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Finally, we will summarize the piecewise linear method.
Firstly, the piecewise linear method is divided into three steps to analyze nonlinear resistance circuits.
The first step, we should get the piecewise linear model
by using continuous piecewise lines to approximate nonlinear curve.
Then for each polygonal line,
we have to get their features and their conditions.
By using the suppose-verify method, we can find out which section it works.
The advantage of this approach is that
if you know which polygonal line it works exactly.
Then for the polygonal line,
it is a linear system.
So methods, such as node method, loop method,
Thevenin theorem, and superposition theorem,
can be used without any taboo.
But it also has some shortcomings.
First, you should be able to find that
it has problem with accuracy.
The example we did just now
is such an example.
It is a straight line here,
and here is also a straight line.
As we mentioned just now,
if the circuit
is either working in this section
or that section,
that is no problem.
Because in these two section,
it has little error.
But unfortunately,
if it works in this section,
then the precision will has problem.
Of course, we also can do this model more accurate.
This is the first section,
this is the second one,
this is the third one,
this is the fourth one,
this is the fifth one,
and this is the sixth one.
We can make a lot of piecewise linear sections
so that it will approximate such a curve under the condition of arbitrary precision.
It can be realized.
But it creates another problem,
that is, as the number of sections increases,
or with the increase of the nonlinear resistance elements in the circuit,
the number of supposition you need to verify
are increased greatly.
What does that mean?
Let's look at such a problem.
Assuming that
there are two nonlinear resistors in it.
A diode
and a common resistor.
The diode
we think it works in two sections.
This is an ideal model of the diode (, which will be discussed later).
The resistor also works two sections.
We leave this question to you.
For such a circuit,
How many sub-circuits do you need to analyze
so that making the problem clear?
If you understand this problem,
you will also understand
the second deficiency of the piecewise linear method
we mentioned earlier.