# Voltage-Controlled Oscillator

Behavioral model of voltage-controlled oscillator

## Library

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:

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

where:

• vin is the voltage applied across the 1+ and 1– ports.

• vout is the voltage across the 2+ and 2– ports.

• fnom is the oscillator frequency when the input control voltage is vnom.

• F is a linear function of vlim or a lookup table function of vlim.

• A is the output voltage peak amplitude.

• t is simulation time.

• iout is the output current.

• Rout 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 vmin and vmax 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 vlim and the value passed to the function F.

## Parameters

### Frequency Tab

Frequency dependence on input voltage

Select one of the following methods for block parameterization:

• `Linear` — Define a linear function by specifying the rate of change of frequency with input voltage. This is the default option.

• `Tabulated` — Provide the vectors of input voltages and corresponding output frequency deviations from nominal. The block determines the frequency deviation by table lookup based on these values.

Nominal frequency

The oscillator frequency when the input control voltage is at the nominal value. The default value is `1000` Hz.

Input voltage corresponding to nominal frequency

The input voltage corresponding to the oscillator nominal frequency. This parameter is visible only if you select `Linear` for the Frequency dependence on input voltage parameter. The default value is `0.5` V.

Rate of change of frequency with input voltage

The linear coefficient defining the rate of change of frequency depending on input voltage. This parameter is visible only if you select `Linear` for the Frequency dependence on input voltage parameter. The default value is `1` Hz/V.

Minimum input voltage

The minimum input voltage that affects VCO frequency. This parameter is visible only if you select `Linear` for the Frequency dependence on input voltage parameter. The default value is `0` V.

Maximum input voltage

The maximum input voltage that affects VCO frequency. This parameter is visible only if you select `Linear` for the Frequency dependence on input voltage parameter. The default value is `1` V.

Input voltage vector

The vector of voltages for the tabulated VCO frequency. This parameter is visible only if you select `Tabulated` for the Frequency dependence on input voltage parameter. The default value is `[0 0.2 0.4 0.6 0.8 1]` V.

Frequency deviation from nominal

The corresponding vector of VCO frequencies relative to the nominal frequency. This parameter is visible only if you select `Tabulated` for the Frequency dependence on input voltage parameter. The default value is `[-1000 -329 -51 162 342 500]` Hz.

### Electrical Characteristics Tab

Output voltage peak amplitude

The peak amplitude of the voltage across the 2+ and 2– terminals. The default value is `1` V.

Input resistance

The resistance seen at the 1+ and 1– terminals. The default value is `Inf` Ohm.

Output resistance

The value of the series output resistance. The default value is `0` Ohm.

### Dynamics Tab

Dynamics

Select one of the following methods for specifying dynamics:

• `No dynamics` — Do not model the time delay between a change in the input control voltage and the oscillator frequency. This is the default option.

• `Model frequency tracking dynamics` — Model a first order dynamic between the input control voltage and the oscillator frequency.

Frequency tracking time constant

Time constant for the first-order filter that delays the measured input control voltage, to model the lag between a change in VCO demanded frequency and the resulting VCO frequency. This parameter is visible only if you select `Model frequency tracking dynamics` for the Dynamics parameter. The default value is `0.001` s.

Initial frequency

The initial VCO output frequency. This parameter is visible only if you select `Model frequency tracking dynamics` for the Dynamics parameter. The default value is `1000` Hz.

## Ports

The block has the following ports:

`1+`

Positive input voltage

`1-`

Negative input voltage

`2+`

Positive output voltage

`2-`

Negative output voltage

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