Definition of Linear Circuit?

  1. 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?
     
  2. jcsd
  3. rude man

    rude man 5,557
    Homework Helper
    Gold Member

    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?
     
  4. This apply only with LINEAR ELEMENTS in circuit. In fact, only independent sources, linear-dependent sources and resistors are allowed.
     
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