# Variable Capacitor

Model linear time-varying capacitor

Passive Devices

## Description

The Variable Capacitor block represents a linear time-varying capacitor. The block provides two options for the relationship between the current i through the capacitor and the voltage v across the device when the capacitance at port C is C. The Equation parameter determines which of the following equations the block uses:

• $i=C\frac{dv}{dt}$

Use the preceding equation when the capacitance is defined as the local gradient of the charge-voltage curve for a given voltage:

$C\left(v\right)=\frac{dQ\left(v\right)}{dv}$

• $i=\frac{dC}{dt}v+C\frac{dv}{dt}$

Use the preceding equation when the capacitance is defined as the ratio of the charge Q to the steady-state voltage:

$C\left(v\right)=\frac{Q\left(v\right)}{v}$

The block includes a resistor in series with the variable capacitor. You can use this resistor to represent the total ohmic connection resistance of the capacitor. You may need to use this resistor to prevent numerical issues for some circuit topologies, such as where a Variable Capacitor block is connected in parallel with another capacitor block that does not have a series resistance.

## Dialog Box and Parameters

Equation

Select one of the following options for block capacitance:

• I = C*dV/dt — This equation assumes the capacitance is defined as the local gradient of the charge-voltage curve for a given voltage. This option is the default.

• I = C*dV/dt + dC/dt*V — This equation assumes the capacitance is defined as the ratio of the charge to the steady-state voltage.

Minimum capacitance C>0

The lower limit on the value of the signal at port C. This limit prevents the signal from reaching a value that has no physical meaning. The default value is 1e-09 F.

Series resistance

The value of the resistance placed in series with the variable capacitor. The default value is 1e-06 Ω.

Initial charge

The charge at the start of the simulation. This parameter is only visible when you select I = C*dV/dt + dC/dt*V for the Equation parameter. The default value is 0 c.

Initial voltage

The output voltage at the start of the simulation. This parameter is only visible when you select I = C*dV/dt for the Equation parameter. The default value is 0 V.

## Ports

The block has the following ports:

C

Capacitance physical signal port (C must be finite and greater than zero)

+

Positive electrical port

-

Negative electrical port