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Definition of Linear Circuit?

by wilsonb
Tags: circuit, definition, linear
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wilsonb
#1
Mar16-12, 12:55 AM
P: 28
1. The problem statement, all variables and given/known data
In the Lectures, we are told that techniques like homogeneity and superposition work only for linear circuits, but in Chapter 3 of the Textbook (which is the only place I can find one) I see a definition of linearity as "A circuit is linear if and only if



2. Relevant equations
f(ax1 + bx2) = af(x1) + bf(x2)"

i.e. if homogeneity and superposition work for it.



3. The attempt at a solution
How do I tell, when confronted with an arbitrary circuit, whether or not it is linear - whether or not homogeneity and superposition are going to work for it?
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rude man
#2
Mar16-12, 03:41 AM
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No circuit is purely linear. Even R's and C's have voltage-varying i-V characteristics. Obviously, a linear model works very well in almost all instances.

Transistor circuits are less linear: usually a linear approximation is made, like an equivalent circuit, constant beta, zero di/dVce in the linear mode, etc.

Diodes are clearly non-linear, since they conduct in one direction but not the other. Zeners are in the same category: their i-V relationships are highly non-linear.

Photodiodes are amazingly linear, providing nearly constant di/dI over as many as 5 orders of magnitude (100,000 to 1). I = intensity.

Got any other devices in mind?
wilsonb
#3
Mar16-12, 05:01 AM
P: 28
This apply only with LINEAR ELEMENTS in circuit. In fact, only independent sources, linear-dependent sources and resistors are allowed.


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