《中国科学》A、E、G与F小开本版式设计

Size: px

Start display at page:

Download "《中国科学》A、E、G与F小开本版式设计"

宋姚
7 years ago
Views:

1 G 2005, 35(): 47~6 47 * ** (, 3620),. 3 : ( ) :. ( ) :,,,,. ( ),,.,, Maxwell 3...,,,., Gustav Kirchhoff [], 960, Gustav Kirchhoff., Gustav Kirchhoff.,, Gustav Kirchhoff , * ( : ) ** snchen@hqu.edu.cn

2 48 G 35 [2].,,.,.,,, ( ),,, (Ohm ) (Kirchhoff ) ;,.., [3,4],., 3.,,. Maxwell,,, [5]. 2. Maxwell 3 ( R) = ε, = µ, + = ρ D E H E k j () N [6] d 0, = j s (2) * ( R) * iω * d d ( * t t lt = ρ t t t lt + µ t t ε t t )dvt j k j j H H E E. (3) kt. (2) N,

3 49 a µ [ ] N [6], N, t (2) a µ t t d µ t = 0 S µ t a j s a j = 0 (µ =, 2,, N ), (4) µ t t, ( jt d sµ t ), = cos( j,d s ) =, ( j d s ), 0, ( jt d sµ t ). µ t t µ t t µ t s µ t µ s µ t j t. Kramer, (4) [6] (4), (6) N, i j j = g j (i =, 2,, N ), (6) i k= N i j ik k (5) Dik gik =. (7) D N + k j k j i k [6], D D (4) a µ 2 [6]. (4) ik (6), D 0 D 0., [6] : ik t () D 0, N i,., i k. (2) D ik 0, D i k i ( i =, 2, ) ik k ( k =). l k,., l k. (3), E E* * H H j j *. (3) E E* * H H, j j *., ρ ( C) ( M) ρ

4 50 G 35 [6] s. cos(, ) ( M ) iωµ jt jg ρtg = dlt 4π h ( C) ρ =, (8) iωε s tg (t = g ), (9) (3) i k, (6),. D 0, i, ; D ik k 0,, i k ( )., (6) (3)., l k N + [6]., N + [6] m+ k ( R) ( C) ( L) ( M) d ( ) d k l = ρ + ρ + ρ j l+ ρtg jg dlg (k = N, N +,, ). lk' lk' g= ( t g) (4) ĵ ( ). I j = s n, Î ) cos( j,d s ) I ds = 0 (µ =, 2,, N ), () t µ t t µ t n n ( R) ( C) ( L) dl cos(,d ) d cos(,d ) ( kt kkt lkt kkt lkt = jkt l kt ρkt + ρkt + ρkt ) Ikt + n e= ( M ) dl cos(,d ) e je l e ρte Ie (k = N, N +,, ) (t e), (2) kt k l k t. Î, (2) 2 : ) ( ) ( ) ( )., 2000, ~27

5 5 ( R) ( R) dlkt kt = ρkt Z, ( M) ( M) dle kte = ρkte ( C) ( C) dlkt kt = ρkt Z, ( L) ( L) dl kt Zkt = ρkt ', Z, ε kt = kkt lkt, (3) n n ( R) ( C) ( L) kkt lkt εkt = jkt l kt Ikt Zkt + Zkt + Zkt cos(,d ) cos(,d ) ( ) n + cos( j,d l ) e= ( M ) e e IZ e kte ε k 't (k = N, N +,, ). (4) ( t e)., (4), () (2) 2 (3) (4) 3. 2, Gustav Kirchhoff ; 5 4 [7,8].,,. 2. ( ) [6]). (3) (2), (2) Î., (8) (9) (3) : 4 R = ( R) d l ρ, t t t tt C =, dl ε () lsl () µ cos( jt, jt ) µ cos( j L = d l d l, e, jt) 4π Mte = d lt d le, h 4π h (3) te (5) ) 50 )

6 52 G 35 ( R) ( C) ( L) ( M) Z = R, Z =, Z = iωl, Z = iω M. (6) iωc. k = E, Ê E d l k d l.,, 4 E d l = ρ j d l, ( R) E dl = j d l, L ρ ( ) ( C E dl = ρ ) j d l, E dl = ρ j d l. e= ( M ) te e e (3) Z, V : V = E d l, 4 IZ (R C L) = V (R C L), ( M) ( M) IZ = V, (7) e te t e=. (6) (7),,, 4 [6,9,0] V (R) = IR, (C) V = I, V (L) = i ω iωc LI, vt () qt () vt ()dt d Φ() t Φ() t R =, C =, L = = =, M it () vt () di d i it () V = I M ( t e). (8) (M) t iω e te e= te ve()d t t d Φe() t Φe() t = = =, dit d it it( t) (9) (5) R, C, L, M 4 ; (9) 4 i, v, q, Φ., (5), (9). (9).,. 2.2 [6] Z M kte (5) (6), ( ) cos(, ) M Z = jt j e Z kte, ( M ) kte ( jt je ), cos( jt, je) = ( jt j e ),

7 53 cos( j,d l ) (4) 3 (, kt kt )., (4) cos(,d ) ( + + ) ± ± = 0 n ( R) ( C) ( L) ( M) jkt l kt Ikt Z kt Zkt Zkt εkt Ie Zkte e= ( t e, k = N, N +,, ), (20) (7), 4 RLC ( R) ( C) ( L) ( M) ( ) t = t + t + t t ± εt ± te e e= V Z Z Z I Z I ( t e) (t =, 2,, ), (2) R C L R C L I ( ) ( ) ( ) ( ) ( ) ( ) t = ( G t + G t + G t ) V t ( G t + G t + G t ) ε t (t = 2 ), (22) G = Z. 2.3 Gustav Kirchhoff [6] (4) Gustav Kirchhoff, (20) (2) Gustav Kirchhoff a µ tit = 0 (µ = 2 N ), (23) b kt Vt = 0 (k = N N + ), (24) ( t lk ), bkt ' = cos( jkt,d l kt ) = ( t lk ), 0 ( t ) a µ t, a µ t (5). (5) (25) Gustav Kirchhoff. (25) (23) (24) Gustav Kirchhoff,,., (23) (24) Gustav Kirchhoff., Gustav Kirchhoff.

8 54 G [6~8] (23) (24) (2) AI = 0, V = 0 V = ZI ±, (26) ε Z Z Z ( RCL) ( M ) ( M ) 2 [ ], [ ], Z Z Z A = aµ t = bkt Z = ( M) ( RCL) ( M) Z Z Z ( M ) ( M) ( RCL) 2 N, N + [8]. []. g ik, ( k = i) = 0, ( k i) (4) (6) N ik k ik k k' = k = N (27) (i =, 2,, N ; k =, 2,. N ), (28) g j g j = 0 (i =, 2,, N ), q ik jk = 0 (i =, 2,, N ). (29) k ' = N (7) (28), (29) q q ik ik QI = 0, D = g = ik (i =, 2,, N ; k = N, N +,, ), D, ( k = i) = gik = 0, ( k i) ik [ ik (30) (i =, 2,, N ; k =, 2,, N ), (3) (30) Q = q ] N (6), (3) D D []. ). (24) (4), (24) ik ),,,. 4, 998, 349~352

9 55 V N = m V (k = N, N +,, ), (32) k' k i i i= (6),, N + (32) N + M = [ m ki ] E m ki MV = 0, (33) Eki = (i =, 2,, N ; k = N, N +,, ), E m k ' i (24) ki E, ( k' = i) = 0, ( k' i) ki (i =N N+; ), (34) b 2. (32), (34) E E ) [6,8] ki (6) j ( i = N, N + ;,, i k j ). k,, (6), k j j ; k, m (6), k j k j., (6), T I = M I m I = T Il., [6,8,2] k k, (24) V N k bki Vi i= = (k = N, N +,, ), V V k i. i l j (35), V ( k =, 2,, N, k V )., V, υ i i ) 54 )

10 56 G 35, Vi υ '., 2 T V = A υ T V = Q υ '. (36),. 3,, Maxwell,,,,.,,, [3] R+ + iωl+ iωm = ( R + R ) + iω( L L ) 2iω M iωc i ± C C ω 2 R+ + iωl R2 + + iωl2 iω M iωc iωc2 R+ + iωl+ iωm = iωc R+ + iωl + R2 + + iωl2 2iω M iωc iωc2 ( ) , (37) (37), RLCM [6] + C C2 ω0 = L + L ± 2 M [4] /2 N υ G = cos( j,d s ) G V cos( j,d s ) I µ t µµ µ µ t µ t µ t sµ t µ t µ t s µ ' =., (38) (39) (µ =, 2,, N ), (40) Ĝµµ ( µ = µ ) ( µ µ ) cos(,d ) cos(,d ) µµ µ t µ t µ t µ t G µ t G = j s j s (µ, µ =, 2,, N ). (4) 3.3 [5] N+ n k Z I = cos( j,d l ) ε (k =, 2,, N + ), (42) kk k kq kg kq k' = q=

11 57 Z kk ( k = k ), ( k k ). n k Z = cos( j,d l )cos( j, j ) Z kk kq kq kq k g kq q= (k, k =, 2,, N ; g =, 2,, 3.4 [6] N G V = cos( j, C ) G V cos( j, C ) I ii i it i it sit it i sit i' = n k ). (43) (i =, 2,, N ), (44) G ii ( i = i ) ( i i ) G' ii ' = cos( j C )cos( j C ) G (i, i =, 2,, N ). (45) it i i' t i' it 3.5 RLC [7] 3.6 [6] 3.7 [6] 3.8 [8] 3.9 [9],,,. (4),, 4, (5),.,. 4 [20,2])., (E, H, j, )

12 58 G 35 ), ), s jt ds t = 0 (µ =, 2,, N ), (46) µ t µ m+ k ( R) ( C) ( L) j d d ( d ) d d ( M ) jg = ρ j l+ ρ j t l+ ρ l+ ρ t l tg g= t ( t g) k l l l l l k' k' k' k' d g (k = N, N +,, ), (47) ρ ( C) cos(, ) ( M ) µ jt jg ρtg = d lt 4π h tg =, ε s ( g ), (48) j j, (47) dt t j,., ) s ji ds i = 0 (µ =, 2,, N ), (49) i= µ i µ m+ k ( ) ( ) ( ) ( ) k dl R d C ( d ) d L j d M j e = ρ j l+ ρ j t l+ ρ l+ t ρ d l t e te t lk' lk' lk' l = = k' ( t e) (k = N, N +,, ), (50) (49) (50) (46) (47), (49) (50) ρ ( R) ( C) ρ ( M ) tg ρ ρ ( M ) 9, = 3 3 4π ρ ρ tg m= n= ik ρ mn ( R) 3 3 = ρ cos( j, e )cos( j, E ), m= n= mn n m 3 3 ( C) s D ε D = mn j en j em m= n= s µ W mn cos(, )cos(, ), cos( j, e )cos( j, e )dlt g n t m /2 3 3 µ jk Rtg, j Rtg, k j= k= ( t = g ), ε mn µ mn e (5) ) 57 )

13 mn mn mnl jl mnlp jj l p l= l= p= ρ = ρ + ρ + ρ mn mn mnl mln l mnlp m p mpln l p l= l= p= ( ) ( ln ) ε = ε + ε + ε E + ε + ε + ε E E mn mn mnl Hl mnlphl Hp l= l= p= µ = µ + µ + µ + W mn,, (52) W = µ 22 µ 33 µ 23 µ 23 ; W 2 = µ 23 µ 3 µ 2 µ 33 ; W 3 = µ 2 µ 23 µ 22 µ 3 ; W = µ µ µ µ W 22 = µ µ 33 µ 3 µ 3 ; W 23 = µ 2 µ 3 µ µ 23 ; (53) ; W 3 = µ 2 µ 32 µ 3 µ 22 ; W 32 = µ 3 µ 2 µ µ 32 ; W 33 = µ µ 22 µ 2 µ 2, (52) ρ mn, mnl ε mn, µ mn, ρ mnl, ε mnl, µ, ρ, ε, µ 3 mnlp [6] mnlp mnlp m = ρmn n + ρmnl n l + ρmnlp n l p n= n= l= n= l= p= +, E j j j j j j m = εmn n + εmnl n l + εmnlp n l p n= n= l= n= l= p= D E E E E E E m = µ mn n + µ mnl n l + µ mnlp n l p n= n= l= n= l= p= +. H H H H H H ρ mn ρ ( m = n), ( ), m = n = εmn = ε 0 ( m n), 0 ( m n), +, (54) ) Maxwell (49)~(53).,, µ mn µ ( m = n), = 0 ( m n), W mn ( µ ) 2 ( m = n), = 0 ( m n),, (5) (48), (49) (50) (46) (47). ) 57 )

14 60 G 35, j k t,, jt () = Im (j ) jt () Im( i = ω j), jt ()dt Im j, t = (55) iω (47) ρ ( ) ρ ( ) ( ) m+ k R C Im d d L d d ( M ) k l j l iω ρ iω ρtg g d g = 0, iω j l j l j l g= ( t g),, (47), ( C) ( C) ( L) ( L) ( M) ( M) ρ = ρ, ρ = iωρ, ρ = iωρ. (56) iω, (55), (49) (50) [20] [2]., 4,., ,, 3. : 4 ( ). 4,, () 3 ;, (3). ()~(3),.,, 3. Gustav Kirchhoff.,., Gustav

15 6 Kirchhoff. Maxwell,,,.,. C. A,.,. :, N., T. A... :, :, 99. ~6 4., 996, 4(5): 345~350 5,,,., 3. :, 2000, 89 6,,.. :, 999 7,.. :, 983, 254~389 8,,.. ( ), 993, 4(2): 59~68 9., 99, 36(): 24~27 0.., 993, 38(6): 527~53. ( ), 994, 5(3): 335~339 2,,., 998, 26(9): 23~26 3, 4. ( ), 999, 20(2): 9~94 4,,., 998, 26(6): 78~8 5,,, 2000, 28(7): 42~45 6 Su W X, Cui S, Wang J C, et al. The deduction of general equation of cut set voltage method in non-linear network by field theory. Chinese Journal of Electronics, 2000, 9(): 08~2 7,,., 998, 26(3): 20~ ( ), 200, 7(4): 48~52 9 Hong Q Q, Wang J C, Chen S N. A general equation derived by field theory for the use of uniform transmission line with mutual inductance. Chinese Journal of Electronics, 2004, 3(2): 24~28 20,.., A, 994, 24(2): 36~326 2,,., 2000, 28(9): 02~04