sin_gen :
An analog sinusoid generator

The sin_gen primitive generates a sinusoidal signal that can optionally be exponentially decaying or frequency/amplitude-modulated.

The generated stimulus waveform V(t) is defined as follows:

for t < delay:
    V(t) = offset + amp*AM_offset*sin(init_phase)
for t >= delay:
    V(t) = offset + amp*exp(-damp(t-delay)) *
           [AM_offset + AM_amp*sin(2*PI*AM_freq*(t-delay)] *
           sin[2*PI*freq*(t-delay)+FM_index*sin(2*PI*FM_freq*(t-delay)) + init_phase]

In the last expression, the first, second, and third lines express the exponentially-decaying amplitude, amplitude modulation, and frequency modulation of the generated sinusoidal signal, respectively. The sinusoidal signal may have an arbitrary DC offset (offset) and start with an arbitrary initial phase (init_phase).

Some examples of generating a simple sinusoid, a sinusoid with exponentially-decaying amplitude, a sinusoid with single-frequency frequency modulation (FM), and a sinusoid with single-frequency amplitude-modulation (AM):

* A simple sinusoid:
    Set damp=0, AM_offset=1, AM_amp=AM_freq=0, FM_index=FM_freq=0
    V(t) = offset + amp*sin(2*PI*freq(t-delay)+init_phase)
    for t >= delay

* A sinusoid with exponentially-decaying amplitude:
    Set AM_offset=1, AM_amp=AM_freq=0, FM_index=FM_freq=0
    V(t) = offset + amp*exp(-damp*(t-delay))*sin(2*PI*freq*(t-delay)+init_phase)
    for t >= delay

* A sinusoid with single-frequency amplitude modulation (AM):
    Set damp=0, FM_index=FM_freq=0, init_phase=0
    V(t) = offset + amp*[AM_offset+AM_amp*sin(2*PI*AM_freq*(t-delay)] *
           sin(2*PI*freq*(t-delay))
    for t >= delay

* A sinusoid with single-frequency frequency modulation (FM):
    Set damp=0, AM_offset=1, AM_amp=AM_freq=0, init_phase=0
    V(t) = offset +
           amp*sin[2*PI*freq*(t-delay)+FM_index*sin(2*PI*FM_freq*(t-delay))]
    for t >= delay

Note: for frequency modulation, the narrowband FM is assumed. In other words, the modulation index, FM_index, which is defined as (max. deviation frequency) / (max. modulation frequency), is assumed to be << 1.

Input/Output Terminals

Name	I/O	Type	Description
out	output	xreal	signal output

Parameters

Name	Type	Default	Unit	Description
offset	real	0.0	None	offset
amp	real	1.0	None	amplitude
freq	real	1.0e9	Hz	frequency
delay	real	0.0	seconds	initial delay
damp	real	0.0	1/sec	damping factor
init_phase	real	0.0	radian	initial phase
AM_offset	real	1.0	None	AM offset
AM_amp	real	0.0	None	AM amplitude
AM_freq	real	0.0	Hz	AM frequency
FM_index	real	0.0	None	FM index
FM_freq	real	0.0	Hz	FM frequency