Ideal diode characteristics

Ideal Diode
Up to this point in your career as an ECE student, you’ve been studying linear electrical components. For example, resistors (R), inductors (L), and capacitors (C) are ideally linear elements (and passive, of course).
Linear Circuit Elements
What do we mean that a component is "linear"? To answer this question, recall there are just two independent qualities of electricity in electrical circuits. These are voltage and current.
A linear circuit element is one that linearly relates the voltage across that element to the current through the element.
Linearity has a precise mathematical statement. If a quantity y is a function of another quantity x, as
y= f( x) (1)
Then y is linearly dependent on x if
my= f( mx) (2)

where m is a constant. In other words, f is a linear function if when quantity x is multiplied by some constant m results in the function simply being multiplied by m.

Here are a couple of examples of linear components in electrical circuits:

This is perhaps a bit tricker, but notice that differentiation is a linear operator: if v increases by a factor m then i does as well.

Ideal Diodes

You will now learn about a new electrical circuit element, the diode. Diodes are made from two different types of semiconducting materials that come together to form a "junction":

The circuit symbol is

which is related to the physical markings on a typical diode as

In stark contrast to resistors, inductors, and capacitors, the diode is a nonlinear element. For an ideal diode, the i-v characteristic curve is

It is apparent from this i-v characteristic curve that there are two distinct regions of operation of the ideal diode:

The ideal diode acts as an electronic "valve" allowing current in only one direction through the diode: in the direction of the arrow in the circuit symbol.
We will find this "valve" behavior very useful in some situations. For example, this is useful to prevent damage to an electronic device when the battery is inserted backwards, for example