Введение
Теорема в электрической физике – теорема о суперпозиции в электрических цепях.
the superposition theorem in electrical circuits
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:
Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i. e. V=0; internal impedance of ideal voltage source is zero (short circuit)). Replacing all other independent current sources with an open circuit (thereby eliminating current i. e. I=0; internal impedance of ideal current source is infinite (open circuit)). This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources. The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent. The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers. Superposition works for voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents. However, if the linear network is operating in steady state and each external independent source has a different frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the same frequency (for example in power systems, where many generators operate at 50 Hz or 60 Hz), then superposition can't be used to determine average power.
Теорема о суперпозиции является производным результатом принципа суперпозиции, применимым к сетевому анализу электрических цепей. Теорема о суперпозиции утверждает, что для линейной системы (в частности, включая подкатегорию линейных систем, инвариантных во времени), отклик (напряжение или ток) в любой ветви двусторонней линейной цепи, содержащей более одного независимого источника, равен алгебраической сумме откликов, вызванных каждым независимым источником, действующим в одиночку, при этом все остальные независимые источники заменяются их внутренними импедансами. Для определения вклада каждого отдельного источника все остальные источники сначала необходимо "выключить" (установить в ноль) следующим образом:
the superposition theorem in electrical circuits
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:
Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i. e. V=0; internal impedance of ideal voltage source is zero (short circuit)). Replacing all other independent current sources with an open circuit (thereby eliminating current i. e. I=0; internal impedance of ideal current source is infinite (open circuit)). This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources. The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent. The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers. Superposition works for voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents. However, if the linear network is operating in steady state and each external independent source has a different frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the same frequency (for example in power systems, where many generators operate at 50 Hz or 60 Hz), then superposition can't be used to determine average power.
Заменить все остальные независимые источники напряжения на короткое замыкание (тем самым устраняя разность потенциалов, то есть V = 0; внутренний импеданс идеального источника напряжения равен нулю – короткое замыкание). Заменить все остальные независимые источники тока на разомкнутую цепь (тем самым устраняя ток, то есть I = 0; внутренний импеданс идеального источника тока бесконечен – разомкнутая цепь).
the superposition theorem in electrical circuits
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:
Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i. e. V=0; internal impedance of ideal voltage source is zero (short circuit)). Replacing all other independent current sources with an open circuit (thereby eliminating current i. e. I=0; internal impedance of ideal current source is infinite (open circuit)). This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources. The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent. The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers. Superposition works for voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents. However, if the linear network is operating in steady state and each external independent source has a different frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the same frequency (for example in power systems, where many generators operate at 50 Hz or 60 Hz), then superposition can't be used to determine average power.
Эта процедура выполняется для каждого источника по очереди, после чего полученные отклики суммируются для определения реальной работы цепи. Итоговая работа цепи является суперпозицией различных источников напряжения и тока. Теорема о суперпозиции имеет большое значение в анализе цепей. Она используется для приведения любой цепи к эквивалентной схеме Нортона или эквивалентной схеме Тевена. Теорема применима к линейным сетям (переменным во времени или инвариантным во времени), состоящим из независимых источников, линейных зависимых источников, линейных пассивных элементов (резисторов, индукторов, конденсаторов) и линейных трансформаторов. Суперпозиция применима к напряжению и току, но не к мощности. Иными словами, сумма мощностей каждого источника при отключенных остальных источниках не равна реальной потребляемой мощности. Для расчета мощности сначала необходимо использовать суперпозицию для определения тока и напряжения каждого линейного элемента, а затем вычислить сумму произведений напряжений и токов. Однако, если линейная сеть работает в установившемся режиме и каждый внешний независимый источник имеет различную частоту, то суперпозицию можно применить для вычисления средней или активной мощности. Если хотя бы два независимых источника имеют одинаковую частоту (например, в энергосистемах, где многие генераторы работают на частоте 50 или 60 Гц), то суперпозицию нельзя использовать для определения средней мощности.
the superposition theorem in electrical circuits
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:
Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i. e. V=0; internal impedance of ideal voltage source is zero (short circuit)). Replacing all other independent current sources with an open circuit (thereby eliminating current i. e. I=0; internal impedance of ideal current source is infinite (open circuit)). This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources. The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent. The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers. Superposition works for voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents. However, if the linear network is operating in steady state and each external independent source has a different frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the same frequency (for example in power systems, where many generators operate at 50 Hz or 60 Hz), then superposition can't be used to determine average power.
Аналогия давления газа
Теорема о суперпозиции в электрических цепях аналогична закону Далтона о парциальном давлении, который гласит, что общее давление, оказываемое идеальной смесью газов в заданном объеме, равно алгебраической сумме давлений, которые оказывал бы каждый газ в отдельности в этом же объеме.