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4.2 Linearity Property 3 Homogeneity property (Scaling) Additivity property

Linear network A linear circuit is one whose output is linearly related (or directly proportional) to its input v V0V0 I0I0 i Linear circuit consist of linear elements linear dependent sources independent sources 4

Non-linear networks Most electronic designs are, in reality, non-linear. There is very little that does not include some semiconductor devices. 5 In an electric circuit, a nonlinear element or nonlinear device is an electrical element which does not have a linear relationship between current and voltage. A diode is a simple example. The current I through a diode is a non-linear function of the voltage V across its terminals:circuit electrical elementlinear currentvoltagediode Nonlinear elements are avoided in some electronic circuits, called linear circuits, because they have the potential to distort electrical signals. A nonlinear curve that consists of linear curves called piece-wise linear.linear circuitselectrical signals Other examples of nonlinear elements are transistors and other semiconductor devices, vacuum tubes, and iron core inductors and transformers when operated above their saturation current.transistors semiconductorvacuum tubesinductors transformerssaturation Examples of linear elements are resistors, capacitors, and air core inductors.resistorscapacitors inductors

Diodes The diode is a 2-terminal device. A diode ideally conducts in only one direction.

Ideal Diode Characteristics Conduction RegionNon-Conduction Region The voltage across the diode is 0 V The current is infinite The forward resistance is defined as R F = V F / I F The diode acts like a short All of the voltage is across the diode The current is 0 A The reverse resistance is defined as R R = V R / I R The diode acts like open

 Forward bias  If the voltage v D across the diode is positive, relatively large amounts of current flow for small voltages.  Reverse bias  For moderately negative values of v D, the current i D is very small. (reverse-biased region)  For sufficiently large reverse-bias voltage v D, currents of large magnitude flow. (reverse- breakdown region) Non-Ideal Diode Characteristics

Nonlinear elements symbol Analytical formula Graphical presentation IU Table presentation

Nonlinear elements analysis Analytical Graphical Load line method (graphical) Piecewise linear method Instrumental analysis

Graphical summation for nonlinear analysis