# Definition of Linear Circuit?

1. Mar 16, 2012

### wilsonb

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. Mar 16, 2012

### rude man

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?

3. Mar 16, 2012

### wilsonb

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