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Inductance controlled by signal
Electrical / Passive Components
This component models a variable inductor. The inductance is determined by the signal fed into the input of the component. The voltage across a variable inductance is determined by the equation
Since is the state variable the equation above must be solved for
. The
control signal must provide the values of both
and
in the following
form:
. It is the responsibility of the
user to provide the appropriate signals for a particular purpose (see further
below).
If the component has multiple phases you can choose to include the inductive
coupling of the phases. In this case the control signal vector must contain
the elements of the inductivity matrix (row by row) and their derivatives
with respect to time. The control signal thus has a width of ,
being the number of phases.
There are two common use cases for variable inductors, which are described in detail below: saturable inductors, in which the inductance is a function of the current and actuators, in which the inductance is a function of an external quantity, such as a solenoid with a movable core.
For a more complex example of a variable inductor that depends on both the inductor current and an external quantity see the Switched Reluctance Machine.
When specifying the characteristic of a saturable inductor, you need to distinguish
carefully between the total inductivity and the differential inductivity
. See also the piece-wise linear Saturable Inductor.
With the total inductivity
you have
which can be implemented as follows:
With the differential inductivity you have
which can be implemented as follows:
Note that in both cases the -input of the Variable Inductor is zero!
In an actuator the inductivity is determined by an external quantity such as the
position of the movable core in a solenoid:
. Therefore you have
which can be implemented as follows:
Note that is preferably calculated as the integral of
rather than
calculating
as the derivative of
.