Voltage-Controlled Oscillator

Behavioral model of voltage-controlled oscillator

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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:

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

$$\dot{\Phi }=2\pi F\left(v_{\lim }\right)$$

$$v_{out}=A\sin \left(2\pi f_{nom}t+\Phi \right)-i_{out}{R}_{out}$$

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

Phase-Locked Loop

How to model a phase-locked loop. The charge pump and filter are modeled using discrete analog components whereas the oscillator is represented as behavioral component using the Simscape™ Electrical™ Voltage-Controlled Oscillator block. The D-type flip-flops in the phase detector are represented in a simplified form using Simulink® blocks to define the behavior, and electrical components are used just at the interface. Non-zero initial conditions are applied to C1 and C2 in order to start the VCO out of phase and test the tracking ability.

• Open Model

Ports

Conserving

1+ — Positive input voltage

electrical

Electrical conserving port associated with the oscillator positive input voltage.

1- — Negative input voltage

electrical

Electrical conserving port associated with the oscillator negative input voltage.

2+ — Positive output voltage

electrical

Electrical conserving port associated with the oscillator positive output voltage.

2- — Negative output voltage

electrical

Electrical conserving port associated with the oscillator negative output voltage.

Parameters

Frequency

Frequency dependence on input voltage — Block parameterization

Linear (default) | Tabulated

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 — Nominal frequency

1000 Hz (default)

The oscillator frequency when the input control voltage is at the nominal value.

Input voltage corresponding to nominal frequency — Input voltage corresponding to nominal frequency

0.5 V (default)

The input voltage corresponding to the oscillator nominal frequency.

Dependencies

This parameter is visible only when you select Linear for the Frequency dependence on input voltage parameter.

Rate of change of frequency with input voltage — Rate of change of frequency with input voltage

1 Hz/V (default)

The linear coefficient defining the rate of change of frequency depending on input voltage.

Dependencies

This parameter is visible only when you select Linear for the Frequency dependence on input voltage parameter.

Minimum input voltage — Minimum input voltage

0 V (default)

The minimum input voltage that affects VCO frequency.

Dependencies

This parameter is visible only when you select Linear for the Frequency dependence on input voltage parameter.

Maximum input voltage — Maximum input voltage

1 V (default)

The maximum input voltage that affects VCO frequency.

Dependencies

This parameter is visible only when you select Linear for the Frequency dependence on input voltage parameter.

Input voltage vector — Input voltage vector

[0, .2, .4, .6, .8, 1] V (default)

The vector of voltages for the tabulated VCO frequency.

Dependencies

This parameter is visible only when you select Tabulated for the Frequency dependence on input voltage parameter.

Frequency deviation from nominal — Frequency deviation from nominal

[-1000, -329, -51, 162, 342, 500] Hz (default)

The corresponding vector of VCO frequencies relative to the nominal frequency.

Dependencies

This parameter is visible only when you select Tabulated for the Frequency dependence on input voltage parameter.

Electrical Characteristics

Output voltage peak amplitude — Output voltage peak amplitude

1 V (default)

The peak amplitude of the voltage across the 2+ and 2– terminals.

Input resistance — Input resistance

inf Ohm (default)

The resistance seen at the 1+ and 1– terminals.

Output resistance — Output resistance

0 Ohm (default)

The value of the series output resistance.

Dynamics

Dynamics — Dynamics specification

No dynamics (default) | Model frequency tracking 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 — Frequency tracking time constant

1e-3 s (default)

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.

Dependencies

This parameter is visible only when you select Model frequency tracking dynamics for the Dynamics parameter.

Initial frequency — Initial frequency

1000 Hz (default)

The initial VCO output frequency.

Extended Capabilities

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

Version History

Introduced in R2013b