Fading LEDs
===========

In addition to turning LEDs on and off, it is also possible to control the brightness of an LED using `Pulse-Width Modulation (PWM) <http://en.wikipedia.org/wiki/Pulse-width_modulation>`_, a common technique for obtaining variable output from a digital pin. This allows us to fade an LED:

.. only:: not latex

   .. image:: http://upload.wikimedia.org/wikipedia/commons/a/a9/Fade.gif

Components
----------

You will need:

- Standard 5 or 3 mm LED
- 100 Ohm resistor
- Wires
- `Breadboard <http://en.wikipedia.org/wiki/Breadboard>`_ (optional, but makes things easier)

Connecting Things Up
--------------------

For this tutorial, we will use the ``X1`` pin. Connect one end of the resistor to ``X1``, and the other end to the **anode** of the LED, which is the longer leg. Connect the **cathode** of the LED to ground.

.. image:: img/fading_leds_breadboard_fritzing.png

Code
----
By examining the :ref:`quickref`, we see that ``X1`` is connected to channel 1 of timer 5 (``TIM5 CH1``). Therefore we will first create a ``Timer`` object for timer 5, then create a ``TimerChannel`` object for channel 1::
    
    from pyb import Timer
    from time import sleep
    
    # timer 5 will be created with a frequency of 100 Hz
    tim = pyb.Timer(5, freq=100)
    tchannel = tim.channel(1, Timer.PWM, pin=pyb.Pin.board.X1, pulse_width=0)

Brightness of the LED in PWM is controlled by controlling the pulse-width, that is the amount of time the LED is on every cycle. With a timer frequency of 100 Hz, each cycle takes 0.01 second, or 10 ms.

To achieve the fading effect shown at the beginning of this tutorial, we want to set the pulse-width to a small value, then slowly increase the pulse-width to brighten the LED, and start over when we reach some maximum brightness::

    # maximum and minimum pulse-width, which corresponds to maximum
    # and minimum brightness
    max_width = 200000
    min_width = 20000

    # how much to change the pulse-width by each step
    wstep = 1500
    cur_width = min_width
    
    while True:
      tchannel.pulse_width(cur_width)
      
      # this determines how often we change the pulse-width. It is
      # analogous to frames-per-second
      sleep(0.01)
    
      cur_width += wstep
    
      if cur_width > max_width:
        cur_width = min_width

Breathing Effect
----------------

If we want to have a breathing effect, where the LED fades from dim to bright then bright to dim, then we simply need to reverse the sign of ``wstep`` when we reach maximum brightness, and reverse it again at minimum brightness. To do this we modify the ``while`` loop to be::

    while True:
      tchannel.pulse_width(cur_width)
    
      sleep(0.01)
    
      cur_width += wstep
    
      if cur_width > max_width:
        cur_width = max_width
        wstep *= -1
      elif cur_width < min_width:
        cur_width = min_width
        wstep *= -1

Advanced Exercise
-----------------

You may have noticed that the LED brightness seems to fade slowly, but increases quickly. This is because our eyes interprets brightness logarithmically (`Weber's Law <http://www.telescope-optics.net/eye_intensity_response.htm>`_
), while the LED's brightness changes linearly, that is by the same amount each time. How do you solve this problem? (Hint: what is the opposite of the logarithmic function?)

Addendum
--------

We could have also used the digital-to-analog converter (DAC) to achieve the same effect. The PWM method has the advantage that it drives the LED with the same current each time, but for different lengths of time. This allows better control over the brightness, because LEDs do not necessarily exhibit a linear relationship between the driving current and brightness.
