(4.15a) Hurwitz (4.15a) {a j } (s ) {a j } n n Hurwitz a n 1 a n 3 a n 5 a n a n 2 a n 4 a n 1 a n 3 H = a n a n 2. (4.16)..... a Hurwitz H i H i i H

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1 6 ( ) u(t) w(t) K w(t) = Ku(t τ) (4.1) τ Ξ(iω) = exp[ α(ω) iβ(ω)] (4.11) (4.1) exp[ α(ω) iβ(ω)] = K exp( iωτ) (4.12) α(ω) = ln(k), β(ω) = ωτ (4.13) dϕ/dω f T 4.3 ( ) OP-amp Nyquist Hurwitz PID Hurwitz U( s) + G( s) W( s) Ξ(s) = G(s) 1 + h(s)g(s) Ξ(s) s n (4.14) h( s) 1 + h(s)g(s) = a n s n + a n 1 s n a = (4.15a) = a n (s p 1 ) (s p n ). (4.15b) 6-1

2 (4.15a) Hurwitz (4.15a) {a j } (s ) {a j } n n Hurwitz a n 1 a n 3 a n 5 a n a n 2 a n 4 a n 1 a n 3 H = a n a n 2. (4.16)..... a Hurwitz H i H i i H 1 = a n 1, H 2 = a n 1 a n a n 3 a n 2, H a n 1 a n 3 a n 5 3 = a n a n 2 a n 4 a n 1 a n 3,. (4.17) Hurwitz Hurwitz (4.15a) H j > (j = 2,, n = 1) (4.18) ( H 1, H n > ) n Hurwitz E(s) O(s) E(s) = O(s) = D(s) N(s) 6-2

3 4.8 Y (s) = G(s) F (s) [G C(s)R(s) + D(s) + G C (s)h(s)n(s)] F (S) 1 + G C (S)G(s)H(s) = W RY (s)r(s) + W DY D(s) + W NY N(s) (4.19) ( D(s) ) PID PID ( ) PID (P, proportional compensation) (I, integral compensation) (D, derivative compensation) ( ) G(s) ( ) G c (s) 4.9 PID s 1 s P K P ( ) I K I /s D K D s PID 4.9 G c (s) = K P + K I s + K Ds (4.2) 4.9 Y (s) = R(s) ( [1] ) P Γ R R /(K P Γ + 1) PID CPU 4.9 PID 4.4 OP pn (bipolar junction transistor, BJT) (field effect transistor, FET) 6-3

4 1 8 j p n 1 6 ev ûœü (a) J / J 1 4 J 1 2 t ûœü 1 ƒvƒ ƒbƒnƒœ [ _ (b) V 1 e V / k B T 2 (c) 4.1 (a) pn ( ) (b) p (c) (4.21) (2 ) 4.1(b) (dv/dj) pn ( ) p,n pn pn 4.1(a) pn 4.1(a) p n n p S ( ) pn U U T S pn *1 ( ) ( ) (built-in field, built-in potential) p n p 4.1(b) ( ) ] ev J(V ) = J [exp 1 (4.21) k B T *1-6-4

5 (4.21) (4.21) 4.1(c) J p n (4.21) (forward bias voltage) (reverse bias voltage) p n n p (minority carrier injection) pn - (Zener tunneling) ( ) pn 3 npn pnp (E) (B) (C) ( 6 pn 8 7 ) (a) ( ) J E = J C + J B (4.22) 2 2 ( ) (J E = ) IV pn 4.12(a) (J C = ) IV (J B = ) 4.11 (a) PNP (b)npn 6-5

6 J C (ma) (a) 2N222a J E = 1mA 2mA 3mA 4mA 5mA J E džq V BC (V) V BC B E n p n J C C J C (ma) N222A J B = 2 A A A A A.5 1 V CE (V) (b) E J E džq n B p J B n V CE C J C 4.12 (a) V BC ( ) - (b) - V CE pn pn 4.12(b) J B J C J E V BE IV 4.12(a) *2 J B J C J E V BE J C 4.13(a) V BE J C 4.13(b) J C J B E B h F E J C = h F E J B (4.23) h F E, 1 1 *2 pn IV 6-6

7 N222A V CE = 6V J C (A) N222A V CE = 6V J C (ma) J C (A) J B (A) (V) V BE J B ( A) (a) (b) V BE džq E n (c) B p J B n C J C 6V 4.13 (c) (a) - - V BE J C (b) J B J C ( ) 1 H ( ) ( ) ( ) ( ) V1 H11 H = 12 J1. (4.24) J 2 H 21 H 22 V 2 H h h ij h 4.14(b) (4.23) h 21 = h F E IV h ( ) ( ) ( ) ( ) ( ) v1 h11 h = 12 j1 hi h = r j1 j 2 h 21 h 22 v 2 h f h o v 2 (4.25) v, j ( ) E, B, C h i h o e, b, c (4.23) h 21 = h F E = h fe (4.23) h F E h fe 4.14(c) h 6-7

8 I C h fe 4.15(a) C d C d R 1, R 2 ( ) 4.15(b) v i } v i = h ie j b + R E (j b + h fe j b ) v o = h fe j b R C A A = v o h fe R C = v i h ie + R E (1 + h fe ) (4.26) h fe 1 A = R C /R E h fe Z i R 1, R 2 Z i Z i Z i = v i j b = h iej b + R E (j b + h fe j b j b = h ie + R E (1 + h fe ) (4.27) 4.14 (a) 4 H( ) (b) 4 (c) npn 2SC373 h 4.15 (a) (b) (a) 6-8

9 Z o Z o = v o j o = h fej b R C j b = R C (4.28) h 4.5 ( ) (field effect transistor, FET) pn FET(JFET) MOS(metal-Oxide- Semiconductor) FET MESFET( FET) HEMT( FET) p n FET MOSFET 2 MOSFET FET (S) (D) (G) G S,D FET 4.16(a) S,D JFET S,D MESFET HEMT MOSFET S (n p ) 4.16(b) (e) ドレイン D D D D D ゲート G G G G G S S S S ソース S (a) (b) (c) (d) (e) 4.16 FET JFET pn pn na G Z in Ω MOSFET pa Z in Ω FET JFET 4.17(a), (b) JFET(n ) JFET V GS V DS J D ( ) V GS J D V GS = V P ( ) V DS V DS J D V GS V GS = J D (V GS ) J DS V GS 6-9

10 ドレイン (ma) JD (a) SK14 V DS 1V ドレイン (ma) 2 V V V V P V ゲートソース V GS (V) ドレインソース (V) (b) JD 6 4 V GS V V V V 4.17 FET (a) V DS (b) V DS 4.18 FET (a) (b) (c) p JFET V GS V P, J D, J DS n MOSFET MOSFET JFET V GS JFET FET V GS = J D ( ) 4.17(a) V GS J D (n ) CMOS MOSFET FET JFET MOSFET n JFET V GS } J G, (4.29) J D = f(v G, V D ) FET

11 Y Y 11 Y 12 Y 21 Y 22 g m r 1 d g m g m + r 1 d g m + r 1 d r 1 d (g m + r 1 d ) r 1 d 4.1 (a) (b) (c) Y f ( ) JD g m, (4.3a) V GS V D =const. ( ) VD r d (4.3b) J D V GS =const. g m r d j d = g m v gs + v d r d (4.31) j, v 4.19(a) µ µ r d g m (4.32) FET (a) (b) (c) (b),(c) FET 4.19 Y Y 4.1 [1] 2. [2] OP (CQ, 199) [3] (CQ, 1991) 6-11

MOS FET c /(17)

MOS FET c /(17) 1 -- 7 1 2008 9 MOS FT 1-1 1-2 1-3 1-4 c 2011 1/(17) 1 -- 7 -- 1 1--1 2008 9 1 1 1 1(a) VVS: Voltage ontrolled Voltage Source v in µ µ µ 1 µ 1 vin 1 + - v in 2 2 1 1 (a) VVS( ) (b) S( ) i in i in 2 2 1