Transcript Ideal Transformer - Keith E. Holbert

EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 12
1
Ideal Transformer
For an ideal transformer (which is coupled with good
magnetic material so that the core permeability and
winding conductivities are assumed infinite, and it is
therefore lossless) the time domain relations are
N1
v1 
v2
N1 i1  N 2 i2  0
N2
where both currents are entering the dots on the
positive terminal.
Lecture 12
2
Ideal Transformer
• Note that the two equations above can be
combined to show that the power into the ideal
transformer is zero, and it is therefore lossless
v1 i1 + v2 i2 = 0 = p1 + p2
• An ideal transformer is very tightly coupled (k1)
N2
n

N1
L2 M L2


L2
L1 M
Lecture 12
3
Ideal Transformer
• Defining the turns ratio, n=N2/N1, provides the
frequency domain equations for an ideal xformer
V2
V1 
n
I1  n I 2
• NOTE: these equations require I2 in the reverse
direction (see Fig. 11.13)---against dot convention
• Each change of voltage or current with respect to
the dot introduces a negative sign in the
corresponding equation
Lecture 12
4
Ideal Transformer
I1
1:n
+
V1
–
I2
+
V2
–
V2
V1 
n
ZL
I1  n I 2
V2
*
n I 2   V2 I*2  S 2
S1  V1 I 
n
*
1
Z input  Z 1 
V1 V2 / n Z L

 2
I1
n I2
n
Lecture 12
5
Class Examples
• Extension Exercise E11.6
• Extension Exercise E11.7
Lecture 12
6
Thevenin Equivalent Circuit
Thevenin's theorem may be used to derive equivalent
circuits for the transformer and either its primary or
secondary circuit
Equivalent Circuit
Voltage Source
Impedance
Current
Replace transformer
and primary circuit
Primary voltage
multiplied by n
Primary
impedance
multiplied by n²
Primary
current divided
by n
Replace transformer
and secondary circuit
Secondary voltage
divided by n
Secondary
impedance divided
by n²
Secondary
current
multiplied by n
Lecture 12
7
Class Examples
• Extension Exercise E11.9
Lecture 12
8