Week 8: Linearity Property and Source Transformation

Linearity Property

What is Linearity Property?

-Linear property is the linear relationship between cause and effect of an element. This property gives linear and nonlinear circuit definition. The property can be applied in various circuit elements. The homogeneity (scaling) property and the additivity property are both the combination of linearity property.

The homogeneity property is that if the input is multiplied by a constant k then the output is also multiplied by the constant k. Input is called excitation and output is called response here. As an example if we consider ohm’s law. Here the law relates the input i to the output v.

Mathematically,                 v= iR

If we multiply the input current  i by a constant k then the output voltage also increases correspondingly by the constant k. The equation stands,      

                                     kiR = kv

The additivity property is that the response to a sum of inputs is the sum of the responses to each input applied separately.

Using voltage-current relationship of a resistor if

                                       v1 = i1R       

and  

                                       v2 = i2R

 Applying (i1 + i2)gives

 V = (i1 + i2)R = i1R+ i2R = v1 + v2

We can say that a resistor is a linear element. Because the voltage-current relationship satisfies both the additivity and the homogeneity properties.

What is linear circuit?

 -A circuit is linear if the output is linearly related with its input.

Example of a Linear Circuit:

See a circuit in figure 1. The box in the circuit is a linear circuit. We cannot see any independent source inside the linear circuit.

Source Transformation

What is Source Transformation?

-Independent current sources can be turned into independent voltage sources, and vice-versa, by methods called "Source Transformations." These transformations are useful for solving circuits. We will explain the two most important source transformations, Thevenin's Source, and Norton's Source, and we will explain how to use these conceptual tools for solving circuits.

For more info about Thevenin's Source, Click here.

For more info about Norton's Source, Click here.

Conversion of Voltage Source to Current Source

To convert a Voltage Source into a current one, We need to follow these steps:

1. Make short circuit between two terminals A and B as we done in figure. Find the short circuit current and let it be I.

2. Measure the resistance at the terminals with load removed and sources of e.m.f s replaced by their internal resistances if any. Let the resistance is R.

3. Then equivalent current source can be represented by a single current source of magnitude I in parallel with resistance R.

Example:

Conversion of Current Source to Voltage Source

To do this, We have to do the same inverse procedure.

Example:

Reflection:

This week, I learned that converting sources is actually very easy. To covert a voltage source into a current one, We simply change the position of the resistors from series to parallel. To convert a current source into a voltage one, We change the position of the resistors from parallel to series. But before we apply source transformation, We must analyze the problem and identify the position of the resistors first. If the source is a voltage one and if the resistor connected to the source is in a parallel connection, then source transformation is not applicable. If the source is a current one and if the resistor connected to the source is in a series connection, then source transformation is also not applicable.

Videos:

Linearity Property:

Source Transformation:

Circuit of Life:

Thanks for visiting my Blog!!. The ninth post will be arriving next week. See ya!!