When  electric  lighting  was  first  used  in  theatre  over  a  century  ago  ,  the  dimming  was  done  by  reducing  the  amount  of  voltage  delivered  to  them .First  it  was  the   resistor  in  series  with  the  lamp  and  when  AC  became  a  standard  , autotransformers  replaced  the  resistors.
An autotransformer  is  a  special   type  of  transformer  with  a  sliding  tap  that  allows  the  output  voltage  to  be  adjusted  from  zero  to  full, so that the autotransformer  produces  an  output  that  is  a  sinewave  with  variable  amplitude.
While  this  type  of  dimmer  had  many  drawbacks  ( large  size , excessive  heat ) they  did  have  one  advantage  :    THE  LAMP  WAS  QUIET  .

Functionally  the Sine  Dimmer  imitates   the  “old “  autotransformer ,  but  due  to use  of  modern  technology  is  able  to  offer  a  viable  product .

 Vout  =  R ( t)  x  V in

Sine Dimmer - Control panel courtesy Compulite

Plug-in Sine Dimmer drawer courtesy Compulite

where  R(t)  is  a dimming  factor  from  0  to  1. in  255  steps  .It  is  implemented  as  duty  cycle  of  high  frequency  carrier 
Vin  is  line  voltage  modulated ( chopped )  by  high  frequency   carrier
Vout  is  a  waveform   whose  amplitude  and  frequency  is  Vin  and   duty  cycle   is  R , This  waveform  cannot  be  directly  used  to  control  the  load. It  must  be  filtered  to  produce  a  sine wave.
The sine dimmer has two stages of circuitry input and output stages.
In the input stage the line voltage is converted to the high frequency, pulse width modulated (PWM) waveform.
Input filter keeps high frequency harmonics inside the dimmer. This means that a sine dimmer introduces no noise into the input line.
The pulse width is proportional to the amplitude of the output voltage equivalent to the phase shift angle of the conventional dimmers.

This high switching frequency reduces the size of the passive filter components and insures that any acoustic noise produced within the dimmer is well above the audible range.

The 50 KHz carrier frequently is divided into 255 steps providing a  voltage resolution on the output of less that 0.5% . There is no minimum load specification and  the Sine Dimmer will produce a sine  waveform at the output with no connected load. 
Besides the variable amplitude sine output the Sine dimmer produces almost no harmonic distortion (typically less  than 1%).
With an incandescent load, current is drawn during the entire power line cycle. For a non- linear load such as a ballast or electronic low-voltage fixture the load characteristics are passed through the power line.
The sine dimmer is transparent to the load and  will  deliver voltage and current to the load the some way as a direct connection to the power line.
Many loads that were not controllable by phase-control dimmers may now be used.
Magnetic  low voltage fixtures, electronic low voltage fixtures, Neon, Cold cathode.
LED’s , fans , small motors will now operate without problems.

But unfortunately not all loads are signed to operate at voltage lower than their ratings.
The sine dimmer generates an output that has no 3rd harmonic and no sharp switching components and as a result will provide quiet loads.

The micro controller on board monitors the output current and module temperature to insure that is within its limits and will shut down if exceeded. Sine dimmer should be considered in any application where silence is important when matching various sources to provide a unified fade without worrying about noisy types.