Electrical circuits wyklad 4

Electrical Circuits

Dr inż. Agnieszka Wardzińska

Room: 105 Polanka

agnieszka.wardzinska@put.poznan.pl

cygnus.et.put.poznan.pl/~award

Źródła sterowane – przykład użycia, kilka

metod

4.2 Linearity Property

3

Homogeneity property (Scaling)

iR

v

i





kiR

kv

ki





Additivity property

R

i

v

i





R

i

v

i





i

(

i

i

)

R

i

R

i

R

v

v

i















Linear network



_{A linear circuit is one whose output is linearly}

related (or directly proportional) to its input

v V₀

I₀ i

 _{Linear circuit consist of}

 _{linear elements}

 _{linear dependent sources}  independent sources 5 mV 1mA A 2 . 0 V 1 A 2 V 10          i v i v i v s s s

nonlinear

R

v

R

i

p

:

_



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:        

 _{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.

 _{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.

 _{Examples of linear elements are resistors, capacitors, and air}

Diodes

The diode is a 2-terminal

device.

A diode ideally

conducts in only one

direction.

Ideal Diode Characteristics

Conduction Region

Non-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

 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)

Nonlinear elements

Nonlinear elements analysis



Analytical



Graphical



Load line method (graphical)



Piecewise linear method