200 2 6 2............................... 2.2.............................. 2.3.............................. 3 2 3 2...................................... 3 2.2.................................. 4 2.3 Op-amp.................................. 7 2.4.............................. 7 2.5 Gyrator GIC..................................... 8 3 0 3................................ 0 3.......................... 3..2....................... 3 3.2........................... 5 3.2............................... 5 3.2.2.............................. 6 3.3................................. 6 3.4..................................... 8 3.4. LC.................................... 8 3.4.2 Brdged................................. 8 4 8 4.................................. 8 4.2......................................... 8 4.3......................................... 8 5 8

.. 2. 00 3. RLC 4..2. 2. 2

A B A B.3 P (The clash of clzatons) (the clash of dscplnes) 2 2 2 2. 2. LC 3 Lossless Hamlton 2. 4 2 3 4 3

G L C G : RLC 2.2 G = g ( G )= g G + g 3 3 G () G, G g,g 3 > 0 (nonlnear element) () d G d G = g +3g 3 2 G (2) (2). 2 G < g 3g 3 d G d G < 0 2. 2 G = g 3g 3 d G d G =0 3. 2 G > g 3g 3 d G d G > 0 2 G > g 3g 3 4

d dt d dt = { g ()} C = (3) L 5 d dt d dt = C { + g } = L (4) (3),, 2 3 (3) C =,L=,g =0.5,g 3 =/3 3 ( 0, 0 )=(0, 0.02) (lmt cycle) 20 (3) 2 d 2 x ( dτ 2 ε x 2) dx + x =0 (5) dτ L ε = g C,x= 3g3, τ = t g LC 6 an der Pol 5 d (0) = g d 6 ε 5

2 lmt cycle -2-2 - -2 2:.5 0.5 0-0.5 0 20 30 40 50 t - -.5 3: 6

R 0 R L C R 4 R 2 0 R VC R 3 (a) (b) 4: (a) (b) (3) 2 d 2 { y dτ 2 ε y = ( ) } dy 2 dy + y =0 (6) dτ dτ g3 L g C, τ = LC t 9 (Raylegh) 3 (3) (5) (6) 2.3 Op-amp 2. 2. 2.4 4 0 ( 0 = + = R + R ) (7) 7

R R 2 C 0 R 5: Gyrator = R ( 0)= R R (8) R R (NIC: negate mpedance conerter) 4(a) 4(b) R 4 2.5 Gyrator GIC 5 + C d ( 0 ) =0 dt = ( 0 ) R (9) 2 = R C d dt (0) L = R C () (GIC: Generalzed Impedance Conerter) GIC 6 8

2 2 B Z Z 2 Z A 3 Z 4 Z 5 3 4 6: Generalzed Impedance Conerter 2 + 3 = 0 Z 2 Z 3 3 + 4 = 0 Z 4 Z 5 (2), 4 2, 3 2 = 3 = ( Z 2Z 4 ( Z 3 Z 5 + Z 4 Z 5 ) + Z 2Z 4 Z 3 Z 5 4 ) Z 4 Z 5 4 (3) = 2 = { ( Z Z 2 = 4 Z 5 Z 2Z 4 Z 3 Z 5 ) Z } 2Z 4 4 = Z 2Z 4 ( 4 ) Z 3 Z 5 Z Z 3 Z 5 (4) Z n = 2 = Z Z 3 Z 5 Z 2 Z 4 Z out = 4 2 = Z 5 (5) (2) 3 2 = Z 2Z 4 Z 3 Z 5 ( 4 ) (6) = Z ( 2 )= Z 2Z 4 Z Z 3 Z 5 ( 4 ) (7) GIC 7 A, B KCL 9

R 2 R 3 B A 3 4 C 4 R 5 7: Smulated Inductor 2 + 3 =0 R 3 4 d + C 4 R 5 dt ( 3 )=0 3 4 = C 4R 3 R 5 d dt ( 3 )= C 4R R 3 R 5 d dt (8) (9) L = C 4R R 3 R 5 (20) 3 3. 0

R L R L C R C C 2 2 2 (a) (b) L R L R C R2 2 L 2 C (c) (d) 8:.. 2. (a) (b) Brdge 3.. 3. 8. (c) 9(a) I

L L R E e jωt C R C (a) (b) 9: (c) (a) (b) ( jωlr R + jωl + + ) I = Ee jωt =0 (2) jωc CR + L = 0 (22) ω 2 LC (R + ) = R R < 0 7 R > 0 < 0 R = L C ω = LC R ( L C ) (23) L R > C (b) C d dt L d dt = + R R + R + = R R + R R + (24) [ µ 2 + C (R + ) + R L (R + ) ] µ + µ = jω (23) R =0 (25) LC (R + ) 7 L>0 C>0 2

Lnear passe RC Lnear passe RC R (a) (b) 0: (a) (b) =0 LCR 8 3..2 0 3 RC (b) d = ( + ) + { + R ( 4 + )} 2 dt C R C R R 3 R d 2 = + (26) R 4 2 dt C 2 C 2 R 3 [ µ 2 + C ( R + R2 ) R 4 C 2 R 3 ] µ + C R C 2 =0 (27) R 4 = ( + ) C 2 R 4 C R (28) ω 2 = C R C 2 8 3

C 2 C C 2 0 R 2 0 R 3 R 3 R 2 R 4 C R 4 (a) (b) R 3 R 3 C 0 C 0 C 2 C 3 R 4 C 2 C 3 2 R 3 R 5 2 R 3 (c) (d) C R 3 C 2 C 3 R 0 2 3 0 C 2 C 3 R 4 R 3 R 4 2 R 3 R 5 C R 5 (e) (f) : 4

ma 6 V 3.6 ma 4 = 3. tanh(0.6 ) = 2.2 tan - ( ) 3 2 750KΩ 750KΩ 2SK30A x axs[v] 2 0-2 0 - R 4 600Ω y axs[v] -4-2 (a) -6-3.6-5 -4-2 0 2 4 5 V (b) -3 2: FET 3.2. 9 2. 3.2. FET 2(a) 2(b) = g () =α tanh (β) (29) = g () =α tan (β) (30) R = 600[Ω] R = Rg () =f () =3. tanh (0.6) (3) 9 5

[ma] 0.04 R=50k 0.03 R 47 x axs 47k 0k 45k 0k 0 y axs 0.02 0.0 0.00-0.0-0.02 40k 25k 40k -0.03 (a) -0.04 -.6 -.2-0.8-0.4 0.0 0.4 0.8.2.6 [V] (b) 3: 3.2.2 3(a) 3(b) 3.3 4 6

4: 7

5: 3.4 3.4. LC 3.4.2 Brdged 4 4. 20 5 3 6 Wen 4.2 4.3 5 8

R 6 3 C 3 2 R 7 C 2 0 E C R 3 R R 4 6: Wen 9