Model linear time-varying capacitor

Passive Devices

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:

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

$$i=\frac{dC}{dt}v+C\frac{dv}{dt}$$

Use the preceding equation when the capacitance is defined as the ratio of the charge

*Q*to the steady-state voltage:$$C(v)=\frac{Q(v)}{v}$$

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.

**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.

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

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