# Voltage-Controlled Oscillator

Behavioral model of voltage-controlled oscillator

**Libraries:**

Simscape /
Electrical /
Integrated Circuits

## Description

The Voltage-Controlled Oscillator block provides a behavioral model of a voltage-controlled oscillator (VCO). The output voltage is defined by the following equations:

$${v}_{\mathrm{lim}}=\{\begin{array}{ll}{v}_{\mathrm{min}}\hfill & \text{for}{v}_{in}{v}_{min}\hfill \\ {v}_{in}\hfill & \text{for}{v}_{min}\le {v}_{in}\le {v}_{\mathrm{max}}\hfill \\ {v}_{\mathrm{max}}\hfill & \text{for}{v}_{in}{v}_{\mathrm{max}}\hfill \end{array}$$

$$\dot{\Phi}=2\pi F\left({v}_{\mathrm{lim}}\right)$$

$${v}_{out}=A\mathrm{sin}\left(2\pi {f}_{nom}t+\Phi \right)-{i}_{out}{R}_{out}$$

where:

*v*_{in}is the voltage applied across the 1+ and 1– ports.*v*_{out}is the voltage across the 2+ and 2– ports.*f*_{nom}is the oscillator frequency when the input control voltage is*v*_{nom}.*F*is a linear function of*v*_{lim}or a lookup table function of*v*_{lim}.*A*is the output voltage peak amplitude.*t*is simulation time.*i*_{out}is the output current.*R*_{out}is the output resistance.

If you choose `Linear`

for the **Frequency dependence
on input voltage** parameter, then the function *F* is
given by:

$$F={f}_{nom}+k\left({v}_{lim}-{v}_{nom}\right)$$

where *k* is the rate of change of frequency with input
voltage.

If you choose `Tabulated`

for the **Frequency
dependence on input voltage** parameter, then the function
*F* is defined by the vectors of input voltages and corresponding
output frequency deviations from nominal that you supply. The values for
*v*_{min} and
*v*_{max} are the first and the last values of
the input voltage vector.

You can model the time delay between a change in the input control voltage and the
oscillator frequency. Do this by modeling a first-order dynamic between
*v*_{lim} and the value passed to the function
*F*.

## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2013b**