Download Electrical circuits wyklad 4

Dr inż. Agnieszka Wardzińska
Room: 105 Polanka
[email protected]
cygnus.et.put.poznan.pl/~award
Advisor hours:
Monday: 9.30-10.15
Wednesday: 10.15-11.00
Źródła sterowane – przykład użycia,
kilka metod
4.2 Linearity Property
Homogeneity property (Scaling)
i  v  iR
ki  kv  kiR
Additivity property
i1  v1  i1 R
i2  v2  i2 R
i1  i2  (i1  i2 ) R  i1 R  i2 R  v1  v2
3
Linear network
 A linear circuit is one whose output is linearly related
(or directly proportional) to its input
i
I0
 Linear circuit consist of
 linear elements
 linear dependent sources
 independent sources
v2
p i R 
: nonlinear
R
v
V0
vs  10V  i  2A
vs  1V
 i  0. 2 A
vs  5mV  i  1mA
2
4
Non-linear networks
 Most electronic designs are, in reality, non-linear. There is very little that
does not include some semiconductor devices.
 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 core
inductors.
5
Diodes
The diode is a 2-terminal device.
A diode ideally conducts in
only one direction.
Ideal Diode Characteristics
Conduction Region
The voltage across the diode is 0 V
The current is infinite
The forward resistance is defined as
RF = VF / IF
The diode acts like a short
Non-Conduction Region
All of the voltage is across the diode
The current is 0 A
The reverse resistance is defined as
RR = VR / IR
The diode acts like open
Non-Ideal Diode Characteristics
 Forward bias
 If the voltage vD across the diode
is positive, relatively large amounts
of current flow for small voltages.
 Reverse bias
 For moderately negative values of
vD, the current iD is very small.
(reverse-biased region)
 For sufficiently large reverse-bias
voltage vD, currents of large
magnitude flow. (reversebreakdown region)
Nonlinear elements
Table presentation
symbol
Analytical formula
I
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2
U( I)  0.5 I
Graphical presentation
10
10
8
8
6
6
I( U )
U( I)
4
4
2
2
0
0
2
4
6
U
8
10
0
0
2
4
6
I
8
10
U
0
0.02
0.08
0.18
0.32
0.5
0.72
0.98
1.28
1.62
2
Nonlinear elements analysis
 Analytical
 Graphical
 Load line method (graphical)
 Piecewise linear method
 Instrumental analysis
Graphical summation for nonlinear
analysis
k1  0.5
k2  0.3
for I from 0 to ?
5
2
U1( I)  k1 I
4
2
U2( I)  k2 I
U3( I)  k1 tan ( I)
U1( I)
3
U2( I)
U3( I)2
1
0
0
0.5
1
I
1.5
Graphical summation for nonlinear
analysis
2
1
1.5
U1( I)
U2( I)
1
U1( I)  U2( I)
0.5
0.5
0.3
0
0
0.5
1
I
U1( 1)  0.5
U2( 1)  0.3
1.5
Graphical summation for nonlinear
analysis
5
4
U1( I)
U2( I)
3
U3( I)
2
U1( I)  U2( I)  U3( I)
1
0
0
0.5
1
I
U1( 1)  0.5
U2( 1)  0.3
1.5
Graphical summation for nonlinear
analysis
0.2
0.315
0.41
0.15
U1( I)
U2( I)
0.1
U4( I)
0.05
0.05
0
0
0.2
0.4
0.6
I
U1( 0.315)  0.05
U2( 0.41)  0.05
U4( 0.315  0.41)  0.05
Graphical summation for nonlinear
analysis
0.8
0.05
0.6
I1( U)
I2( U)
0.41
0.4
I1( U)  I2( U)
0.315
0.2
0
0
0.05
0.1
U
0.15
0.2