Описание элементов программы.

Отчёт

Задание №1.

Расчёт параметров диодной цепи с колебательным контуром.

 

 

Выполнил

студент гр. 4025/10 (___________) Рыженков В.С.

 

Руководитель:

доцент, к.т.н. (____________) Карпенко Л.Н.

 

 

Санкт-Петербург

1)Постановка задачи:

Дано: С, L, R1, R2, R3, Uco

Найти: i1(t), i2(t), i3(t), uc(t), Wм(t), Wдж(t), ul(t) и ε(t) – погрешность.

Построить графики указанных зависимостей.

2) Разработка математической модели:

1) Цепь до коммутации(t<=0)

i1= i2= i3= 0 (A)

uc=Uco

 

2) Цепь после коммутации, в устоявшемся режиме (t>>0)

i1’=i2’=i3’= 0 (A)

uc’=o

 

3) Цепь в момент коммутации(t=>0)

С условием:

 

Сформируем два дифференциальных уравнения первого порядка и избавимся от переменных i1(t) и i3(t).

В итоге:

Из уравнений производных:

Получаем конечные выражения:

 

 

4)Баланс энергий: ,

где - начальная энергия в конденсаторе;

- тепло, выделяющееся на активных сопротивлениях R₁, R₂, R₃ и диоде;

- энергия магнитного поля в катушках индуктивности;

- энергия электрического поля в конденсаторе.

5) В программе используются следующие обозначения:

Задаём величины параметров: U_C0=300 В, C=10^-5 Ф, R₁=0.5 Ом, R₂=0.2 Ом, R_пр =100000 Ом, R_обр =0.01 Ом, L=0.005 Гн.

Задаём параметры интегрирования дифференциального уравнения (используется встроенная подпрограмма IVPRK):

 

Tb =0 – начальный момент времени счёта,

Tk =0.02 – конечный момент времени счёта,

HT =0.00005 – шаг счета,

TOL =0.005 – погрешность счёта.

 

Баланс энергии соблюдается тем точнее, чем меньше шаг счета ht.

 

Y(1) – массив содержащий значения Uc(t)

Y(2) – массив сожержащий значения i2(t)

YPR(2) – производная тока в катушке (di2/dt)

YPR(1) – производная напряжения на конденсаторе

npoint - номер текущей точки, для заполнения массива Egrafic

I1, i2, i3 -токи соответственно в текущий момент времени t

I1pred, i2pred, i3pred -токи соответственно в предыдущий момент времени t

Uc, Ul - напряжения соответственно в текущий момент времени t

wc, wl, wdg – энергии соответственно в конденсаторе, в катушке и выделившаяся на активных элементах.

ERR – погрешность

xarr, yarr – массивы абсциссы и ординаты для построения графиков

 

6) Блок схема задачи:

Описание элементов программы.

1) Задаём имя программы и открываем необходимые библиотеки:

PROGRAM Zadacha1

use msimsl

implicit none

 

2) Задаём тип и характер представляемых чисел(количество графиков, параметры программы IVPRK, число производных, начальные данные и промежуточные величины):

integer npoint*4, ncurv*2/5/, ido, istep, mxparam, n, s/50/

parameter (mxparam=50, n=2)

real param(mxparam), t, tend, tk, tol, ht

real l,c,r1,r2,r3,rpr,robr

real Uc0, uc, ul, i1, i2, i3, wdg, wc, wl, wc0, wm, err, poligrf

real Tpred, I1pred, I2pred, I3pred, ucpred, ulpred

real y(2), ypr(2), TARR(15000)

real delenx/1.15/, deleny/1.3/

real xarr(100000), yarr(5,100000), yarr1(3,100000), yarr2(1,100000)

LOGICAL smenaRd

external fcn

 

3) Обращаемся к текстовому файлу с начальными данными записываем и выводим их на экран:

common r1, r2, r3, rpr, robr, l, c, Uc0

namelist /LIST1/ r1, r2, r3, rpr, robr, l, c, Uc0, tend, tk, tol, ht

open(3,file='Data.txt')

open(8,file='Result.txt')

read(3,list1); write(*,list1); write(8,list1)

read(*,*)

close(3)

 

4) Считаем значение энергии до зпуска схемы:

Wc0=C*Uc0**2/2

 

5) Считаем параметры цепи в момент запуска (при t=0), записываем полученные значения в массив результатов как первую точку и выводим её на график:

npoint=1

t=0; tend=0

r3=robr; smenaRd=.false.

 

xarr(npoint)=T

yarr(1,npoint)=Uc0

yarr(2,npoint)=-Uc0

yarr(3,npoint)=-Uc0/(R1+R3)

yarr(4,npoint)=0

yarr(5,npoint)=-Uc0/(R1+R3)

yarr1(1,npoint)=0

yarr1(2,npoint)=Wc0

yarr1(3,npoint)=0

yarr2(1,npoint)=0

 

6) Задаём занчения для расчёта дифференциального уравнения в первой точке и значение для сопротивления резистора и условия для значения сопротивления диода:

IF (uc0>0) Rd=Robr

if(uc0<=0) Rd=Rpr

r3=robr; smenaRd=.false.

y(1)=Uc0; y(2)=0

ido=1; param=0

param(4)=30000; PARAM(10)=1

 

7) Строим тело программы цикла с шагом по времени и условием выхода из цыкла по достижению заданного времени и записью каждого шага в массив результатов:

Do

npoint=npoint+1

Tend= Tend+HT

IF(T>Tk) EXIT

if(smenaRd) then

end do

 

8) Программа вычисления всех параметров цепи с телом IVPRK:

i3= -(y(1)+y(2)*R1)/(R1+R3)

CALL R_and_Tok_Dioda(R3,i3)

CALL IVPRK(IDO, N, FCN, T, Tend, TOL, PARAM, y)

IF (i3.GT.0) smenaRd=.true.

i1=y(2)-(y(1)+y(2)*R1)/(R1+R3)

i2=Y(2);

Uc=Y(1);

Ul=R3*I3-R2*I2;

 

WC=C*Uc**2/2

WL=L*Y(2)**2/2

Wdg=Wdg+0.5*(Tend-Tpred)*(R1*(i1**2+I1pred**2)+R2*(i2**2+I2pred**2)+R3*(i3**2+I3pred**2))

err=100*(Wc0-Wdg-WL-WC)/Wc0

 

9) Введение предыдущих значений параметров цепи(t=t-ht):

Tpred=Tend

I3pred=I3

I1pred=i1

I2pred=i2

10) Тело вспомогательной программы для IVPRK:

SUBROUTINE FCN(N, T, Y, YPR)

INTEGER N

REAL T, Y(2), YPR(2), L,C,R1,R2, Rpr, Robr, R3, Uc0, i3, i1

common r1, r2, r3, rpr, robr, l, c, Uc0

 

i3= -(y(1)+y(2)*R1)/(R1+R3)

CALL R_and_Tok_Dioda(R3,i3)

i1=y(2)-(y(1)+y(2)*R1)/(R1+R3)

 

YPR(1)=((R3)*Y(2)-Y(1))/(C*(R1+R3))

YPR(2)= (Y(2)*((R3)/(R1+R3)-R2-R3)-Y(1))/L

END

 

11) Подпрограмма определяющая значение сопротивления диода:

SUBROUTINE R_and_Tok_Dioda(R3,i3)

IMPLICIT none

REAL R1,R2,r3,Rpr,Robr,L,C,i3,uc0

COMMON r1, r2, rpr, robr, l, c, Uc0

 

IF (i3.GT.0) THEN

R3=Robr

ELSE

R3=Rpr

ENDIF

END

 

Программа

use msimsl

IMPLICIT none

INTEGER MXPARM,N,npoint,IDO,NP

PARAMETER (MXPARM=50,N=2,NP=100000)

REAL PARAM(MXPARM),T,Tend,Tk,TOL,HT,y(N),UC0,C,R1,R2,R3,L,Rd,Rpr,Robr,i,R

REAL XARR(100000),Y1(5,100000),Y2(3,100000),Y3(1,100000)

REAL W0,Wr,Wm,We,err,i1,i3,uL,i1pred,i2pred,i3pred,uL1,uC1,T1

EXTERNAL FCN

 

COMMON R1,R2,R3,L,C,Rpr,Robr, Rd

NAMELIST /dif/ Tend,Tk,HT,TOL

NAMELIST /par/ UC0,C,R1,R2,R3,L,Rpr,Robr

OPEN(8,FILE='result.txt')

OPEN(3,FILE='data.txt')

READ(3,dif); WRITE(8,dif); WRITE(*,dif)

READ(3,par); WRITE(8,par); WRITE(*,par)

READ(*,*)

CLOSE(3)

y(1)=UC0; y(2)=0

IF (uc0>0) Rd=Robr

if(uc0<=0) Rd=Rpr

T=0; Tend=HT; IDO=1; PARAM=0

CALL IVPRK(IDO,2,FCN,T,Tend,TOL,PARAM,y)

i3=UC0/(R1+R3+Rd)

CALL R_and_Tok_Dioda(Rd,i3)

W0=0.5*C*UC0*UC0; Wr=0; Wm=0; We=W0

 

XARR(1)=T; Y1(1,1)=UC0; Y1(2,1)=0; Y1(3,1)=i3; Y1(4,1)=0; Y1(5,1)=UC0/(R1+R3+Rd)

Y2(1,1)=0; Y2(2,1)=0

Y3(1,1)=UC0/(R1+R3+Rd); Y3(1,1)=0

 

ido=3;CALL IVPRK(IDO,2,FCN,T,Tend,TOL,PARAM,y)

CALL SSET(MXPARM,0.0,PARAM,1)

PARAM(10)=1.0; PARAM(4)=100000; IDO=1

WRITE(8,20)

WRITE(8,'(f6.5,2X,8f11.5,e12.4)') T,y(1),i1,uL,y(2),i3,Wm,Wr,We,err

npoint=1

10 CONTINUE

npoint=npoint+1;

CALL IVPRK(IDO,2,FCN,T,Tend,TOL,PARAM,y)

i3=(y(1)-y(2)*R1)/(R1+Rd+R3)

if(npoint/=2) CALL R_and_Tok_Dioda(Rd,i3)

IF (i3>0)then; Rd=Robr

if(i3<0) Rd=Rpr

endif

i1=y(2)+i3

uL=(R3+Rd)*i3-y(2)*R2

Wr=Wr+0.5*HT*(R1*(i1pred**2+i1**2)+R2*(i2pred**2+y(2)**2)+(R3+Rd)*(i3pred**2+i3**2))

Wm=L*y(2)**2/2

We=C*y(1)**2/2

err=100*(W0-Wr-Wm-We)/W0

 

XARR(npoint)=T; Y1(1,npoint)=y(1); Y1(2,npoint)=uL; Y1(3,npoint)=i1; Y1(4,npoint)=y(2); Y1(5,npoint)=i3

Y2(1,npoint)=Wm; Y2(2,npoint)=Wr; Y2(3,npoint)=We

Y3(1,npoint)=err

 

i1pred=i1; i2pred=y(2); i3pred=i3; T1=T

Uc1=y(1); uL1=uL

WRITE(8,'(f6.5,2X,8f11.5,e12.4)') T,y(1),i1,uL,y(2),i3,Wm,Wr,We,err

Tend=Tend+HT

IF (Tend.LE.(Tk+0.1*HT)) GOTO 10

20 FORMAT(2X,'Time',7X,'uC',10X,'i1',8X,'uL',10X,'i2',9X,'i3',9X,'Wm',9X,'Wr',9X,'We',7X,'err,%')

CLOSE(8)

CALL EGRAFIC(npoint,XARR,5,Y1,1.3,2.5,.false.)

CALL EGRAFIC(npoint,XARR,3,Y2,1.3,2.5,.false.)

CALL EGRAFIC(npoint,XARR,1,Y3,1.3,2.5,.false.)

 

END

 

SUBROUTINE FCN(N,T,y,YPRIME)

IMPLICIT none

INTEGER N

REAL YPRIME(N),y(N),R1,R2,R3,Rd,Rpr,Robr,L,C,i1,i3,T

COMMON R1,R2,R3,L,C,Rpr,Robr, Rd

 

i3=(y(1)-y(2)*R1)/(R1+Rd+R3)

i1=y(2)+i3

YPRIME(1)=-i1/C

YPRIME(2)=((R3+Rd)*i3-y(2)*R2)/L

 

END

SUBROUTINE R_and_Tok_Dioda(RDiod,i3)

IMPLICIT none

REAL R1,R2,Rpr,Robr,L,C,i3,RDiod,R3

COMMON R1,R2,R3,L,C,Rpr,Robr

 

IF (i3>0) THEN

RDiod=Robr

ELSE

RDiod=Rpr

ENDIF

 

END

 

9) Результаты расчёта:

1)В случае когда напряжение на конденсаторе прямой полярности. Сопротивление диодной ветви становится равным сопротивлению диода в закрытом состоянии. Поэтому ток течёт сначала в контуре конденсатов-катушка и со сменой полярности напряжения на катушке переходит в ветвь катушка-диод.

 

Исходные данные:

&dif Tend=0,Tk=0.01,HT=5e-7,TOL=5e-3/

&par UC0=-300,C=1e-3,R1=0.5,R2=0.2,R3=0.,L=5e-3,Rpr=1e-2,Robr=1e4/

Рис. 2. Кривые токов и напряжения:1- uc; 2 – uL; 3- i1; 4 – i2; 5 – i3.

 

По рисунку 2 видно, что: при замыкании схемы, напряжение на конденсаторе(1) падает до нуля за 5мс, Напряжение на катушке(2) становится равным обратному на конденсаторе и переходит через нулевое значение, когда достигает величины большей чем uc ток начинает течь в контуре катушка-диод. Токи в ветви конденсатора(3) и катушки(4) совпадают до того момента как ток не потечёт через диод, татем появляется ток в диоде(5) который становится равным по модулю току в катушке.

 

Рис. 3. Кривые энергий:

1- энергия в катушке; 2 – энергия в конденсаторе; 3 – энергия выделившаяся в активных элементах.

Рис. 4. Кривая погрешности баланса энергий.

 

Погрешность расчёта можно охарактеризовать балансом энергий. При данных параметрах баланс энергий сходится до точности в 0,06%.

 

 

Результаты вычислений программы:

Time uC i1 uL i2 i3 Wm Wr We err,%

.00005 299.92368 0.00000 - 0.00000 2.98912 0.03000 0.00000 0.00000 45.00000 0.0000E+00

.00005 299.92368 3.01896 -297.81638 2.98912 0.02984 0.02234 0.00038 44.97711 0.3945E-03

.00010 299.69852 5.98555 -295.51456 5.95588 0.02967 0.08868 0.00161 44.90960 0.2480E-03

.00015 299.32556 8.92846 -293.08154 8.89897 0.02949 0.19798 0.00406 44.79790 0.1431E-03

.00020 298.80609 11.84637 -290.51947 11.81708 0.02929 0.34911 0.00834 44.64254 0.2635E-04

.00025 298.14136 14.73802 -287.83057 14.70894 0.02908 0.54088 0.01501 44.44414 -0.6783E-04

.00030 297.33273 17.60213 -285.01700 17.57328 0.02885 0.77205 0.02465 44.20338 -0.1671E-03

.00035 296.38162 20.43749 -282.08112 20.40887 0.02862 1.04131 0.03778 43.92104 -0.2639E-03

.00040 295.28949 23.24287 -279.02515 23.21450 0.02837 1.34728 0.05494 43.59794 -0.3556E-03

.00045 294.05786 26.01709 -275.85150 25.98898 0.02810 1.68857 0.07662 43.23502 -0.4517E-03

.00050 292.68832 28.75898 -272.56262 28.73115 0.02783 2.06370 0.10332 42.83323 -0.5348E-03

.00055 291.18253 31.46740 -269.16086 31.43986 0.02754 2.47116 0.13549 42.39363 -0.6220E-03

.00060 289.54218 34.14124 -265.64874 34.11399 0.02725 2.90941 0.17357 41.91734 -0.7076E-03

.00065 287.76901 36.77941 -262.02884 36.75247 0.02694 3.37686 0.21799 41.40551 -0.7831E-03

.00070 285.86484 39.38083 -258.30356 39.35421 0.02662 3.87189 0.26914 40.85936 -0.8412E-03

.00075 283.83154 41.94448 -254.47566 41.91819 0.02629 4.39284 0.32740 40.28017 -0.9017E-03

.00080 281.67102 44.46933 -250.54767 44.44339 0.02594 4.93804 0.39311 39.66928 -0.9539E-03

.00085 279.38525 46.95441 -246.52229 46.92882 0.02559 5.50578 0.46661 39.02806 -0.1001E-02

.00090 276.97626 49.39874 -242.40218 49.37352 0.02523 6.09436 0.54819 38.35793 -0.1056E-02

.00095 274.44608 51.80140 -238.19006 51.77655 0.02485 6.70203 0.63815 37.66032 -0.1097E-02

.00100 271.79681 54.16149 -233.88867 54.13702 0.02447 7.32704 0.73672 36.93676 -0.1138E-02

.00105 269.03064 56.47812 -229.50078 56.45404 0.02408 7.96765 0.84414 36.18874 -0.1174E-02

.00110 266.14975 58.75043 -225.02917 58.72676 0.02368 8.62208 0.96062 35.41785 -0.1217E-02

.00115 263.15637 60.97762 -220.47670 60.95435 0.02327 9.28858 1.08635 34.62564 -0.1256E-02

.00120 260.05276 63.15888 -215.84612 63.13603 0.02285 9.96540 1.22146 33.81372 -0.1274E-02

.00125 256.84125 65.29345 -211.14032 65.27103 0.02242 10.65077 1.36610 32.98372 -0.1291E-02

.00130 253.52420 67.38058 -206.36218 67.35860 0.02198 11.34295 1.52038 32.13726 -0.1303E-02

.00135 250.10399 69.41958 -201.51459 69.39804 0.02154 12.04022 1.68437 31.27600 -0.1318E-02

.00140 246.58305 71.40976 -196.60045 71.38867 0.02109 12.74086 1.85814 30.40160 -0.1324E-02

.00145 242.96384 73.35047 -191.62263 73.32984 0.02063 13.44316 2.04172 29.51571 -0.1328E-02

.00150 239.24884 75.24109 -186.58412 75.22092 0.02016 14.14547 2.23513 28.62000 -0.1326E-02

.00155 235.44057 77.08102 -181.48778 77.06133 0.01969 14.84612 2.43834 27.71613 -0.1316E-02

.00160 231.54158 78.86971 -176.33662 78.85050 0.01921 15.54350 2.65134 26.80575 -0.1309E-02

.00165 227.55446 80.60662 -171.13356 80.58790 0.01873 16.23602 2.87405 25.89052 -0.1295E-02

.00170 223.48180 82.29125 -165.88158 82.27302 0.01823 16.92212 3.10640 24.97206 -0.1282E-02

.00175 219.32622 83.92312 -160.58359 83.90538 0.01774 17.60028 3.34829 24.05200 -0.1260E-02

.00180 215.09038 85.50179 -155.24258 85.48455 0.01723 18.26902 3.59961 23.13194 -0.1242E-02

.00185 210.77693 87.02682 -149.86150 87.01010 0.01673 18.92689 3.86019 22.21346 -0.1207E-02

.00190 206.38858 88.49787 -144.44331 88.48166 0.01621 19.57251 4.12990 21.29812 -0.1175E-02

.00195 201.92804 89.91455 -138.99100 89.89886 0.01570 20.20451 4.40854 20.38747 -0.1138E-02

.00200 197.39803 91.27655 -133.50748 91.26138 0.01518 20.82160 4.69591 19.48299 -0.1089E-02

.00205 192.80130 92.58356 -127.99574 92.56891 0.01465 21.42251 4.99180 18.58617 -0.1046E-02

.00210 188.14061 93.83532 -122.45871 93.82120 0.01412 22.00604 5.29597 17.69845 -0.1003E-02

.00215 183.41872 95.03159 -116.89932 95.01801 0.01359 22.57105 5.60817 16.82121 -0.9537E-03

.00220 178.63840 96.17217 -111.32049 96.15912 0.01306 23.11644 5.92813 15.95584 -0.9060E-03

.00225 173.80244 97.25687 -105.72514 97.24435 0.01252 23.64116 6.25558 15.10365 -0.8488E-03

.00230 168.91367 98.28555 -100.11618 98.27357 0.01198 24.14423 6.59021 14.26591 -0.7915E-03

.00235 163.97485 99.25807 -94.49649 99.24664 0.01143 24.62474 6.93172 13.44388 -0.7375E-03

.00240 158.98882 100.17435 -88.86894 100.16347 0.01089 25.08180 7.27979 12.63872 -0.6771E-03

.00245 153.95837 101.03434 -83.23640 101.02399 0.01034 25.51462 7.63407 11.85159 -0.6125E-03

.00250 148.88634 101.83798 -77.60172 101.82819 0.00980 25.92245 7.99423 11.08357 -0.5478E-03

.00255 143.77553 102.58527 -71.96769 102.57603 0.00925 26.30460 8.35991 10.33570 -0.4811E-03

.00260 138.62877 103.27625 -66.33714 103.26755 0.00870 26.66047 8.73076 9.60897 -0.4133E-03

.00265 133.44887 103.91094 -60.71284 103.90279 0.00815 26.98948 9.10639 8.90430 -0.3497E-03

.00270 128.23863 104.48943 -55.09755 104.48183 0.00760 27.29113 9.48642 8.22257 -0.2797E-03

.00275 123.00088 105.01183 -49.49401 105.00478 0.00705 27.56501 9.87048 7.56461 -0.2087E-03

.00280 117.73840 105.47826 -43.90492 105.47176 0.00650 27.81073 10.25817 6.93117 -0.1388E-03

.00285 112.45400 105.88889 -38.33297 105.88293 0.00595 28.02799 10.64909 6.32295 -0.6252E-04

.00290 107.15046 106.24389 -32.78082 106.23849 0.00540 28.21654 11.04285 5.74061 0.9537E-05

.00295 101.83055 106.54348 -27.25108 106.53863 0.00486 28.37620 11.43904 5.18473 0.7947E-04

.00300 96.49705 106.78790 -21.74638 106.78359 0.00431 28.50684 11.83726 4.65584 0.1558E-03

.00305 91.15269 106.97742 -16.26926 106.97365 0.00377 28.60840 12.23709 4.15441 0.2278E-03

.00310 85.80023 107.11230 -10.82226 107.10908 0.00322 28.68089 12.63814 3.68084 0.3041E-03

.00315 80.44238 107.19289 - 5.40790 107.19020 0.00268 28.72435 13.04000 3.23549 0.3756E-03

.00320 75.08186 107.21950 - 0.02863 107.21735 0.00215 28.73890 13.44226 2.81864 0.4514E-03

.00325 69.72134 107.19251 5.31309 107.19090 0.00161 28.72472 13.84451 2.43053 0.5182E-03

.00330 64.36351 107.11231 10.61489 107.11123 0.00108 28.68204 14.24637 2.07133 0.5918E-03

.00335 59.01101 106.97929 15.87439 106.97874 0.00055 28.61113 14.64743 1.74115 0.6660E-03

.00340 53.66647 106.79392 21.08927 106.79389 0.00003 28.51234 15.04729 1.44004 0.7277E-03

.00345 48.33250 106.55663 21.31143 106.55712 -0.00049 28.38605 15.44558 1.16802 0.7971E-03

.00350 43.71949 87.80965 21.45389 106.34280 -18.53316 28.27198 15.79729 0.95570 -0.5548E-01

.00355 39.53747 79.60539 21.49084 106.12807 -26.52268 28.15792 16.08601 0.78161 -0.5674E-01

.00360 35.74620 72.16731 21.52006 105.91302 -33.74571 28.04392 16.34319 0.63890 -0.5777E-01

.00365 32.30918 65.42383 21.54228 105.69770 -40.27387 27.93001 16.57443 0.52194 -0.5862E-01

.00370 29.19333 59.31010 21.55816 105.48219 -46.17209 27.81623 16.78434 0.42613 -0.5931E-01

.00375 26.36866 53.76731 21.56830 105.26656 -51.49924 27.70262 16.97668 0.34765 -0.5988E-01

.00380 23.80798 48.74214 21.57326 105.05084 -56.30870 27.58920 17.15455 0.28341 -0.6034E-01

.00385 21.48664 44.18626 21.57351 104.83511 -60.64885 27.47600 17.32050 0.23084 -0.6073E-01

.00390 19.38228 40.05582 21.56951 104.61938 -64.56356 27.36304 17.47660 0.18784 -0.6104E-01

.00395 17.47464 36.31113 21.56167 104.40372 -68.09260 27.25034 17.62456 0.15268 -0.6129E-01

.00400 15.74535 32.91613 21.55035 104.18816 -71.27203 27.13793 17.76579 0.12396 -0.6151E-01

.00405 14.17775 29.83819 21.53589 103.97273 -74.13454 27.02582 17.90143 0.10050 -0.6168E-01

.00410 12.75674 27.04768 21.51859 103.75746 -76.70978 26.91403 18.03243 0.08137 -0.6183E-01

.00415 11.46864 24.51778 21.49872 103.54237 -79.02460 26.80256 18.15956 0.06576 -0.6195E-01

.00420 10.30103 22.22414 21.47653 103.32750 -81.10336 26.69143 18.28344 0.05306 -0.6205E-01

.00425 9.24266 20.14469 21.45225 103.11285 -82.96816 26.58065 18.40460 0.04271 -0.6213E-01

.00430 8.28333 18.25945 21.42608 102.89846 -84.63902 26.47023 18.52345 0.03431 -0.6219E-01

.00435 7.41379 16.55026 21.39821 102.68434 -86.13408 26.36018 18.64035 0.02748 -0.6225E-01

.00440 6.62565 15.00069 21.36880 102.47050 -87.46981 26.25051 18.75557 0.02195 -0.6229E-01

.00445 5.91131 13.59585 21.33801 102.25697 -88.66113 26.14122 18.86936 0.01747 -0.6232E-01

.00450 5.26388 12.32220 21.30597 102.04375 -89.72156 26.03232 18.98189 0.01385 -0.6236E-01

.00455 4.67711 11.16749 21.27281 101.83086 -90.66338 25.92381 19.09333 0.01094 -0.6239E-01

.00460 4.14534 10.12063 21.23864 101.61831 -91.49768 25.81570 19.20379 0.00859 -0.6241E-01

.00465 3.66342 9.17153 21.20357 101.40610 -92.23457 25.70799 19.31339 0.00671 -0.6242E-01

.00470 3.22671 8.31108 21.16768 101.19424 -92.88316 25.60069 19.42221 0.00521 -0.6244E-01

.00475 2.83098 7.53099 21.13107 100.98275 -93.45176 25.49379 19.53031 0.00401 -0.6245E-01

.00480 2.47240 6.82375 21.09380 100.77162 -93.94787 25.38730 19.63775 0.00306 -0.6245E-01

.00485 2.14750 6.18257 21.05596 100.56087 -94.37830 25.28122 19.74458 0.00231 -0.6246E-01

.00490 1.85314 5.60127 21.01760 100.35051 -94.74924 25.17556 19.85084 0.00172 -0.6247E-01

.00495 1.58647 5.07426 20.97877 100.14053 -95.06626 25.07031 19.95655 0.00126 -0.6248E-01

.00500 1.34490 4.59648 20.93953 99.93093 -95.33445 24.96548 20.06174 0.00090 -0.6247E-01

.00505 1.12608 4.16333 20.89993 99.72173 -95.55840 24.86106 20.16642 0.00063 -0.6247E-01

.00510 0.92789 3.77063 20.86001 99.51293 -95.74230 24.75706 20.27063 0.00043 -0.6247E-01

.00515 0.74841 3.41461 20.81981 99.30453 -95.88992 24.65348 20.37436 0.00028 -0.6248E-01

.00520 0.58588 3.09185 20.77936 99.09654 -96.00469 24.55031 20.47764 0.00017 -0.6248E-01

.00525 0.43872 2.79923 20.73869 98.88895 -96.08972 24.44756 20.58046 0.00010 -0.6249E-01

.00530 0.30550 2.53395 20.69783 98.68177 -96.14782 24.34523 20.68285 0.00005 -0.6248E-01

.00535 0.18491 2.29346 20.65681 98.47500 -96.18154 24.24331 20.78479 0.00002 -0.6249E-01

.00540 0.07578 2.07542 20.61566 98.26864 -96.19321 24.14181 20.88631 0.00000 -0.6250E-01

.00545 -0.02297 1.87776 20.57439 98.06269 -96.18493 24.04073 20.98740 0.00000 -0.6250E-01

.00550 -0.11230 1.69856 20.53302 97.85715 -96.15859 23.94006 21.08807 0.00001 -0.6250E-01

.00555 -0.19310 1.53611 20.49157 97.65203 -96.11592 23.83980 21.18831 0.00002 -0.6250E-01

.00560 -0.26617 1.38883 20.45005 97.44733 -96.05849 23.73995 21.28814 0.00004 -0.6250E-01

.00565 -0.33222 1.25532 20.40848 97.24303 -95.98772 23.64052 21.38756 0.00006 -0.6250E-01

.00570 -0.39191 1.13428 20.36688 97.03915 -95.90487 23.54149 21.48656 0.00008 -0.6250E-01

.00575 -0.44583 1.02456 20.32525 96.83569 -95.81113 23.44288 21.58515 0.00010 -0.6250E-01

.00580 -0.49453 0.92509 20.28361 96.63265 -95.70757 23.34467 21.68334 0.00012 -0.6251E-01

.00585 -0.53850 0.83491 20.24196 96.43002 -95.59512 23.24687 21.78111 0.00014 -0.6251E-01

.00590 -0.57816 0.75317 20.20031 96.22781 -95.47465 23.14948 21.87848 0.00017 -0.6250E-01

.00595 -0.61394 0.67906 20.15867 96.02602 -95.34695 23.05249 21.97545 0.00019 -0.6250E-01

.00600 -0.64619 0.61189 20.11706 95.82464 -95.21275 22.95590 22.07202 0.00021 -0.6250E-01

.00605 -0.67523 0.55099 20.07546 95.62367 -95.07269 22.85972 22.16819 0.00023 -0.6250E-01

.00610 -0.70138 0.49579 20.03390 95.42313 -94.92734 22.76393 22.26395 0.00025 -0.6250E-01

.00615 -0.72490 0.44575 19.99237 95.22299 -94.77724 22.66854 22.35932 0.00026 -0.6250E-01

.00620 -0.74603 0.40039 19.95088 95.02328 -94.62289 22.57356 22.45429 0.00028 -0.6250E-01

.00625 -0.76501 0.35928 19.90944 94.82397 -94.46470 22.47897 22.54887 0.00029 -0.6250E-01

.00630 -0.78202 0.32201 19.86805 94.62508 -94.30307 22.38477 22.64306 0.00031 -0.6250E-01

.00635 -0.79727 0.28823 19.82671 94.42661 -94.13838 22.29096 22.73685 0.00032 -0.6250E-01

.00640 -0.81090 0.25761 19.78542 94.22855 -93.97094 22.19755 22.83025 0.00033 -0.6250E-01

.00645 -0.82308 0.22987 19.74419 94.03091 -93.80104 22.10453 22.92327 0.00034 -0.6251E-01

.00650 -0.83393 0.20472 19.70302 93.83367 -93.62895 22.01189 23.01589 0.00035 -0.6251E-01

.00655 -0.84359 0.18192 19.66192 93.63685 -93.45493 21.91965 23.10813 0.00036 -0.6251E-01

.00660 -0.85216 0.16127 19.62088 93.44044 -93.27917 21.82779 23.19998 0.00036 -0.6251E-01

.00665 -0.85975 0.14255 19.57990 93.24443 -93.10188 21.73631 23.29145 0.00037 -0.6251E-01

.00670 -0.86644 0.12558 19.53900 93.04884 -92.92326 21.64521 23.38254 0.00038 -0.6251E-01

.00675 -0.87233 0.11021 19.49817 92.85365 -92.74345 21.55450 23.47325 0.00038 -0.6252E-01

.00680 -0.87749 0.09628 19.45740 92.65887 -92.56260 21.46417 23.56358 0.00038 -0.6251E-01

.00685 -0.88198 0.08366 19.41671 92.46451 -92.38085 21.37421 23.65354 0.00039 -0.6252E-01

.00690 -0.88587 0.07222 19.37609 92.27055 -92.19833 21.28463 23.74311 0.00039 -0.6252E-01

.00695 -0.88922 0.06186 19.33555 92.07699 -92.01513 21.19543 23.83232 0.00040 -0.6252E-01

.00700 -0.89207 0.05247 19.29508 91.88383 -91.83136 21.10660 23.92114 0.00040 -0.6253E-01

.00705 -0.89448 0.04398 19.25469 91.69109 -91.64711 21.01814 24.00960 0.00040 -0.6252E-01

.00710 -0.89649 0.03628 19.21437 91.49874 -91.46246 20.93005 24.09769 0.00040 -0.6252E-01

.00715 -0.89812 0.02930 19.17414 91.30680 -91.27750 20.84233 24.18541 0.00040 -0.6252E-01

.00720 -0.89943 0.02299 19.13397 91.11526 -91.09227 20.75497 24.27276 0.00040 -0.6252E-01

.00725 -0.90043 0.01727 19.09389 90.92412 -90.90685 20.66799 24.35975 0.00041 -0.6253E-01

.00730 -0.90116 0.01210 19.05389 90.73338 -90.72128 20.58137 24.44637 0.00041 -0.6253E-01

.00735 -0.90165 0.00742 19.01397 90.54305 -90.53563 20.49511 24.53263 0.00041 -0.6253E-01

.00740 -0.90191 0.00317 18.97412 90.35310 -90.34993 20.40921 24.61853 0.00041 -0.6253E-01

.00745 -0.90197 -0.00066 18.93435 90.16356 -90.16422 20.32367 24.70407 0.00041 -0.6253E-01

.00750 -0.90185 -0.00414 18.89467 89.97441 -89.97855 20.23849 24.78925 0.00041 -0.6252E-01

.00755 -0.90157 -0.00727 18.85506 89.78566 -89.79293 20.15366 24.87407 0.00041 -0.6252E-01

.00760 -0.90113 -0.01011 18.81553 89.59731 -89.60741 20.06919 24.95854 0.00041 -0.6252E-01

.00765 -0.90056 -0.01268 18.77609 89.40935 -89.42203 19.98508 25.04265 0.00041 -0.6252E-01

.00770 -0.89987 -0.01500 18.73672 89.22179 -89.23679 19.90132 25.12642 0.00040 -0.6252E-01

.00775 -0.89906 -0.01709 18.69744 89.03461 -89.05170 19.81791 25.20983 0.00040 -0.6252E-01

.00780 -0.89816 -0.01898 18.65824 88.84784 -88.86682 19.73485 25.29289 0.00040 -0.6253E-01

.00785 -0.89717 -0.02069 18.61911 88.66145 -88.68214 19.65213 25.37561 0.00040 -0.6253E-01

.00790 -0.89609 -0.02223 18.58007 88.47546 -88.49769 19.56977 25.45798 0.00040 -0.6253E-01

.00795 -0.89495 -0.02362 18.54111 88.28985 -88.31347 19.48774 25.54000 0.00040 -0.6253E-01

.00800 -0.89373 -0.02488 18.50222 88.10463 -88.12951 19.40606 25.62168 0.00040 -0.6252E-01

.00805 -0.89246 -0.02601 18.46342 87.91980 -87.94581 19.32473 25.70301 0.00040 -0.6253E-01

.00810 -0.89113 -0.02702 18.42470 87.73536 -87.76238 19.24373 25.78401 0.00040 -0.6252E-01

.00815 -0.88976 -0.02794 18.38605 87.55131 -87.57925 19.16308 25.86467 0.00040 -0.6253E-01

.00820 -0.88834 -0.02876 18.34749 87.36764 -87.39639 19.08276 25.94498 0.00039 -0.6252E-01

.00825 -0.88689 -0.02950 18.30901 87.18436 -87.21385 19.00278 26.02497 0.00039 -0.6252E-01

.00830 -0.88539 -0.03016 18.27061 87.00146 -87.03162 18.92313 26.10461 0.00039 -0.6253E-01

.00835 -0.88387 -0.03075 18.23229 86.81895 -86.84969 18.84382 26.18393 0.00039 -0.6253E-01

.00840 -0.88232 -0.03128 18.19404 86.63682 -86.66810 18.76484 26.26291 0.00039 -0.6253E-01

.00845 -0.88074 -0.03175 18.15588 86.45507 -86.48682 18.68620 26.34156 0.00039 -0.6253E-01

.00850 -0.87915 -0.03217 18.11780 86.27370 -86.30588 18.60788 26.41988 0.00039 -0.6253E-01

.00855 -0.87753 -0.03255 18.07980 86.09272 -86.12527 18.52989 26.49787 0.00039 -0.6254E-01

.00860 -0.87589 -0.03288 18.04187 85.91211 -85.94499 18.45223 26.57553 0.00038 -0.6254E-01

.00865 -0.87424 -0.03318 18.00403 85.73188 -85.76506 18.37489 26.65287 0.00038 -0.6253E-01

.00870 -0.87257 -0.03344 17.96626 85.55203 -85.58547 18.29787 26.72989 0.00038 -0.6253E-01

.00875 -0.87090 -0.03367 17.92857 85.37256 -85.40623 18.22118 26.80658 0.00038 -0.6253E-01

.00880 -0.86921 -0.03387 17.89096 85.19346 -85.22733 18.14481 26.88295 0.00038 -0.6254E-01

.00885 -0.86751 -0.03404 17.85344 85.01474 -85.04878 18.06876 26.95901 0.00038 -0.6254E-01

.00890 -0.86580 -0.03419 17.81598 84.83640 -84.87059 17.99303 27.03474 0.00037 -0.6254E-01

.00895 -0.86409 -0.03432 17.77861 84.65842 -84.69275 17.91762 27.11015 0.00037 -0.6254E-01

.00900 -0.86237 -0.03444 17.74132 84.48083 -84.51527 17.84253 27.18525 0.00037 -0.6255E-01

.00905 -0.86065 -0.03453 17.70410 84.30360 -84.33813 17.76774 27.26004 0.00037 -0.6255E-01

.00910 -0.85892 -0.03461 17.66696 84.12675 -84.16136 17.69327 27.33451 0.00037 -0.6255E-01

.00915 -0.85719 -0.03468 17.62990 83.95026 -83.98494 17.61912 27.40867 0.00037 -0.6255E-01

.00920 -0.85545 -0.03473 17.59292 83.77415 -83.80888 17.54527 27.48252 0.00037 -0.6255E-01

.00925 -0.85371 -0.03477 17.55601 83.59840 -83.63317 17.47173 27.55606 0.00036 -0.6255E-01

.00930 -0.85198 -0.03480 17.51918 83.42303 -83.45782 17.39850 27.62929 0.00036 -0.6255E-01

.00935 -0.85024 -0.03481 17.48243 83.24802 -83.28283 17.32558 27.70221 0.00036 -0.6255E-01

.00940 -0.84849 -0.03482 17.44576 83.07338 -83.10820 17.25297 27.77483 0.00036 -0.6256E-01

.00945 -0.84675 -0.03483 17.40916 82.89911 -82.93394 17.18065 27.84714 0.00036 -0.6256E-01

.00950 -0.84501 -0.03482 17.37264 82.72520 -82.76002 17.10864 27.91915 0.00036 -0.6255E-01

.00955 -0.84327 -0.03481 17.33619 82.55165 -82.58646 17.03694 27.99086 0.00036 -0.6255E-01

.00960 -0.84153 -0.03480 17.29983 82.37847 -82.41327 16.96553 28.06227 0.00035 -0.6255E-01

.00965 -0.83979 -0.03477 17.26354 82.20566 -82.24043 16.89442 28.13338 0.00035 -0.6255E-01

.00970 -0.83805 -0.03474 17.22732 82.03320 -82.06795 16.82362 28.20419 0.00035 -0.6255E-01

.00975 -0.83632 -0.03471 17.19118 81.86111 -81.89583 16.75311 28.27470 0.00035 -0.6256E-01

.00980 -0.83458 -0.03468 17.15512 81.68938 -81.72407 16.68289 28.34492 0.00035 -0.6256E-01

.00985 -0.83285 -0.03465 17.11913 81.51801 -81.55266 16.61297 28.41484 0.00035 -0.6256E-01

.00990 -0.83112 -0.03460 17.08322 81.34700 -81.38160 16.54333 28.48447 0.00035 -0.6256E-01

.00995 -0.82939 -0.03456 17.04738 81.17635 -81.21091 16.47400 28.55381 0.00034 -0.6256E-01

.01000 -0.82766 -0.03452 17.01162 81.00605 -81.04057 16.40495 28.62286 0.00034 -0.6255E-01

 

 

2) В случае когда напряжение на конденсаторе обратной полярности. Сопротивление диодной ветви становится равным сопротивлению диода в открытом состоянии. Поэтому ток течёт в контуре конденсатов-диод, не проходя в ветвь с катушкой.

 

Исходные данные:

&dif Tend=0,Tk=0.01,HT=5e-7,TOL=5e-3/

&par UC0=-300,C=1e-3,R1=0.5,R2=0.2,R3=0.,L=5e-3,Rpr=1e-2,Robr=1e4/

 

Рис. 5. Кривые токов и напряжения:

1- uc; 2 – uL; 3- i1; 4 – i2; 5 – i3.

 

Скачёт напряжении на ul, обусловлен выбросом погрешности при расчёте.

 

Рис. 6. Кривые энергий:

1- энергия в катушке; 2 – энергия в конденсаторе; 3 – энергия выделившаяся в активных элементах.

Рис. 7. Кривая погрешности баланса энергий.

 

Погрешность расчёта можно охарактеризовать балансом энергий. При данных параметрах баланс энергий сходится до точности в 0,1%.

Результаты вычислений программы:

Time uC i1 uL i2 i3 Wm Wr We err,%

.00005 -271.98398 0.00000 0.00000 -0.05597 -588.23529 0.00000 0.00000 45.00000 0.0000E+00

.00005 -271.98398 -533.30304 5.32128 -0.05597 -533.24707 0.00001 3.62624 36.98764 0.9747E-01

.00010 -246.58424 -483.50061 4.81262 -0.10660 -483.39401 0.00003 10.23306 30.40190 0.9700E-01

.00015 -223.55646 -438.34897 4.35149 -0.15238 -438.19659 0.00006 15.66351 24.98875 0.9662E-01

.00020 -202.67911 -397.41382 3.93345 -0.19377 -397.22003 0.00009 20.12706 20.53941 0.9630E-01

.00025 -183.75139 -360.30136 3.55447 -0.23118 -360.07019 0.00013 23.79585 16.88229 0.9604E-01

.00030 -166.59123 -326.65466 3.21090 -0.26498 -326.38968 0.00018 26.81140 13.87632 0.9582E-01

.00035 -151.03357 -296.15005 2.89944 -0.29551 -295.85455 0.00022 29.29002 11.40557 0.9565E-01

.00040 -136.92876 -268.49408 2.61710 -0.32307 -268.17102 0.00026 31.32730 9.37474 0.9550E-01

.00045 -124.14113 -243.42079 2.36114 -0.34794 -243.07286 0.00030 33.00184 7.70551 0.9539E-01

.00050 -112.54768 -220.68898 2.12911 -0.37037 -220.31860 0.00034 34.37821 6.33349 0.9529E-01

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.00900 0.66758 0.24783 -0.49411 0.24778 0.00005 0.00015 40.73237 0.00022 0.9483E-01

.00905 0.65507 0.25269 -0.47819 0.25264 0.00005 0.00016 40.73238 0.00021 0.9483E-01

.00910 0.64231 0.25739 -0.46215 0.25734 0.00005 0.00017 40.73238 0.00021 0.9483E-01

.00915 0.62933 0.26193 -0.44599 0.26188 0.00005 0.00017 40.73238 0.00020 0.9483E-01

.00920 0.61612 0.26631 -0.42972 0.26626 0.00005 0.00018 40.73239 0.00019 0.9483E-01

.00925 0.60270 0.27052 -0.41335 0.27048 0.00005 0.00018 40.73239 0.00018 0.9483E-01

.00930 0.58907 0.27457 -0.39688 0.27453 0.00005 0.00019 40.73240 0.00017 0.9483E-01

.00935 0.57525 0.27846 -0.38034 0.27841 0.00004 0.00019 40.73240 0.00017 0.9483E-01

.00940 0.56123 0.28218 -0.36372 0.28213 0.00004 0.00020 40.73240 0.00016 0.9483E-01

.00945 0.54703 0.28573 -0.34703 0.28569 0.00004 0.00020 40.73241 0.00015 0.9483E-01

.00950 0.53266 0.28911 -0.33029 0.28907 0.00004 0.00021 40.73241 0.00014 0.9483E-01

.00955 0.51812 0.29233 -0.31350 0.29229 0.00004 0.00021 40.73241 0.00013 0.9483E-01

.00960 0.50343 0.29538 -0.29667 0.29534 0.00004 0.00022 40.73242 0.00013 0.9483E-01

.00965 0.48859 0.29826 -0.27981 0.29823 0.00003 0.00022 40.73242 0.00012 0.9483E-01

.00970 0.47361 0.30097 -0.26293 0.30094 0.00003 0.00023 40.73243 0.00011 0.9483E-01

.00975 0.45849 0.30352 -0.24604 0.30349 0.00003 0.00023 40.73243 0.00011 0.9483E-01

.00980 0.44326 0.30589 -0.22914 0.30586 0.00003 0.00023 40.73243 0.00010 0.9483E-01

.00985 0.42791 0.30810 -0.21225 0.30807 0.00003 0.00024 40.73244 0.00009 0.9483E-01

.00990 0.41245 0.31013 -0.19537 0.31011 0.00003 0.00024 40.73244 0.00009 0.9483E-01

3)В случае когда напряжение на конденсаторе прямой полярности. Но сопротивление диодной ветви равно в прямом и обратном направлении сопротивлению диода в закрытом состоянии. Ток течёт в контуре конденсатов-катушка. Процесс периодический. Энергия контура переходит из конденсатора в катушку и обратно, до того момента пока вся энергия не перейдёт в джоулевы потери.

Исходные данные:

&dif Tend=0,Tk=0.01,HT=5e-7,TOL=5e-3/

&par UC0=300,C=1e-3,R1=0.5,R2=0.2,R3=0.,L=5e-3,Rpr=1e4,Robr=1e4/

 

Рис. 8. Кривые токов и напряжения:1- uc; 2 – uL; 3- i1; 4 – i2; 5 – i3.

 

Рис. 9. Кривые энергий:

1- энергия в катушке; 2 – энергия в конденсаторе; 3 – энергия выделившаяся в активных элементах.

 

Рис. 7. Кривая погрешности баланса энергий.

 

Погрешность расчёта можно охарактеризовать балансом энергий. При данных параметрах баланс энергий сходится до точности в 0,07%.

 

Результаты вычислений программы:

Time uC i1 uL i2 i3 Wm Wr We err,%

.00010 -299.69849 0.00000 0.00000 -5.95588 -0.03000 0.00000 0.00000 45.00000 0.0000E+00

.00010 -299.69849 -5.98555 -295.51453 -5.95588 -0.02967 0.08868 0.00169 44.90959 0.8934E-04

.00020 -298.80615 -11.84637 -290.51953 -11.81709 -0.02929 0.34911 0.00871 44.64256 -0.8421E-03

.00030 -297.33279 -17.60213 -285.01706 -17.57328 -0.02885 0.77205 0.02530 44.20340 -0.1648E-02

.00040 -295.28955 -23.24287 -279.02521 -23.21451 -0.02837 1.34728 0.05585 43.59796 -0.2416E-02

.00050 -292.68839 -28.75898 -272.56265 -28.73115 -0.02783 2.06370 0.10446 42.83325 -0.3122E-02

.00060 -289.54221 -34.14125 -265.64877 -34.11400 -0.02725 2.90941 0.17493 41.91735 -0.3750E-02

.00070 -285.86487 -39.38085 -258.30362 -39.35423 -0.02662 3.87189 0.27069 40.85936 -0.4315E-02

.00080 -281.67105 -44.46935 -250.54768 -44.44341 -0.02594 4.93804 0.39483 39.66929 -0.4808E-02

.00090 -276.97629 -49.39877 -242.40219 -49.37354 -0.02523 6.09437 0.55006 38.35793 -0.5238E-02

.00100 -271.79684 -54.16151 -233.88869 -54.13704 -0.02447 7.32705 0.73871 36.93676 -0.5590E-02

.00110 -266.14978 -58.75045 -225.02921 -58.72677 -0.02368 8.62208 0.96271 35.41785 -0.5881E-02

.00120 -260.05280 -63.15889 -215.84615 -63.13604 -0.02285 9.96540 1.22362 33.81373 -0.6097E-02

.00130 -253.52425 -67.38058 -206.36223 -67.35860 -0.02198 11.34295 1.52259 32.13727 -0.6237E-02

.00140 -246.58310 -71.40976 -196.60048 -71.38867 -0.02109 12.74086 1.86037 30.40161 -0.6305E-02

.00150 -239.24889 -75.24109 -186.58415 -75.22092 -0.02016 14.14547 2.23736 28.62002 -0.6306E-02

.00160 -231.54164 -78.86971 -176.33670 -78.85049 -0.01921 15.54350 2.65354 26.80577 -0.6235E-02

.00170 -223.48186 -82.29124 -165.88164 -82.27300 -0.01823 16.92212 3.10856 24.97207 -0.6102E-02

.00180 -215.09044 -85.50176 -155.24266 -85.48453 -0.01723 18.26901 3.60170 23.13195 -0.5907E-02

.00190 -206.38866 -88.49785 -144.44341 -88.48164 -0.01621 19.57250 4.13191 21.29814 -0.5653E-02

.00200 -197.39812 -91.27653 -133.50758 -91.26135 -0.01518 20.82159 4.69781 19.48301 -0.5344E-02

.00210 -188.14067 -93.83531 -122.45878 -93.82119 -0.01412 22.00604 5.29775 17.69846 -0.4982E-02

.00220 -178.63843 -96.17216 -111.32052 -96.15911 -0.01306 23.11644 5.92978 15.95584 -0.4567E-02

.00230 -168.91367 -98.28555 -100.11618 -98.27357 -0.01198 24.14423 6.59171 14.26591 -0.4111E-02

.00240 -158.98878 -100.17436 -88.86890 -100.16348 -0.01089 25.08180 7.28112 12.63872 -0.3629E-02

.00250 -148.88628 -101.83799 -77.60165 -101.82819 -0.00980 25.92245 7.99539 11.08356 -0.3105E-02

.00260 -138.62868 -103.27625 -66.33704 -103.26756 -0.00870 26.66047 8.73173 9.60896 -0.2552E-02

.00270 -128.23851 -104.48944 -55.09742 -104.48184 -0.00760 27.29114 9.48720 8.22256 -0.1986E-02

.00280 -117.73825 -105.47827 -43.90476 -105.47177 -0.00650 27.81074 10.25875 6.93115 -0.1404E-02

.00290 -107.15028 -106.24390 -32.78064 -106.23849 -0.00540 28.21654 11.04323 5.74059 -0.8096E-03

.00300 -96.49685 -106.78791 -21.74617 -106.78360 -0.00431 28.50684 11.83744 4.65582 -0.2109E-03

.00310 -85.80001 -107.11231 -10.82204 -107.10909 -0.00322 28.68089 12.63812 3.68082 0.3884E-03

.00320 -75.08161 -107.21950 -0.02839 -107.21735 -0.00215 28.73890 13.44203 2.81862 0.9924E-03

.00330 -64.36324 -107.11230 10.61515 -107.11122 -0.00108 28.68203 14.24594 2.07131 0.1582E-02

.00340 -53.66618 -106.79391 21.08955 -106.79388 -0.00003 28.51233 15.04667 1.44003 0.2161E-02

.00350 -43.01137 -106.26788 31.37635 -106.26889 0.00101 28.23269 15.84110 0.92499 0.2719E-02

.00360 -32.41938 -105.53815 41.45774 -105.54019 0.00203 27.84683 16.62620 0.52551 0.3261E-02

.00370 -21.91037 -104.60902 51.31655 -104.61206 0.00304 27.35921 17.39906 0.24003 0.3781E-02

.00380 -11.50406 -103.48510 60.93631 -103.48912 0.00402 26.77499 18.15692 0.06617 0.4268E-02

.00390 -1.21967 -102.17132 70.30125 -102.17631 0.00499 26.09999 18.89714 0.00074 0.4718E-02

.00400 8.92406 -100.67294 79.39631 -100.67887 0.00593 25.34059 19.61728 0.03982 0.5138E-02

.00410 18.90894 -98.99551 88.20717 -99.00236 0.00684 24.50367 20.31508 0.17877 0.5518E-02

.00420 28.71736 -97.14485 96.72030 -97.15258 0.00773 23.59656 20.98847 0.41234 0.5855E-02

.00430 38.33231 -95.12703 104.92295 -95.13562 0.00859 22.62696 21.63558 0.73468 0.6161E-02

.00440 47.73737 -92.94839 112.80313 -92.95782 0.00942 21.60289 22.25480 1.13943 0.6418E-02

.00450 56.91681 -90.61550 120.34971 -90.62572 0.01022 20.53255 22.84470 1.61976 0.6635E-02

.00460 65.85552 -88.13513 127.55231 -88.14613 0.01099 19.42435 23.40412 2.16847 0.6810E-02

.00470 74.53912 -85.51427 134.40144 -85.52599 0.01173 18.28674 23.93210 2.77804 0.6939E-02

.00480 82.95390 -82.76006 140.88841 -82.77249 0.01243 17.12821 24.42796 3.44067 0.7022E-02

.00490 91.08689 -79.87984 147.00539 -79.89294 0.01310 15.95720 24.89121 4.14841 0.7065E-02

.00500 98.92588 -76.88107 152.74538 -76.89480 0.01374 14.78202 25.32163 4.89317 0.7067E-02

.00510 106.45938 -73.77135 158.10219 -73.78568 0.01433 13.61082 25.71922 5.66680 0.7026E-02

.00520 113.67668 -70.55842 163.07056 -70.57331 0.01490 12.45148 26.08421 6.46119 0.6943E-02

.00530 120.56786 -67.25008 167.64600 -67.26550 0.01542 11.31162 26.41702 7.26830 0.6817E-02

.00540 127.12376 -63.85423 171.82489 -63.87013 0.01591 10.19848 26.71830 8.08022 0.6657E-02

.00550 133.33603 -60.37882 175.60448 -60.39517 0.01635 9.11894 26.98890 8.88925 0.6466E-02

.00560 139.19711 -56.83187 178.98277 -56.84864 0.01676 8.07942 27.22986 9.68792 0.6246E-02

.00570 144.70027 -53.22142 181.95869 -53.23856 0.01713 7.08586 27.44236 10.46908 0.5991E-02

.00580 149.83954 -49.55553 184.53191 -49.57299 0.01746 6.14370 27.62779 11.22594 0.5707E-02

.00590 154.60977 -45.84222 186.70288 -45.85997 0.01775 5.25784 27.78764 11.95209 0.5408E-02

.00600 159.00665 -42.08955 188.47293 -42.10756 0.01801 4.43262 27.92354 12.64156 0.5080E-02

.00610 163.02663 -38.30551 189.84413 -38.32373 0.01822 3.67177 28.03726 13.28884 0.4739E-02

.00620 166.66696 -34.49805 190.81927 -34.51644 0.01839 2.97846 28.13063 13.88894 0.4379E-02

.00630 169.92570 -30.67506 191.40195 -30.69358 0.01853 2.35524 28.20559 14.43737 0.4011E-02

.00640 172.80170 -26.84434 191.59647 -26.86296 0.01862 1.80405 28.26411 14.93021 0.3636E-02

.00650 175.29456 -23.01361 191.40782 -23.03229 0.01868 1.32622 28.30823 15.36409 0.3256E-02

.00660 177.40466 -19.19048 190.84174 -19.20918 0.01870 0.92248 28.34002 15.73621 0.2869E-02

.00670 179.13315 -15.38243 189.90459 -15.40111 0.01868 0.59299 28.36156 16.04434 0.2483E-02

.00680 180.48189 -11.59681 188.60338 -11.61544 0.01863 0.33730 28.37490 16.28686 0.2101E-02

.00690 181.45349 -7.84083 186.94579 -7.85936 0.01854 0.15442 28.38212 16.46268 0.1731E-02

.00700 182.05127 -4.12153 184.94003 -4.13994 0.01841 0.04285 28.38521 16.57133 0.1367E-02

.00710 182.27925 -0.44579 182.59494 -0.46404 0.01825 0.00054 28.38615 16.61286 0.1012E-02

.00720 182.14211 3.17970 179.91992 3.16165 0.01806 0.02499 28.38684 16.58787 0.6783E-03

.00730 181.64520 6.74844 176.92487 6.73061 0.01783 0.11325 28.38910 16.49749 0.3556E-03

.00740 180.79453 10.25413 173.62015 10.23656 0.01757 0.26197 28.39468 16.34333 0.5205E-04

.00750 179.59668 13.69069 170.01666 13.67342 0.01728 0.46741 28.40522 16.12749 -0.2340E-03

.00760 178.05888 17.05226 166.12570 17.03530 0.01695 0.72550 28.42224 15.85248 -0.4915E-03

.00770 176.18892 20.33319 161.95901 20.31659 0.01660 1.03191 28.44715 15.52127 -0.7266E-03

.00780 173.99512 23.52812 157.52869 23.51189 0.01622 1.38202 28.48125 15.13715 -0.9388E-03

.00790 171.48634 26.63187 152.84720 26.61606 0.01582 1.77104