Variable Capacitor
Purpose
Capacitance controlled by signal
Library
Electrical / Passive Components
Description
This component models a variable capacitor. The capacitance is determined by the signal fed into the input of the component. The current through a variable capacitance 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 capacitive
coupling of the phases. In this case the control signal vector must contain
the elements of the capacitance matrix (row by row) and their derivatives
with respect to time. The control signal thus has a width of ,
being the number of phases.
Note The momentary capacitance may not be set to zero. In case of coupled capacitors, the capacitance matrix may not be singular.
There are two common use cases for variable capacitors, which are described in detail below: saturable capacitors, in which the capacitance is a function of the voltage and electrostatic actuators, in which the capacitance is a function of an external quantity, such as a capacitor with movable plates.
Saturable Capacitor Modeling
When specifying the characteristic of a saturable capacitor, you need to distinguish
carefully between the total capacitance and the differential
capacitance
.
With the total capacitance you have
which can be implemented as follows:
With the differential capacitance you have
which can be implemented as follows:
Note that in both cases the -input of the Variable Capacitor is
zero!
Actuator Modeling
In an electrostatic actuator the capacitance is determined by an external quantity
such as the distance between the movable plates of a capacitor:
.
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
.
Parameters
- Capacitive coupling
- Specifies whether the phases should be coupled capacitively. This parameter determines how the elements of the control signal are interpreted. The default is off.
- Initial voltage
- The initial voltage of the capacitor at simulation start, in volts (V). This parameter may either be a scalar or a vector corresponding to the implicit width of the component. The positive pole is marked with a "+". The initial voltage default is 0.
Probe Signals
- Capacitor voltage
- The voltage measured across the capacitor, in volts (V). A positive voltage is measured when the potential at the terminal marked with "+" is greater than the potential at the unmarked terminal.
- Capacitor current
- The current flowing through the capacitor, in amperes (A).