Variable Capacitor

Linear time-varying capacitor

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Libraries:
Simscape / Electrical / Passive

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:

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

• $$i=\frac{dC}{dt}v+C\frac{dv}{dt}$$

  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.

Examples

AM Radio Receiver

A simplified AM radio receiver. A single tone signal at 2kHz is transmitted with a carrier frequency of 600kHz. The variable capacitor, Cres, in the resonant circuit is used in order to sweep through a certain frequency span. When the resonance passes through 600kHz, the signal is picked up and amplified by a two-stage Class A RF power amplifier. The signal is finally extracted by a diode detector, where it would normally be passed on to an audio amplifier (not included here). The Scope displays the final output, the value of the resonant capacitance, and the received and amplified signals.

• Open Model

Ports

Input

C — Capacitance

physical signal

Physical signal input port associated with the capacitance. C must be finite and greater than zero

Conserving

+ — Positive terminal

electrical

Electrical conserving port associated with the capacitor positive voltage.

- — Negative terminal

electrical

Electrical conserving port associated with the capacitor negative voltage.

Parameters

Equation — Equation for block capacitance

I = C*dV/dt (default) | I = C*dV/dt + dC/dt*V

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 — Minimum capacitance

1e-9 F (default)

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 — Series resistance

1e-6 Ohm (default)

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

Initial voltage — Initial output voltage

0 V (default)

The output voltage at the start of the simulation.

Dependencies

This parameter is visible only when you select I = C*dV/dt for the Equation parameter.

Initial charge — Initial charge

0 C (default)

The charge at the start of the simulation.

Dependencies

This parameter is visible only when you select I = C*dV/dt + dC/dt*V for the Equation parameter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2008a