Roy Lewallen wrote:
I'm sure that somewhere in one of your texts you can find the definition
of linear as applied to networks. Once you do, though, a little thought
is required to discover that y = mx + b doesn't satisfy the criteria for
network linearity.

To be linear, a network has to satisfy superposition. This means that:

If y1 is the response to excitation x1 and y2 is the response to
excitation x2, then the response to x1 + x2 must be y1 + y2.

Let's try that with your function.

The response to x1 is:

y(x1) = mx1 + b

The response to x2 is:

y(x2) = mx2 + b

The sum of y(x1) and y(x2) is:

y(x1) + y(x2) = m(x1 + x2) + 2b

But response to x1 + x2 is:

y(x1 + x2) = m(x1 + x2) + b

These are not equal as they must be to satisfy superposition and
therefore the requirements for linearity.

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy Lewallen, W7EL wrote:
"But of course you realize that the function y = mx + b doesn`t meet the
requirements of a linear function when applied to network theory."

Works for me.

Linear means the graph of the function is a straight line.

f(x) = y = mx + b is called linear because its graph is a straight line.

A straight line is the shortest distance between two points.

In y = mx + b, m is a constant determining the slope of the line. x is
is the independent variable. b is the offset or point along the x-axis
where the line crosses.

y then is a linear function of x because its slope is always mx, but
displaced in the x-direction by a constant value, namely b.

y is linear the same as IR is linear, or by substitution, E is linear in
Ohm`s law where E=IR. For any value of I, voltage = IR and the graph of
I versus E is a straight line with a slope equal to R.

Resistance is a common factor in network theory.

Best regards, Richard Harrison, KB5WZI

Not that it means anything, but the linearity requirement is met when
b = 0, which, of course, is a subset of the family of equations of the
form y = mx + b.

73,

Chuck
NT3G