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# Sinusoid

Model DC offset and sinusoidal modulation

Sources

## Description

The Sinusoid block implements a voltage or current source that provides a DC offset and sine wave modulation. This block can be used with each listed block carrier in the circuit envelope environment.

The block implements the following voltage (or current) relationships for the in-phase, (ui), and quadrature, (uq), components of the kth listed block carrier:

$\begin{array}{l}{u}_{k,i}\left(t\right)={D}_{i}+{A}_{i}\mathrm{sin}\left({w}_{k}\left(t-\tau \right)\right)\\ {u}_{k,q}\left(t\right)={D}_{q}+{A}_{q}\mathrm{sin}\left({w}_{k}\left(t-\tau \right)\right)\end{array}$

where:

• Di and Dq are DC offsets.

• Ai and Aq are in-phase and quadrature amplitudes.

• τ is the time delay.

• ωk is the specified modulation frequency at a given carrier frequency fk.

• t is the time.

## Dialog Box and Parameters

Source type

Specify the wave type as:

• Ideal Voltage — The block simulates a voltage envelope v(t) at the specified Carrier frequencies.

• Ideal Current — The block simulates a current envelope i(t) at the specified Carrier frequencies.

The default value of this parameter is Ideal Voltage.

Offset in-phase

Specify the in-phase offset, Di, as a scalar or vector. Specify the units of the offset from the corresponding drop-down list. The default value of this parameter is 0 V for a voltage signal or 0 A for a current signal.

Specify the quadrature offset, Dq, as a scalar or vector. Specify the units of the offset from the corresponding drop-down list. The default value of this parameter is 0 V for a voltage signal or 0 A for a current signal.

Sinusoidal amplitude in-phase

Specify the in-phase amplitude, Ai, as a scalar or vector. Specify the units of the offset from the corresponding drop-down list. The default value of this parameter is 0 V for a voltage signal or 0 A for a current signal.

Specify the quadrature amplitude, Aq, as a scalar or vector. Specify the units of the offset from the corresponding drop-down list. The default value of this parameter is 0 V for a voltage signal or 0 A for a current signal.

Sinusoidal modulation frequency

At each carrier fk specified by the Carrier frequencies parameter, specify the modulation frequency mk. Specify the units from the corresponding drop-down list. The default value of this parameter is 0 Hz.

Time delay

Specify the time delay, τ, of the modulation as a scalar or vector. Specify the units from the corresponding drop-down list. The default value of this parameter is 0 s.

Damping factor (1/s)

Specify the damping factor, ζ, of the modulation as a nonzero scalar or vector with nonzero elements. The default value of this parameter is 0 s-1, representing an undamped sinusoid.

Carrier frequencies

Enter a vector of carrier frequencies whose elements are combinations of fundamental tones and corresponding harmonics in the Configuration block. Specify the units from the corresponding drop-down list. The default value of this parameter is 0 Hz.

Ground and hide negative terminals

Select this option to internally ground and hide the negative terminals. Clear this to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.