Variable Resistor with Variable Capacitor

Purpose

Controlled resistance in parallel with controlled capacitance

Library

Electrical / Passive Components

Description

This component models a variable resistor with a variable capacitor connected in parallel. The resistance and capacitance are determined by the signals fed into the inputs of the component. The current through this component is determined by the equation:

\[i = \left(\frac1R + \frac{\mathrm{d}}{\mathrm{d}t}C\right)\cdot v + C\cdot\frac{\mathrm{d}}{\mathrm{d}t}v\]

The control signal for the capacitor must provide the values of both \(C\) and \(\frac{\mathrm{d}}{\mathrm{d}t}C\) in the following form: \(\left[ C_1\; C_2 \ldots C_n\; \frac{\mathrm{d}}{\mathrm{d}t}C_1\; \frac{\mathrm{d}}{\mathrm{d}t}C_2 \ldots \frac{\mathrm{d}}{\mathrm{d}t}C_n\right]\). It is the responsibility of the user to provide the appropriate signals for a particular purpose. For detailed information see the Variable Capacitor

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) followed by their derivatives with respect to time, e.g. for two coupled phases: \(\left[ C_{11}\; C_{12}\; C_{21}\; C_{22}\; \frac{\mathrm{d}}{\mathrm{d}t}C_{11}\; \frac{\mathrm{d}}{\mathrm{d}t}C_{12}\; \frac{\mathrm{d}}{\mathrm{d}t}C_{21}\; \frac{\mathrm{d}}{\mathrm{d}t}C_{22}\right]\). The control signal thus has a width of \(2\cdot n^2\), \(n\) being the number of phases.

Note

The momentary capacitance and the resistance may not be set to zero. In case of coupled capacitors, the capacitance matrix may not be singular.

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 \((\mathrm{V})\). 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 \((\mathrm{V})\). A positive voltage is measured when the potential at the terminal marked with “+” is greater than the potential at the unmarked terminal.