交流阻抗谱的表示及应用_崔晓莉.pdf-道客多多

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1、30 4 Z =Sv(1 S) Vol. 30, No. 42001 M12 Journal of Shanghai Teachers University(Natural Sciences) Dec . 2 0 0 1 E F V U#崔晓莉,江志裕(复旦大学化学系,上海 200433)K 1: 介绍了交流阻抗谱不同的表示形式,依据4种典型的等效电路的理论阻抗绘制了它们的 Nyquist图、导纳图、电容图、Bode图和 Warburg图,并对不同形式图谱的特点及应用范围进行了概述.1oM: 交流阻抗谱;Nyquist图;导纳图;电容图; Bode图;Warburg图ms |: O646.5

3、 F.E F L q1,#Z k- 1/2m, XWarburgmBL.Lk- 1/2 , W Rs.55 4 ak ,: E F V U#3 AE V m 3. 1 Nyquistmr mm(b), E FVr TZ= 1/(1/Rct)+ jkCd . (17)Z = Z+ jZ= Rct1+ k2C2d R2ct- j kCd R2ct1+ k2C2d R2ct. (18)N T V,(Z- Rct /2)2+ (- Z)2 = (Rct /2)2. (19)T(19)NyquistmBRct /2,Nyquistm V pQERct.ZKv, qk*#QE, V p ,Cd =1/(k

5、logf- logk= - log Cd - logk= - logCd - log 2f . (25) u, Xlog|Z|logfWm| q- 1L,logf = 0 H,Llog|Z| (- log Cd - log 2). V p .tg(- ) = RctkCd. (26) T(26) VBodem,k 0 H, 0.k H,- 90.3. 5 WarburgmZ= Rct /(1+ k2C2d R2ct),Z k- 1 /2m,k 0,k- 1/2 H,Z Rct;k,k- 1/2 0 H,Z 0.4 AE ? m 4. 1 Nyquistm56 Z =Sv(1 S) 2001 M

6、r mm(c), E FVr T VZ = Rs + 1/(1/Rct)+ jkCd . (27) T(27) VZ = Rs + Rct1+ k2C2d R2ct- j kCd R2ct1+ k2C2d R2ct. (28)(Z- Rs - Rct /2)2+ (- Z)2 = (Rct /2)2. (29)E F Nyquistm T, L(Rs+ Rct /2, 0),Rct /2.Nyquistm,QE , AE . qk* = 1/(RctCd ), V p 4.4. 2 ,m , VY = (Rs+ Rct+ k2C2d R2ctRs)(1+ k2C2d R2ct)+ jkCd R

7、2ct (1+ k2C2d R2ct)(Rs+ Rct+ k2C2d R2ct Rs)2+ k2C2d R4ct. (30) q H, VeY = k2C2d Rs+ jkCd1+ k2C2d R2s. , LiVh k,Y- 1/(2Rs) 2+ (Y)2 = 1/(2Rs) 2. (31) T(31) A ,m H T, L 1/(2Rs ),0,1/(2Rs),Nm V pERs. q H,k 0, k2,k3, VY = 1/(Rs+ Rct) .k 0 H, , l Y B, 1/(Rs + Rct).M H, Vr Cd8 .4. 3 m VC = kCd R2ct (1+ k2C

8、2d R2ct) - j(Rs+ Rct + k2C2d R2ctRs)(1+ k2C2d R2ct)k(Rs + Rct+ k2C2d R2ct Rs )2+ k3C2dR4ct. (32) q H,k2R2ctC2d 1, T Rs, Rct1, LiVh k, VBZ T(33). L (Cd /2,0),Cd, qk* = 1/(RsCd ).(C- Cd /2)2+ (C)2 = (Cd /2)2. (33) q,k2R2ctC2d 1,kf2 1,5 T(36),log|Z|= log Rs, u,|Z| Rs, VVBodemRs .tg(- ) = R2ctkCdRs+ Rct

9、+ RsR2ctk2C2d. (37)V(37) V A, u, tg(-) 0, 0; u,9 tg(-) 0, 0.W q u,0- 90WM.4. 5 WarburgmZ= Rs+ Rct /(1+ k2R2ctC2d ),#k,k- 1/2 0 H,Z Rs;k 0,k- 1/2 H,Z Rs + Rct.5 i Him 5. 1 Nyquistmr m(d), E FVr T3,4Z = Rs+ ab2+ k2C2da2 - jkCda2+ ek- 1/2bb2+ k2C2da2 . (38)T(38)a= Rct+ ek- 1/2, b= 1+ Cdek1/2,eWarburg“

10、, “ 、 i1,WarburgEF VVrRW = 1/(kCW ) = ek- 1/2. (39) AiB 0O H,e= RT /( 2n2F2c0O DO). (40)T, DOc0OsY 0O “ i.e, V T(40) p “ . q H,WarburgE Fl, i V , T(38) Ve T(28).E FNyquistmB3,4. u VRs,Rct,Cd . q H,b 1, k1/2,k,k2, VZ = Rs + Rct+ ek- 1/2 - j(2Cde2+ ek- 1/2). (41)Z= Rs+ Rct+ ek- 1/2. (42)- Z= 2Cde2+ ek

11、- 1/2. (43)Z= Rs + Rct - 2Cde2+ (- Z). (44)E FNyquistm| q1L,Z Rs+ Rct - 2Cde2. uRs,Rct,Cd , Warburg“ e, V p “ . qS =,VCBBL.m sRs, Rct, Cd#eMvl qSY, ,zS qS =A U+.5. 2 ,m ,Vr T:Y = (b2+ k2C2da2) a+ Rs (b2+ k2C2da2)+ j(kCd a2+ ak- 1/2b)a+ Rs(b2+ k2C2d a2) 2+ (kCda2+ ak- 1/2b)2 . (45)k H, i V , ,Vr T V

12、T(30)(31)V U, ,mVCT.k 0 H, T(45) k,k2, V58 Z =Sv(1 S) 2001 MY= (Rs+ Rct+ ek- 1/2)+ j(2Cde2+ ek- 1/2)(Rs+ Rct+ ek- 1/2)2+ (2Cde2+ ek- 1/2)2. (46)ek- 1 /2 (Rs+ Rct) H,Y 0, Y 0, tUS.5. 3 m Vr T:C = (b2+ k2C2da2)(kCd a2+ ak- 1 /2b)k- j(b2+ k2C2da2)ak+ kRs(b2+ k2C2da2)ak+ kRs(b2+ k2C2da2) 2+ k2(kCda2+ ak

13、- 1/2b)2 . (47)k H,M i V ,T AE ? f B, mB.k H, T(47) k,k2 T(48).C = ek- 1/2 - j(Rs+ Rct+ ek- 1/2)/2e2, (48)C= C- (Rs + Rct) /(2e2). (49) T(49) V, qRctl H, i i H m| q1L.m sRs,Rct,eMvl# qSY v,Hq/,Sm,A U +.1q E F mY, | 6) .5. 4 BodemBodem, u,M i V ,T AE ? f B.|Z| Rs ,tg(- ) 0, 0. qv H,8“ q Tv A, i V ,lo

14、g|Z|logfW| q- 1; q H,8“ i,N H,Rs , Rct ( V ,y F(kCd )- 1,7WarburgE Fek- 1/2,yN,kl H,r Cdg V , H,Z = ek- 1/2 - jek- 1/2,log|Z|= logek- 1/2+ log 2 = log(e/ ) - (1/2)logf .#log|Z| logfL| q- 1/2.5. 5 Warburgm8“Kil WarburgmZ k- 1 /2m. T(42)、(43) V A, uZk- 1 /2VCL,Z k- 1/2L w: (Rs+ Rct). - Z k- 1/29L, 2Cde2,| qe, V pCd “ .6 YV s V A,BFE F , VNZ TV U , L 8Hq,4 aV UZE ?ZL q ,iB Q .+Yt LHq/,Bm, H Tm, 8“T .6, V UZE VM.“ E F V U T, V L() q m T, EG Nyquist plot; Admittanceplot; capacitanceplaneplot; Bode plot; Warburgplot61 4 ak ,: E F V U#

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