Behavioral model of voltage-controlled oscillator

Integrated Circuits

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*.

**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.

**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**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.

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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