 1) ?? ??, ?? n F =1 T L1 = 10 (20 dB) ??xp ?? = T L2 = 25 µF · kω(ms) P = 4. 44 dB = 2. 83 (6. 25) fp = = ωp 1 = = 2. 25 [Hz] 2π 2πT L1 x p 10 xp T L2 n P = 0. 74 dB n = 0. 1 xp ?? = 6. 28 = 250 µF · kΩ f p = 1. 01 [Hz] P 3 T L2 = 2. 5 µF · kΩ = 0. 628 f p = 10. 1 [Hz] = 0. 74 dB 6. 3 AM , 3 T L1 , T L2 , T L3 AL AL = AM 1 1 + jωT L1 1 · 1 1 + jωT L2 1 · 1 1 + jωT L3 1 115 −10 −15. 56 −20 Response (dB) −30 −19. 26 10 n=1 0. 1 −40 −50 1. 01 0. 2 1 2. 25 10. 10 10 20 Frequency (Hz) 6. 6: (F = 10) = x AM 1 1 − j ωT L1 1 · 1 1 1 − j ωT L2 1 1 − j ωT L3 1 = 1/ωT L1 , T L2 = nT L1 , T L3 = mT L1 AL = = AM 1 1 − jx · 1 n 1 1 − 1 m jx/n · 1 1 1 − jx/m AM 1 −x 2 ( + + AL 1 nm ) − jx(1 + 1 n + 1 m − x2 nm ) β AL = = AL 1 + AL β AM 1 −x 2 ( 1 n + 1 m + 1 nm ) − jx(1 AM + − 1 n + 1 m − 1 n x2 nm ) + AM β − x2 nm = 1 1 1 + + A M β − x2 ( n 1 m + 1 nm ) jx(1 + + 1 m ) + AM β = AL FM = FM AM − x2 ( n + 1 1 m + 1 nm ) − jx(1 + 1 n + 1 m − x2 nm (6. 26) ) | AL | | AL | = = AM FM X x 2 1 − x2 ( n + 1 m 1 + 1 nm ) 2 (6. 27) + x2 (1 + 1 n + 1 m − x2 nm )2 (??) FM −X 1 n + 1 m + 1 nm 2 +X 1 + 1 n + 1 m − X nm 2 116 = X 3 n2 m2 + + 1 n 3 1 n + 1 1 m 2 + 1 nm 2 −2 1 n 1 1 + 1 n + 1 1 1 m nm X X 2 + = 1 1 1 + m − 2F M + m + nm + F2 M (6. 28) n m2 2 [X + (n2 + m2 + 1)X 2 + {(nm + n + m)2 − 2F M nm(n + m + 1)}X + n2 m2 F 2 ] M −a + √ a2 − 3b > −b > 0 0 0 2 F M nm(n + m + 1) − (nm + n + m)2 FM > > + n + m)2 2nm(n + m + 1) (nm x 2 = X = −a + √ a2 − 3b 3 = −a + 3 √ D (6. 30) | AL p | | AL p | = = AM 2 27 nm D(a − √ D) − 1 9 ab +c AM nm −2 DX − 9 1 9 ab +c 1 f ( x) = x 3 + ax2 + bx + c f ( x) x f ( x) =0 x = = 3x + 2ax + b = 0 √ −a ± a2 − 3b 3 2 D fmin fmin = a − 3b 2 D >0 D <0 = 2 27 D(a − √ D) − 1 9 ab +c (6. 29) 117 A A. 1 A. 1. 1 ??R iR , R vR vR iR R = = = iR R vR R vR iR (A. 1) (A. 2) (A. 3) iR R vR A. 1: A. 1. 2 ??L vL vL iL ∆t ∆iL = L ∆iL ∆t (A. 4) ∆t → 0 vL iL = = L 1 L diL dt vL dt (A. 5) (A. 6) iL L vL A. 2: 118 ZL vL iL ZL 2 = = = = (ω jω L iL ZL vL ZL vL iL (A. 7) (A. 8) (A. 9) (A. 10) j (j = −1) ω = 2π f ) f A. 1. 3 ??q C iL vC iC ∆t iC ∆t ∆vC (A. 11) (A. 12) ∆q = ∆q = C ∆vC ∆vC = C ∆t ∆t → 0 iC vC = = C 1 C dvC dt iC dt (A. 13) (A. 14) iC C vC A. 3: ZC vC iC ZC = = = = 1 jωC iC ZC vC ZC vC iC (A. 15) (A. 16) (A. 17) (A. 18) A. 2 A. 2. 1 ??2 2 ( ) R1 , R2 I V 119 V1 , V2 V1 V2 = = IR1 IR2 V 2 = V1 + V2 = IR1 R + IR2 = I (R1 + R2 ) (A. 19) R 2 = V I = R1 + R2 2 (A. 20) I I V1 V V2 R2 R1 ⇒ V R = R1 + R2 A. 4: V2 V2 V V R2 = IR2 = R1 + R2 =V R2 R1 + R2 (A. 21) R ZL , ZC A. 2. 2 ??2 ( ) R1 , R2 I1 , I2 V I1 I2 I I 2 R 1 R = = V R1 V R2 = I1 + I2 = V R1 + R V R2 =V 1 R1 + 1 R2 (A. 22) = = V I 1 R1 = + 1 1 R1 + 1 R2 = R1 R2 R1 + R2 (A. 23) 1 R2 (A. 24) 120 I I1 V R1 I2 R2 I ⇒ V R = 1 1 R1 1 +R 2 A. 5: 2 ( ) 2 I2 V R2 IR R2 1 R2 I 1 1 R1 1 1 R2 I2 = = = I · + = I R2 1 R1 + 1 R2 (A. 25) A. 3 A. 3. 1 2 2 2 R a a 1 1 ( ??) ⇔ b V b A. 6: ?? a–b R1 4 Ω a 6V 8Ω R2 VL RL b A. 7: Vo Vo a–b =V R2 R1 + R2 Ri =6 8 4 +8 = 4 [V] Ri = R1 //R2 = 4//8 = ·8 = 2. 667 [Ω] 4+8 4 121 ?? [. . . ] a–b VL RL Ri RL 2. 667 a–b = Vo + RL =4 + RL RI 2. 667 Ω a 4V VL RL b A. 8: 122 B B. 1 B. 1. 1 [1] 1. 0V −0. 5 ∼ −0. 8 V 2. 3. µ (µc ) µ µ µm µm = 1. 5µc 4. E p / E g gm Ip 0. 6 µ I p (E p , Eg ) 3 I p (E p , Eg ) =G − 3α 2 1 −α 1 1 µc − 1 3 µm Ep 2 1 − 1− α E gg + Ep 1 −α 1 µc ≥ −µc Egg (B. 1) E gg = Eg + 0. 6 α 0. 6 E gg ≤0 Ep B. 1. 2 gm gm = = = ∂I p ∂Eg 1 1 −α Ip G 3 − 3α 2 1 1 −α 1 1 µc Ep − 1 3 µm Ep 2 1 − 1− α E gg + Ep 1 −α 1 −1 (B. 2) µc 1 −α · E gg + (B. 3) µc rp rp 1 rp = ∂I p ∂E p 123 = G 3 − 3α 2 1 − 1− 2 α 3 1 −α 1 1 µc 1 1 − 1 1 3 2 1 − 1− α 3 2 µm E gg 1 − −1 1 1 3 −α Ep 2 1 − 1− α −1 E gg + Ep 1 −α 1 µc + Ep = G 3 · − α µc 1 −α 1 + 3 2 Ep 1 −α 1 µc 3 − 3α 2 1 1 µc 1 Ep − + 1 − 1− α µm 1 1 Ep 2 1 − 1− α E gg 1 + Ep 1−α 1 µc − 3α × · 2(1 − α) = µ Ip 1 1 · · − α µc 1 1 E gg + Ep µc (B. 4) − 3α 2 −α rp · 1 Ep + µc · E gg 1 + Ep µc gm µ = = gm r p = E gg 1 1 + Ep · 1 1−3α 2 µc · 3 1 Ep + µc 1 · 1 1 E gg + Ep µc E gg Ep + µc 1 1−3α 2 + µc 1 = 1 − 3α 2 · µc + 1 − 3α 2 · E gg Ep ?? (B. 5) (??) ?? Ip Eg = −0. 6 Ep (??) 1. 5 E gg + E p /µc = 0 µ µc ?? (??) E gg 0 µm µm = 2 3 − 3α µc ≈ 1. 67µc (B. 6) ?? (??), (??) 1−α E gg + E p /µc (??) E gg + Ep µc = G 1−α Ip 3 − 3α 2 1 µc − 1 1 −3 α 2 1−3α (B. 7) µm 1−α Ep 2 (??) E gg + Ep µc = G 1−α {(1 − α)gm } α α 3 − 3α 2 α 1 1 µc − 1 1−3α 2α 1−3α (B. 8) µm 1 −3 α 2α Ep 2α (??) (??) 1 −α gm 3 {(1 − α)gm } 1 −α G α − 3α 2 α 1 1 α = G µc 1 − 1 1 −3 α µm 1 1 −3 α 2 Ep 2α 3 1−α − 3α) 2 µc 1−α − 1 −3 α Ip 1−α µm − 1 1 Ep 2 = gm G (1−α) 2 α 3 − 3α 2 α 1 (1−3α)(1−α) 2α (1−3α)(1−α) µc 1 µm 1 2 Ep 2α Ip 1−α = 3 3 α 1−α 1 −2 α 2 Ip G Ep 2 µc − −3 α 2 µm (B. 9) 124 (??) ?? [1, p. 124] (??) 1 B. 1. 3 E gg E gg ≤ 0 2 E gg > 0 >0 ( µ ) E st µm ( ) = E gg + Ep µm (B. 10) ( ) 1. 5 Ep 1. 5 Ik G G E gg =G E st 1. 5 =G E gg + µm (B. 11) =0 Ip Ip (??) 1 −α 1 =G 3 − 3α 2 1 µc − 1 3 2 1 − 1− α 1 1 −α 1 µm 1. 5 µc Ep 3/2 E gg =0 Ik (??) Ik =G Ep µm 1 3 2 1 − 1− α G (??) G =G 3 − 3α 2 1−α 1 1 µc 1 1 − 1 1−α 1 µm 1 − 1− α µc /2 µ3 m = = = G µm 1 − 1− α 3 2 µc 1 − µm 1 3 2 1 − 1− α /2 µ3 m G µm G µc −1 3 − 3α 3α − 3 2 µm 1 − 1− α =G µm −1 µc 3 2 1 − 1− α (B. 12) ?? [. . . ]