In yesterday’s post we saw how a digital signal gets turned into something a lot more gradual, i.e. analog.

The reason for this is what I described as capacitors “dampening change” in an earlier post. This is incredibly useful in the world of Physical Computing. We can do “gradual” things with nothing but 0/1 signals coming out of a microcontroller!

The reason this works, is that capacitors mess around with the time domain. Put a “1” on them, and they will follow along eventually, i.e. a little while later. And likewise for a “0” – to bring up a previous diagram again:

This is especially useful with the timer hardware built into an ATmega. You can set up some of the pins to toggle at the rate of a hardware-controlled counter. From the ATmega328 datasheet:

This is a pin which is set up to generate a pulse repeatedly, and the clever bit is that you can control not just the rate, but also the ratio between on and off times. This is amazingly useful:

• if the ratio is all the way off, i.e. the pin is permanently “0”, the the voltage on the capacitor in the above circuit will be 0V

• if the ratio is all the way on (100% on), then the voltage of the capacitor will stabilize to 3.3V if you wait a little while

• anywhere in between, and the capacitor will be charged while high and discharged while low, and end up being some intermediate voltage between 0 and 3.3V on average

On average: that’s the key. The voltage will still go up and down, but if we choose a high-enough pulse rate, then that variation will be minimal.

This is one useful way of looking at Pulse Width Modulation (PWM): 0 = 0V, 255 (on an 8-bit counter) = 3.3V, and everything in between is N/255 * 3.3V – IOW, we’ve just created a digital-to-analog converter (DAC)!

There are more ways to generate such an adjustable output voltage – see the Bleep! weblog post, for example. But if you just want a slowly adjustable analog voltage, then all it takes is one resistor and one capacitor.

And all it needs on the microcontroller, is one pin which pulses up and down in a specified ratio. The faster it does, the smoother the output voltage. The more accurately the time-off vs time-on ratio is, the more accurately we can set that output voltage. An 8-bit timer will not be able to divide the 3.3V supply voltage into more accurate steps than 0.013V, i.e. 13 millivolt, for example.

It doesn’t really matter how the pulse is generated. There are six pins on an ATmega which can generate pulses with hardware support. This is why the very confusingly-named analogWrite() function in the Arduino library can only be used on 6 specific (digital!) output pins. And it’s not really analog at all, it just becomes analog if you attach a resistor and a capacitor.

The benefit of hardware PWM, as this is called, is that the timer pulses can be made to repeat very quickly (up to some 64,000 times per second). That means a smaller capacitor will often be sufficient, and you can get either a very smooth output voltage or one which can be adjusted rapidly (but never both at the same time).

With software PWM, the pin toggling is done with software loops or timer interrupts. In that case, any output pin can be used. But this incurs a lot more processor overhead, and the pulse rates are far more limited. A while back, I posted a software PWM example to drive some LED strips (the PWM being used for brightness control in this case, even though no caps are involved). That code was almost too slow to avoid visible flickering, although some software tricks can be used to improve the pulse rate a bit.

To be continued, probably about a week from now…