40 lines
1.7 KiB
HTML
40 lines
1.7 KiB
HTML
Clarification of the term "Linear"
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<p>
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The term "linear" is very clear when applied to a
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mathematical function. A function F is linear if and only
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if it obeys homogeneity and superposition:
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</p><p>
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Homogeneity: F(cx) = cF(x)
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<br/>
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Superposition: F(x+y) = F(x) + F(y)
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</p><p>
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In the context of what we have seen so far, the only
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elements that are linear as mathematical functions are
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resistors. An independent voltage source or an independent
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current source is not a linear element. (There are also
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linear dependent sources, linear capacitors and linear
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inductors, but we have not yet introduced them in our class.
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You will see them later.)
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</p><p>
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Formally, a circuit composed of only linear elements is a
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linear circuit. When we add independent sources to a linear
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circuit as inputs, we get a circuit that is not linear
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because it has an offset: its v-i characteristic at a pair
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of exposed terminals may not pass through the origin.
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However, we can make a Thevenin or Norton equivalent model
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of such a circuit: the Thevenin resistance summarizes the
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effect of the linear elements and the Thevenin voltage
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summarizes the effect of the independent sources.
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</p><p>
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However the term "linear," when applied to an electrical
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circuit often takes on an informal meaning. We often say
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that a circuit containing only linear elements and
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independent sources is a "linear circuit." So, in the
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informal sense, a linear circuit is one where we can apply
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the Thevenin or Norton theorems to summarize the behavior at
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a pair of exposed terminals.
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</p><p>
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Sorry for the confusion of words — natural language is like
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that!
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</p>
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