Digital Signal Processing Reference
In-Depth Information
B
1
I
2
+
−
+
−
dI
1
dI
2
L
21
L
2
dt
dt
dI
2
dI
1
L
12
L
1
dt
dt
−
+
−
+
−
+
I
1
V
1
Figure 2-20
Voltage sources induced by the time-varying currents in loop 1.
voltage in loop 2. Faraday's law can be rewritten in terms of circuit parameters:
dψ
2
dt
=−
L
21
dI
1
dt
v
2
=−
(2-96)
Therefore, every time you change the current in loop 1, an electromotive force
(i.e., a voltage) is induced in loop 2, which causes current to flow. In addition to
inducing a voltage on loops in the vicinity, changing current in loop 1 will change
the magnetic flux flowing through itself and, consequently, induce a voltage in
itself. This is called the
self-inductance:
ψ
1
I
1
L
11
≡
(2-97)
Similar to the mutual inductance, if the current changes a voltage is induced in
the loop:
v
=−
L
11
dI
1
dt
(2-98)
By observing (2-98), the units of inductance are determined to be volt
seconds
per ampere, also known as henries. Figure 2-20 shows the voltage elements
superimposed on the magnetically coupled loops corresponding to the mutual and
self-inductance values calculated with (2-96) and (2-98). Note that the voltage
sources were chosen to be positive and the negative sign is accounted for with
the direction of current flow.
·
Example 2-5
Equivalent Circuit of a Magnetically Coupled System The mag-
netically coupled circuit can be understood more easily if conventional circuit
theory is applied. Figure 2-21 shows the circuit for the magnetically coupled
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