Основные положения теории переходных процессов в электрических цепях

12

Академия России

Кафедра физики

Реферат

Основные положения теории переходных процессов

в электрических цепях

Орел 2009

Содержание

Условия возникновения переходных колебаний в электрических цепях

Законы коммутации и начальные условия

Сущность классического метода анализа переходных колебаний в
электрических цепях

Библиографический список

Условия возникновения переходных колебаний в электрических цепях

Ранее мы анализировали установившийся (стационарный) режим колебаний,
когда напряжение на элементах и ток ветвей изменялись по гармоническому
закону на бесконечно большом интервале времени. К установившемуся режиму
относятся также режим постоянного тока и режим обесточенной цепи.

На практике часто возникает необходимость анализа электрической цепи при
переходе от одного стационарного состояния к другому.

Если цепь содержит только элементы активного сопротивления, то такой
переход происходит мгновенно, так как эти элементы на запасают энергии.

При наличии в цепи реактивных элементов L и С для перехода от одного
состояния к другому требуется некоторое конечное время. Это объясняется
тем, что реактивные элементы могут запасать энергию, а затем
отдавать ее.

Процесс перехода электрической цепи от одного установившегося состояния
к другому установившемуся состоянию называется переходным
(нестационарным) процессом. 

Колебания, существующие при этом в цепи, называют переходными
(нестационарными). 

Частным случаем переходных колебаний являются свободные колебания. Они
существуют в электрической цепи после прекращения внешнего воздействия
за счет энергии, запасенной в реактивных элементах.

Таким образом, условиями возникновения переходных колебаний в
электрической цепи являются:

– наличие в цепи реактивных элементов;

– наличие коммутации.

При этом под коммутацией понимают любые действия в цепи, приводящие к
возникновению переходных процессов.

Приведем примеры коммутаций:

а) механическое соединение или разъединение на отдельных участках цепи.
В теории считают, что такое действие осуществляется с помощью идеального
ключа. На рисунке 1, а показан случай, когда идеальный ключ замыкается,
а на рисунке 1, б – когда размыкается;
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а) б)

Рис. 1

б) включение или выключение ЭДС или задающего тока источников.

picscalex84010009000003410d000009000001000000000400000003010800050000000
b0200000000050000000c026602de11030000001e0008000000fa0200001000000000000
000040000002d01000007000000fc020100000000000000040000002d010100000100002
4037e003301340133012a01340120013501170137010d01390105013c01fb003f01f2004
101e9004601e2004a01d9004f01d2005401c9005901c1005f01bb006c01ae007201a7007
901a10080019b00880196009001910098018c00a0018800a9018400b2018100ba017e00c
4017c00cd017900d7017700e0017700ea017600f3017600fe01760008027700110277001
b02790024027c002e027e00360281003f028400470288004f028c0058029100600296006
8029b006f02a1007502a7007c02ae008802bb008e02c1009302c9009902d2009e02d900a
202e200a602e900a902f200ac02fb00ae020501b1020d01b2021701b4022001b5022a01b
5023401b5023401b5023e01b4024801b2025101b1025b01ae026301ac026d01a9027601a
6027f01a20287019e028f019902980193029f018e02a6018802ae017c02bc017502c2016
f02c7016802cd016002d2015802d7014f02dc014702e0013f02e3013602e7012e02eb012
402ed011b02ef011102f1010802f201fe01f201f301f201ea01f201e001f201d701f101c
d01ef01c401ed01ba01eb01b201e701a901e301a001e0019801dc019001d7018801d2018
001cd017901c7017201c2016c01bc015f01ae015901a60154019f014f0198014a018f014
601870141017f013f0176013c016d013901630137015b01350151013401480133013e013
301340108000000fa0200000000000000000000040000002d01020007000000fc020000f
fffff000000040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000800000025030200f8014e02f801170004000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000800000025030200fb011a01c8014b0104000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000800000025030200fb011a0128024b0104000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000001000024037e00cb0a3401cb0a2a01cd0a2
001ce0a1701cf0a0d01d20a0501d50afb00d70af200da0ae900de0ae200e20ad900e80ad
200ed0ac900f10ac200f80abb00040bae000b0ba700120ba100190b9b00210b9600290b9
100310b8c00390b8800410b85004b0b8100530b7e005c0b7c00660b79006f0b7700790b7
700820b76008c0b7600970b7600a00b7700aa0b7700b30b7900bd0b7c00c60b7e00ce0b8
100d80b8500e00b8800e80b8c00f00b9100f80b9600010c9b00070ca1000e0ca700150ca
e00210cbb00270cc2002c0cc900310cd200370cd9003b0ce2003f0ce900420cf200440cf
b00470c05014a0c0d014b0c17014d0c20014e0c2a014e0c34014e0c34014e0c3e014d0c4
8014b0c51014a0c5b01470c6301440c6d01420c76013f0c7f013b0c8701370c8f01310c9
8012c0c9f01270ca701210cae01150cbc010e0cc201070cc701010ccd01f80bd201f00bd
701e80bdc01e00be001d80be301ce0be701c60beb01bd0bed01b30bef01aa0bf101a00bf
201970bf2018c0bf201820bf201790bf2016f0bf101660bef015c0bed01530beb014b0be
701410be301390be001310bdc01290bd701210bd201190bcd01120bc7010b0bc201040bb
c01f80aae01f10aa701ed0a9f01e80a9801e20a8f01de0a8701da0a7f01d70a7601d50a6
d01d20a6301cf0a5b01ce0a5101cd0a4801cb0a3e01cb0a3401040000002d01020004000
0002d01030004000000f001000008000000fa0200001000000000000000040000002d010
000040000002d0101000800000025030200910b4e02910b1700040000002d01020004000
0002d01030004000000f001000008000000fa0200001000000000000000040000002d010
000040000002d0101000800000025030200940b1a01610b4b01040000002d01020004000
0002d01030004000000f001000008000000fa0200001000000000000000040000002d010
000040000002d0101000800000025030200940b1a01c10b4b01040000002d01020004000
0002d01030004000000f001000008000000fa0200001000000000000000040000002d010
000040000002d0101000001000024037e00a0053001a0052601a2051c01a3051401a4050
a01a7050101aa05f800ac05ef00af05e700b305df00b705d700bc05d000c205c700c605c
000cc05ba00d805ac00df05a600e505a000ec059a00f4059500fc05900004068b000c068
800140684001d06800025067e002e067c0038067900410677004a067700530676005d067
60067067600710677007a067700830679008c067c0096067e009e068000a7068400af068
800b7068b00bf069000c7069500cf069a00d506a000dc06a600e306ac00ef06ba00f406c
000f906c700ff06d0000407d7000807df000c07e7000e07ef001107f8001407010116070
a011807140119071c011a0726011a0730011a0730011a0739011907430118074c0116075
50114075e01110768010e0770010c0779010807810104078901ff069101f9069801f406a
001ef06a701e306b401dc06ba01d506bf01cf06c501c706ca01bf06cf01b706d401af06d
801a706db019e06df019606e3018c06e5018306e6017a06e9017106ea016706ea015d06e
a015306ea014a06ea014106e9013806e6012e06e5012506e3011d06df011406db010c06d
8010406d401fc05cf01f405ca01ec05c501e505bf01df05ba01d805b401cc05a701c605a
001c2059801bc059101b7058901b3058101af057901ac057001aa056801a7055e01a4055
501a3054c01a2054301a0053901a0053001040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
10008000000250302005d064e025d064e01040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
10008000000250302005d0617005d06f100040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
10008000000250302006006ee002e062001040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
10008000000250302006006ee008d062001040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
100080000002503020060063a012e066b01040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
100080000002503020060063a018d066b01040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
1000001000024037e00390f3001390f26013b0f1c013c0f14013d0f0a01400f0201430ff
800450fef00480fe7004c0fe000500fd700550fd0005a0fc7005e0fc000650fba00710fa
c00780fa6007e0fa000850f9a008d0f9500950f90009d0f8c00a50f8800ad0f8400b60f8
100be0f7e00c70f7c00d00f7900da0f7700e30f7700ec0f7600f60f7600001076000a107
700131077001c10790025107c002f107e0037108100401084004810880050108c0058109
0006010950068109a006e10a0007510a6007c10ac008810ba008d10c0009210c7009710d
0009d10d700a110e000a510e700a710ef00aa10f800ad100201af100a01b1101401b2101
c01b3102601b3103001b3103001b3103a01b2104301b1104c01af105601ad105e01aa106
801a7107001a5107901a11081019d10890197109101921099018d10a0018810a7017c10b
5017510bb016e10bf016810c6016010ca015810cf015010d4014810d8014010db013710d
f012f10e3012510e5011c10e6011310e9010a10ea010010ea01f60fea01ec0fea01e30fe
a01da0fe901d00fe601c70fe501be0fe301b60fdf01ad0fdb01a50fd8019d0fd401950fc
f018d0fca01850fc6017e0fbf01780fbb01710fb501650fa7015e0fa0015a0f9901550f9
101500f89014c0f8101480f7901450f7001430f6801400f5e013d0f56013c0f4c013b0f4
301390f3a01390f3001040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f60f4e02f60f4e01040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f60f1700f60ff100040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f90fef00c60f2001040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f90fef0026102001040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f90f3a01c60f6b01040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000800000025030
200f90f3a0126106b01040000002d010200040000002d01030004000000f001000008000
000fa0200001000000000000000040000002d010000040000002d0101000c00000025030
400d40076007a0076007900f0011700f001040000002d010200040000002d01030004000
000f001000008000000fa0200001000000000000000040000002d010000040000002d010
1000c0000002503040042057600e8047600e704f0018504f001040000002d01020004000
0002d01030004000000f001000008000000fa0200001000000000000000040000002d010
000040000002d0101000c00000025030400b00976000a0a76000b0af0016d0af00104000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000c000000250304001e0e7600770e7600780ef
001db0ef001040000002d010200040000002d01030004000000f0010000030000001e000
30000001e00030000001e00040000002d010300040000002d0102001c000000fb0210000
70000000000bc02000000cc0102022253797374656d00007f0b0a2de0ef1200d89ff377e
19ff3772020f577a109667f040000002d010000050000000102ffffff000500000009020
000000005000000020102000000050000000601010000000500000004010d00000005000
000070101000000050000002e0100000000050000001402000000001c000000fb0209000
40000000000bc02000000cc0702022253797374656d0000720b0a63e0ef1200d89ff377e
19ff3772020f577a109667f040000002d010400050000000102ffffff000500000002010
2000000040000002d0103001c000000fb020900040000000000bc02000000cc070202225
3797374656d00007c0b0a4ae0ef1200d89ff377e19ff3772020f577a109667f040000002
d010500040000002d01020005000000090200000000050000002e0100000000030000001
e00070000001604f001ce11bd00df1005000000090200000000050000000201010000000
50000000102ffffff00050000002e01180000001c000000fb0246ff000000000000bc020
00000000702001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577a
109667f040000002d01060009000000320acf015e110100000030105d001c000000fb022
bff000000000000bc02010000000702001054696d6573204e657720526f6d616e00d89ff
377e19ff3772020f577a109667f040000002d01070004000000f001060009000000320a8
501001101000000491053001c000000fb020700030000000000bc02000000cc070202225
3797374656d0000800b0a7de0ef1200d89ff377e19ff3772020f577a109667f040000002
d01060004000000f0010700040000002d010200040000002d010300040000002d0105000
70000001604ef01ce11bd00df1004000000f0010600040000002701ffff040000002701f
fff040000002701ffff1c000000fb021000070000000000bc02000000cc0102022253797
374656d0000800b0a7ee0ef1200d89ff377e19ff3772020f577a109667f040000002d010
60004000000f001040004000000f0010500040000002701ffff030000001e00030000001
e00030000001e00040000002d010300040000002d010200040000002d010000050000000
102ffffff000500000009020000000005000000020102000000050000000601010000000
500000004010d00000005000000070101000000050000002e01000000000500000014020
00000001c000000fb020900040000000000bc02000000cc0702022253797374656d00007
c0b0a4be0ef1200d89ff377e19ff3772020f577a109667f040000002d010400050000000
102ffffff0005000000020102000000040000002d0103001c000000fb020900040000000
000bc02000000cc0702022253797374656d0000720b0a64e0ef1200d89ff377e19ff3772
020f577a109667f040000002d010500040000002d0102000500000009020000000005000
0002e0100000000030000001e00070000001604f0013508bd00460705000000090200000
00005000000020101000000050000000102ffffff00050000002e01180000001c000000f
b0246ff000000000000bc02000000000702001054696d6573204e657720526f6d616e00d
89ff377e19ff3772020f577a109667f040000002d01070009000000320acf01c50701000
00030105d001c000000fb022bff000000000000bc02010000000702001054696d6573204
e657720526f6d616e00d89ff377e19ff3772020f577a109667f040000002d01080004000
000f001070009000000320a8501670701000000491053001c000000fb020700030000000
000bc02000000cc0702022253797374656d0000780b0aade0ef1200d89ff377e19ff3772
020f577a109667f040000002d01070004000000f0010800040000002d010200040000002
d010300040000002d010500070000001604ef013508bd00460704000000f001070004000
0002701ffff040000002701ffff040000002701ffff040000002d01060004000000f0010
40004000000f0010500040000002701ffff030000001e00030000001e00030000001e000
40000002d010300040000002d010200040000002d010000050000000102ffffff0005000
00009020000000005000000020102000000050000000601010000000500000004010d000
00005000000070101000000050000002e0100000000050000001402000000001c000000f
b020600030000000000bc02000000cc0702022253797374656d0000720b0a65e0ef1200d
89ff377e19ff3772020f577a109667f040000002d010400050000000102ffffff0005000
000020102000000040000002d0103001c000000fb020600030000000000bc02000000cc0
702022253797374656d00007c0b0a4ce0ef1200d89ff377e19ff3772020f577a109667f0
40000002d010500040000002d01020005000000090200000000050000002e01000000000
30000001e000700000016049c01610dd4008c0c050000000902000000000500000002010
1000000050000000102ffffff00050000002e01180000001c000000fb022cff000000000
000bc02010000000702001054696d6573204e657720526f6d616e00d89ff377e19ff3772
020f577a109667f040000002d01070009000000320a8101ad0c0100000045108e001c000
000fb020700030000000000bc02000000cc0702022253797374656d00007b0b0a1fe0ef1
200d89ff377e19ff3772020f577a109667f040000002d01080004000000f001070004000
0002d010200040000002d010300040000002d0105000700000016049b01600dd4008c0c0
4000000f0010800040000002701ffff040000002701ffff040000002701ffff040000002
d01060004000000f001040004000000f0010500040000002701ffff030000001e0003000
0001e00030000001e00040000002d010300040000002d010200040000002d01000005000
0000102ffffff00050000000902000000000500000002010200000005000000060101000
0000500000004010d00000005000000070101000000050000002e0100000000050000001
402000000001c000000fb020600030000000000bc02000000cc0702022253797374656d0
0007c0b0a4de0ef1200d89ff377e19ff3772020f577a109667f040000002d01040005000
0000102ffffff0005000000020102000000040000002d0103001c000000fb02060003000
0000000bc02000000cc0702022253797374656d0000720b0a66e0ef1200d89ff377e19ff
3772020f577a109667f040000002d010500040000002d010200050000000902000000000
50000002e0100000000030000001e000700000016049c01a803d400d3020500000009020
000000005000000020101000000050000000102ffffff00050000002e01180000001c000
000fb022cff000000000000bc02010000000702001054696d6573204e657720526f6d616
e00d89ff377e19ff3772020f577a109667f040000002d01070009000000320a8101f4020
100000045108e001c000000fb020700030000000000bc02000000cc07020222537973746
56d0000780b0aafe0ef1200d89ff377e19ff3772020f577a109667f040000002d0108000
4000000f0010700040000002d010200040000002d010300040000002d010500070000001
6049b01a703d400d30204000000f0010800040000002701ffff040000002701ffff04000
0002701ffff040000002d01060004000000f001040004000000f0010500040000002701f
fff040000002701ffff04000000f0010000030000000000

а) Включение б) Выключение

Рис. 2

На рисунке 2, а показано схемное обозначение включения постоянной ЭДС и
постоянного тока, а на рисунке 2, б их выключение.

Такое воздействие принято называть ступенчатым (перепадом, или скачком
напряжения или тока). В случае 2,б иногда говорят, что “гасится”
источник постоянной ЭДС или источник постоянного тока. При этом сам
источник (его внутреннее сопротивление) механически из схемы не
исключается. Отметим, что ступенчатое воздействие является простейшей
функцией. Нахождение реакции на такое воздействие является одной из
важных задач в теории переходных процессов (аналогично задаче нахождения
реакции цепи на гармоническое воздействие в стационарном режиме).

в) другие воздействия, например, в виде импульсов различной формы,
включение и выключение источников гармонических колебаний и др.

Переходные процессы играют важную роль в технике связи.

Они используются для получения напряжения или тока специальной формы
(остроконечные импульсы, пилообразное напряжение и т. п.).

С другой стороны, за счет переходных процессов могут возникать искажения
формы сигналов, что является нежелательным. Анализ переходных процессов
позволяет оценить эти искажения, а также другие характеристики,
составляющие основу методов синтеза устройств, предназначенных для
оптимальной обработки сигналов.

В технике связи переходные процессы учитывают при расчете усилителей
дискретных сигналов, фазосдвигающих цепочек, линий задержки и других
устройств.

При анализе переходных процессов необходимо применять особые правила –
законы коммутации и начальные условия.

Законы коммутации и начальные условия

Будем считать, что коммутация происходит в момент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, а все переходные процессы в цепи начинаются с момента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, т. е. непосредственно после
коммутации. Состояние цепи до коммутации оценивается в момент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.

Законы коммутации относятся к энергоемким (реактивным) элементам, т.
е. к емкости и индуктивности. Они гласят: напряжение на емкости и ток в
индуктивности при конечных по величине воздействиях являются
непрерывными функциями времени, т. е. не могут изменяться скачком.

Математически эта формулировка может быть записана следующим образом
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 для
емкости;
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 для
индуктивности.

Законы коммутации являются следствием определений элементов емкости и
индуктивности.

Так для емкости
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,

а для индуктивности
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.

Полученные интегралы с переменными верхними пределами являются
непрерывными функциями их пределов (времени
picscalex1000100090000038f0000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c028001e0001200000026060f001a00ffffffff00001000
0000c0ffffff06000000a0000000860100000b00000026060f000c004d61746854797065
0000300017000000fb0280fe0000000000009001010000cc0402001054696d6573204e65
7720526f6d616e2043797200cce2040000002d01000008000000320a20012e0001000000
74000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01010004000000f00100000300
00000000) при ограниченных значениях
picscalex1000100090000038f0000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a001e0001200000026060f001a00ffffffff00001000
0000c0ffffffe6ffffffa0000000860100000b00000026060f000c004d61746854797065
0000300017000000fb0280fe0000000000009001010000cc0402001054696d6573204e65
7720526f6d616e2043797200ccf6040000002d01000008000000320a40012e0001000000
69000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01010004000000f00100000300
00000000 и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, которые являются именно таковыми.

Физически закон коммутации для индуктивности объясняется
противодействием ЭДС самоиндукции изменению тока, а закон коммутации для
емкости – противодействием напряженности электрического поля
конденсатора изменению внешнего напряжения.

При количественном анализе переходных колебаний в условия каждой
конкретной задачи должны входить значения напряжений на емкостях и токов
в индуктивностях цепи в момент коммутации, т. е. в начальный момент. Эти
значения образуют начальные условия задачи. Ими, в силу законов
коммутации, задаются те напряжения и токи в цепи, которые сохраняют свои
значения в момент времени непосредственно после коммутации. Если в
момент коммутации напряжение на всех емкостях цепи и токи во всех
индуктивностях цепи равны нулю, то соответствующие начальные условия
называются нулевыми.

Если же это не выполняется хотя бы в одном реактивном элементе цепи, то
задача решается при ненулевых начальных условиях.

На практике при решении задач важное значение имеет умение находить
начальные и конечные значения реакций.

Безошибочно это сделать можно только при твердом знании законов
коммутации и их правильном применении. Проиллюстрируем это на примере.

Пусть в цепи, изображенной на схеме (рис. 3) и находящейся при нулевых
начальных условиях в момент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 включается источник постоянного напряжения путем замыкания ключа.
Требуется определить начальные (для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) и конечные (для
picscalex100010009000003b70000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02800180031200000026060f001a00ffffffff00001000
0000c0ffffff0600000040030000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a2001250201000000a50008000000320a200103010100
00003d0017000000fb0280fe0000000000009001010000cc0402001054696d6573204e65
7720526f6d616e2043797200cc24040000002d01010004000000f001000008000000320a
20012e000100000074000a00000026060f000a00ffffffff01000000000010000000fb02
1000070000000000bc02000000cc0102022253797374656d00cc040000002d0100000400
0000f0010100030000000000) значения реакций.
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0000000000000000040000002d010e0009000000320ac001dc050100000032323a001c00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Рис. 3

Решение.

Изобразим схему для
picscalex100010009000003de0000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00100041200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffffc0030000860100000b00000026060f000c004d61746854797065
0000300017000000fb0280fe0000000000009001000000cc0402001054696d6573204e65
7720526f6d616e2043797200cc83040000002d01000008000000320a6001fc0201000000
300010000000fb0280fe0000000000009001000000020002001053796d626f6c00020400
00002d01010004000000f001000008000000320a60012b02010000002b0008000000320a
60010301010000003d0017000000fb0280fe0000000000009001010000cc040200105469
6d6573204e657720526f6d616e2043797200cc83040000002d01000004000000f0010100
08000000320a60012e000100000074000a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000cc0102022253797374656d00cc04000000
2d01010004000000f0010000030000000000 (рис. 4) с учетом законов
коммутации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 (КЗ);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 обрыв (ХХ),
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4308210346082203480824034a0825034c0828034d0829034e082d034e082f034e082f03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Рис. 4

Откуда
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;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;
picscalex100010009000003740100000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024004e00a1200000026060f001a00ffffffff00001000
0000c0ffffffbaffffffa00a0000fa0300000b00000026060f000c004d61746854797065
0000f00009000000fa02000010000000000000002200040000002d010000050000001402
000213060500000013020002950a17000000fb0220ff0000000000009001000000cc0402
001054696d6573204e657720526f6d616e2043797200ccee040000002d01010008000000
320aeb03e60901000000320008000000320aeb030a0701000000310008000000320acc01
690901000000320008000000320ac002540101000000320017000000fb0280fe00000000
00009001000000cc0402001054696d6573204e657720526f6d616e2043797200ccee0400
00002d01020004000000f001010008000000320a6002100401000000290008000000320a
6002500301000000300008000000320a6002f50101000000280017000000fb0280fe0000
000000009001010000cc0402001054696d6573204e657720526f6d616e2043797200ccee
040000002d01010004000000f001020008000000320a8b03fc0801000000520008000000
320a8b03390601000000520008000000320a6c017f0801000000520008000000320a6c01
b70601000000450008000000320a6002160001000000550010000000fb0280fe00000000
00009001000000020002001053796d626f6c0002040000002d01020004000000f0010100
08000000320a8b03d607010000002b0008000000320a6c01e30701000000d70008000000
320a6002e504010000003d0008000000320a60027f02010000002b000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f0010200030000000000;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.

Теперь определим реакции для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 с учетом того, что режим установился. Емкость
при этом уже зарядится, и будет представлять собой обрыв. Следовательно,
все реакции будут равны нулю, за исключением напряжения на емкости,
которое будет
равно picscalex1000100090000038f0000000200170000000000050000000902000000
000400000002010100050000000102ffffff00040000002e011800050000003102010000
00050000000b0200000000050000000c02a00180011200000026060f001a00ffffffff00
0010000000c0ffffffc6ffffff40010000660100000b00000026060f000c004d61746854
7970650000200017000000fb0280fe0000000000009001010000cc0402001054696d6573
204e657720526f6d616e2043797200cc2f040000002d01000008000000320a6001460001
00000045000a00000026060f000a00ffffffff01000000000010000000fb021000070000
000000bc02000000cc0102022253797374656d00cc040000002d01010004000000f00100
00030000000000.

При анализе переходных колебаний в электрических цепях применяются
следующие методы для нахождения реакций:

– классический, основанный на составлении и решении дифференциальных
уравнений;

– операторный, основанный на применении преобразования Лапласа;

– временной, использующий переходные и импульсные характеристики;

– частотный, базирующийся на спектральном представлении воздействия
(преобразование Фурье).

Укажем, что последних три метода применимы только для линейных
электрических цепей, поскольку в их основе лежит метод наложения
(суперпозиции).

Сущность классического метода анализа переходных колебаний в
электрических цепях

Переходные процессы в электрических цепях описываются уравнениями,
составленными на основании законов Кирхгофа для мгновенных значений
напряжений и токов. Эти уравнения для различных цепей после
соответствующих преобразований могут быть приведены к какому-либо из
следующих видов:

1)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;

2)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;

3)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Первое уравнение – линейное, с постоянными коэффициентами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 характеризует
линейную цепь.

Второе, в котором, по крайней мере, один из коэффициентов (в данном
случае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) является функцией
времени, описывает линейную цепь с переменными параметрами (т. е.
параметрические цепи).

Третье, в котором хотя бы один из коэффициентов (в данном случае
picscalex1000100090000039101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600260061200000026060f001a00ffffffff000010000000c0ffffff
b7ffffff20060000170200000b00000026060f000c004d61746854797065000060001c00
0000fb02bbfd0901000000009001000000020002001053796d626f6c0000890c0a5630f0
1200d89ff377e19ff3772020f577830c66d9040000002d01000008000000320a9f012004
0100000028791c000000fb02bbfd0901000000009001000000020002001053796d626f6c
00008b0c0a1730f01200d89ff377e19ff3772020f577830c66d9040000002d0101000400
0000f001000008000000320a9f0146050100000029791c000000fb02a6fd090100000000
9001000000020002001053796d626f6c0000890c0a57d0f01200d89ff377e19ff3772020
f577830c66d9040000002d01000004000000f001010008000000320a9e01c20101000000
5b791c000000fb02a6fd0901000000009001000000020002001053796d626f6c00008b0c
0a18d0f01200d89ff377e19ff3772020f577830c66d9040000002d01010004000000f001
000008000000320a9e01c005010000005d791c000000fb0240fe00000000000090010100
00cc0402001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577830c
66d9040000002d01000004000000f001010008000000320aa0019f040100000074790800
0000320aa001940201000000667908000000320aa00139000100000061791c000000fb02
80fe0000000000009001000000cc0402001054696d6573204e657720526f6d616e00d89f
f377e19ff3772020f577830c66d9040000002d01010004000000f001000008000000320a
1002300301000000327908000000320a1002f9000100000031790a00000026060f000a00
ffffffff0100000000001c000000fb021000070000000000bc02000000cc010202225379
7374656d00d9830c66d900000a0021008a010000000000000000bcf31200040000002d01
000004000000f0010100030000000000) является функцией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, описывает нелинейную
цепь и является, в отличие от первых двух, нелинейным дифференциальным
уравнением.

Рассмотрим пример.

Пусть на последовательный контур (рис. 5), находящийся при нулевых
начальных условиях в момент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 посредством замыкания ключа начинает действовать источник
напряжения величиной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. Требуется определить реакции.

picscalex800100090000034b1300000b000001000000000400000003010800050000000
b0200000000050000000c024806860e030000001e0008000000fa0200001000000000000
000040000002d01000007000000fc020100000000000000040000002d010100000100002
4037e00a101fa03a101f003a301e603a401dd03a501d303a801cb03ab01c103ad01b803b
001af03b401a803b8019f03be019803c3018f03c7018803ce018103da017403e1016d03e
8016703ef016103f7015c03ff015703070252030f024e0317024b0321024703290244033
20242033c023f0345023d034f023d0358023c0362023c036d023c0376023d0380023d038
9023f03930242039c024403a4024703ae024b03b6024e03be025203c6025703ce025c03d
7026103dd026703e4026d03eb027403f7028103fd02880302038f03070398030d039f031
103a8031503af031803b8031a03c1031d03cb032003d3032103dd032203e6032403f0032
403fa032403fa032403040422030e0421031704200321041d0329041a03330418033c041
503450411034d040d03550407035e0402036504fd026d04f7027404eb028204e4028804d
d028d04d7029304ce029804c6029d04be02a204b602a604ae02aa04a402ad049c02b1049
302b3048902b5048002b7047602b8046d02b8046202b8045802b8044f02b8044502b7043
c02b5043202b3042902b1042102ad041702aa040f02a6040702a204ff019d04f7019804e
f019304e8018d04e1018804da018204ce017404c7016d04c3016504be015e04b8015504b
4014d04b0014504ad013c04ab013304a8012904a5012104a4011704a3010e04a1010404a
101fa0308000000fa0200000000000000000000040000002d01020007000000fc020000f
fffff000000040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d0101000800000025030200670214056702dd0204000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d01010008000000250302006a02e0033702110404000
0002d010200040000002d01030004000000f001000008000000fa0200001000000000000
000040000002d010000040000002d01010008000000250302006a02e0039702110404000
0002d010200040000002d01030004000000f001000007000000fc020000ffffff0000000
40000002d01000008000000fa0205000100000000000000040000002d0104000e0000002
40305004f0876014f080d02c9090d02c90976014f087601040000002d010200040000002
d01030008000000fa0200001000000000000000040000002d010500040000002d0101000
e000000240305004f080d02c9090d02c90976014f0876014f080d02040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101000800000025030200900ccf03700bcf03040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101000800000025030200900c0904700b0904040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101000800000025030200000c0d04000cb604040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101000800000025030200000ccf03000c3603040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d01010008000000250302009504c201e704c201040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d01010008000000250302008306c201d506c201040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101004600000025032100e704c201e704ba01e804b201e904ab01e
b04a401ed049d01f0049701f3049101f6048b01fa048601fe04820102057e0106057b010
b05780110057601150575011a05750120057501250576012a0578012e057b0133057e013
70582013b0586013f058b01420591014505970148059d014a05a4014c05ab014d05b2014
e05ba014e05c201040000002d010200040000002d01030004000000f001050008000000f
a0200001000000000000000040000002d010500040000002d01010046000000250321004
e05c2014e05ba014f05b2015005ab015205a40154059d01570597015a0591015d058b016
10586016505820169057e016d057b0172057801770576017c05750181057501870575018
c0576019105780195057b019a057e019e058201a2058601a6058b01a9059101ac059701a
f059d01b105a401b205ab01b405b201b405ba01b505c201040000002d010200040000002
d01030004000000f001050008000000fa0200001000000000000000040000002d0105000
40000002d0101004600000025032100b505c201b505ba01b605b201b705ab01b905a401b
b059d01be059701c0059101c4058b01c7058601cb058201d0057e01d4057b01d9057801d
e057601e3057501e8057501ed057501f3057601f7057801fc057b0101067e01050682010
90686010d068b01100691011306970115069d011806a4011906ab011b06b2011b06ba011
c06c201040000002d010200040000002d01030004000000f001050008000000fa0200001
000000000000000040000002d010500040000002d01010046000000250321001c06c2011
c06ba011d06b2011e06ab012006a40122069d0124069701270691012b068b012e0686013
206820137067e013b067b0140067801450676014a0675014f06750154067501590676015
e06780163067b0168067e016c0682017006860173068b01770691017a0697017c069d017
e06a4018006ab018106b2018206ba018206c201040000002d010200040000002d0103000
4000000f001050008000000fa0200001000000000000000040000002d010500040000002
d0101000a000000250303006702dd026702c201c502c201040000002d010200040000002
d01030004000000f001050008000000fa0200001000000000000000040000002d0105000
40000002d0101000a00000025030300c404c2013504c201c5022b01040000002d0102000
40000002d01030004000000f001050008000000fa0200001000000000000000040000002
d010500040000002d0101000800000025030200c502c201c5028901040000002d0102000
40000002d01030004000000f001050004000000f001000007000000fc020000000000000
000040000002d01000005000000060101000000040000002d01040048000000240322002
904c2012904bd012b04b9012d04b5012f04b2013304af013704ad013b04ac013f04ab014
404ac014804ad014c04af014f04b2015204b5015404b9015504bd015604c2015604c2015
504c6015404ca015204ce014f04d2014c04d4014804d6014404d8013f04d8013b04d8013
704d6013304d4012f04d2012d04ce012b04ca012904c6012904c201040000002d0102000
5000000060101000000040000002d01030008000000fa0200000a0000000000000004000
0002d010500040000002d01010048000000250322002904c2012904bd012b04b9012d04b
5012f04b2013304af013704ad013b04ac013f04ab014404ac014804ad014c04af014f04b
2015204b5015404b9015504bd015604c2015604c2015504c6015404ca015204ce014f04d
2014c04d4014804d6014404d8013f04d8013b04d8013704d6013304d4012f04d2012d04c
e012b04ca012904c6012904c201040000002d010200040000002d01030004000000f0010
50008000000fa0200000a00000000000000040000002d010500040000002d01010040000
00025031e00e1030501da030401d4030501cd030501c7030601c0030801b9030901b3030
c01ac030e01a6031101a00315019903190193031d018d0321018703260181032c017b033
101750337016f033d016a03440164034b015f0352015a03590155036101500369014b037
101470379013f038b0137039e013103b101040000002d010200040000002d01030004000
000f0010500040000002d01000005000000060101000000040000002d0104002e0000002
40315002403f1010b0394010f03970114039a0119039d011e039f012303a2012803a3012
e03a5013303a6013903a7013e03a8014403a8014903a8014f03a8015403a7015a03a6016
003a5016003a5012403f1012403f101040000002d0102000500000006010100000004000
0002d01030008000000fa0200001000000000000000040000002d010500040000002d010
1000800000025030200d506c2014f08c201040000002d010200040000002d01030004000
000f001050008000000fa0200001000000000000000040000002d010500040000002d010
1000a00000025030300c909c201000cc201000c3c03040000002d010200040000002d010
30004000000f001050008000000fa0200001000000000000000040000002d01050004000
0002d0101000c00000025030400000c3104000c30066702300667020305040000002d010
200040000002d01030004000000f0010500030000001e00030000001e00030000001e000
40000002d010300040000002d0102001c000000fb021000070000000000bc02000000cc0
102022253797374656d0000770c0a58e0ef1200d89ff377e19ff3772020f577230c66990
40000002d010500050000000102ffffff000500000009020000000005000000020102000
000050000000601010000000500000004010d00000005000000070101000000050000002
e0100000000050000001402000000001c000000fb020600030000000000bc02000000cc0
702022253797374656d00002b0c0a77e0ef1200d89ff377e19ff3772020f577230c66990
40000002d010600050000000102ffffff0005000000020102000000040000002d0103001
c000000fb020600030000000000bc02000000cc0702022253797374656d00007a0c0a31e
0ef1200d89ff377e19ff3772020f577230c6699040000002d010700040000002d0102000
5000000090200000000050000002e0100000000030000001e00070000001604360116066
e005b050500000009020000000005000000020101000000050000000102ffffff0005000
0002e01180000001c000000fb022cff000000000000bc02010000000702001054696d657
3204e657720526f6d616e00d89ff377e19ff3772020f577230c6699040000002d0108000
9000000320a1b017c05010000004c0182001c000000fb020700030000000000bc0200000
0cc0702022253797374656d0000270c0a8de0ef1200d89ff377e19ff3772020f577230c6
699040000002d01090004000000f0010800040000002d010200040000002d01030004000
0002d010700070000001604350115066e005b0504000000f0010900040000002701ffff0
40000002701ffff040000002701ffff1c000000fb021000070000000000bc02000000cc0
102022253797374656d0000270c0a8ee0ef1200d89ff377e19ff3772020f577230c66990
40000002d01080004000000f001060004000000f0010700040000002701ffff030000001
e00030000001e00030000001e00040000002d010300040000002d010200040000002d010
500050000000102ffffff000500000009020000000005000000020102000000050000000
601010000000500000004010d00000005000000070101000000050000002e01000000000
50000001402000000001c000000fb020600030000000000bc02000000cc0702022253797
374656d00007a0c0a32e0ef1200d89ff377e19ff3772020f577230c6699040000002d010
600050000000102ffffff0005000000020102000000040000002d0103001c000000fb020
600030000000000bc02000000cc0702022253797374656d00002b0c0a78e0ef1200d89ff
377e19ff3772020f577230c6699040000002d010700040000002d0102000500000009020
0000000050000002e0100000000030000001e00070000001604430176097b00ae0805000
00009020000000005000000020101000000050000000102ffffff00050000002e0118000
0001c000000fb022cff000000000000bc02010000000702001054696d6573204e6577205
26f6d616e00d89ff377e19ff3772020f577230c6699040000002d01090009000000320a2
801cf080100000052018e001c000000fb020700030000000000bc02000000cc070202225
3797374656d0000100c0a43e0ef1200d89ff377e19ff3772020f577230c6699040000002
d010a0004000000f0010900040000002d010200040000002d010300040000002d0107000
70000001604420175097b00ae0804000000f0010a00040000002701ffff040000002701f
fff040000002701ffff040000002d01080004000000f001060004000000f001070004000
0002701ffff030000001e00030000001e00030000001e00040000002d010300040000002
d010200040000002d010500050000000102ffffff0005000000090200000000050000000
20102000000050000000601010000000500000004010d000000050000000701010000000
50000002e0100000000050000001402000000001c000000fb020600030000000000bc020
00000cc0702022253797374656d00002b0c0a79e0ef1200d89ff377e19ff3772020f5772
30c6699040000002d010600050000000102ffffff0005000000020102000000040000002
d0103001c000000fb020600030000000000bc02000000cc0702022253797374656d00007
a0c0a33e0ef1200d89ff377e19ff3772020f577230c6699040000002d010700040000002
d01020005000000090200000000050000002e0100000000030000001e000700000016045
804430b82037b0a0500000009020000000005000000020101000000050000000102fffff
f00050000002e01180000001c000000fb022bff000000000000bc02010000cc070200105
4696d6573204e657720526f6d616e00d89ff377e19ff3772020f577230c6699040000002
d01090009000000320a2f048c0a01000000d1018d001c000000fb020700030000000000b
c02000000cc0702022253797374656d0000220c0ad0e0ef1200d89ff377e19ff3772020f
577230c6699040000002d010a0004000000f0010900040000002d010200040000002d010
300040000002d0107000700000016045704420b82037b0a04000000f0010a00040000002
701ffff040000002701ffff040000002701ffff040000002d01080004000000f00106000
4000000f0010700040000002701ffff08000000fa0200001000000000000000040000002
d010600040000002d01010008000000250302007606200247052002040000002d0102000
40000002d01030004000000f0010600040000002d0100000500000006010100000004000
0002d0104002c00000024031400fc0420025f05ef015d05f5015a05fb015805010257050
70255050d025405130254051a02540520025405270254052d025505330257053a0258054
0025a0546025d054c025f055202fc042002fc042002040000002d0102000500000006010
1000000040000002d01030008000000fa0200001000000000000000040000002d0106000
40000002d0101000800000025030200c9097f029a087f02040000002d010200040000002
d01030004000000f0010600040000002d01000005000000060101000000040000002d010
4002e000000240315004f087f02b2084d02af085302ad085902ab085f02a9086502a8086
c02a7087202a6087802a6087f02a6088502a7088b02a8089202a9089802ab089e02ad08a
402af08aa02b208b002b208b0024f087f024f087f02040000002d0102000500000006010
1000000040000002d01030008000000fa0200001000000000000000040000002d0106000
40000002d0101000800000025030200e20cdb04e20c8703040000002d010200040000002
d01030004000000f0010600040000002d01000005000000060101000000040000002d010
4002e00000024031500e20c3c03b10c9f03b70c9c03bd0c9a03c30c9803c90c9603cf0c9
503d60c9403dc0c9303e20c9303e90c9303ef0c9403f50c9503fc0c9603020d9803080d9
a030e0d9c03140d9f03140d9f03e20c3c03e20c3c03040000002d0102000500000006010
1000000040000002d010300030000001e00030000001e00030000001e00040000002d010
300040000002d010200040000002d010500050000000102ffffff0005000000090200000
00005000000020102000000050000000601010000000500000004010d000000050000000
70101000000050000002e0100000000050000001402000000001c000000fb020e0006000
0000000bc02000000cc0702022253797374656d00007a0c0a37e0ef1200d89ff377e19ff
3772020f577230c6699040000002d010600050000000102ffffff0005000000020102000
000040000002d0103001c000000fb020e00060000000000bc02000000cc0702022253797
374656d00002b0c0a7ae0ef1200d89ff377e19ff3772020f577230c6699040000002d010
700040000002d01020005000000090200000000050000002e0100000000030000001e000
70000001604e40023030f005201050000000902000000000500000002010100000005000
0000102ffffff00050000002e01180000001c000000fb022bff000000000000bc0200000
0000702001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577230c6
699040000002d01090009000000320abc00a10201000000300c6a001c000000fb022bff0
00000000000bc02000000020702001053796d626f6c0000100c0a45e0ef1200d89ff377e
19ff3772020f577230c6699040000002d010a0004000000f001090009000000320abc00e
e01010000003d0c75001c000000fb022bff000000000000bc02010000000702001054696
d6573204e657720526f6d616e00d89ff377e19ff3772020f577230c6699040000002d010
90004000000f0010a0009000000320abc00690101000000740c3b001c000000fb0207000
30000000000bc02000000cc0702022253797374656d0000100c0a46e0ef1200d89ff377e
19ff3772020f577230c6699040000002d010a0004000000f0010900040000002d0102000
40000002d010300040000002d010700070000001604e40023030f00520104000000f0010
a00040000002701ffff040000002701ffff040000002701ffff040000002d01080004000
000f001060004000000f0010700040000002701ffff030000001e00030000001e0003000
0001e00040000002d010300040000002d010200040000002d010500050000000102fffff
f00050000000902000000000500000002010200000005000000060101000000050000000
4010d00000005000000070101000000050000002e0100000000050000001402000000001
c000000fb020a00040000000000bc02000000cc0702022253797374656d00002b0c0a7be
0ef1200d89ff377e19ff3772020f577230c6699040000002d010600050000000102fffff
f0005000000020102000000040000002d0103001c000000fb020a00040000000000bc020
00000cc0702022253797374656d00007a0c0a38e0ef1200d89ff377e19ff3772020f5772
30c6699040000002d010700040000002d01020005000000090200000000050000002e010
0000000030000001e000700000016047603760644022a050500000009020000000005000
000020101000000050000000102ffffff00050000002e01180000001c000000fb0246ff0
00000000000bc02010000000702001054696d6573204e657720526f6d616e00d89ff377e
19ff3772020f577230c6699040000002d01090009000000320a5603e605010000004c0c7
2001c000000fb022bff000000000000bc02010000000702001054696d6573204e6577205
26f6d616e00d89ff377e19ff3772020f577230c6699040000002d010a0004000000f0010
90009000000320a0c03340501000000550c9a001c000000fb020700030000000000bc020
00000cc0702022253797374656d0000100c0a48e0ef1200d89ff377e19ff3772020f5772
30c6699040000002d01090004000000f0010a00040000002d010200040000002d0103000
40000002d0107000700000016047603760644022a0504000000f0010900040000002701f
fff040000002701ffff040000002701ffff040000002d01080004000000f001060004000
000f0010700040000002701ffff030000001e00030000001e00030000001e00040000002
d010300040000002d010200040000002d010500050000000102ffffff000500000009020
000000005000000020102000000050000000601010000000500000004010d00000005000
000070101000000050000002e0100000000050000001402000000001c000000fb020a000
40000000000bc02000000cc0702022253797374656d00007a0c0a39e0ef1200d89ff377e
19ff3772020f577230c6699040000002d010600050000000102ffffff000500000002010
2000000040000002d0103001c000000fb020a00040000000000bc02000000cc070202225
3797374656d00002b0c0a7ce0ef1200d89ff377e19ff3772020f577230c6699040000002
d010700040000002d01020005000000090200000000050000002e0100000000030000001
e00070000001604cc04750e9b031b0d05000000090200000000050000000201010000000
50000000102ffffff00050000002e01180000001c000000fb0246ff000000000000bc020
10000000702001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f5772
30c6699040000002d01090009000000320aac04ca0d01000000430c7c001c000000fb022
cff000000000000bc02010000000702001054696d6573204e657720526f6d616e00d89ff
377e19ff3772020f577230c6699040000002d010a0004000000f001090009000000320a6
204250d01000000550c99001c000000fb020700030000000000bc02000000cc070202225
3797374656d0000100c0a4ae0ef1200d89ff377e19ff3772020f577230c6699040000002
d01090004000000f0010a00040000002d010200040000002d010300040000002d0107000
70000001604cc04750e9b031b0d04000000f0010900040000002701ffff040000002701f
fff040000002701ffff040000002d01080004000000f001060004000000f001070004000
0002701ffff030000001e00030000001e00030000001e00040000002d010300040000002
d010200040000002d010500050000000102ffffff0005000000090200000000050000000
20102000000050000000601010000000500000004010d000000050000000701010000000
50000002e0100000000050000001402000000001c000000fb020a00040000000000bc020
00000cc0702022253797374656d00002b0c0a7de0ef1200d89ff377e19ff3772020f5772
30c6699040000002d010600050000000102ffffff0005000000020102000000040000002
d0103001c000000fb020a00040000000000bc02000000cc0702022253797374656d00007
a0c0a3ae0ef1200d89ff377e19ff3772020f577230c6699040000002d010700040000002
d01020005000000090200000000050000002e0100000000030000001e00070000001604d
403a909a3024f080500000009020000000005000000020101000000050000000102fffff
f00050000002e01180000001c000000fb0246ff000000000000bc0201000000070200105
4696d6573204e657720526f6d616e00d89ff377e19ff3772020f577230c6699040000002
d01090009000000320ab4030c0901000000520c7c001c000000fb022cff000000000000b
c02010000000702001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f
577230c6699040000002d010a0004000000f001090009000000320a6a035908010000005
50c99001c000000fb020700030000000000bc02000000cc0702022253797374656d00001
00c0a4ce0ef1200d89ff377e19ff3772020f577230c6699040000002d01090004000000f
0010a00040000002d010200040000002d010300040000002d010700070000001604d403a
909a3024f0804000000f0010900040000002701ffff040000002701ffff040000002701f
fff040000002d01080004000000f001060004000000f0010700040000002701ffff03000
0001e00030000001e00030000001e00040000002d010300040000002d010200040000002
d010500050000000102ffffff00050000000902000000000500000002010200000005000
0000601010000000500000004010d00000005000000070101000000050000002e0100000
000050000001402000000001c000000fb020b00050000000000bc02000000cc070202225
3797374656d00007a0c0a3be0ef1200d89ff377e19ff3772020f577230c6699040000002
d010600050000000102ffffff0005000000020102000000040000002d0103001c000000f
b020b00050000000000bc02000000cc0702022253797374656d00002b0c0a7ee0ef1200d
89ff377e19ff3772020f577230c6699040000002d010700040000002d010200050000000
90200000000050000002e0100000000030000001e00070000001604b50484019e030f000
500000009020000000005000000020101000000050000000102ffffff00050000002e011
80000001c000000fb02fafe810000000000bc02000000020702001053796d626f6c00001
00c0a4de0ef1200d89ff377e19ff3772020f577230c6699040000002d010900090000003
20a6204890001000000280c48001c000000fb02fafe810000000000bc020000000207020
01053796d626f6c0000220c0ad6e0ef1200d89ff377e19ff3772020f577230c669904000
0002d010a0004000000f001090009000000320a6204280101000000290c49001c000000f
b022bff000000000000bc02010000000702001054696d6573204e657720526f6d616e00d
89ff377e19ff3772020f577230c6699040000002d01090004000000f0010a00090000003
20a6504d50001000000740c3c0009000000320a6504230001000000650c5f001c000000f
b020700030000000000bc02000000cc0702022253797374656d0000220c0ad7e0ef1200d
89ff377e19ff3772020f577230c6699040000002d010a0004000000f0010900040000002
d010200040000002d010300040000002d010700070000001604b50484019e030f0004000
000f0010a00040000002701ffff040000002701ffff040000002701ffff040000002d010
80004000000f001060004000000f0010700040000002701ffff040000002701ffff04000
000f001000004000000f0010500030000000000

Рис. 5

Составим уравнение по второму закону Кирхгофа:
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или
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.
(1)

Пусть все элементы цепи линейны. Тогда уравнение (1) преобразуется к
виду:
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Или
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,

где: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;
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;
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;
picscalex1000100090000031c0100000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02800400071200000026060f001a00ffffffff00001000
0000c0ffffffb7ffffffc0060000370400000b00000026060f000c004d61746854797065
0000e00009000000fa02000010000000000000002200040000002d010000050000001402
5002f4030500000013025002a10617000000fb0240fe0000000000009001010000cc0402
001054696d6573204e657720526f6d616e2043797200cca5040000002d01010008000000
320a20040904020000004c4308000000320ac0023b0001000000610017000000fb0240fe
0000000000009001000000cc0402001054696d6573204e657720526f6d616e2043797200
cca5040000002d01020004000000f001010008000000320aa401d8040100000031001700
0000fb0280fe0000000000009001000000cc0402001054696d6573204e657720526f6d61
6e2043797200cca5040000002d01010004000000f001020008000000320a300318010100
0000320010000000fb0240fe0000000000009001000000020002001053796d626f6c0002
040000002d01020004000000f001010008000000320ac0028902010000003d000a000000
26060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000cc
0102022253797374656d00cc040000002d01010004000000f0010200030000000000.

Получено линейное, в общем случае неоднородное дифференциальное
уравнение второго порядка, которое решается относительно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 известными из математики методами.

Аналогичное уравнение получается и для параметрической цепи. Пусть
теперь цепь является нелинейной, например, допустим, что индуктивность
является функцией тока, т.е.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.

Тогда
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и уравнение (1) будет иметь вид
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.

Оно может быть преобразовано в нелинейное уравнение второго порядка.
Решение нелинейных дифференциальных уравнений, даже первого порядка,
является весьма сложной, а иногда и неразрешимой задачей.

На практике для нахождения реакций в режиме переходных колебаний широкое
применение получил метод “переменных состояния”, в основу которого
положено определение токов через индуктивности и напряжений на емкостях.
С данным методом необходимо ознакомиться самостоятельно.

Библиографический список

1. Белецкий А. Ф. Теория линейных электрических цепей. – М.: Радио и
связь, 1986

2. Шалашов Г. В. Переходные процессы в электрических цепях. – Орел:
ОВВКУС 1981

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